StudentAid
HomeLearn
9th Class10th Class11th Class12th ClassCambridge past papersBrowse everything
Attendance
Class attendanceVisitor register
For schoolsFor driversFor parentsBook a demo
Learn/ A Level Mathematics/ Past Papers/ 2024/ May/June 2024 /Paper 1 (Variant 2)

Pure Mathematics 1 — Variant 2

A Level Mathematics · 9709/12 · May/June 2024

Question Paper

PDF · 1.0 MB · 20 pages

Mark Scheme

PDF · 352 KB · 25 pages

This browser cannot show the PDF inline.

Open the question paper · Open the mark scheme

Questions

5 of 10 questions shown here, checked against the paper. The others are in the PDF above — they contain diagrams or maths we could not yet verify, and we would rather show you the original than a transcription we are not sure of.

1 [3]
The coefficient of x2x^{2} in the expansion of (1−4x)6(1 - 4x)^{6} is 12 times the coefficient of x2x^{2} in the expansion of (2+ax)5(2 + ax)^{5}. Find the value of the positive constant aa.
2 [5]
The curve y=x2y = x^{2} is transformed to the curve y=4(x−3)2−8y = 4(x-3)^{2} - 8. Describe fully a sequence of transformations that have been combined, making clear the order in which the transformations have been applied.
7
The equation of a circle is (x−6)2+(y+a)2=18(x-6)^{2} + (y+a)^{2} = 18. The line with equation y=2a−xy = 2a - x is a tangent to the circle.
7(a) [5]
Find the two possible values of the constant aa.
7(b) [3]
For the greater value of aa, find the equation of the diameter which is perpendicular to the given tangent.
9
A function f is such that f′(x)=6(2x−3)2−6xf'(x) = 6(2x-3)^{2} - 6x for x∈Rx \in \mathbb{R}.
9(a) [4]
Determine the set of values of xx for which f(x)f(x) is decreasing.
9(b) [4]
Given that f(1)=−1f(1) = -1, find f(x)f(x).
10
The equation of a curve is y=(5−2x)32+5y = (5-2x)^{\frac{3}{2}} + 5 for x<52x < \frac{5}{2}.
10(a) [4]
A point PP is moving along the curve in such a way that the yy-coordinate of point PP is decreasing at 5 units per second. Find the rate at which the xx-coordinate of point PP is increasing when y=32y = 32.
10(b) [6]
Point AA on the curve has yy-coordinate 32. Point BB on the curve is such that the gradient of the curve at BB is −3-3. Find the equation of the perpendicular bisector of ABAB. Give your answer in the form ax+by+c=0ax + by + c = 0, where aa, bb and cc are integers.

Published by Cambridge Assessment International Education. Reproduced for study use.