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This page covers Questions and Worked Solutions for CIE Pure Maths Paper 3 May/June 2021, 9709/33.

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CIE May 2021 9709 Pure Maths Paper 3 (pdf)

- Expand (1 + 3x)
^{2/3}in ascending powers of x, up to and including the term in x^{3}, simplifying the coefficients. - Solve the equation 4x = 3 + 4
^{-x}. Give your answer correct to 3 decimal places - 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 - let f(x) =
- (a) By first expanding tan(2θ + 2θ), show that the equation tan 4θ =/2 = tan θ may be expressed as tan
^{4}θ + 2 tan^{2}θ − 7 = 0. - (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. - 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
- The diagram shows the curve y = ln x/x
^{4}and its maximum point M. - The quadrilateral ABCD is a trapezium in which AB and DC are parallel.
- (a) Verify that

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