{"article_info":{"article_id":133061,"cat_id":1097,"cat_title":"Đề thi, đề kiểm tra Toán lớp 7 - Kết nối tri thức","publish_time":1673254740,"cat_id2":1097,"is_link":0,"thumbnail":"","title":"Đề thi giữa kì 2 Toán 7 - Đề số 4 - Kết nối tri thức","label":"Đề thi giữa kì 2 - Đề số 4","alias":"de-kiem-tra-giua-hoc-ki-2-toan-7-de-so-4-ket-noi-tri-thuc","introtext":"I. TRẮC NGHIỆM (2,0 điểm)\r\nHãy chọn phương án trả lời đúng và viết chữ cái đứng trước đáp án đó vào bài làm.","content":"<p><strong class=\"sub_question_head\" id=\"sub_question_head_1\">Đề bài</strong></p><p><strong>I. TRẮC NGHIỆM (<em>2,0 điểm</em>)</strong></p>\r\n<p>Hãy chọn phương án trả lời đúng và viết chữ cái đứng trước đáp án đó vào bài làm.</p>\r\n<p><strong>Câu 1. </strong>Hai đại lượng \\(x,y\\) trong công thức nào tỉ lệ nghịch với nhau:<strong></strong></p>\r\n<p><strong>     A. </strong>\\(y = 5 + x\\)                    <strong>B. </strong>\\(x = \\dfrac{5}{y}\\)              <strong>C. </strong>\\(y = 5x\\)                            <strong>D. </strong>\\(x = 5y\\)</p>\r\n<p><strong>Câu 2. </strong>Biểu thức đại số biểu thị bình phương của một tổng hai số \\(a\\) và \\(b\\) là: <strong></strong></p>\r\n<p><strong>     A. </strong>\\({a^2} - {b^2}\\)              <strong>B. </strong>\\({a^2} + {b^2}\\)                  <strong>C. </strong>\\({\\left( {a - b} \\right)^2}\\)   <strong>D. </strong>\\({\\left( {a + b} \\right)^2}\\)<strong>                                                                             </strong></p>\r\n<p><strong>Câu 3.</strong> Giá trị của biểu thức: \\({x^3} - 2{x^2}\\) tại \\(x =  - 2\\) là:<strong></strong></p>\r\n<p><strong>     A. </strong>\\( - 16\\)                          <strong>B. </strong>\\(16\\)                                  <strong>C. </strong>\\(0\\)                                   <strong>D. </strong>\\( - 8\\)<strong>     </strong></p>\r\n<p><strong>Câu 4.</strong> Biểu thức nào sau đây <strong>không </strong>là đơn thức?</p>\r\n<p><strong>     A. </strong>\\(4{x^2}y\\left( { - 2x} \\right)\\)                                         <strong>B. </strong>\\(2x\\)                                  <strong>C. </strong>\\(2xy - {x^2}\\) <strong>D. </strong>\\(2021\\)<strong>                                   </strong></p>\r\n<p><strong>Câu 5.</strong> Sắp xếp các hạng tử của đa thức \\(P\\left( x \\right) = 2{x^3} - 7{x^2} + {x^4} - 4\\) theo lũy thừa giảm dần của biến ta được:<strong></strong></p>\r\n<p><strong>     A. </strong>\\(P\\left( x \\right) = {x^4} + 2{x^3} - 7{x^2} - 4\\)                 <strong>B. </strong>\\(P\\left( x \\right) = 7{x^2} + 2{x^3} + {x^4} - 4\\)</p>\r\n<p>     <strong>C. </strong>\\(P\\left( x \\right) =  - 4 - 7{x^2} + 2{x^3} + {x^4}\\)             <strong>D. </strong>\\(P\\left( x \\right) = {x^4} - 2{x^3} - 7{x^2} - 4\\)<strong> </strong></p>\r\n<p><strong>Câu 6.</strong> Cho tam giác \\(MNP\\) có \\(NP = 1cm,MP = 7cm\\). Độ dài cạnh \\(MN\\) là một số nguyên (cm). Độ dài cạnh \\(MN\\) là:</p>\r\n<p><strong>     A. </strong>\\(8cm\\)                          <strong>B. </strong>\\(5cm\\)                               <strong>C. </strong>\\(6cm\\)                               <strong>D. </strong>\\(7cm\\)<strong>   </strong></p>\r\n<p><strong>Câu 7. </strong>Cho tam giác \\(ABC\\), có \\(\\angle A = {90^0};\\angle C = {30^0}\\). Khi đó quan hệ giữa ba cạnh \\(AB,AC,BC\\) là:<strong></strong></p>\r\n<p><strong>     A. </strong>\\(BC &gt; AB &gt; AC\\)             <strong>B. </strong> \\(AC &gt; AB &gt; BC\\)                 <strong>C. </strong>\\(AB &gt; AC &gt; BC\\)                  <strong>D. </strong>\\(BC &gt; AC &gt; AB\\)</p>\r\n<p><strong>Câu 8.</strong> Giao điểm của 3 đường trung trực của tam giác</p>\r\n<p>A. cách đều 3 cạnh của tam giác.</p>\r\n<p>B. được gọi là trực tâm của tam giác.</p>\r\n<p>C. cách đều 3 đỉnh của tam giác.</p>\r\n<p>D. cách đỉnh một đoạn bằng \\(\\dfrac{2}{3}\\) độ dài đường trung tuyến đi qua đỉnh đó.</p>\r\n<p><strong>II. PHẦN TỰ LUẬN <em>(8,0 điểm)</em></strong></p>\r\n<p><strong>Bài 1. <em>(1 điểm)</em></strong> Tìm \\(x\\) biết:</p>\r\n<p>a)       \\(\\dfrac{{5x - 2}}{3} = \\dfrac{{ - 3}}{4}\\)                           b) \\(\\left( {{x^2} - \\dfrac{1}{4}} \\right).\\left( {x + \\dfrac{2}{5}} \\right) = 0\\)<strong></strong></p>\r\n<p><strong>Bài 2. <em>(1,5 điểm)</em></strong> Ba lớp 7A, 7B, 7C cùng tham gia lao động trồng cây. Biết số cây ở lớp 7A, 7B, 7C được trồng tỉ lệ với các số \\(3\\,;\\,5\\,;\\,8\\) và hai lần số cây của lớp 7A cộng với \\(4\\) lần số cây lớp 7B trồng được nhiều hơn số cây lớp 7C trồng được là \\(108\\) cây. Tính số cây trồng được của mỗi lớp</p>\r\n<p><strong>Bài 3. <em>(1,5 điểm)</em></strong> Cho hai đa thức: \\(f\\left( x \\right) = {x^5} + {x^3} - 4x - {x^5} + 3x + 7\\) và \\(g\\left( x \\right) = 3{x^2} - {x^3} + 8x - 3{x^2} - 14\\).</p>\r\n<p>a) Thu gọn và sắp xếp hai đa thức \\(f\\left( x \\right)\\) và \\(g\\left( x \\right)\\) theo lũy thừa giảm dần của biến.</p>\r\n<p>b) Tính \\(f\\left( x \\right) + g\\left( x \\right)\\) và tìm nghiệm của đa thức \\(f\\left( x \\right) + g\\left( x \\right)\\).    </p>\r\n<p><strong>Bài 4. <em>(3,5 điểm)</em></strong> Cho tam giác \\(ABC\\) cân tại \\(A\\), kẻ \\(AH\\)vuông góc với \\(BC\\)\\(\\left( {H \\in BC} \\right)\\). Gọi \\(P\\) là trung điểm của \\(HC\\). Trên tia đối của tia \\(PA\\) lấy điểm \\(Q\\) sao cho \\(QP = PA\\).</p>\r\n<p>a) Chứng minh rằng: \\(\\Delta APH = \\Delta QPC\\) và \\(QC\\) vuông góc với\\(BC\\).</p>\r\n<p>b) Chứng minh rằng: \\(QC = AH\\)từ đó suy ra \\(AC &gt; QC\\).</p>\r\n<p>c) Chứng minh rằng: \\(\\angle PAC &lt; \\angle HAP\\)</p>\r\n<p>d) Gọi \\(I\\) là trung điểm của \\(BQ\\). Chứng minh rằng ba điểm \\(A,H,I\\) thẳng hàng.</p>\r\n<p><strong>Bài 5. <em>(0,5 điểm) </em></strong>Cho các số thực \\(a,b,c,d,e\\) thỏa mãn: \\(\\dfrac{a}{b} = \\dfrac{b}{c} = \\dfrac{c}{d} = \\dfrac{d}{e}\\).</p>\r\n<p>Chứng minh rằng: \\({\\left( {\\dfrac{{2019b + 2020c - 2021d}}{{2019c + 2020d - 2021e}}} \\right)^3} = \\dfrac{{{a^2}}}{{bc}}\\).</p>\r\n<p align=\"center\"><em>(Giả thiết các tỉ số đều có nghĩa)</em></p><hr/><p><strong class=\"sub_question_head\" id=\"sub_question_head_2\">Lời giải</strong></p><p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">I. Trắc nghiệm</span></strong></p>\r\n<table class=\"MsoNormalTable\" style=\"width: 430px; border-collapse: collapse; border: none;\" border=\"1\" cellspacing=\"0\" cellpadding=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"border: solid #DDDDDD 1.0pt; mso-border-alt: solid #DDDDDD .75pt; padding: 6.0pt 6.0pt 6.0pt 6.0pt;\" valign=\"top\">\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: center; line-height: 18.0pt;\" align=\"center\"><strong><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">1.B</span></strong></strong></p>\r\n</td>\r\n<td style=\"border: solid #DDDDDD 1.0pt; border-left: none; mso-border-left-alt: solid #DDDDDD .75pt; mso-border-alt: solid #DDDDDD .75pt; padding: 6.0pt 6.0pt 6.0pt 6.0pt;\" valign=\"top\">\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: center; line-height: 18.0pt;\" align=\"center\"><strong><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">2.</span></strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\"> D</span></strong></p>\r\n</td>\r\n<td style=\"border: solid #DDDDDD 1.0pt; border-left: none; mso-border-left-alt: solid #DDDDDD .75pt; mso-border-alt: solid #DDDDDD .75pt; padding: 6.0pt 6.0pt 6.0pt 6.0pt;\" valign=\"top\">\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: center; line-height: 18.0pt;\" align=\"center\"><strong><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">3. </span></strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">A</span></strong></p>\r\n</td>\r\n<td style=\"border: solid #DDDDDD 1.0pt; border-left: none; mso-border-left-alt: solid #DDDDDD .75pt; mso-border-alt: solid #DDDDDD .75pt; padding: 6.0pt 6.0pt 6.0pt 6.0pt;\" valign=\"top\">\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: center; line-height: 18.0pt;\" align=\"center\"><strong><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">4.</span></strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\"> C</span></strong></p>\r\n</td>\r\n</tr>\r\n<tr>\r\n<td style=\"border: solid #DDDDDD 1.0pt; border-top: none; mso-border-top-alt: solid #DDDDDD .75pt; mso-border-alt: solid #DDDDDD .75pt; padding: 6.0pt 6.0pt 6.0pt 6.0pt;\" valign=\"top\">\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: center; line-height: 18.0pt;\" align=\"center\"><strong><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">5.</span></strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\"> A</span></strong></p>\r\n</td>\r\n<td style=\"border-top: none; border-left: none; border-bottom: solid #DDDDDD 1.0pt; border-right: solid #DDDDDD 1.0pt; mso-border-top-alt: solid #DDDDDD .75pt; mso-border-left-alt: solid #DDDDDD .75pt; mso-border-alt: solid #DDDDDD .75pt; padding: 6.0pt 6.0pt 6.0pt 6.0pt;\" valign=\"top\">\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: center; line-height: 18.0pt;\" align=\"center\"><strong><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">6.</span></strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\"> D</span></strong></p>\r\n</td>\r\n<td style=\"border-top: none; border-left: none; border-bottom: solid #DDDDDD 1.0pt; border-right: solid #DDDDDD 1.0pt; mso-border-top-alt: solid #DDDDDD .75pt; mso-border-left-alt: solid #DDDDDD .75pt; mso-border-alt: solid #DDDDDD .75pt; padding: 6.0pt 6.0pt 6.0pt 6.0pt;\" valign=\"top\">\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: center; line-height: 18.0pt;\" align=\"center\"><strong><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">7.</span></strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\"> D</span></strong></p>\r\n</td>\r\n<td style=\"border-top: none; border-left: none; border-bottom: solid #DDDDDD 1.0pt; border-right: solid #DDDDDD 1.0pt; mso-border-top-alt: solid #DDDDDD .75pt; mso-border-left-alt: solid #DDDDDD .75pt; mso-border-alt: solid #DDDDDD .75pt; padding: 6.0pt 6.0pt 6.0pt 6.0pt;\" valign=\"top\">\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: center; line-height: 18.0pt;\" align=\"center\"><strong><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">8.</span></strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\"> C</span></strong></p>\r\n</td>\r\n</tr>\r\n</tbody>\r\n</table>\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">Câu 1.</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Phương pháp:</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Vận dụng định nghĩa về đại lượng tỉ lệ nghịch.<strong></strong></span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Cách giải: </span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: 14.2pt 5.0cm 10.0cm 15.0cm 482.7pt;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Ta có: </span><span class=\"MTConvertedEquation\">\\(x = \\dfrac{5}{y}\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> là hai đại lượng tỉ lệ nghịch với nhau.</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: 14.2pt 5.0cm 10.0cm 15.0cm 482.7pt;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Chọn B.</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">Câu 2.</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: 125.5pt;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Phương pháp:                 </span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: 125.5pt;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Dùng các chữ, các số và các phép toán để diễn đạt các mệnh đề phát biểu bằng lời.<strong></strong></span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Cách giải: </span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: 374.95pt;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Bình phương của một tổng hai số </span><span class=\"MTConvertedEquation\">\\(a\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> và </span><span class=\"MTConvertedEquation\">\\(b\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> là: </span><span class=\"MTConvertedEquation\">\\({\\left( {a + b} \\right)^2}\\)</span><strong></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: 14.2pt 5.0cm 10.0cm 15.0cm 482.7pt;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Chọn D.</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">Câu 3.</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Phương pháp:</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Thay </span><span class=\"MTConvertedEquation\">\\(x =  - 2\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> vào biểu thức </span><span class=\"MTConvertedEquation\">\\({x^3} - 2{x^2}\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> để tính.<strong></strong></span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Cách giải: </span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Thay </span><span class=\"MTConvertedEquation\">\\(x =  - 2\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> vào biểu thức </span><span class=\"MTConvertedEquation\">\\({x^3} - 2{x^2}\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> ta có: </span><span class=\"MTConvertedEquation\">\\({\\left( { - 2} \\right)^3} - 2.