CIE May 2021 9709 Pure Maths Paper 11

CIE May/June 2021 9709 Pure Maths Paper 11 (pdf)

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1. The equation of a curve is such that
2. The sum of the first 20 terms of an arithmetic progression is 405 and the sum of the first 40 terms is 1410.
   Find the 60th term of the progression
3. (a) Find the first three terms in the expansion of (3 − 2x)⁵ in ascending powers of x
4. The diagram shows part of the graph of y = a tan(x − b) + c.
   Given that 0 < b < π, state the values of the constants a, b and c.
5. The fifth, sixth and seventh terms of a geometric progression are 8k, −12 and 2k respectively. Given that k is negative, find the sum to infinity of the progression.
6. The equation of a curve is y = (2k − 3)x² − kx − (k − 2), where k is a constant. The line y = 3x − 4 is a tangent to the curve.
   Find the value of k. 7 (a) Prove the identity

8. The diagram shows a symmetrical metal plate. The plate is made by removing two identical pieces from a circular disc with centre C. The boundary of the plate consists of two arcs PS and QR of the original circle and two semicircles with PQ and RS as diameters. The radius of the circle with centre C is 4 cm, and PQ = RS = 4 cm also.
   (a) Show that angle PCS = 2/3 π radians
   
9. Functions f and g are defined as follows:
   f(x) = (x − 2)² − 4 for x ≥ 2,
   
   g(x) = ax + 2 for x ∈ R,
   where a is a constant.
   (a) State the range of f.
   
10. The equation of a circle is x² + y² − 4x + 6y − 77 = 0. (a) Find the x-coordinates of the points A and B where the circle intersects the x-axis.
11. The equation of a curve is

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