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 2023, 9709/12.

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CIE May/June 2023 9709 Pure Maths Paper 12 (pdf)

- The equation of a curve is such that dy/dx = 4/(x − 3)
^{3}for x > 3. The curve passes through the point (4, 5). Find the equation of the curve. - The coefficient of x
^{4}in the expansion of (x + a)^{6}is p and the coefficient of x^{2}in the expansion of (ax + 3)^{4}is q. It is given that p + q = 276.

Find the possible values of the constant - (a) Express 4x
^{2}− 24x + p in the form a(x + b)^{2}+ c, where a and b are integers and c is to be given in terms of the constant p. - Solve the equation 8x
^{6}+ 215x^{3}− 27 = 0. - The diagram shows the curve with equation
- The diagram shows a sector OAB of a circle with centre O. Angle AOB = θ radians and OP = AP = x.

(a) Show that the arc length AB is 2xθ cos θ

- By first expanding (cos θ + sin θ)
^{2}, find the three solutions of the equation

(cos θ + sin θ)^{2}= 1 - The diagram shows the graph of y = f(x) where the function f is defined b
- The second term of a geometric progression is 16 and the sum to infinity is 100.

(a) Find the two possible values of the first term. - The equation of a circle is (x − a)
^{2}+ (y − 3)^{2}= 20. The line y = 1/2 x + 6 is a tangent to the circle at the point P.

(a) Show that one possible value of a is 4 and find the other possible valu - The equation of a curve is

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