Geometry and measures worksheet — GCSE Foundation

1.Write down the exact value of sin 45°.

2.Put sin 30°, tan 30° and cos 30° in order of size, starting with the smallest.

3.A sector of a circle has radius 7 cm and angle 90°. Using π = 3.14, work out the arc length of the sector, to 1 decimal place.

4.A circle has circumference 31.4 cm. Using π = 3.14, work out the radius of the circle.

5.A rhombus has all four sides equal in length, but it is not a square — its angles are not all 90°. How many lines of symmetry does this rhombus have?

6.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.

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

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

9.All four sides of a rhombus are the same length. One side of a rhombus is 7 cm long. Work out the perimeter of the rhombus.

11.A bead starts at position (2, −1) on a grid, in centimetres. It is moved by the column vector u, with top number 3 and bottom number 5, and then moved by the column vector v, with top number −7 and bottom number 2. Work out the coordinates of the bead's final position.

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

13.Line 1 passes through (0, 1) and (2, 5). Line 2 passes through (3, 2) and (5, 6). Work out the gradient of each line. Then write down whether the two lines are parallel.

14.A sector of a circle has an angle of 90° at the centre. Write down what fraction of the whole circle this sector represents.

15.Write down the name given to a quadrilateral with exactly one pair of parallel sides.