## Exam-Style Questions.## Problems adapted from questions set for previous Mathematics exams. |

## 1. | GCSE Higher |

\(ABC\) is a right-angled triangle.

John has a method for finding the length of \(AC\)

$$AC^2 = AB^2 - BC^2$$ $$AC^2 = 13^2 - 5^2$$ $$AC^2 = 169 - 25$$ $$AC^2 = 144$$ $$AC = \sqrt{144}$$ $$AC = 12$$John's answer of \(12cm\) is not correct.

(a) What mistake has he made with his method?

(b) Show the correct method and the correct answer to 3 significant figures.

## 2. | GCSE Higher |

The diagram, not drawn to scale, show a polygon with one line of symmetry, AE.

Angle HAB is 90° and interior angle DEF is 220°.

Work out the size of angle ABC which is half the size of interior angle BCD and twice the size of angle CDE.

## 3. | GCSE Higher |

A point P is marked on side BC of parallelogram ABCD such that AB = BP.

Find the value of angle \(x\).

## 4. | GCSE Higher |

The diagram shows a quadrilateral ABCD in which angle DAB equals angle CDA and AB = CD.

Prove that the diagonals of this quadrilateral are of equal length.

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