CIE May/June 2021 9709 Pure Maths Paper 12 (pdf)
- (a) Express 16x2 − 24x + 10 in the form (4x + a)2 + b
(b) It is given that the equation 16x2 − 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
(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) = 2x2 + 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.
- 8 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 y2 = x − 2 and the lines x = 5 and y = 1. The
shaded region enclosed by the curve and the lines is rotated through 360Å 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.
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