{\\left( { - 2} \\right)^2} = \\left( { - 8} \\right) - 2.4 =  - 16\\)</span><strong></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: 14.2pt 5.0cm 10.0cm 15.0cm 482.7pt;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Chọn A.</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">Câu 4.</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Phương pháp:</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Đơn thức là biểu thức đại số chỉ gồm một số, hoặc một biến, hoặc một tích giữa các số và các biến.<strong></strong></span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Cách giải: </span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Biểu thức: </span><span class=\"MTConvertedEquation\">\\(2xy - {x^2}\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> không là một đơn thức.</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: 14.2pt 5.0cm 10.0cm 15.0cm 482.7pt;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Chọn C.</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">Câu 5.</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Phương pháp:</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Thu gọn đa thức bằng cách nhóm các hạng tử đồng dạng lại rồi thu gọn chúng. Sau đó sắp xếp theo lũy thừa giảm dần của biến.<strong></strong></span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Cách giải: </span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Sắp xếp theo lũy thừa giảm dần của biến: </span><span class=\"MTConvertedEquation\">\\(P\\left( x \\right) = {x^4} + 2{x^3} - 7{x^2} - 4\\)</span><strong></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: 14.2pt 5.0cm 10.0cm 15.0cm 482.7pt;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Chọn A.</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">Câu 6.</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Phương pháp:</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Sử dụng hệ quả của bất đẳng thức trong tam giác:</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">+ Tồn tại một tam giác có độ dài ba cạnh là </span><span class=\"MTConvertedEquation\">\\(a,b,c\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> nếu </span><span class=\"MTConvertedEquation\">\\(\\left| {b - c} \\right| &lt; a &lt; b + c\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">.</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">+ Trong trường hợp xác định được </span><span class=\"MTConvertedEquation\">\\(a\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> là số lớn nhất trong ba số </span><span class=\"MTConvertedEquation\">\\(a,b,c\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> thì điều kiện tồn tại tam giác là </span><span class=\"MTConvertedEquation\">\\(a &lt; b + c\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">. <strong></strong></span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Cách giải: </span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: center 269.3pt;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Xét tam giác </span><span class=\"MTConvertedEquation\">\\(MNP\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">, ta có: </span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: center 269.3pt;\"><span class=\"MTConvertedEquation\">\\(\\begin{array}{l}\\,\\,\\,\\,\\,\\,\\,\\left| {NP - MP} \\right| &lt; MN &lt; NP + MP\\\\ \\Rightarrow \\left| {1 - 7} \\right| &lt; MN &lt; 1 + 7\\\\ \\Rightarrow 6 &lt; MN &lt; 8\\end{array}\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: center 269.3pt;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Vì độ dài cạnh </span><span class=\"MTConvertedEquation\">\\(MN\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> là một số nguyên nên </span><span class=\"MTConvertedEquation\">\\(MN = 7\\,\\left( {cm} \\right)\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">     <strong></strong></span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: 14.2pt 5.0cm 10.0cm 15.0cm 482.7pt;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Chọn D.</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">Câu 7.</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Phương pháp:</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 13.8px;\"><span style=\"font-family: 'Times New Roman', serif; font-size: 12pt;\">Sử dụng quan hệ giữa góc và cạnh đối diện trong tam giác.</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 13.8px;\"><strong><span style=\"font-size: 12pt; line-height: 18.4px; font-family: 'Times New Roman', serif;\">Cách giải:</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 13.8px;\"><span style=\"font-size: 12pt; line-height: 18.4px; font-family: 'Times New Roman', serif;\">Xét </span><span class=\"MTConvertedEquation\">\\(\\Delta ABC\\)</span><span style=\"font-size: 12pt; line-height: 18.4px; font-family: 'Times New Roman', serif;\"> có: </span><span class=\"MTConvertedEquation\">\\(\\angle A + \\angle B + \\angle C = {180^0}\\)</span><span style=\"font-size: 12pt; line-height: 18.4px; font-family: 'Times New Roman', serif;\"> (định lý tổng ba góc trong một tam giác)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 13.8px;\">\\(\\begin{array}{l} \\Rightarrow {90^0} + \\angle B + {30^0} = {180^0}\\\\ \\Rightarrow \\angle B + {120^0} = {180^0}\\\\ \\Rightarrow \\angle B = {60^0}\\end{array}\\)</p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 13.8px;\"><span style=\"font-size: 12pt; line-height: 18.4px; font-family: 'Times New Roman', serif;\">Ta có: </span><span class=\"MTConvertedEquation\">\\(\\angle C &lt; \\angle B &lt; \\angle A\\)</span><span style=\"font-size: 12pt; line-height: 18.4px; font-family: 'Times New Roman', serif;\"> (vì </span><span class=\"MTConvertedEquation\">\\({30^0} &lt; {60^0} &lt; {90^0}\\)</span><span style=\"font-size: 12pt; line-height: 18.4px; font-family: 'Times New Roman', serif;\">)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 13.8px;\"><span class=\"MTConvertedEquation\">\\( \\Rightarrow AB &lt; AC &lt; BC\\)</span><span style=\"font-size: 12pt; line-height: 18.4px; font-family: 'Times New Roman', serif;\"> (quan hệ giữa góc và cạnh đối diện trong tam giác)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 13.8px;\"><strong><span style=\"font-size: 12pt; line-height: 18.4px; font-family: 'Times New Roman', serif;\">Chọn D.</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">Câu 8.</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">Phương pháp</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">Tính chất đồng quy của 3 đường trung trực của tam giác</span></p>\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">Lời giải</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">3 đường trung trực của tam giác đồng quy tại 1 điểm, điểm này cách đều 3 đỉnh của tam giác.</span></p>\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">Chọn C.</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: .0001pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">II. PHẦN TỰ LUẬN <em>(8,0 điểm)</em></span></strong></p>\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">Bài 1.</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">Phương pháp</span></p>\r\n<p class=\"MsoNormal\" style=\"line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">a) Vận dụng định nghĩa hai phân số bằng nhau: Nếu </span><span class=\"MTConvertedEquation\">\\(\\dfrac{a}{b} = \\dfrac{c}{d}\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> thì </span><span class=\"MTConvertedEquation\">\\(ad = bc\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">.</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">b) Phương trình </span><span class=\"MTConvertedEquation\">\\(A\\left( x \\right).B\\left( x \\right) = 0\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> , chia hai trường hợp để giải:</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">+ Trường hợp 1: </span><span class=\"MTConvertedEquation\">\\(A\\left( x \\right) = 0\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">+ Trường hợp 2: </span><span class=\"MTConvertedEquation\">\\(B\\left( x \\right) = 0\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify;\"><strong><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">Cách giải:</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"margin-bottom: 0.0001pt; text-align: justify; line-height: 13.8px;\"><span style=\"font-size: 12pt; line-height: 18.4px; font-family: 'Times New Roman', serif;\">a) </span><span class=\"MTConvertedEquation\">\\(\\dfrac{{5x - 2}}{3} = \\dfrac{{ - 3}}{4}\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"margin-bottom: 0.0001pt; text-align: justify; line-height: 13.8px;\"><span class=\"MTConvertedEquation\">\\(\\begin{array}{l}4.\\left( {5x - 2} \\right) = \\left( { - 3} \\right).3\\\\20x - 8 =  - 9\\\\20x =  - 9 + 8\\\\20x =  - 1\\\\x = \\dfrac{{ - 1}}{{20}}\\end{array}\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"margin-bottom: 0.0001pt; text-align: justify; line-height: 13.8px;\"><span style=\"font-size: 12pt; line-height: 18.4px; font-family: 'Times New Roman', serif;\">Vậy </span><span class=\"MTConvertedEquation\">\\(x = \\dfrac{{ - 1}}{{20}}\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"margin-bottom: 0.0001pt; text-align: justify; line-height: 13.8px;\"><span style=\"font-size: 12pt; line-height: 18.4px; font-family: 'Times New Roman', serif;\">b) </span><span class=\"MTConvertedEquation\">\\(\\left( {{x^2} - \\dfrac{1}{4}} \\right).\\left( {x + \\dfrac{2}{5}} \\right) = 0\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"margin-bottom: 0.0001pt; text-align: justify; line-height: 13.8px;\"><span style=\"font-size: 12pt; line-height: 18.4px; font-family: 'Times New Roman', serif;\">Trường hợp 1:</span></p>\r\n<p class=\"MsoNormal\" style=\"margin-bottom: 0.0001pt; text-align: justify; line-height: 13.8px;\"><span class=\"MTConvertedEquation\">\\(\\begin{array}{l}{x^2} - \\dfrac{1}{4} = 0\\\\{x^2} = \\dfrac{1}{4} = {\\left( { \\pm \\dfrac{1}{2}} \\right)^2}\\\\ \\Rightarrow x = \\dfrac{1}{2};x =  - \\dfrac{1}{2}\\end{array}\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"margin-bottom: 0.0001pt; text-align: justify; line-height: 13.8px;\"><span style=\"font-size: 12pt; line-height: 18.4px; font-family: 'Times New Roman', serif;\">Trường hợp 2:</span></p>\r\n<p class=\"MsoNormal\" style=\"margin-bottom: 0.0001pt; text-align: justify; line-height: 13.8px;\"><span class=\"MTConvertedEquation\">\\(\\begin{array}{l}x + \\dfrac{2}{5} = 0\\\\x = \\dfrac{{ - 2}}{5}\\end{array}\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"margin-bottom: 0.0001pt; text-align: justify; line-height: 13.8px;\"> </p>\r\n<p class=\"MsoNormal\" style=\"margin-bottom: 0.0001pt; text-align: justify; line-height: 13.8px;\"><span style=\"font-size: 12pt; line-height: 18.4px; font-family: 'Times New Roman', serif;\">Vậy </span><span class=\"MTConvertedEquation\">\\(x = \\dfrac{1}{2};x =  - \\dfrac{1}{2};x = \\dfrac{{ - 2}}{5}\\)</span></p>\r\n<p> </p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify;\"><strong><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\" lang=\"VI\">Câu 2</span></strong><strong></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Phương pháp:</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Gọi số cây ba lớp </span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\" lang=\"VI\">7A, 7B, 7C trồng được lần lượt là </span><span class=\"MTConvertedEquation\">\\(x,y,z\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\" lang=\"VI\"> (cây) (điều kiện: </span><span class=\"MTConvertedEquation\">\\(x,y,z \\in {\\mathbb{N}^*}\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\" lang=\"VI\">)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Áp dụng tính chất của dãy tỉ số bằng nhau để giải toán.