CIE May 2022 9709 Pure Maths Paper 12

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

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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 = 5x^1/2 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

7. 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.
8. The equation of a curve is y = 3x + 1 − 4(3x + 1)^1/2 for x > −1/3
9. Functions f and g are defined as follows:
10. 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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