CIE May 2021 9709 Pure Maths Paper 32

CIE May 2021 9709 Pure Maths Paper 3 (pdf)

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1. Solve the inequality |2x − 1| < 3|x + 1|.
2. On a sketch of an Argand diagram, shade the region whose points represent complex numbers z satisfying the inequalities |z + 1 − i| ≤ 1 and arg|z − 1| ≤ 3/4 π
3. The variables x and y satisfy the equation x = A(3^−y), where A is a constant.
   (a) Explain why the graph of y against ln x is a straight line and state the exact value of the gradient of the line
4. Using integration by parts, find the exact value of
5. The complex number u is given by u = 10 − 4√6i.
   Find the two square roots of u, giving your answers in the form a + ib, where a and b are real and exact.
6. (a) Prove that cosec 2θ − cot 2&theta= tan θ.
7. A curve is such that the gradient at a general point with coordinates x, y is proportional to y/√(x + 1).
   The curve passes through the points with coordinates (0,1)and (3, e)
8. The equation of a curve is
9. Let f(x) =
10. The diagram shows a trapezium ABCD in which AD = BC = r and AB = 2r. The acute angles BAD and ABC are both equal to x radians. Circular arcs of radius r with centres A and B meet at M, the midpoint of AB.

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