CIE Oct/Nov 2021 9709 Pure Maths Paper 11

CIE Oct/Nov 2021 9709 Pure Maths Paper 11 Questions (pdf)

CIE Oct/Nov 2021 9709 Pure Maths Paper 11 Mark Scheme (pdf)

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1. (a) Expand (1 - 1/2x)² (b) Find the first four terms in the expansion, in ascending powers of x, of (1 + 2x)⁶ (c) Hence find the coefficient of x in the expansion of (1 - 1/2x)²(1 + 2x)⁶
2. A curve has equation y = kx² + 2x − k and a line has equation y = kx − 2, where k is a constant. Find the set of values of k for which the curve and line do not intersect.
3. Solve, by factorising, the equation 6 cos 1 tan 1 − 3 cos 1 + 4 tan 1 − 2 = 0
4. The first term of an arithmetic progression is a and the common difference is −4. The first term of a geometric progression is 5a and the common ratio is −1/4. The sum to infinity of the geometric progression is equal to the sum of the first eight terms of the arithmetic progression. (a) Find the value of a. The kth term of the arithmetic progression is zero. (b) Find the value of k.
5. The diagram shows part of the graph of y = a cos(bx) + c. (a) Find the values of the positive integers a, b and c (b) For these values of a, b and c, use the given diagram to determine the number of solutions in the interval 0 ≤ x ≤ 2π for each of the following equation
6. The diagram shows a metal plate ABC in which the sides are the straight line AB and the arcs AC and BC. The line AB has length 6 cm. The arc AC is part of a circle with centre B and radius 6 cm, and the arc BC is part of a circle with centre A and radius 6 cm. (a) Find the perimeter of the plate, giving your answer in terms of π. (b) Find the area of the plate, giving your answer in terms of π and √3.

7. A circle with centre (5, 2) passes through the point (7, 5). (a) Find an equation of the circle The line y = 5x − 10 intersects the circle at A and B. (b) Find the exact length of the chord A
8. (a) Express −3x² + 12x + 2 in the form −3(x − a)² + b, where a and b are constants
9. A curve has equation y = f(x), and it is given that f′(x) = 2x² − 7 − 4/x². (a) Given that f(1) = −1/3, find f(x). (b) Find the coordinates of the stationary points on the curve (c) Find f′′(x) (d) Hence, or otherwise, determine the nature of each of the stationary points
10. The diagram shows the curve with equation The normal to the curve at the point (1, 1) crosses the y-axis at the point A. (c) Find the y-coordinate of

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