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Temporary Maths Page

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TSR Wiki > Study Help > Subjects and Revision > Subject Guides > Mathematics > Example Questions and Exam Papers > Temporary Maths Page

Welcome to the Temporary Maths Page.

The aim of this page is to compile a selection of revision questions and their worked solutions. Questions will eventually be categorised by module and topic across several pages, but this is the place where they all begin.

Please read before contributing

If you would like to contribute, that would be much appreciated.

Write your question as a bullet point under the appropriate section below. Try to present it clearly, using TeX if necessary.
All questions are linked to their solutions by a unique ID (for example M0123). Write your full worked solution at the bottom of the answers page, using the next available ID as a section heading. Important: Even if you would like to leave the solution for someone else to complete, you must create a blank entry on the solutions page.
If you took the question from a thread in the TSR Forum, include a link in your solution.
Come back here, and link your question to its answer.

Please contact jamesgurung if you have any queries or suggestions.

KS3 Questions

(None submitted.)

GCSE Questions

Algebra

Express $\frac{x}{(x+1)(x+3)} + \frac{x+12}{x^{2}-9}$ as a single fraction in its simplest form. Solution (M0001)

Inequalities

Solve the inequality $x^{2} + 2x \ge 3$ . Solution (M0002)

A Level Questions

Different exam boards have different syllabi. If any questions come under different modules for different exam boards, please make a note by the question. Please do not mark categorisation for the IB or any other exam system; this will be implemented later.

Further Pure 2

Show that S(rt3,0) is a focus of the ellipse with the equations The origin is O and P is any point on the ellipse. A line is drawn from O perpendicular to the tangent to the ellipse at P and this line meets the line SP, produced if necessary, in the point Q. Show that the locus of Q is a circle.Solution (M0010)

Further Pure 1

Find the general solution to $x\frac{d^2y}{dx^2}-2\frac{dy}{dx} + x = 0$ using the substitution $\frac{dy}{dx} = v$ . Solution (M0003)
Find the general solution of the differential equation $\frac{dy}{dx} - 2ycosecx = tan \frac{x}{2}$ . Solution (M0009)

Core 3

Differentiate $\frac{e^{x}}{x-1}$ twice with respect to . Solution (M0004)

Differentiate $\ln(x + \sqrt{x^{2} +1})$ - Solution (M0005)

H is a function such that . What is 80 times? And 81 times? Solution (M0006)

NB This question is possible to do with C3 maths knowledge but is not in the style of any of the current exam boards.

Core 2

Find all solutions to the equation . Solution (M0008)

Mechanics 1

A particle P moves in a straight line with acceleration (6t-10) ms^-2. Initially P is at O, a fixed point on the line, and has velocity 3ms^-1. Show that, during the first 2 seconds, P travels a distance of $\frac{188}{27}$ m. Solution (M0007)