CIE May 2022 9709 Pure Maths Paper 12

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This page covers Questions and Worked Solutions for CIE Pure Maths Paper 1 May/June 2022, 9709/12.

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CIE May/June 2022 9709 Pure Maths Paper 12 (pdf)

  1. The coefficient of x4 in the expansion of (3 + x)5 is equal to the coefficient of x2 in the expansion …
  2. The second and third terms of a geometric progression are 10 and 8 respectively.
    Find the sum to infinity.
  3. The equation of a curve is such that
  4. The first, second and third terms of an arithmetic progression are k, 6k and k + 6 respectively.
    (a) Find the value of the constant k.
    (b) Find the sum of the first 30 terms of the progression
  5. The equation of a curve is y = 4x2 − kx + 1/2 k2 and the equation of a line is y = x − a, where k and a are constants.
    (a) Given that the curve and the line intersect at the points with x-coordinates 0 and 34, find the values of k and a.
  6. The diagram shows the curve with equation y = 5x1/2 and the line with equation y = 2x + 2.
    Find the exact area of the shaded region which is bounded by the line and the curve

  1. The diagram shows a sector OBAC of a circle with centre O and radius 10 cm. The point P lies on OC and BP is perpendicular to OC. Angle AOC = 1/6 π and the length of the arc AB is 2 cm.
    (a) Find the angle BOC8. The equation of a circle is x2 + y2 + ax + by − 12 = 0. The points A(1,1) and B(2,−6) lie on the circle.
    (a) Find the values of a and b and hence find the coordinates of the centre of the circle.
  2. The equation of a curve is y = 3x + 1 − 4(3x + 1)1/2 for x > −1/3
  3. Functions f and g are defined as follows:
  4. The function f is given by f(x) = 4 cos4x + cos2x − k for 0 ≤ x ≤ 2π, where k is a constant.
    (a) Given that k = 3, find the exact solutions of the equation f(x) =

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