CIE May 2021 9709 Pure Maths Paper 33

CIE May 2021 9709 Pure Maths Paper 3 (pdf)

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1. Expand (1 + 3x)^2/3 in ascending powers of x, up to and including the term in x³, simplifying the coefficients.
2. Solve the equation 4x = 3 + 4^-x. Give your answer correct to 3 decimal places
3. The parametric equations of a curve are
   x = t + ln(t + 2), y = (t − 1)e^-2t, where t > −2.
   (a) Express dy/dx in terms of t, simplifying your answer.
   (b) Find the exact y-coordinate of the stationary point of the curve
4. let f(x) =
5. (a) By first expanding tan(2θ + 2θ), show that the equation tan 4θ =/2 = tan θ may be expressed as tan⁴θ + 2 tan²θ − 7 = 0.
6. (a) By sketching a suitable pair of graphs, show that the equation cot 1/2x = 1 + e^-x has exactly one root in the interval 0 < x ≤ π.
7. For the curve shown in the diagram, the normal to the curve at the point P with coordinates (x, y) meets the x-axis at N. The point M is the foot of the perpendicular from P to the x-axis
8. The diagram shows the curve y = ln x/x⁴ and its maximum point M.
9. The quadrilateral ABCD is a trapezium in which AB and DC are parallel.
10. (a) Verify that

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