CIE March 2020 9709 Pure Maths Paper 2 (pdf)
- Solve the equation 2 sin(θ + 30° + 5 cos θ = 2 sin θ for 0° < θ < 90°.
- (a) Find the quotient when 4x3 + 17x2 + 9x is divided by x2 + 5x + 6, and show that the remainder
(b) Hence solve the equation 4x3 + 17x2 + 9x − 18 = 0.
- It is given that
Find the value of the positive constant a.
- A curve has equation
3x2 − y2 − 4 ln(2y + 3) = 26.
Find the equation of the tangent to the curve at the point (3, −1).
- (a) Sketch, on the same diagram, the graphs of y = |x + 2k| and y = |2x − 3k|, where k is a positive
Give, in terms of k, the coordinates of the points where each graph meets the axes.
(b) Find, in terms of k, the coordinates of each of the two points where the graphs intersect.
(c) Find, in terms of k, the largest value of t satisfying the inequality
- A curve has equation y = x3e0.2x where x ≥ 0. At the point P on the curve, the gradient of the curve
(a) Show that the x-coordinate of P satisfies the equation x =
(b) Use the equation in part (a) to show by calculation that the x-coordinate of P lies between 1.7
(c) Use an iterative formula, based on the equation in part (a), to find the x-coordinate of P correct
to 4 significant figures. Give the result of each iteration to 6 significant figures.
- The diagram shows part of the curve with equation
y = 4 sin2x + 8 sin x + 3,
where x is measured in radians. The curve crosses the x-axis at the point A and the shaded region is
bounded by the curve and the lines x = 0 and y = 0.
(a) Find the exact x-coordinate of A.
(b) Find the exact gradient of the curve at A.
(c) Find the exact area of the shaded region.
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