CIE March 2020 9709 Pure Maths Paper 2

CIE March 2020 9709 Pure Maths Paper 2 (pdf)

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1. Solve the equation 2 sin(θ + 30° + 5 cos θ = 2 sin θ for 0° < θ < 90°.
2. (a) Find the quotient when 4x³ + 17x² + 9x is divided by x² + 5x + 6, and show that the remainder is 18.
   (b) Hence solve the equation 4x³ + 17x² + 9x − 18 = 0.
3. It is given that
   Find the value of the positive constant a.
4. 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).
5. (a) Sketch, on the same diagram, the graphs of y = |x + 2k| and y = |2x − 3k|, where k is a positive constant.
   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

6. A curve has equation y = x³e^0.2x where x ≥ 0. At the point P on the curve, the gradient of the curve is 15.
   (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 and 1.8.
   (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.
   
7. 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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