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 2021, 9709/12.

**Related Pages**

More A Levels Past Papers

CIE May/June 2021 9709 Pure Maths Paper 12 (pdf)

- (a) Express 16x
^{2}− 24x + 10 in the form (4x + a)^{2}+ b

(b) It is given that the equation 16x^{2}− 24x + 10 = k, where k is a constant, has exactly one root. Find the value of this root - (a) The graph of y = f(x) is transformed to the graph of y = 2f(x − 1).

Describe fully the two single transformations which have been combined to give the resulting transformation.

(b) The curve y = sin 2x − 5x is reflected in the y-axis and then stretched by scale factor 1/3 in the x-direction.

Write down the equation of the transformed curve. - The equation of a curve is y = (x − 3)√(x + 1) + 3. The following points lie on the curve. Non-exact values are rounded to 4 decimal places
- The coefficient of x in the expansion of (4x + 10/x)
^{3}is p - The function f is defined by f(x) = 2x
^{2}+ 3 for x ge; 0.

(a) Find and simplify an expression for ff(x) - Points A and B have coordinates (8, 3) and (p, q) respectively. The equation of the perpendicular
bisector of AB is y = −2x + 4.

Find the values of p and q

- The point A has coordinates (1, 5) and the line l has gradient −2/3 and passes through A. A circle has
centre (5, 11) and radius √52.

(a) Show that l is the tangent to the circle at A. - The first, second and third terms of an arithmetic progression are a, 3/2a and b respectively, where
a and b are positive constants. The first, second and third terms of a geometric progression are
a, 18 and b + 3 respectively.

(a) Find the values of a and b - The diagram shows part of the curve with equation y
^{2}= x − 2 and the lines x = 5 and y = 1. The shaded region enclosed by the curve and the lines is rotated through 360° about the x-axis.

Find the volume obtained - (a) Prove the identity
- The gradient of a curve is given by
- The diagram shows a cross-section of seven cylindrical pipes, each of radius 20 cm, held together by a thin rope which is wrapped tightly around the pipes. The centres of the six outer pipes are A, B, C, D, E and F. Points P and Q are situated where straight sections of the rope meet the pipe with centre A.

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.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.