This is part of a collection of videos showing step-by-step solutions for CIE A-Level Mathematics past papers.

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)

- The coefficient of x
^{4}in the expansion of (3 + x)^{5}is equal to the coefficient of x^{2}in the expansion … - The second and third terms of a geometric progression are 10 and 8 respectively.

Find the sum to infinity. - The equation of a curve is such that
- 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 - The equation of a curve is y = 4x
^{2}− kx + 1/2 k^{2}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. - 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

- 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 x^{2}+ y^{2}+ 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. - The equation of a curve is y = 3x + 1 − 4(3x + 1)
^{1/2}for x > −1/3 - Functions f and g are defined as follows:
- The function f is given by f(x) = 4 cos
^{4}x + cos^{2}x − 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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