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

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

- Given that 2
^{y}= 9^{3x}, 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 = 5xe
^{1/2x}. - 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 the diagram.

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) = 6x^{3}+ ax^{2}− 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 cos
^{2}θ.

(b) Solve the equation 3 sin 2θ cot θ = 5 for 0 < 1 < π.

(c) Find the exact value of

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