Geometry and measures worksheet — GCSE Higher

1.A triangular prism has a cross-section that is a triangle with a base of 3.5 cm and a perpendicular height of 4 cm. The prism is 10 cm long. Work out the volume of the prism.

2.Triangle T has a vertex at (2, 1). It is enlarged by a scale factor of 3, centre (0, 0). Work out the coordinates of the image of this vertex.

3.Every diameter of a circle is an example of a more general type of straight line joining two points on the circle. Which term names that more general type of line?

4.A quadrilateral has two pairs of parallel sides. All four of its interior angles are right angles, but its sides are not all the same length. Which quadrilateral is this?

5.ABCD is a cyclic quadrilateral, with its vertices in that order around the circle. Angle DAB = 108°. Work out the size of angle BCD.

6.A right-angled triangle has two sides of length 5 cm and 12 cm, and the angle between those two sides is 90°. Work out the length of the hypotenuse.

7.A hexagonal prism has 8 faces and 12 vertices. Using F + V − E = 2, work out how many edges it has.

8.Triangle PQR has vertices P(0, 0), Q(9, 0) and R(0, 4). Work out the area of triangle PQR.

9.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?

10.A cube has all of its edges the same length. How many planes of symmetry does it have?

11.A market stall sells apples at £2.40 per kilogram. Which of these expressions gives the cost, in pounds, of buying m kilograms of apples?

12.A trapezium has vertices (2, 1), (6, 1), (5, 4) and (3, 4). It is rotated 180° about the vertex (2, 1). Work out the number of points on the trapezium — including its vertices, edges and interior — that are invariant under this rotation.

13.Point A and point B are 5 cm apart. How many points are exactly 4 cm from A and exactly 3 cm from B?

14.In triangle ABC and triangle DEF, AB = DE, AC = DF, and the angle at A equals the angle at D. Write down the congruence condition that proves the two triangles are congruent.

15.A surveyor is marking out field ABCD for a new crop. The plan states that side AB is parallel to side DC, but AB and DC are not equal in length, and sides BC and AD are not parallel to each other. Which term correctly describes the shape of field ABCD?