# CIE May 2020 9709 Pure Maths Paper 23

This is part of a collection of videos showing step-by-step solutions for CIE A-Level Mathematics past papers.

This page covers Questions and Worked Solutions for CIE Pure Maths Paper 2 May/June 2020, 9709/23.

Related Pages
More A Levels Past Papers

CIE May/June 2020 9709 Pure Maths Paper 23 (pdf)

1. Given that 2y = 93x, use logarithms to show that y = kx and find the value of k correct to 3 significant figures.
2. Find the exact coordinates of the stationary point on the curve with equation y = 5xe1/2x.
3. The equation of a curve is cos 3x + 5 sin y = 3.
Find the gradient of the curve at the point (1/9π,1/6π).
4. The variables x and y satisfy the equation y = Ax−2p, where A and p are constants. The graph of ln y against ln x is a straight line passing through the points (−0.68, 3.02) and (1.07, −1.53), as shown in the diagram.
Find the values of A and p.
5. (a) Sketch, on the same diagram, the graphs of y = |2x − 3| and y = 3x + 5.
(b) Solve the inequality 3x + 5 < |2x − 3|.

1. The polynomial p(x) is defined by
p(x) = 6x3 + ax2 − 4x − 3,
where a is a constant. It is given that (x + 3) is a factor of p(x).
(a) Find the value of a.
(b) Using this value of a, factorise p(x) completely.
(c) Hence solve the equation p(cosec θ) = 0 for 0° < 1 < 360°.
2. It is given that
(a) Show that a =
(b) Using the equation in part (a), show by calculation that 1 < a < 2.
(c) Use an iterative formula, based on the equation in part (a), to find the value of a correct to 4 significant figures. Give the result of each iteration to 6 significant figures.
3. (a) Show that 3 sin 2θ cot θ = 6 cos2θ.
(b) Solve the equation 3 sin 2θ cot θ = 5 for 0 < 1 < π.
(c) Find the exact value of

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 