Geometry and measures worksheet — GCSE Foundation

1.A solid is built from five centimetre cubes, standing side by side on a table in a single straight row. Looking down from directly above (the plan view), how many squares are visible?

2.A circle has a diameter of 4 cm. Work out the radius of the circle.

3.Each of these has an exact value. Write down the one whose value is the greatest.

4.Two sides of a triangle are 20 cm and 8 cm long. Write down which one of these lengths is possible for the third side.

5.A ship's radar shows a lighthouse at the point (12, −4) on a grid measured in nautical miles. The ship is at (2, 5). The ship sails along the vector that takes it directly to the lighthouse, then sails along that same vector again. Work out the ship's final position.

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

7.Triangle ABC is similar to triangle PQR. AB corresponds to PQ, and BC corresponds to QR. AB = 5 cm, PQ = 15 cm and BC = 7 cm. Work out the length of QR.

8.Two angles lie on a straight line. One angle is 118°. Which reason correctly explains why the other angle is 62°?

9.In this question, a curved surface counts as a face. How many faces does a cone have?

10.A train leaves Leeds at 08:47 and arrives in London at 11:05. Work out how long the journey takes.

11.How many edges does a cube have?

12.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.

13.Two angles are complementary. One of them is 35°. Work out the size of the other angle.

14.A cable supporting a flagpole is anchored to the ground 5 m from the base of the pole. The cable makes an angle of 60° with the ground. Using the exact value of tan 60°, work out the exact height of the flagpole.

15.Point B is at (1, 6). It is reflected in the x-axis. Work out the coordinates of the image of point B.