CIE May/June 2020 9709 Pure Maths Paper 23 (pdf)
- Given that 2y = 93x, use logarithms to show that y = kx and find the value of k correct to 3 significant figures.
- Find the exact coordinates of the stationary point on the curve with equation y = 5xe1/2x.
- 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).
- 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
Find the values of A and p.
- (a) Sketch, on the same diagram, the graphs of y = |2x − 3| and y = 3x + 5.
(b) Solve the inequality 3x + 5 < |2x − 3|.
- 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°.
- 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.
- (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
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