</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Cách giải: </span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Gọi số cây ba lớp </span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\" lang=\"VI\">7A, 7B, 7C trồng được lần lượt là </span><span class=\"MTConvertedEquation\">\\(x,y,z\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\" lang=\"VI\"> (cây) (điều kiện: </span><span class=\"MTConvertedEquation\">\\(x,y,z \\in {\\mathbb{N}^*}\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\" lang=\"VI\">)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\" lang=\"VI\">Vì </span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">số cây ở lớp 7A, 7B, 7C được trồng tỉ lệ với các số </span><span class=\"MTConvertedEquation\">\\(3\\,;\\,5\\,;\\,8\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\" lang=\"VI\"> nên ta có: </span><span class=\"MTConvertedEquation\">\\(\\dfrac{x}{3} = \\dfrac{y}{5} = \\dfrac{z}{8}\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\" lang=\"VI\">Vì </span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">hai lần số cây của lớp 7A cộng với </span><span class=\"MTConvertedEquation\">\\(4\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> lần số cây lớp 7B trồng được nhiều hơn số cây lớp 7C trồng được là </span><span class=\"MTConvertedEquation\">\\(108\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> cây</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\" lang=\"VI\"> nên ta có: </span><span class=\"MTConvertedEquation\">\\(2x + 4y - z = 108\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\" lang=\"VI\">Áp dụng tính chất của dãy tỉ số bằng nhau, ta có: </span><span class=\"MTConvertedEquation\">\\(\\dfrac{x}{3} = \\dfrac{y}{5} = \\dfrac{z}{8} = \\dfrac{{2x}}{6} = \\dfrac{{4y}}{{20}} = \\dfrac{z}{8} = \\dfrac{{2x + 4y - z}}{{6 + 20 - 8}} = \\dfrac{{108}}{{18}} = 6\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\" lang=\"VI\">Khi đó, </span><span class=\"MTConvertedEquation\">\\(\\dfrac{x}{3} = 6 \\Rightarrow x = 18\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\" lang=\"VI\"> (tmđk)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\" lang=\"VI\">            </span><span class=\"MTConvertedEquation\">\\(\\dfrac{y}{5} = 6 \\Rightarrow y = 30\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\" lang=\"VI\"> (tmđk)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; text-indent: 36.0pt; line-height: 115%;\"><span class=\"MTConvertedEquation\">\\(\\dfrac{z}{8} = 6 \\Rightarrow y = 48\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\" lang=\"VI\"> (tmđk)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\" lang=\"VI\">Vậy số cây ba lớp trồng được là: Lớp 7A: 18 cây; lớp 7B: 30 cây, lớp 7C: 48 cây.</span></p>\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">Bài 3.</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Phương pháp:</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">a) Thu gọn đa thức bằng cách nhóm các hạng tử đồng dạng lại rồi thu gọn chúng. Sau đó sắp xếp theo lũy thừa giảm dần của biến.</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">b) Tính </span><span class=\"MTConvertedEquation\">\\(f\\left( x \\right) + g\\left( x \\right)\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> ta nhóm các hạng tử đồng dạng lại rồi thu gọn chúng.</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Tìm nghiệm của đa thức </span><span class=\"MTConvertedEquation\">\\(f\\left( x \\right) + g\\left( x \\right)\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">, ta giải phương trình </span><span class=\"MTConvertedEquation\">\\(f\\left( x \\right) + g\\left( x \\right) = 0\\)</span><strong></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Cách giải: </span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">a) </span><span class=\"MTConvertedEquation\">\\(f\\left( x \\right) = {x^5} + {x^3} - 4x - {x^5} + 3x + 7\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">    </span><span class=\"MTConvertedEquation\">\\(\\begin{array}{l}f\\left( x \\right) = \\left( {{x^5} - {x^5}} \\right) + {x^3} + \\left( { - 4x + 3x} \\right) + 7\\\\f\\left( x \\right) = {x^3} - x + 7\\end{array}\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span class=\"MTConvertedEquation\">\\(\\begin{array}{l}g\\left( x \\right) = 3{x^2} - {x^3} + 8x - 3{x^2} - 14\\\\g\\left( x \\right) =  - {x^3} + \\left( {3{x^2} - 3{x^2}} \\right) + 8x - 14\\\\g\\left( x \\right) =  - {x^3} + 8x - 14\\end{array}\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">b) </span><span class=\"MTConvertedEquation\">\\(f\\left( x \\right) + g\\left( x \\right) = {x^3} - x + 7 - {x^3} + 8x - 14\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">   </span><span class=\"MTConvertedEquation\">\\(\\begin{array}{l}\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\, = {x^3} - x + 7 - {x^3} + 8x - 14\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\, = \\left( {{x^3} - {x^3}} \\right) + \\left( { - x + 8x} \\right) + \\left( {7 - 14} \\right)\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\, = 7x - 7\\end{array}\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Ta có: </span><span class=\"MTConvertedEquation\">\\(f\\left( x \\right) + g\\left( x \\right) = 0\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; text-indent: 36.0pt; line-height: 115%;\"><span class=\"MTConvertedEquation\">\\(\\begin{array}{l}7x - 7 = 0\\\\7x = 7\\\\\\,\\,\\,x = 1\\end{array}\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Vậy </span><span class=\"MTConvertedEquation\">\\(x = 1\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> là nghiệm của đa thức </span><span class=\"MTConvertedEquation\">\\(f\\left( x \\right) + g\\left( x \\right)\\)</span><strong></strong></p>\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">Bài 4.</span></strong></p>\r\n<p class=\"MsoNormal\"><strong><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">Phương pháp:</span></strong></p>\r\n<p class=\"MsoNormal\"><strong><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">+ </span></strong><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">Sử dụng các cách chứng minh hai tam giác bằng nhau.</span></p>\r\n<p class=\"MsoNormal\"><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">+ Mối quan hệ giữa góc và cạnh trong tam giác (Cạnh đối diện với góc lớn hơn thì lớn hơn)</span></p>\r\n<p class=\"MsoNormal\"><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">+ Tính chất trọng tâm của tam giác.</span></p>\r\n<p class=\"MsoNormal\"><strong><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">Cách giải:</span></strong></p>\r\n<p class=\"MsoNormal\"><img src=\"https://img.loigiaihay.com/picture/2023/0109/2023-01-09-160328_1.png\" style=\"text-align: center;\" /></p>\r\n<p class=\"MsoNormal\"><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">a. Xét </span><span class=\"MTConvertedEquation\">\\(\\Delta APH\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">và </span><span class=\"MTConvertedEquation\">\\(\\Delta QPC\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">có:</span></p>\r\n<p class=\"MsoNormal\"><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">+ </span><span class=\"MTConvertedEquation\">\\(HP = PC\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">(gt)</span></p>\r\n<p class=\"MsoNormal\"><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">+ </span><span class=\"MTConvertedEquation\">\\(\\angle APH = \\angle QPC\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">(đối đỉnh)</span></p>\r\n<p class=\"MsoNormal\"><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">+ </span><span class=\"MTConvertedEquation\">\\(QP = PA\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\"> (gt)</span></p>\r\n<p class=\"MsoNormal\"><span class=\"MTConvertedEquation\">\\( \\Rightarrow \\)\\(\\Delta APH = \\Delta QPC\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\"> (c.g.c) (đpcm).</span></p>\r\n<p class=\"MsoNormal\"><span class=\"MTConvertedEquation\">\\( \\Rightarrow \\angle AHP = \\angle QCP = {90^o}\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">(hai góc tương ứng)</span></p>\r\n<p class=\"MsoNormal\" style=\"margin-bottom: 12.0pt;\"><span class=\"MTConvertedEquation\">\\( \\Rightarrow QC \\bot BC\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">(đpcm).</span></p>\r\n<p class=\"MsoNormal\"><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">b. Theo (a) </span><span class=\"MTConvertedEquation\">\\(\\Delta APH = \\Delta QPC\\)</span></p>\r\n<p class=\"MsoNormal\"><span class=\"MTConvertedEquation\">\\( \\Rightarrow QC = AH\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">(hai cạnh tương ứng) (1)</span></p>\r\n<p class=\"MsoNormal\"><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">Mà </span><span class=\"MTConvertedEquation\">\\(\\Delta AHC\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">vuông tại H </span><span class=\"MTConvertedEquation\">\\( \\Rightarrow AH &lt; AC\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">(cạnh góc vuông &lt;cạnh huyền) (2)</span></p>\r\n<p class=\"MsoNormal\"><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">Từ (1) và (2), suy ra </span><span class=\"MTConvertedEquation\">\\(QC &lt; AC\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">(đpcm).</span></p>\r\n<p class=\"MsoNormal\"><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">c. Xét </span><span class=\"MTConvertedEquation\">\\(\\Delta AQC\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">có </span><span class=\"MTConvertedEquation\">\\(QC &lt; AC\\)\\( \\Rightarrow \\angle QAC &lt; \\angle AQC\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">                (3)  (Mối quan hệ giữa cạnh- góc trong tam giác)</span></p>\r\n<p class=\"MsoNormal\"><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">Mặt khác </span><span class=\"MTConvertedEquation\">\\(\\Delta APH = \\Delta QPC \\Rightarrow \\angle HAP = \\angle PQC = \\angle AQC\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">          (4)</span></p>\r\n<p class=\"MsoNormal\" style=\"margin-bottom: 12.0pt;\"><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">Từ (3) và (4) </span><span class=\"MTConvertedEquation\">\\( \\Rightarrow \\angle HAP &lt; \\angle QAC\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\"> hay </span><span class=\"MTConvertedEquation\">\\(\\angle HAP &lt; \\angle PAC\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">(đpcm).</span></p>\r\n<p class=\"MsoNormal\"><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">d. Xét </span><span class=\"MTConvertedEquation\">\\(\\Delta ABQ\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">có </span><span class=\"MTConvertedEquation\">\\(BP\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">là trung tuyến ứng với cạnh </span><span class=\"MTConvertedEquation\">\\(AQ\\)</span></p>\r\n<p class=\"MsoNormal\"><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">Mà </span><span class=\"MTConvertedEquation\">\\(BH = 2HP\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">(do </span><span class=\"MTConvertedEquation\">\\(H\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\"> là trung điểm của </span><span class=\"MTConvertedEquation\">\\(BC\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">, </span><span class=\"MTConvertedEquation\">\\(P\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">là trung điểm của </span><span class=\"MTConvertedEquation\">\\(HC\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">) </span><span class=\"MTConvertedEquation\">\\( \\Rightarrow H\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">là trọng tâm </span><span class=\"MTConvertedEquation\">\\(\\Delta ABQ\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">  (5)</span></p>\r\n<p class=\"MsoNormal\"><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">Lại có </span><span class=\"MTConvertedEquation\">\\(I\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">là trung điểm của </span><span class=\"MTConvertedEquation\">\\(BQ\\)</span><span class=\"MTConvertedEquation\">\\( \\Rightarrow AI\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">là trung tuyến ứng với cạnh </span><span class=\"MTConvertedEquation\">\\(BQ\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">     (6)</span></p>\r\n<p class=\"MsoNormal\"><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">Từ (5), (6)  </span><span class=\"MTConvertedEquation\">\\( \\Rightarrow H \\in AI\\)</span></p>\r\n<p class=\"MsoNormal\"><span class=\"MTConvertedEquation\">\\( \\Rightarrow A,H,I\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">thẳng hàng (đpcm)</span></p>\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">Bài 5.</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Phương pháp:</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Áp dụng tính chất của dãy tỉ số bằng nhau.</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Cách giải:</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Ta có: </span><span class=\"MTConvertedEquation\">\\(\\dfrac{a}{b} = \\dfrac{b}{c} = \\dfrac{c}{d} = \\dfrac{d}{e}\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> nên </span><span class=\"MTConvertedEquation\">\\(\\dfrac{a}{b} = \\dfrac{{2019b}}{{2019c}} = \\dfrac{{2020c}}{{2020d}} = \\dfrac{{2021d}}{{2021e}}\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Áp dụng tính chất của dãy tỉ số bằng nhau, ta có: </span><span class=\"MTConvertedEquation\">\\(\\dfrac{{2019b}}{{2019c}} = \\dfrac{{2020c}}{{2020d}} = \\dfrac{{2021d}}{{2021e}} = \\dfrac{{2019b + 2020c - 2021d}}{{2019c + 2020d - 2021e}}\\)</span></p>\r\n<p> </p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Mà </span><span class=\"MTConvertedEquation\">\\(\\dfrac{a}{b} = \\dfrac{{2019b}}{{2020c}}\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> và </span><span class=\"MTConvertedEquation\">\\(\\dfrac{a}{b} = \\dfrac{b}{c}\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> (gt) nên </span><span class=\"MTConvertedEquation\">\\({\\left( {\\dfrac{{2019b + 2020c - 2021d}}{{2019c + 2020d - 2021e}}} \\right)^3} = {\\left( {\\dfrac{a}{b}} \\right)^3} = \\dfrac{{{a^2}}}{{{b^2}}}.