49 a C1 3 C1 for choosing three inequalities that will define a M In this example, and are values x y 2 region satisfying the conditions: x y x y + 5 > 1 > 2 ≤ These are drawn on the diagram. C1 C1 for a clear diagram illustrating the chosen Any region needs a minimum of three inequalities straight lines to enclose it. The region R above is where the solutions satisfying all three inequalities lie. y) Point (x, is inside the region if the point satisfies all three inequalities. For example, (1.5 , 3) is inside the region since 1.5 + 3 5, 1.5 >1 and 3 > ≤ 2. y) Point (x, is outside the region if it does not satisfy at least one of the inequalities. C1 C1 for clear explanation linking the chosen inequalities For example, (2, 4) satisfies two of the y with the diagram conditions (x > 1 and > 2) but does x y not satisfy + 5. ≤ Point (x,y) is on the boundary of the b i region if the point satisfies one of the C1 C1 for clear correct explanation inequalities but only as a equality. C1 C1 for use of an example to illustrate this For example, (2, 3) is on the boundary x y of + 5 as 2 + 3 = 5. ≤ C1 C1 for clear correct explanation ii C1 C1 for use of an example to illustrate this C1 C1 for clear correct explanation iii C1 C1 for use of an example to illustrate this 9
49 a b i ii iii In this example, x and y are values satisfying the conditions: x + y ≤ 5 x > 1 y > 2 These are drawn on the diagram. Any region needs a minimum of three straight lines to enclose it. The region R above is where the solutions satisfying all three inequalities lie. Point (x, y) is inside the region if the point satisfies all three inequalities. For example, (1.5 , 3) is inside the region since 1.5 + 3 ≤ 5, 1.5 >1 and 3 > 2. Point (x, y) is outside the region if it does not satisfy at least one of the inequalities. For example, (2, 4) satisfies two of the conditions (x > 1 and y > 2) but does not satisfy x + y ≤ 5. Point (x,y) is on the boundary of the region if the point satisfies one of the inequalities but only as a equality. For example, (2, 3) is on the boundary of x + y ≤ 5 as 2 + 3 = 5. C1 C1 C1 C1 C1 C1 C1 C1 C1 3 2 C1 for choosing three inequalities that will define a region C1 for a clear diagram illustrating the chosen inequalities C1 for clear explanation linking the chosen inequalities with the diagram C1 for clear correct explanation C1 for use of an example to illustrate this C1 for clear correct explanation C1 for use of an example to illustrate this C1 for clear correct explanation C1 for use of an example to illustrate this M 9
Higher_Skills_Algebra_MarkScheme_Edexcel.docx