 # 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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