\\dfrac{a}{b} = \\dfrac{{{a^2}}}{{{b^2}}}.\\dfrac{b}{c} = \\dfrac{{{a^2}}}{{bc}}\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> (đpcm)</span></p>\r\n<p class=\"MsoNormal\" style=\"line-height: 150%; tab-stops: 14.15pt 5.0cm 269.3pt 396.85pt;\"><strong><span style=\"font-size: 12.0pt; line-height: 150%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\">I. TRẮC NGHIỆM (<em>2,0 điểm</em>)</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"margin-bottom: .0001pt; text-align: justify; line-height: 150%;\"><span style=\"font-size: 12.0pt; line-height: 150%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\">Hãy chọn phương án trả lời đúng và viết chữ cái đứng trước đáp án đó vào bài làm.</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\">Câu 1. </span></strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\">Hai đại lượng </span><span class=\"MTConvertedEquation\">\\(x,y\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"> trong công thức nào tỉ lệ nghịch với nhau:<strong></strong></span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: 14.2pt 5.0cm 10.0cm 15.0cm 482.7pt;\"><strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">     </span>A. </span></strong><span class=\"MTConvertedEquation\">\\(y = 5 + x\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">                    </span><strong>B. </strong></span><span class=\"MTConvertedEquation\">\\(x = \\dfrac{5}{y}\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">              </span><strong>C. </strong></span><span class=\"MTConvertedEquation\">\\(y = 5x\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">                            </span><strong>D. </strong></span><span class=\"MTConvertedEquation\">\\(x = 5y\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; mso-fareast-font-family: 'Times New Roman'; color: black; mso-themecolor: text1;\">Câu 2. </span></strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\">Biểu thức đại số biểu thị bình phương của một tổng hai số </span><span class=\"MTConvertedEquation\">\\(a\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"> và </span><span class=\"MTConvertedEquation\">\\(b\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"> là: <strong></strong></span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: 14.2pt 5.0cm 10.0cm 15.0cm 454.55pt 482.7pt;\"><strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">     </span>A. </span></strong><span class=\"MTConvertedEquation\">\\({a^2} - {b^2}\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">              </span><strong>B. </strong></span><span class=\"MTConvertedEquation\">\\({a^2} + {b^2}\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">                  </span><strong>C. </strong></span><span class=\"MTConvertedEquation\">\\({\\left( {a - b} \\right)^2}\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">   </span><strong>D. </strong></span><span class=\"MTConvertedEquation\">\\({\\left( {a + b} \\right)^2}\\)</span><strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 2;\">                                                                             </span></span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; mso-fareast-font-family: 'Times New Roman'; color: black; mso-themecolor: text1;\">Câu 3.</span></strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; mso-fareast-font-family: 'Times New Roman'; color: black; mso-themecolor: text1;\"> </span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\">Giá trị của biểu thức: </span><span class=\"MTConvertedEquation\">\\({x^3} - 2{x^2}\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"> tại </span><span class=\"MTConvertedEquation\">\\(x =<span style=\"mso-spacerun: yes;\">  </span>- 2\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"> là:<strong></strong></span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: 14.2pt 5.0cm 10.0cm 15.0cm 482.7pt;\"><strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">     </span>A. </span></strong><span class=\"MTConvertedEquation\">\\( - 16\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">                          </span><strong>B. </strong></span><span class=\"MTConvertedEquation\">\\(16\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">                                  </span><strong>C. </strong></span><span class=\"MTConvertedEquation\">\\(0\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">                                   </span><strong>D. </strong></span><span class=\"MTConvertedEquation\">\\( - 8\\)</span><strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">     </span></span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; mso-fareast-font-family: 'Times New Roman'; color: black; mso-themecolor: text1;\">Câu 4.</span></strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; mso-fareast-font-family: 'Times New Roman'; color: black; mso-themecolor: text1;\"> </span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\">Biểu thức nào sau đây <strong>không </strong>là đơn thức?</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: 14.2pt 5.0cm 10.0cm 15.0cm 482.7pt;\"><strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">     </span>A. </span></strong><span class=\"MTConvertedEquation\">\\(4{x^2}y\\left( { - 2x} \\right)\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">                                         </span><strong>B. </strong></span><span class=\"MTConvertedEquation\">\\(2x\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">                                  </span><strong>C. </strong></span><span class=\"MTConvertedEquation\">\\(2xy - {x^2}\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><strong>D. </strong></span><span class=\"MTConvertedEquation\">\\(2021\\)</span><strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">                                   </span></span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; mso-fareast-font-family: 'Times New Roman'; color: black; mso-themecolor: text1;\">Câu 5.</span></strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; mso-fareast-font-family: 'Times New Roman'; color: black; mso-themecolor: text1;\"> </span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\">Sắp xếp các hạng tử của đa thức </span><span class=\"MTConvertedEquation\">\\(P\\left( x \\right) = 2{x^3} - 7{x^2} + {x^4} - 4\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"> theo lũy thừa giảm dần của biến ta được:<strong></strong></span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: 14.2pt 5.0cm 10.0cm 15.0cm 482.7pt;\"><strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">     </span>A. </span></strong><span class=\"MTConvertedEquation\">\\(P\\left( x \\right) = {x^4} + 2{x^3} - 7{x^2} - 4\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">                 </span><strong>B. </strong></span><span class=\"MTConvertedEquation\">\\(P\\left( x \\right) = 7{x^2} + 2{x^3} + {x^4} - 4\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: 14.2pt 5.0cm 10.0cm 15.0cm 482.7pt;\"><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">     </span><strong>C. </strong></span><span class=\"MTConvertedEquation\">\\(P\\left( x \\right) =<span style=\"mso-spacerun: yes;\">  </span>- 4 - 7{x^2} + 2{x^3} + {x^4}\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">             </span><strong>D. </strong></span><span class=\"MTConvertedEquation\">\\(P\\left( x \\right) = {x^4} - 2{x^3} - 7{x^2} - 4\\)</span><strong></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; mso-fareast-font-family: 'Times New Roman'; color: black; mso-themecolor: text1;\">Câu 6.</span></strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; mso-fareast-font-family: 'Times New Roman'; color: black; mso-themecolor: text1;\"> </span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\">Cho tam giác </span><span class=\"MTConvertedEquation\">\\(MNP\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"> có </span><span class=\"MTConvertedEquation\">\\(NP = 1cm,MP = 7cm\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\">. Độ dài cạnh </span><span class=\"MTConvertedEquation\">\\(MN\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"> là một số nguyên (cm). Độ dài cạnh </span><span class=\"MTConvertedEquation\">\\(MN\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"> là:</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: 14.2pt 5.0cm 10.0cm 15.0cm 482.7pt;\"><strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">     </span>A. </span></strong><span class=\"MTConvertedEquation\">\\(8cm\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">                          </span><strong>B. </strong></span><span class=\"MTConvertedEquation\">\\(5cm\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">                               </span><strong>C. </strong></span><span class=\"MTConvertedEquation\">\\(6cm\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">                               </span><strong>D. </strong></span><span class=\"MTConvertedEquation\">\\(7cm\\)</span><strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">   </span></span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; mso-fareast-font-family: 'Times New Roman'; color: black; mso-themecolor: text1;\">Câu 7. </span></strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\">Cho tam giác </span><span class=\"MTConvertedEquation\">\\(ABC\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\">, có </span><span class=\"MTConvertedEquation\">\\(\\angle A = {90^0};\\angle C = {30^0}\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\">. Khi đó quan hệ giữa ba cạnh </span><span class=\"MTConvertedEquation\">\\(AB,AC,BC\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"> là:<strong></strong></span></p>","common_article":"","display_type":2,"vungoi_exam_id":"","article_type":1,"cmt_count":1,"zip_status":1,"last_modified_time":1707118261,"last_zip_time":1707118261,"zip_link":"https://offline.loigiaihay.com/articles/1097/133061/133061_1707118261.zip","picture":"","youtube_id":"","url_upload_pdf":"https://img.loigiaihay.com/picture/share_img/2023/0109/de-kiem-tra-giua-hoc-ki-2-toan-7-de-so-4-ket-noi-tri-thuc-1673255368.pdf","video_start_time":"0","quizlet_id":"0","ref_article_id":0,"readmore_display_type":0,"wiki":0,"sub_articles":[{"id":"705056","group_title":"","sub_article_link":"0","order_in_article":"1","title":"Đề bài","content":"<p><strong>I. TRẮC NGHIỆM (<em>2,0 điểm</em>)</strong></p>\r\n<p>Hãy chọn phương án trả lời đúng và viết chữ cái đứng trước đáp án đó vào bài làm.</p>\r\n<p><strong>Câu 1. </strong>Hai đại lượng \\(x,y\\) trong công thức nào tỉ lệ nghịch với nhau:<strong></strong></p>\r\n<p><strong>     A. </strong>\\(y = 5 + x\\)                    <strong>B. </strong>\\(x = \\dfrac{5}{y}\\)              <strong>C. </strong>\\(y = 5x\\)                            <strong>D. </strong>\\(x = 5y\\)</p>\r\n<p><strong>Câu 2. </strong>Biểu thức đại số biểu thị bình phương của một tổng hai số \\(a\\) và \\(b\\) là: <strong></strong></p>\r\n<p><strong>     A. </strong>\\({a^2} - {b^2}\\)              <strong>B. </strong>\\({a^2} + {b^2}\\)                  <strong>C. </strong>\\({\\left( {a - b} \\right)^2}\\)   <strong>D. </strong>\\({\\left( {a + b} \\right)^2}\\)<strong>                                                                             </strong></p>\r\n<p><strong>Câu 3.</strong> Giá trị của biểu thức: \\({x^3} - 2{x^2}\\) tại \\(x =  - 2\\) là:<strong></strong></p>\r\n<p><strong>     A. </strong>\\( - 16\\)                          <strong>B. </strong>\\(16\\)                                  <strong>C. </strong>\\(0\\)                                   <strong>D. </strong>\\( - 8\\)<strong>     </strong></p>\r\n<p><strong>Câu 4.</strong> Biểu thức nào sau đây <strong>không </strong>là đơn thức?</p>\r\n<p><strong>     A. </strong>\\(4{x^2}y\\left( { - 2x} \\right)\\)                                         <strong>B. </strong>\\(2x\\)                                  <strong>C. </strong>\\(2xy - {x^2}\\) <strong>D. </strong>\\(2021\\)<strong>                                   </strong></p>\r\n<p><strong>Câu 5.</strong> Sắp xếp các hạng tử của đa thức \\(P\\left( x \\right) = 2{x^3} - 7{x^2} + {x^4} - 4\\) theo lũy thừa giảm dần của biến ta được:<strong></strong></p>\r\n<p><strong>     A. </strong>\\(P\\left( x \\right) = {x^4} + 2{x^3} - 7{x^2} - 4\\)                 <strong>B. </strong>\\(P\\left( x \\right) = 7{x^2} + 2{x^3} + {x^4} - 4\\)</p>\r\n<p>     <strong>C. </strong>\\(P\\left( x \\right) =  - 4 - 7{x^2} + 2{x^3} + {x^4}\\)             <strong>D. </strong>\\(P\\left( x \\right) = {x^4} - 2{x^3} - 7{x^2} - 4\\)<strong> </strong></p>\r\n<p><strong>Câu 6.