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/ 2020/ May/June 2020 /Paper 1 (Variant 3)

Pure Mathematics 1 — Variant 3

A Level Mathematics · 9709/13 · May/June 2020

Question Paper

PDF · 130 KB · 20 pages

Mark Scheme

PDF · 327 KB · 14 pages

This browser cannot show the PDF inline.

Open the question paper · Open the mark scheme

Questions

6 of 11 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 [4]
Find the set of values of mm for which the line with equation y=mx+1y = mx + 1 and the curve with equation y=3x2+2x+4y = 3x^{2} + 2x + 4 intersect at two distinct points.
2 [4]
The equation of a curve is such that dydx=3x12−3x−12\frac{\mathrm{d}y}{\mathrm{d}x} = 3x^{\frac{1}{2}} - 3x^{-\frac{1}{2}}. It is given that the point (4,7)(4, 7) lies on the curve. Find the equation of the curve.
4
4(a) [1]
Expand (1+a)5(1 + a)^{5} in ascending powers of aa up to and including the term in a3a^{3}.
4(b) [3]
Hence expand [1+(x+x2)]5[1 + (x + x^{2})]^{5} in ascending powers of xx up to and including the term in x3x^{3}, simplifying your answer.
6
A point PP is moving along a curve in such a way that the xx-coordinate of PP is increasing at a constant rate of 2 units per minute. The equation of the curve is y=(5x−1)12y = (5x - 1)^{\frac{1}{2}}.
6(a) [4]
Find the rate at which the yy-coordinate is increasing when x=1x = 1.
6(b) [3]
Find the value of xx when the yy-coordinate is increasing at 58\frac{5}{8} units per minute.
7
7(a) [4]
Show that tan⁡θ1+cos⁡θ+tan⁡θ1−cos⁡θ≡2sin⁡θcos⁡θ\frac{\tan\theta}{1 + \cos\theta} + \frac{\tan\theta}{1 - \cos\theta} \equiv \frac{2}{\sin\theta\cos\theta}.
7(b) [4]
Hence solve the equation tan⁡θ1+cos⁡θ+tan⁡θ1−cos⁡θ=6tan⁡θ\frac{\tan\theta}{1 + \cos\theta} + \frac{\tan\theta}{1 - \cos\theta} = \frac{6}{\tan\theta} for 0∘<θ<180∘0^\circ < \theta < 180^\circ.
10
10(a) [4]
The coordinates of two points AA and BB are (−7,3)(-7, 3) and (5,11)(5, 11) respectively. Show that the equation of the perpendicular bisector of ABAB is 3x+2y=113x + 2y = 11.
10(b) [5]
A circle passes through AA and BB and its centre lies on the line 12x−5y=7012x - 5y = 70. Find an equation of the circle.

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