## 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 ex

## 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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