Geometry and measures worksheet — GCSE Higher

1.A circle has centre O. PQ, RS and TU are three chords of the circle, and only one of them passes through O. Write down what this tells you about that chord.

2.A cuboid has length 3 cm, width 4 cm and height 12 cm. Work out the length of the diagonal that runs from one corner of the cuboid to the opposite corner.

3.A, B, C and D are points on a circle, with B and D both on the same major arc AC. E lies on the straight line through A and B, beyond B, so that angle CBE = 145°. Work out the size of angle ADC.

4.In triangle ABC, AB = 9 cm, AC = 6 cm, and angle BAC = 65°. Work out the length of BC. Give your answer to 1 decimal place.

5.A straight line crosses two parallel lines. One of the angles formed is (2x + 10)°, and the angle alternate to it is 74°. Work out the value of x.

6.Point P has coordinates (2, 1). Transformation A reflects a point in the x-axis. Transformation B translates a point by the vector (0, 4). Work out the coordinates of the image of P when A is applied first, followed by B.

7.Triangle A has vertices (2, 1), (5, 1) and (2, 4). It is translated by the vector (−3, 2) and the image is then reflected in the x-axis. Work out the coordinates of the image of (5, 1).

8.A chocolate bar is a prism. Its cross-section is a triangle with a base of 6 cm and a perpendicular height of 5 cm, and the bar is 12 cm long. Work out the volume of the bar.

9.A tile manufacturer cuts a hexagonal tile so that all six sides measure exactly 4 cm, but a check shows only two pairs of the six interior angles are equal to each other, not all six angles. The customer's order specifies regular hexagonal tiles. Based on the check, is this tile a regular hexagon?

10.Shape S is enlarged by scale factor −1, centre (0, 0). Which single transformation has the same overall effect as this enlargement, for every point?

11.A regular nonagon has 9 sides. Work out the sum of its interior angles.

12.A cone is cut by a flat plane parallel to its circular base, partway up between the base and the apex. What shape is the cross-section?

13.In triangle ABC and triangle DEF, the angle at A equals the angle at D, and AB ÷ DE = AC ÷ DF. Write down what this proves about the two triangles.

14.Which of these correctly compares a 'line' with a 'line segment'?

15.A parallelogram has an area of 96 cm² and a base of 8 cm. Work out the perpendicular height of the parallelogram.