</strong> Cho tam giác \\(MNP\\) có \\(NP = 1cm,MP = 7cm\\). Độ dài cạnh \\(MN\\) là một số nguyên (cm). Độ dài cạnh \\(MN\\) là:</p>\r\n<p><strong>     A. </strong>\\(8cm\\)                          <strong>B. </strong>\\(5cm\\)                               <strong>C. </strong>\\(6cm\\)                               <strong>D. </strong>\\(7cm\\)<strong>   </strong></p>\r\n<p><strong>Câu 7. </strong>Cho tam giác \\(ABC\\), có \\(\\angle A = {90^0};\\angle C = {30^0}\\). Khi đó quan hệ giữa ba cạnh \\(AB,AC,BC\\) là:<strong></strong></p>\r\n<p><strong>     A. </strong>\\(BC &gt; AB &gt; AC\\)             <strong>B. </strong> \\(AC &gt; AB &gt; BC\\)                 <strong>C. </strong>\\(AB &gt; AC &gt; BC\\)                  <strong>D. </strong>\\(BC &gt; AC &gt; AB\\)</p>\r\n<p><strong>Câu 8.</strong> Giao điểm của 3 đường trung trực của tam giác</p>\r\n<p>A. cách đều 3 cạnh của tam giác.</p>\r\n<p>B. được gọi là trực tâm của tam giác.</p>\r\n<p>C. cách đều 3 đỉnh của tam giác.</p>\r\n<p>D. cách đỉnh một đoạn bằng \\(\\dfrac{2}{3}\\) độ dài đường trung tuyến đi qua đỉnh đó.</p>\r\n<p><strong>II. PHẦN TỰ LUẬN <em>(8,0 điểm)</em></strong></p>\r\n<p><strong>Bài 1. <em>(1 điểm)</em></strong> Tìm \\(x\\) biết:</p>\r\n<p>a)       \\(\\dfrac{{5x - 2}}{3} = \\dfrac{{ - 3}}{4}\\)                           b) \\(\\left( {{x^2} - \\dfrac{1}{4}} \\right).\\left( {x + \\dfrac{2}{5}} \\right) = 0\\)<strong></strong></p>\r\n<p><strong>Bài 2. <em>(1,5 điểm)</em></strong> Ba lớp 7A, 7B, 7C cùng tham gia lao động trồng cây. Biết số cây ở lớp 7A, 7B, 7C được trồng tỉ lệ với các số \\(3\\,;\\,5\\,;\\,8\\) và hai lần số cây của lớp 7A cộng với \\(4\\) lần số cây lớp 7B trồng được nhiều hơn số cây lớp 7C trồng được là \\(108\\) cây. Tính số cây trồng được của mỗi lớp</p>\r\n<p><strong>Bài 3. <em>(1,5 điểm)</em></strong> Cho hai đa thức: \\(f\\left( x \\right) = {x^5} + {x^3} - 4x - {x^5} + 3x + 7\\) và \\(g\\left( x \\right) = 3{x^2} - {x^3} + 8x - 3{x^2} - 14\\).</p>\r\n<p>a) Thu gọn và sắp xếp hai đa thức \\(f\\left( x \\right)\\) và \\(g\\left( x \\right)\\) theo lũy thừa giảm dần của biến.</p>\r\n<p>b) Tính \\(f\\left( x \\right) + g\\left( x \\right)\\) và tìm nghiệm của đa thức \\(f\\left( x \\right) + g\\left( x \\right)\\).    </p>\r\n<p><strong>Bài 4. <em>(3,5 điểm)</em></strong> Cho tam giác \\(ABC\\) cân tại \\(A\\), kẻ \\(AH\\)vuông góc với \\(BC\\)\\(\\left( {H \\in BC} \\right)\\). Gọi \\(P\\) là trung điểm của \\(HC\\). Trên tia đối của tia \\(PA\\) lấy điểm \\(Q\\) sao cho \\(QP = PA\\).</p>\r\n<p>a) Chứng minh rằng: \\(\\Delta APH = \\Delta QPC\\) và \\(QC\\) vuông góc với\\(BC\\).</p>\r\n<p>b) Chứng minh rằng: \\(QC = AH\\)từ đó suy ra \\(AC &gt; QC\\).</p>\r\n<p>c) Chứng minh rằng: \\(\\angle PAC &lt; \\angle HAP\\)</p>\r\n<p>d) Gọi \\(I\\) là trung điểm của \\(BQ\\). Chứng minh rằng ba điểm \\(A,H,I\\) thẳng hàng.</p>\r\n<p><strong>Bài 5. <em>(0,5 điểm) </em></strong>Cho các số thực \\(a,b,c,d,e\\) thỏa mãn: \\(\\dfrac{a}{b} = \\dfrac{b}{c} = \\dfrac{c}{d} = \\dfrac{d}{e}\\).</p>\r\n<p>Chứng minh rằng: \\({\\left( {\\dfrac{{2019b + 2020c - 2021d}}{{2019c + 2020d - 2021e}}} \\right)^3} = \\dfrac{{{a^2}}}{{bc}}\\).</p>\r\n<p align=\"center\"><em>(Giả thiết các tỉ số đều có nghĩa)</em></p>","youtube_id":"","video_start_time":"0"},{"id":"705057","group_title":"","sub_article_link":"0","order_in_article":"2","title":"Lời giải","content":"<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">I. Trắc nghiệm</span></strong></p>\r\n<table class=\"MsoNormalTable\" style=\"width: 430px; border-collapse: collapse; border: none;\" border=\"1\" cellspacing=\"0\" cellpadding=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"border: solid #DDDDDD 1.0pt; mso-border-alt: solid #DDDDDD .75pt; padding: 6.0pt 6.0pt 6.0pt 6.0pt;\" valign=\"top\">\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: center; line-height: 18.0pt;\" align=\"center\"><strong><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">1.B</span></strong></strong></p>\r\n</td>\r\n<td style=\"border: solid #DDDDDD 1.0pt; border-left: none; mso-border-left-alt: solid #DDDDDD .75pt; mso-border-alt: solid #DDDDDD .75pt; padding: 6.0pt 6.0pt 6.0pt 6.0pt;\" valign=\"top\">\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: center; line-height: 18.0pt;\" align=\"center\"><strong><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">2.</span></strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\"> D</span></strong></p>\r\n</td>\r\n<td style=\"border: solid #DDDDDD 1.0pt; border-left: none; mso-border-left-alt: solid #DDDDDD .75pt; mso-border-alt: solid #DDDDDD .75pt; padding: 6.0pt 6.0pt 6.0pt 6.0pt;\" valign=\"top\">\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: center; line-height: 18.0pt;\" align=\"center\"><strong><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">3. </span></strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">A</span></strong></p>\r\n</td>\r\n<td style=\"border: solid #DDDDDD 1.0pt; border-left: none; mso-border-left-alt: solid #DDDDDD .75pt; mso-border-alt: solid #DDDDDD .75pt; padding: 6.0pt 6.0pt 6.0pt 6.0pt;\" valign=\"top\">\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: center; line-height: 18.0pt;\" align=\"center\"><strong><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">4.</span></strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\"> C</span></strong></p>\r\n</td>\r\n</tr>\r\n<tr>\r\n<td style=\"border: solid #DDDDDD 1.0pt; border-top: none; mso-border-top-alt: solid #DDDDDD .75pt; mso-border-alt: solid #DDDDDD .75pt; padding: 6.0pt 6.0pt 6.0pt 6.0pt;\" valign=\"top\">\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: center; line-height: 18.0pt;\" align=\"center\"><strong><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">5.</span></strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\"> A</span></strong></p>\r\n</td>\r\n<td style=\"border-top: none; border-left: none; border-bottom: solid #DDDDDD 1.0pt; border-right: solid #DDDDDD 1.0pt; mso-border-top-alt: solid #DDDDDD .75pt; mso-border-left-alt: solid #DDDDDD .75pt; mso-border-alt: solid #DDDDDD .75pt; padding: 6.0pt 6.0pt 6.0pt 6.0pt;\" valign=\"top\">\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: center; line-height: 18.0pt;\" align=\"center\"><strong><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">6.</span></strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\"> D</span></strong></p>\r\n</td>\r\n<td style=\"border-top: none; border-left: none; border-bottom: solid #DDDDDD 1.0pt; border-right: solid #DDDDDD 1.0pt; mso-border-top-alt: solid #DDDDDD .75pt; mso-border-left-alt: solid #DDDDDD .75pt; mso-border-alt: solid #DDDDDD .75pt; padding: 6.0pt 6.0pt 6.0pt 6.0pt;\" valign=\"top\">\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: center; line-height: 18.0pt;\" align=\"center\"><strong><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">7.</span></strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\"> D</span></strong></p>\r\n</td>\r\n<td style=\"border-top: none; border-left: none; border-bottom: solid #DDDDDD 1.0pt; border-right: solid #DDDDDD 1.0pt; mso-border-top-alt: solid #DDDDDD .75pt; mso-border-left-alt: solid #DDDDDD .75pt; mso-border-alt: solid #DDDDDD .75pt; padding: 6.0pt 6.0pt 6.0pt 6.0pt;\" valign=\"top\">\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: center; line-height: 18.0pt;\" align=\"center\"><strong><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">8.</span></strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\"> C</span></strong></p>\r\n</td>\r\n</tr>\r\n</tbody>\r\n</table>\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">Câu 1.</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Phương pháp:</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Vận dụng định nghĩa về đại lượng tỉ lệ nghịch.<strong></strong></span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Cách giải: </span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: 14.2pt 5.0cm 10.0cm 15.0cm 482.7pt;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Ta có: </span><span class=\"MTConvertedEquation\">\\(x = \\dfrac{5}{y}\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> là hai đại lượng tỉ lệ nghịch với nhau.</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: 14.2pt 5.0cm 10.0cm 15.0cm 482.7pt;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Chọn B.</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">Câu 2.</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: 125.5pt;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Phương pháp:                 </span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: 125.5pt;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Dùng các chữ, các số và các phép toán để diễn đạt các mệnh đề phát biểu bằng lời.<strong></strong></span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Cách giải: </span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: 374.95pt;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Bình phương của một tổng hai số </span><span class=\"MTConvertedEquation\">\\(a\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> và </span><span class=\"MTConvertedEquation\">\\(b\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> là: </span><span class=\"MTConvertedEquation\">\\({\\left( {a + b} \\right)^2}\\)</span><strong></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: 14.2pt 5.0cm 10.0cm 15.0cm 482.7pt;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Chọn D.</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">Câu 3.</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Phương pháp:</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Thay </span><span class=\"MTConvertedEquation\">\\(x =  - 2\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> vào biểu thức </span><span class=\"MTConvertedEquation\">\\({x^3} - 2{x^2}\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> để tính.<strong></strong></span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Cách giải: </span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Thay </span><span class=\"MTConvertedEquation\">\\(x =  - 2\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> vào biểu thức </span><span class=\"MTConvertedEquation\">\\({x^3} - 2{x^2}\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> ta có: </span><span class=\"MTConvertedEquation\">\\({\\left( { - 2} \\right)^3} - 2.{\\left( { - 2} \\right)^2} = \\left( { - 8} \\right) - 2.4 =  - 16\\)</span><strong></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: 14.2pt 5.0cm 10.0cm 15.0cm 482.7pt;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Chọn A.</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">Câu 4.</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Phương pháp:</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Đơn thức là biểu thức đại số chỉ gồm một số, hoặc một biến, hoặc một tích giữa các số và các biến.<strong></strong></span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Cách giải: </span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Biểu thức: </span><span class=\"MTConvertedEquation\">\\(2xy - {x^2}\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> không là một đơn thức.</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: 14.2pt 5.0cm 10.0cm 15.0cm 482.7pt;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Chọn C.</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">Câu 5.</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Phương pháp:</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Thu gọn đa thức bằng cách nhóm các hạng tử đồng dạng lại rồi thu gọn chúng. Sau đó sắp xếp theo lũy thừa giảm dần của biến.<strong></strong></span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Cách giải: </span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Sắp xếp theo lũy thừa giảm dần của biến: </span><span class=\"MTConvertedEquation\">\\(P\\left( x \\right) = {x^4} + 2{x^3} - 7{x^2} - 4\\)</span><strong></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: 14.2pt 5.0cm 10.0cm 15.0cm 482.7pt;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Chọn A.</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">Câu 6.</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Phương pháp:</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Sử dụng hệ quả của bất đẳng thức trong tam giác:</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">+ Tồn tại một tam giác có độ dài ba cạnh là </span><span class=\"MTConvertedEquation\">\\(a,b,c\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> nếu </span><span class=\"MTConvertedEquation\">\\(\\left| {b - c} \\right| &lt; a &lt; b + c\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">.