Geometry and measures worksheet — GCSE Foundation

1.A water tank holds 2.5 m³. Work out this volume in cm³.

2.The point (0, −5) lies on one of the two coordinate axes. Write down which axis this is.

3.The point (2, 5) is translated 3 units right and 4 units down. Work out the coordinates of the image point.

4.A treasure map has a scale of 1 cm to 4 m. A path from the start to a rock is drawn as two straight sections, measuring 3 cm and 2.5 cm. Work out the total real distance from the start to the rock, in metres.

5.Point E is at (4, 2). It is rotated 180° about the point (1, 1). Work out the coordinates of the image of point E.

6.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?

7.A sailmaker cuts two triangular sail panels from a pattern. Panel X has a 10 m side, with angles of 50° and 75° at its two ends. Panel Y also has a 10 m side, with angles of 50° and 75° at its two ends, in the same arrangement. The sailmaker wants to check the panels will match exactly, without cutting a third measurement. Which condition proves the two panels are congruent?

8.A locus is described as the set of points exactly 4 cm from a fixed point O. What shape is this locus?

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

10.A plan of a car park is drawn to a scale of 1 : 500. A parking bay is drawn as a rectangle measuring 1.2 cm by 0.6 cm. The real width of the bay corresponds to the 0.6 cm side. What is the real width of the bay, in metres?

11.A rectangular bookmark measures 2 cm by 25 cm. Work out the area of the bookmark.

12.Two similar hexagonal tiles have lengths in the ratio 4 : 7. A side of the smaller tile is 8.4 cm long. Work out the length of the corresponding side of the larger tile.

13.A cylinder has a radius of 3 cm and a height of 10 cm. Using π = 3.14, work out the volume of the cylinder.

14.A sector of a circle has radius 5 cm and angle 72°. Work out the arc length of the sector, in terms of π.

15.A regular polygon has an interior angle of 156°. Work out the number of sides of the polygon.