# CIE Oct/Nov 2021 9709 Pure Maths Paper 13

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This page covers Questions and Worked Solutions for CIE Pure Maths Paper 1 Oct/Nov 2021, 9709/13.

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CIE Oct/Nov 2021 9709 Pure Maths Paper 13 Questions (pdf)

CIE Oct/Nov 2021 9709 Pure Maths Paper 13 Mark Scheme (pdf)

1. The graph of y = f(x) is transformed to the graph of y = 3 − f(x). Describe fully, in the correct order, the two transformations that have been combine
2. (a) Find the first three terms, in ascending powers of x, in the expansion of (1 + ax)6 (b) Given that the coefficient of x2 in the expansion of (1 − 3x)(1 + ax)6 is −3, find the possible values of the constant
3. (a) Express 5y2 − 30y + 50 in the form (5y + a)2 + b, where a and b are constants (b) The function f is defined by f(x) = x5 − 10x3 + 50x. Determine whether f is an increasing function, a decreasing function or neither
4. The first term of an arithmetic progression is 84 and the common difference is −3. (a) Find the smallest value of n for which the nth term is negative. It is given that the sum of the first 2k terms of this progression is equal to the sum of the first k terms. (b) Find the value of k.
5. In the diagram, X and Y are points on the line AB such that BX = 9 cm and AY = 11 cm. Arc BC is part of a circle with centre X and radius 9 cm, where CX is perpendicular to AB. Arc AC is part of a circle with centre Y and radius 11 cm. (a) Show that angle XYC = 0.9582 radians, correct to 4 significant figures. (b) Find the perimeter of ABC
6. The diagram shows the graph of y = f(x).

1. (a) Show that the equation
2. The diagram shows the curves with equation
3. The line y = 2x + 5 intersects the circle with equation x2 + y2 = 20 at A and B. (a) Find the coordinates of A and B in surd form and hence find the exact length of the chord AB A straight line through the point (10, 0) with gradient m is a tangent to the circle. (b) Find the two possible values of
4. A curve has equation y = f(x) and it is given that

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