</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">+ Trong trường hợp xác định được </span><span class=\"MTConvertedEquation\">\\(a\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> là số lớn nhất trong ba số </span><span class=\"MTConvertedEquation\">\\(a,b,c\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> thì điều kiện tồn tại tam giác là </span><span class=\"MTConvertedEquation\">\\(a &lt; b + c\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">. <strong></strong></span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Cách giải: </span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: center 269.3pt;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Xét tam giác </span><span class=\"MTConvertedEquation\">\\(MNP\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">, ta có: </span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: center 269.3pt;\"><span class=\"MTConvertedEquation\">\\(\\begin{array}{l}\\,\\,\\,\\,\\,\\,\\,\\left| {NP - MP} \\right| &lt; MN &lt; NP + MP\\\\ \\Rightarrow \\left| {1 - 7} \\right| &lt; MN &lt; 1 + 7\\\\ \\Rightarrow 6 &lt; MN &lt; 8\\end{array}\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: center 269.3pt;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Vì độ dài cạnh </span><span class=\"MTConvertedEquation\">\\(MN\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> là một số nguyên nên </span><span class=\"MTConvertedEquation\">\\(MN = 7\\,\\left( {cm} \\right)\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">     <strong></strong></span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: 14.2pt 5.0cm 10.0cm 15.0cm 482.7pt;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Chọn D.</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">Câu 7.</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Phương pháp:</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 13.8px;\"><span style=\"font-family: 'Times New Roman', serif; font-size: 12pt;\">Sử dụng quan hệ giữa góc và cạnh đối diện trong tam giác.</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 13.8px;\"><strong><span style=\"font-size: 12pt; line-height: 18.4px; font-family: 'Times New Roman', serif;\">Cách giải:</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 13.8px;\"><span style=\"font-size: 12pt; line-height: 18.4px; font-family: 'Times New Roman', serif;\">Xét </span><span class=\"MTConvertedEquation\">\\(\\Delta ABC\\)</span><span style=\"font-size: 12pt; line-height: 18.4px; font-family: 'Times New Roman', serif;\"> có: </span><span class=\"MTConvertedEquation\">\\(\\angle A + \\angle B + \\angle C = {180^0}\\)</span><span style=\"font-size: 12pt; line-height: 18.4px; font-family: 'Times New Roman', serif;\"> (định lý tổng ba góc trong một tam giác)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 13.8px;\">\\(\\begin{array}{l} \\Rightarrow {90^0} + \\angle B + {30^0} = {180^0}\\\\ \\Rightarrow \\angle B + {120^0} = {180^0}\\\\ \\Rightarrow \\angle B = {60^0}\\end{array}\\)</p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 13.8px;\"><span style=\"font-size: 12pt; line-height: 18.4px; font-family: 'Times New Roman', serif;\">Ta có: </span><span class=\"MTConvertedEquation\">\\(\\angle C &lt; \\angle B &lt; \\angle A\\)</span><span style=\"font-size: 12pt; line-height: 18.4px; font-family: 'Times New Roman', serif;\"> (vì </span><span class=\"MTConvertedEquation\">\\({30^0} &lt; {60^0} &lt; {90^0}\\)</span><span style=\"font-size: 12pt; line-height: 18.4px; font-family: 'Times New Roman', serif;\">)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 13.8px;\"><span class=\"MTConvertedEquation\">\\( \\Rightarrow AB &lt; AC &lt; BC\\)</span><span style=\"font-size: 12pt; line-height: 18.4px; font-family: 'Times New Roman', serif;\"> (quan hệ giữa góc và cạnh đối diện trong tam giác)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 13.8px;\"><strong><span style=\"font-size: 12pt; line-height: 18.4px; font-family: 'Times New Roman', serif;\">Chọn D.</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">Câu 8.</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">Phương pháp</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">Tính chất đồng quy của 3 đường trung trực của tam giác</span></p>\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">Lời giải</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">3 đường trung trực của tam giác đồng quy tại 1 điểm, điểm này cách đều 3 đỉnh của tam giác.</span></p>\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">Chọn C.</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: .0001pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">II. PHẦN TỰ LUẬN <em>(8,0 điểm)</em></span></strong></p>\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">Bài 1.</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">Phương pháp</span></p>\r\n<p class=\"MsoNormal\" style=\"line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">a) Vận dụng định nghĩa hai phân số bằng nhau: Nếu </span><span class=\"MTConvertedEquation\">\\(\\dfrac{a}{b} = \\dfrac{c}{d}\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> thì </span><span class=\"MTConvertedEquation\">\\(ad = bc\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">.</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">b) Phương trình </span><span class=\"MTConvertedEquation\">\\(A\\left( x \\right).B\\left( x \\right) = 0\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> , chia hai trường hợp để giải:</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">+ Trường hợp 1: </span><span class=\"MTConvertedEquation\">\\(A\\left( x \\right) = 0\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">+ Trường hợp 2: </span><span class=\"MTConvertedEquation\">\\(B\\left( x \\right) = 0\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify;\"><strong><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">Cách giải:</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"margin-bottom: 0.0001pt; text-align: justify; line-height: 13.8px;\"><span style=\"font-size: 12pt; line-height: 18.4px; font-family: 'Times New Roman', serif;\">a) </span><span class=\"MTConvertedEquation\">\\(\\dfrac{{5x - 2}}{3} = \\dfrac{{ - 3}}{4}\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"margin-bottom: 0.0001pt; text-align: justify; line-height: 13.8px;\"><span class=\"MTConvertedEquation\">\\(\\begin{array}{l}4.\\left( {5x - 2} \\right) = \\left( { - 3} \\right).3\\\\20x - 8 =  - 9\\\\20x =  - 9 + 8\\\\20x =  - 1\\\\x = \\dfrac{{ - 1}}{{20}}\\end{array}\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"margin-bottom: 0.0001pt; text-align: justify; line-height: 13.8px;\"><span style=\"font-size: 12pt; line-height: 18.4px; font-family: 'Times New Roman', serif;\">Vậy </span><span class=\"MTConvertedEquation\">\\(x = \\dfrac{{ - 1}}{{20}}\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"margin-bottom: 0.0001pt; text-align: justify; line-height: 13.8px;\"><span style=\"font-size: 12pt; line-height: 18.4px; font-family: 'Times New Roman', serif;\">b) </span><span class=\"MTConvertedEquation\">\\(\\left( {{x^2} - \\dfrac{1}{4}} \\right).\\left( {x + \\dfrac{2}{5}} \\right) = 0\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"margin-bottom: 0.0001pt; text-align: justify; line-height: 13.8px;\"><span style=\"font-size: 12pt; line-height: 18.4px; font-family: 'Times New Roman', serif;\">Trường hợp 1:</span></p>\r\n<p class=\"MsoNormal\" style=\"margin-bottom: 0.0001pt; text-align: justify; line-height: 13.8px;\"><span class=\"MTConvertedEquation\">\\(\\begin{array}{l}{x^2} - \\dfrac{1}{4} = 0\\\\{x^2} = \\dfrac{1}{4} = {\\left( { \\pm \\dfrac{1}{2}} \\right)^2}\\\\ \\Rightarrow x = \\dfrac{1}{2};x =  - \\dfrac{1}{2}\\end{array}\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"margin-bottom: 0.0001pt; text-align: justify; line-height: 13.8px;\"><span style=\"font-size: 12pt; line-height: 18.4px; font-family: 'Times New Roman', serif;\">Trường hợp 2:</span></p>\r\n<p class=\"MsoNormal\" style=\"margin-bottom: 0.0001pt; text-align: justify; line-height: 13.8px;\"><span class=\"MTConvertedEquation\">\\(\\begin{array}{l}x + \\dfrac{2}{5} = 0\\\\x = \\dfrac{{ - 2}}{5}\\end{array}\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"margin-bottom: 0.0001pt; text-align: justify; line-height: 13.8px;\"> </p>\r\n<p class=\"MsoNormal\" style=\"margin-bottom: 0.0001pt; text-align: justify; line-height: 13.8px;\"><span style=\"font-size: 12pt; line-height: 18.4px; font-family: 'Times New Roman', serif;\">Vậy </span><span class=\"MTConvertedEquation\">\\(x = \\dfrac{1}{2};x =  - \\dfrac{1}{2};x = \\dfrac{{ - 2}}{5}\\)</span></p>\r\n<p> </p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify;\"><strong><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\" lang=\"VI\">Câu 2</span></strong><strong></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Phương pháp:</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Gọi số cây ba lớp </span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\" lang=\"VI\">7A, 7B, 7C trồng được lần lượt là </span><span class=\"MTConvertedEquation\">\\(x,y,z\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\" lang=\"VI\"> (cây) (điều kiện: </span><span class=\"MTConvertedEquation\">\\(x,y,z \\in {\\mathbb{N}^*}\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\" lang=\"VI\">)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Áp dụng tính chất của dãy tỉ số bằng nhau để giải toán.</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Cách giải: </span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Gọi số cây ba lớp </span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\" lang=\"VI\">7A, 7B, 7C trồng được lần lượt là </span><span class=\"MTConvertedEquation\">\\(x,y,z\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\" lang=\"VI\"> (cây) (điều kiện: </span><span class=\"MTConvertedEquation\">\\(x,y,z \\in {\\mathbb{N}^*}\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\" lang=\"VI\">)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\" lang=\"VI\">Vì </span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">số cây ở lớp 7A, 7B, 7C được trồng tỉ lệ với các số </span><span class=\"MTConvertedEquation\">\\(3\\,;\\,5\\,;\\,8\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\" lang=\"VI\"> nên ta có: </span><span class=\"MTConvertedEquation\">\\(\\dfrac{x}{3} = \\dfrac{y}{5} = \\dfrac{z}{8}\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\" lang=\"VI\">Vì </span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">hai lần số cây của lớp 7A cộng với </span><span class=\"MTConvertedEquation\">\\(4\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> lần số cây lớp 7B trồng được nhiều hơn số cây lớp 7C trồng được là </span><span class=\"MTConvertedEquation\">\\(108\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> cây</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\" lang=\"VI\"> nên ta có: </span><span class=\"MTConvertedEquation\">\\(2x + 4y - z = 108\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\" lang=\"VI\">Áp dụng tính chất của dãy tỉ số bằng nhau, ta có: </span><span class=\"MTConvertedEquation\">\\(\\dfrac{x}{3} = \\dfrac{y}{5} = \\dfrac{z}{8} = \\dfrac{{2x}}{6} = \\dfrac{{4y}}{{20}} = \\dfrac{z}{8} = \\dfrac{{2x + 4y - z}}{{6 + 20 - 8}} = \\dfrac{{108}}{{18}} = 6\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\" lang=\"VI\">Khi đó, </span><span class=\"MTConvertedEquation\">\\(\\dfrac{x}{3} = 6 \\Rightarrow x = 18\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\" lang=\"VI\"> (tmđk)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\" lang=\"VI\">            </span><span class=\"MTConvertedEquation\">\\(\\dfrac{y}{5} = 6 \\Rightarrow y = 30\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\" lang=\"VI\"> (tmđk)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; text-indent: 36.0pt; line-height: 115%;\"><span class=\"MTConvertedEquation\">\\(\\dfrac{z}{8} = 6 \\Rightarrow y = 48\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\" lang=\"VI\"> (tmđk)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\" lang=\"VI\">Vậy số cây ba lớp trồng được là: Lớp 7A: 18 cây; lớp 7B: 30 cây, lớp 7C: 48 cây.</span></p>\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">Bài 3.</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Phương pháp:</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">a) Thu gọn đa thức bằng cách nhóm các hạng tử đồng dạng lại rồi thu gọn chúng. Sau đó sắp xếp theo lũy thừa giảm dần của biến.</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">b) Tính </span><span class=\"MTConvertedEquation\">\\(f\\left( x \\right) + g\\left( x \\right)\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> ta nhóm các hạng tử đồng dạng lại rồi thu gọn chúng.