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Exam-Style Questions.Problems adapted from questions set for previous Mathematics exams. |
1. | GCSE Higher |
The diagram shows an isosceles triangle (not drawn to scale).
Angle ABC = angle ACB, AB = \(3x+8\) and AC = \(5x-7\).
Use an algebraic method to find the value of \(x\).
2. | GCSE Higher |
Solve the following linear equation to find the value of \(x\).
$$ \frac{5x+4}{3} - \frac{2x-3}{5} = \frac{10+x}{2} $$3. | GCSE Higher |
The trapezium and rectangle shown here have the same perimeters. The diagrams are not drawn to scale and the measurements are in centimetres. Calculate the area of the trapezium.
6. | GCSE Higher |
The area of rectangle PQRS (not to scale) is 80cm2.
(a) Show that \( x^2 + 14x = 40\).
(b) Find the value of \( x \) giving your answer correct to three significant figures.
7. | IGCSE Extended |
(a) Show that the equation \(\frac{3}{x+1}+\frac{3x-9}{2}=1\) can be simplified to \(3x^2-8x-5=0\).
(b) Solve the equation \(3x^2-8x-5=0\) showing all of your working and giving answers to three significant figures.
(c) The total surface area of a cone with radius \(x\) and slant height \(8x\) is equal to the area of a circle with radius r. Show that \(r = 3x\).
[The curved surface area, \(A\), of a cone with radius \(r\) and slant height \(l\) is \(A=\pi rl\).]
8. | GCSE Higher |
A rectangular sheet of paper can be cut into two identical rectangular pieces in two different ways, either by cutting along line A or by cutting along line B.
When the original sheet of paper is cut along line A, the perimeter of each of the two pieces is 56 cm.
When the original sheet of paper is cut along line B, the perimeter of each of the two pieces is 64 cm.
What is the perimeter of the original sheet of paper?
9. | GCSE Higher |
Show that you understand equations and inequalities by answering the following:
(a) Solve \(5x^2=80\)
(b) Solve \(8x + 2 \gt x + 7\)
(c) Write down the largest integer that satisfies \(8x - 2 \lt 25\)
(d) Solve the following pair of equations
$$3x + 5y = 21$$ $$8x - 5y = 1$$10. | IB Studies |
A red rug has a width of \(x-3\) cm and a length of \(4x\) cm.
(a) Write down an ex
The area of the rug is 3240 cm2.
(b) Calculate the value of \(x\).
(c) Hence, write down the value of the length and of the width of the rug in centimetres.
11. | GCSE Higher |
Two numbers are chosen so that the sum of their squares is 25.
If those numbers are represented by \(x\) and \(y\) they will also satisfy the equation:
$$y-3x=13$$Use an algebraic method to find two possible values of \(x\) and \(y\) .
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The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.
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