# CIE May 2023 9709 Pure Maths Paper 12 (9709/12/m/j/23)

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.

Related Pages
More A Levels Past Papers

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

1. 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.
2. The coefficient of x4 in the expansion of (x + a)6 is p and the coefficient of x2 in the expansion of (ax + 3)4 is q. It is given that p + q = 276.
Find the possible values of the constant
3. (a) Express 4x2 − 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.
4. Solve the equation 8x6 + 215x3 − 27 = 0.
5. The diagram shows the curve with equation
6. 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

1. By first expanding (cos θ + sin θ)2, find the three solutions of the equation
(cos θ + sin θ)2 = 1
2. The diagram shows the graph of y = f(x) where the function f is defined b
3. 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.
4. 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
5. The equation of a curve is

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.