7 27 a = 180° (90° + 15°) M1 M1 using angles in a triangle M x – = 180° 105° 75° A1 A1 cao – b Angle ACD = 15° B1 B1 for recognition of alternate angles Alternate angles M1 M1 for using angles in a triangle and adding BCD = 90° + 15° 105° A1 A1 cao 5 28 Their interior angles are 120° and 3 × B1 2 B1 for a clear explanation M 120° = 360° This is the total of the angles around a point. 1 29 M1 3 M1 for process of applying Pythagoras theorem M Using Pythagoras 1.52 = 52 x2+ = 25 2.25 x2 – = = 4.734165 x M1 M1 for correct Pythagoras statement A1 A1 for 4.73 m A1 A1 for 4.73 correct to 2 or 3 dp 5 30 a Scale factor is 3 B1 2 B1 cao M 3 b The side lengths of A are one-third the side lengths of C, so the scale factor will be . B1 for scale factor Where the lines cross is the centre of B1 B1 for explaining the lines enlargement, this point is (–18, 14) B1 for correct centre. B1 B1 4 31 The sum of the areas of the two smaller B1 2 B1 for a clear explanation H semicircles is equal to the area of the 3 larger semicircle. 1 32 AC is 5 cm because, triangle ABC is a 5, B1 2 B1 for explaining AC as being 5 cm H 12, 13 special right-angled triangle. 3 Triangle ACD is a right-angled triangle B1 B1 for completing the explanation for DC to be 4 cm and a 3, 4, 5 triangle, giving CD the length 4. 2
7 27 a b x = 180° – (90° + 15°) = 180° – 105° Angle ACD = 15° Alternate angles BCD = 90° + 15° 75° 105° M1 A1 B1 M1 A1 M1 using angles in a triangle A1 cao B1 for recognition of alternate angles M1 for using angles in a triangle and adding A1 cao M 5 28 Their interior angles are 120° and 3 × 120° = 360° This is the total of the angles around a point. B1 2 B1 for a clear explanation M 1 29 Using Pythagoras x2+ 1.52 = 52 x2 = 25 – 2.25 x = = 4.734165 4.73 m M1 M1 A1 A1 3 M1 for process of applying Pythagoras theorem M1 for correct Pythagoras statement A1 for A1 for 4.73 correct to 2 or 3 dp M 5 30 a b Scale factor is 3 The side lengths of A are one-third the side lengths of C, so the scale factor will be . Where the lines cross is the centre of enlargement, this point is (–18, 14) B1 B1 B1 B1 2 3 B1 cao B1 for scale factor B1 for explaining the lines B1 for correct centre. M 4 31 The sum of the areas of the two smaller semicircles is equal to the area of the larger semicircle. B1 2 3 B1 for a clear explanation H 1 32 AC is 5 cm because, triangle ABC is a 5, 12, 13 special right-angled triangle. Triangle ACD is a right-angled triangle and a 3, 4, 5 triangle, giving CD the length 4. B1 B1 2 3 B1 for explaining AC as being 5 cm B1 for completing the explanation for DC to be 4 cm H 2
Foundation_Skills_Geometry%20MarkScheme_AQA.docx