CIE March 2021 9709 Pure Maths Paper 2

CIE March 2021 9709 Pure Maths Paper 2 (pdf)

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1. (a) Sketch, on the same diagram, the graphs of y = |3x − 5| and y = x + 2.
   (b) Solve the equation |3x − 5| = x + 2.
2. Solve the equation sec²θ cot θ = 8 for 0 < θ < π
3. The parametric equations of a curve are
   x = e^2tcos 4t, y = 3 sin 2t.
   Find the gradient of the curve at the point for which t = 0.
4. The diagram shows part of the curve with equation
   (b) Use the trapezium rule with two intervals to find an approximation to the area of the shaded region. Give your answer correct to 2 significant figures.
   (c) State, with a reason, whether your answer to part (b) is an over-estimate or under-estimate of the exact area of the shaded region
5. (a) Given that 2 ln(x + 1) + ln x = ln(x + 9), show that x
   (b) It is given that the equation x =
   (c) Use an iterative formula, based on the equation in part (b), to find the root correct to 3 significant figures. Give the result of each iteration to 5 significant figures.
   

6. The polynomial p(x) is defined by
   p(x) = x³ + ax + b,
   where a and b are constants. It is given that (x + 2) is a factor of p(x) and that the remainder is 5 when p(x) is divided by (x − 3).
   (a) Find the values of a and b.
   (b) Hence find the exact root of the equation p(e^2y) = 0.
7. (a) Express 5√3 cos x + 5 sin x in the form R(cosx − α), where R > 0 and 0 < α < 1/2π
   (b) As x varies, find the least possible value of 4 + 5√3 cos x + 5 sin x, and determine the corresponding value of x where −pi; < x < π
   (c) Find

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