</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Tìm nghiệm của đa thức </span><span class=\"MTConvertedEquation\">\\(f\\left( x \\right) + g\\left( x \\right)\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">, ta giải phương trình </span><span class=\"MTConvertedEquation\">\\(f\\left( x \\right) + g\\left( x \\right) = 0\\)</span><strong></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Cách giải: </span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">a) </span><span class=\"MTConvertedEquation\">\\(f\\left( x \\right) = {x^5} + {x^3} - 4x - {x^5} + 3x + 7\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">    </span><span class=\"MTConvertedEquation\">\\(\\begin{array}{l}f\\left( x \\right) = \\left( {{x^5} - {x^5}} \\right) + {x^3} + \\left( { - 4x + 3x} \\right) + 7\\\\f\\left( x \\right) = {x^3} - x + 7\\end{array}\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span class=\"MTConvertedEquation\">\\(\\begin{array}{l}g\\left( x \\right) = 3{x^2} - {x^3} + 8x - 3{x^2} - 14\\\\g\\left( x \\right) =  - {x^3} + \\left( {3{x^2} - 3{x^2}} \\right) + 8x - 14\\\\g\\left( x \\right) =  - {x^3} + 8x - 14\\end{array}\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">b) </span><span class=\"MTConvertedEquation\">\\(f\\left( x \\right) + g\\left( x \\right) = {x^3} - x + 7 - {x^3} + 8x - 14\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">   </span><span class=\"MTConvertedEquation\">\\(\\begin{array}{l}\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\, = {x^3} - x + 7 - {x^3} + 8x - 14\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\, = \\left( {{x^3} - {x^3}} \\right) + \\left( { - x + 8x} \\right) + \\left( {7 - 14} \\right)\\\\\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\, = 7x - 7\\end{array}\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Ta có: </span><span class=\"MTConvertedEquation\">\\(f\\left( x \\right) + g\\left( x \\right) = 0\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; text-indent: 36.0pt; line-height: 115%;\"><span class=\"MTConvertedEquation\">\\(\\begin{array}{l}7x - 7 = 0\\\\7x = 7\\\\\\,\\,\\,x = 1\\end{array}\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Vậy </span><span class=\"MTConvertedEquation\">\\(x = 1\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> là nghiệm của đa thức </span><span class=\"MTConvertedEquation\">\\(f\\left( x \\right) + g\\left( x \\right)\\)</span><strong></strong></p>\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">Bài 4.</span></strong></p>\r\n<p class=\"MsoNormal\"><strong><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">Phương pháp:</span></strong></p>\r\n<p class=\"MsoNormal\"><strong><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">+ </span></strong><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">Sử dụng các cách chứng minh hai tam giác bằng nhau.</span></p>\r\n<p class=\"MsoNormal\"><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">+ Mối quan hệ giữa góc và cạnh trong tam giác (Cạnh đối diện với góc lớn hơn thì lớn hơn)</span></p>\r\n<p class=\"MsoNormal\"><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">+ Tính chất trọng tâm của tam giác.</span></p>\r\n<p class=\"MsoNormal\"><strong><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">Cách giải:</span></strong></p>\r\n<p class=\"MsoNormal\"><img src=\"https://img.loigiaihay.com/picture/2023/0109/2023-01-09-160328_1.png\" style=\"text-align: center;\" /></p>\r\n<p class=\"MsoNormal\"><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">a. Xét </span><span class=\"MTConvertedEquation\">\\(\\Delta APH\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">và </span><span class=\"MTConvertedEquation\">\\(\\Delta QPC\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">có:</span></p>\r\n<p class=\"MsoNormal\"><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">+ </span><span class=\"MTConvertedEquation\">\\(HP = PC\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">(gt)</span></p>\r\n<p class=\"MsoNormal\"><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">+ </span><span class=\"MTConvertedEquation\">\\(\\angle APH = \\angle QPC\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">(đối đỉnh)</span></p>\r\n<p class=\"MsoNormal\"><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">+ </span><span class=\"MTConvertedEquation\">\\(QP = PA\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\"> (gt)</span></p>\r\n<p class=\"MsoNormal\"><span class=\"MTConvertedEquation\">\\( \\Rightarrow \\)\\(\\Delta APH = \\Delta QPC\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\"> (c.g.c) (đpcm).</span></p>\r\n<p class=\"MsoNormal\"><span class=\"MTConvertedEquation\">\\( \\Rightarrow \\angle AHP = \\angle QCP = {90^o}\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">(hai góc tương ứng)</span></p>\r\n<p class=\"MsoNormal\" style=\"margin-bottom: 12.0pt;\"><span class=\"MTConvertedEquation\">\\( \\Rightarrow QC \\bot BC\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">(đpcm).</span></p>\r\n<p class=\"MsoNormal\"><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">b. Theo (a) </span><span class=\"MTConvertedEquation\">\\(\\Delta APH = \\Delta QPC\\)</span></p>\r\n<p class=\"MsoNormal\"><span class=\"MTConvertedEquation\">\\( \\Rightarrow QC = AH\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">(hai cạnh tương ứng) (1)</span></p>\r\n<p class=\"MsoNormal\"><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">Mà </span><span class=\"MTConvertedEquation\">\\(\\Delta AHC\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">vuông tại H </span><span class=\"MTConvertedEquation\">\\( \\Rightarrow AH &lt; AC\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">(cạnh góc vuông &lt;cạnh huyền) (2)</span></p>\r\n<p class=\"MsoNormal\"><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">Từ (1) và (2), suy ra </span><span class=\"MTConvertedEquation\">\\(QC &lt; AC\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">(đpcm).</span></p>\r\n<p class=\"MsoNormal\"><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">c. Xét </span><span class=\"MTConvertedEquation\">\\(\\Delta AQC\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">có </span><span class=\"MTConvertedEquation\">\\(QC &lt; AC\\)\\( \\Rightarrow \\angle QAC &lt; \\angle AQC\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">                (3)  (Mối quan hệ giữa cạnh- góc trong tam giác)</span></p>\r\n<p class=\"MsoNormal\"><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">Mặt khác </span><span class=\"MTConvertedEquation\">\\(\\Delta APH = \\Delta QPC \\Rightarrow \\angle HAP = \\angle PQC = \\angle AQC\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">          (4)</span></p>\r\n<p class=\"MsoNormal\" style=\"margin-bottom: 12.0pt;\"><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">Từ (3) và (4) </span><span class=\"MTConvertedEquation\">\\( \\Rightarrow \\angle HAP &lt; \\angle QAC\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\"> hay </span><span class=\"MTConvertedEquation\">\\(\\angle HAP &lt; \\angle PAC\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">(đpcm).</span></p>\r\n<p class=\"MsoNormal\"><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">d. Xét </span><span class=\"MTConvertedEquation\">\\(\\Delta ABQ\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">có </span><span class=\"MTConvertedEquation\">\\(BP\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">là trung tuyến ứng với cạnh </span><span class=\"MTConvertedEquation\">\\(AQ\\)</span></p>\r\n<p class=\"MsoNormal\"><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">Mà </span><span class=\"MTConvertedEquation\">\\(BH = 2HP\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">(do </span><span class=\"MTConvertedEquation\">\\(H\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\"> là trung điểm của </span><span class=\"MTConvertedEquation\">\\(BC\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">, </span><span class=\"MTConvertedEquation\">\\(P\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">là trung điểm của </span><span class=\"MTConvertedEquation\">\\(HC\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">) </span><span class=\"MTConvertedEquation\">\\( \\Rightarrow H\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">là trọng tâm </span><span class=\"MTConvertedEquation\">\\(\\Delta ABQ\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">  (5)</span></p>\r\n<p class=\"MsoNormal\"><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">Lại có </span><span class=\"MTConvertedEquation\">\\(I\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">là trung điểm của </span><span class=\"MTConvertedEquation\">\\(BQ\\)</span><span class=\"MTConvertedEquation\">\\( \\Rightarrow AI\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">là trung tuyến ứng với cạnh </span><span class=\"MTConvertedEquation\">\\(BQ\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">     (6)</span></p>\r\n<p class=\"MsoNormal\"><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">Từ (5), (6)  </span><span class=\"MTConvertedEquation\">\\( \\Rightarrow H \\in AI\\)</span></p>\r\n<p class=\"MsoNormal\"><span class=\"MTConvertedEquation\">\\( \\Rightarrow A,H,I\\)</span><span style=\"font-size: 12pt; line-height: 107%; font-family: 'Times New Roman', serif;\">thẳng hàng (đpcm)</span></p>\r\n<p class=\"MsoNormal\" style=\"margin-top: 0cm; margin-right: 2.4pt; margin-bottom: 12.0pt; margin-left: 2.4pt; text-align: justify; line-height: 18.0pt;\"><strong><span style=\"font-size: 12pt; font-family: 'Times New Roman', serif;\">Bài 5.</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Phương pháp:</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Áp dụng tính chất của dãy tỉ số bằng nhau.</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Cách giải:</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Ta có: </span><span class=\"MTConvertedEquation\">\\(\\dfrac{a}{b} = \\dfrac{b}{c} = \\dfrac{c}{d} = \\dfrac{d}{e}\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> nên </span><span class=\"MTConvertedEquation\">\\(\\dfrac{a}{b} = \\dfrac{{2019b}}{{2019c}} = \\dfrac{{2020c}}{{2020d}} = \\dfrac{{2021d}}{{2021e}}\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Áp dụng tính chất của dãy tỉ số bằng nhau, ta có: </span><span class=\"MTConvertedEquation\">\\(\\dfrac{{2019b}}{{2019c}} = \\dfrac{{2020c}}{{2020d}} = \\dfrac{{2021d}}{{2021e}} = \\dfrac{{2019b + 2020c - 2021d}}{{2019c + 2020d - 2021e}}\\)</span></p>\r\n<p> </p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\">Mà </span><span class=\"MTConvertedEquation\">\\(\\dfrac{a}{b} = \\dfrac{{2019b}}{{2020c}}\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> và </span><span class=\"MTConvertedEquation\">\\(\\dfrac{a}{b} = \\dfrac{b}{c}\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> (gt) nên </span><span class=\"MTConvertedEquation\">\\({\\left( {\\dfrac{{2019b + 2020c - 2021d}}{{2019c + 2020d - 2021e}}} \\right)^3} = {\\left( {\\dfrac{a}{b}} \\right)^3} = \\dfrac{{{a^2}}}{{{b^2}}}.\\dfrac{a}{b} = \\dfrac{{{a^2}}}{{{b^2}}}.\\dfrac{b}{c} = \\dfrac{{{a^2}}}{{bc}}\\)</span><span style=\"font-size: 12pt; line-height: 115%; font-family: 'Times New Roman', serif;\"> (đpcm)</span></p>\r\n<p class=\"MsoNormal\" style=\"line-height: 150%; tab-stops: 14.15pt 5.0cm 269.3pt 396.85pt;\"><strong><span style=\"font-size: 12.0pt; line-height: 150%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\">I. TRẮC NGHIỆM (<em>2,0 điểm</em>)</span></strong></p>\r\n<p class=\"MsoNormal\" style=\"margin-bottom: .0001pt; text-align: justify; line-height: 150%;\"><span style=\"font-size: 12.0pt; line-height: 150%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\">Hãy chọn phương án trả lời đúng và viết chữ cái đứng trước đáp án đó vào bài làm.</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\">Câu 1. </span></strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\">Hai đại lượng </span><span class=\"MTConvertedEquation\">\\(x,y\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"> trong công thức nào tỉ lệ nghịch với nhau:<strong></strong></span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: 14.2pt 5.0cm 10.0cm 15.0cm 482.7pt;\"><strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">     </span>A. </span></strong><span class=\"MTConvertedEquation\">\\(y = 5 + x\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">                    </span><strong>B. </strong></span><span class=\"MTConvertedEquation\">\\(x = \\dfrac{5}{y}\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">              </span><strong>C. </strong></span><span class=\"MTConvertedEquation\">\\(y = 5x\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">                            </span><strong>D. </strong></span><span class=\"MTConvertedEquation\">\\(x = 5y\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; mso-fareast-font-family: 'Times New Roman'; color: black; mso-themecolor: text1;\">Câu 2. </span></strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\">Biểu thức đại số biểu thị bình phương của một tổng hai số </span><span class=\"MTConvertedEquation\">\\(a\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"> và </span><span class=\"MTConvertedEquation\">\\(b\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"> là: <strong></strong></span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: 14.2pt 5.0cm 10.0cm 15.0cm 454.55pt 482.7pt;\"><strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">     </span>A. </span></strong><span class=\"MTConvertedEquation\">\\({a^2} - {b^2}\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">              </span><strong>B. </strong></span><span class=\"MTConvertedEquation\">\\({a^2} + {b^2}\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">                  </span><strong>C. </strong></span><span class=\"MTConvertedEquation\">\\({\\left( {a - b} \\right)^2}\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">   </span><strong>D. </strong></span><span class=\"MTConvertedEquation\">\\({\\left( {a + b} \\right)^2}\\)</span><strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 2;\">                                                                             </span></span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; mso-fareast-font-family: 'Times New Roman'; color: black; mso-themecolor: text1;\">Câu 3.