# Exam-Style Questions.

## Problems adapted from questions set for previous Mathematics exams.

### 1.

GCSE Higher

Solve the following linear equations showing clearly each step of your working.

(a) $$\frac{6}{x} = 24$$.

(b) $$11x - 5 = 9(x + 9)$$.

### 2.

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 $$x$$.

### 3.

GCSE Higher

The perimeter of the triangle is the same length as the perimeter of the square.

Find an expression for the length of one side of the square in terms of a. Give your answer in its simplest form.

### 4.

GCSE Higher

Aimee, Natasha and Ruby play hockey.

• Aimee has scored 6 more goals than Natasha.
• Ruby has scored 5 more goals than Aimee.

If altogether they have scored 35 goals, how many goals did they each score?

### 5.

GCSE Higher

Solve the following linear equation to find the value of $$x$$.

$$\frac{5x+4}{3} - \frac{2x-3}{5} = \frac{10+x}{2}$$

### 6.

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.

### 7.

GCSE Higher

Two rectangles, not drawn to scale, are shown below. All measurements are in centimetres. Both rectangles have the same areas. Work out the perimeter of the rectangle on the left.

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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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