</span></strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; mso-fareast-font-family: 'Times New Roman'; color: black; mso-themecolor: text1;\"> </span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\">Giá trị của biểu thức: </span><span class=\"MTConvertedEquation\">\\({x^3} - 2{x^2}\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"> tại </span><span class=\"MTConvertedEquation\">\\(x =<span style=\"mso-spacerun: yes;\">  </span>- 2\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"> là:<strong></strong></span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: 14.2pt 5.0cm 10.0cm 15.0cm 482.7pt;\"><strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">     </span>A. </span></strong><span class=\"MTConvertedEquation\">\\( - 16\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">                          </span><strong>B. </strong></span><span class=\"MTConvertedEquation\">\\(16\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">                                  </span><strong>C. </strong></span><span class=\"MTConvertedEquation\">\\(0\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">                                   </span><strong>D. </strong></span><span class=\"MTConvertedEquation\">\\( - 8\\)</span><strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">     </span></span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; mso-fareast-font-family: 'Times New Roman'; color: black; mso-themecolor: text1;\">Câu 4.</span></strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; mso-fareast-font-family: 'Times New Roman'; color: black; mso-themecolor: text1;\"> </span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\">Biểu thức nào sau đây <strong>không </strong>là đơn thức?</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: 14.2pt 5.0cm 10.0cm 15.0cm 482.7pt;\"><strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">     </span>A. </span></strong><span class=\"MTConvertedEquation\">\\(4{x^2}y\\left( { - 2x} \\right)\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">                                         </span><strong>B. </strong></span><span class=\"MTConvertedEquation\">\\(2x\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">                                  </span><strong>C. </strong></span><span class=\"MTConvertedEquation\">\\(2xy - {x^2}\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><strong>D. </strong></span><span class=\"MTConvertedEquation\">\\(2021\\)</span><strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">                                   </span></span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; mso-fareast-font-family: 'Times New Roman'; color: black; mso-themecolor: text1;\">Câu 5.</span></strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; mso-fareast-font-family: 'Times New Roman'; color: black; mso-themecolor: text1;\"> </span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\">Sắp xếp các hạng tử của đa thức </span><span class=\"MTConvertedEquation\">\\(P\\left( x \\right) = 2{x^3} - 7{x^2} + {x^4} - 4\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"> theo lũy thừa giảm dần của biến ta được:<strong></strong></span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: 14.2pt 5.0cm 10.0cm 15.0cm 482.7pt;\"><strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">     </span>A. </span></strong><span class=\"MTConvertedEquation\">\\(P\\left( x \\right) = {x^4} + 2{x^3} - 7{x^2} - 4\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">                 </span><strong>B. </strong></span><span class=\"MTConvertedEquation\">\\(P\\left( x \\right) = 7{x^2} + 2{x^3} + {x^4} - 4\\)</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: 14.2pt 5.0cm 10.0cm 15.0cm 482.7pt;\"><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">     </span><strong>C. </strong></span><span class=\"MTConvertedEquation\">\\(P\\left( x \\right) =<span style=\"mso-spacerun: yes;\">  </span>- 4 - 7{x^2} + 2{x^3} + {x^4}\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">             </span><strong>D. </strong></span><span class=\"MTConvertedEquation\">\\(P\\left( x \\right) = {x^4} - 2{x^3} - 7{x^2} - 4\\)</span><strong></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; mso-fareast-font-family: 'Times New Roman'; color: black; mso-themecolor: text1;\">Câu 6.</span></strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; mso-fareast-font-family: 'Times New Roman'; color: black; mso-themecolor: text1;\"> </span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\">Cho tam giác </span><span class=\"MTConvertedEquation\">\\(MNP\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"> có </span><span class=\"MTConvertedEquation\">\\(NP = 1cm,MP = 7cm\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\">. Độ dài cạnh </span><span class=\"MTConvertedEquation\">\\(MN\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"> là một số nguyên (cm). Độ dài cạnh </span><span class=\"MTConvertedEquation\">\\(MN\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"> là:</span></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%; tab-stops: 14.2pt 5.0cm 10.0cm 15.0cm 482.7pt;\"><strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">     </span>A. </span></strong><span class=\"MTConvertedEquation\">\\(8cm\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">                          </span><strong>B. </strong></span><span class=\"MTConvertedEquation\">\\(5cm\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">                               </span><strong>C. </strong></span><span class=\"MTConvertedEquation\">\\(6cm\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">                               </span><strong>D. </strong></span><span class=\"MTConvertedEquation\">\\(7cm\\)</span><strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"><span style=\"mso-tab-count: 1;\">   </span></span></strong></p>\r\n<p class=\"MsoNormal\" style=\"text-align: justify; line-height: 115%;\"><strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; mso-fareast-font-family: 'Times New Roman'; color: black; mso-themecolor: text1;\">Câu 7. </span></strong><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\">Cho tam giác </span><span class=\"MTConvertedEquation\">\\(ABC\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\">, có </span><span class=\"MTConvertedEquation\">\\(\\angle A = {90^0};\\angle C = {30^0}\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\">. Khi đó quan hệ giữa ba cạnh </span><span class=\"MTConvertedEquation\">\\(AB,AC,BC\\)</span><span style=\"font-size: 12.0pt; line-height: 115%; font-family: 'Times New Roman',serif; color: black; mso-themecolor: text1;\"> là:<strong></strong></span></p>","youtube_id":"","video_start_time":"0"}],"comment_url":"https://loigiaihay.com/comment/de-kiem-tra-giua-hoc-ki-2-toan-7-de-so-4-ket-noi-tri-thuc-c1097a133061.html","origin_url":"https://loigiaihay.com/de-kiem-tra-giua-hoc-ki-2-toan-7-de-so-4-ket-noi-tri-thuc-c1097a133061.html","relate_link":[]},"callouts":[],"relate_articles":[],"others_in_cat":[{"article_id":133110,"cat_id":1097,"publish_time":1673427300,"is_link":0,"thumbnail":"","title":"Đề thi giữa kì 2 Toán 7 - Đề số 5 - Kết nối tri thức","alias":"de-kiem-tra-giua-hoc-ki-2-toan-7-de-so-5-ket-noi-tri-thuc","introtext":"I. TRẮC NGHIỆM ( 2 điểm)\r\nHãy chọn phương án trả lời đúng và viết chữ cái đứng trước đáp án đó vào bài làm.","display_type":2,"article_type":1},{"article_id":155574,"cat_id":1097,"publish_time":1706520240,"is_link":0,"thumbnail":"https://img.loigiaihay.com/picture/article/2024/0129/resize_1-0.png","title":"Đề thi giữa kì 2 Toán 7 Kết nối tri thức - Đề số 6","alias":"de-thi-giua-ki-2-toan-7-ket-noi-tri-thuc-de-so-6","introtext":"Phần trắc nghiệm (3 điểm)\r\nCâu 1: Trong các cặp tỉ số sau, cặp tỉ số nào lập thành một tỉ lệ thức?\r\n","display_type":5,"article_type":1},{"article_id":155575,"cat_id":1097,"publish_time":1706520420,"is_link":0,"thumbnail":"https://img.loigiaihay.com/picture/article/2024/0129/resize_1-0_1.png","title":"Đề thi giữa kì 2 Toán 7 Kết nối tri thức - Đề số 7","alias":"de-thi-giua-ki-2-toan-7-ket-noi-tri-thuc-de-so-7","introtext":"Phần trắc nghiệm (3 điểm)\r\nCâu 1: Nếu 4.b = 5.c và b, c ≠ 0 thì:\r\n","display_type":5,"article_type":1},{"article_id":155576,"cat_id":1097,"publish_time":1706520780,"is_link":0,"thumbnail":"https://img.loigiaihay.com/picture/article/2024/0129/resize_1-0_2.png","title":"Đề thi giữa kì 2 Toán 7 Kết nối tri thức - Đề số 8","alias":"de-thi-giua-ki-2-toan-7-ket-noi-tri-thuc-de-so-8","introtext":"Phần trắc nghiệm (3 điểm)\r\nCâu 1: Nếu 2.b = 5.c và b, c ≠ 0 thì:\r\n","display_type":5,"article_type":1},{"article_id":155578,"cat_id":1097,"publish_time":1706521080,"is_link":0,"thumbnail":"https://img.loigiaihay.com/picture/article/2024/0129/resize_1-0_3.png","title":"Đề thi giữa kì 2 Toán 7 Kết nối tri thức - Đề số 9","alias":"de-thi-giua-ki-2-toan-7-ket-noi-tri-thuc-de-so-9","introtext":"Phần trắc nghiệm (3 điểm)\r\nCâu 1: Thay tỉ số 1,2 : 1,35 bằng tỉ số giữa các số nguyên ta được:\r\n","display_type":5,"article_type":1},{"article_id":155580,"cat_id":1097,"publish_time":1706521380,"is_link":0,"thumbnail":"https://img.loigiaihay.com/picture/article/2024/0129/resize_1-0_4.png","title":"Đề thi giữa kì 2 Toán 7 Kết nối tri thức - Đề số 10","alias":"de-thi-giua-ki-2-toan-7-ket-noi-tri-thuc-de-so-10","introtext":"Phần trắc nghiệm (3 điểm)\r\nCâu 1: Từ tỉ lệ thức $\\frac{a}{b}=\\frac{c}{d}$ (giả thiết các tỉ số đều có nghĩa) ta suy ra đẳng thức:\r\n","display_type":5,"article_type":1},{"article_id":133044,"cat_id":1097,"publish_time":1673080440,"is_link":0,"thumbnail":"","title":"Đề thi giữa kì 2 Toán 7 - Đề số 3 - Kết nối tri thức","alias":"de-kiem-tra-giua-hoc-ki-2-toan-7-de-so-3-ket-noi-tri-thuc","introtext":"I. TRẮC NGHIỆM ( 2 điểm)\r\nHãy chọn phương án trả lời đúng và viết chữ cái đứng trước đáp án đó vào bài làm.","display_type":2,"article_type":1},{"article_id":133024,"cat_id":1097,"publish_time":1672908960,"is_link":0,"thumbnail":"","title":"Đề thi giữa kì 2 Toán 7 - Đề số 2 - Kết nối tri thức","alias":"de-kiem-tra-giua-hoc-ki-2-toan-7-de-so-2-ket-noi-tri-thuc","introtext":"I. TRẮC NGHIỆM ( 3 điểm)\r\nHãy chọn phương án trả lời đúng và viết chữ cái đứng trước đáp án đó vào bài làm.","display_type":2,"article_type":1},{"article_id":133012,"cat_id":1097,"publish_time":1672823100,"is_link":0,"thumbnail":"","title":"Đề thi giữa kì 2 Toán 7 - Đề số 1 - Kết nối tri thức","alias":"de-kiem-tra-giua-hoc-ki-2-toan-7-de-so-1-ket-noi-tri-thuc","introtext":"I. TRẮC NGHIỆM ( 2 điểm)\r\nHãy chọn phương án trả lời đúng và viết chữ cái đứng trước đáp án đó vào bài làm.","display_type":2,"article_type":1}],"event_info":{"title":"Đề thi giữa kì 2 Toán 7 Kết nối tri thức","cat_id":1097,"alias":"de-kiem-tra-giua-hoc-ki-2-toan-7-ket-noi-tri-thuc","introtext":"","type":"event","item_id":30387,"item_type":2},"banner":[],"top_banner":"","content_expanded":[],"child_events":[{"id":"30387","title":"Đề thi giữa kì 2 Toán 7 Kết nối tri thức","short_title":"Đề thi giữa kì 2","alias":"de-kiem-tra-giua-hoc-ki-2-toan-7-ket-noi-tri-thuc","picture":"","is_link":"0","links":"","is_hot":"0","is_all":"0","category_id":"1097","ordering":"30387","parent_id":"0"}],"parent_events":[],"cfg_info":{"last_cfg_time":"1521866679","ad.popup_frequency":"0","ad.adsense.detail_bottom.unit_id":"ca-app-pub-8529835372050931/9927553003","ad.adsense.popup.unit_id":"ca-app-pub-8529835372050931/2161779402","current.force.update.version":"181","support.email":"loigiaihay.com@gmail.com","support.fanpage":"https://www.facebook.com/Loigiaihay/","popup_rating_after":"86400","admob.app_id":"ca-app-pub-8529835372050931~4358271409","admob.unit.article_detail_bottom":"ca-app-pub-8529835372050931/1883637630","admob.unit.article_detail_top":"ca-app-pub-8529835372050931/8604898230","admob.unit.event_article_top":"ca-app-pub-8529835372050931/7406887709","admob.unit.interestial":"ca-app-pub-8529835372050931/2741937409","ios_appstore_link":"https://itunes.apple.com/us/app/loigiaihay/id1209891610?mt=8","android_appstore_link":"https://play.google.com/store/apps/details?id=com.tp.loigiaihay","min_version":"2.1.3","latest_version":"1.3.9","force_update":false},"popup_ads":[]}