Geometry and measures worksheet — GCSE Foundation

1.How many edges does a cube have?

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

3.Which of the following is NOT one of the four basic conditions used to prove two triangles are congruent?

4.Freya is designing a triangular flower bed. Two of its corners have equal angles, and the angle at the third corner is 40°. Work out the size of one of the two equal corner angles.

5.Write down which one of these quadrilaterals always has diagonals that are equal in length and that cross at right angles.

6.Work out the distance between the points (−3, 4) and (5, −2).

7.Two sides of a triangle are 9 cm and 15 cm long. Write down which one of these lengths is possible for the third side.

8.A triangle has a base of 8 cm and a perpendicular height of 5 cm. Work out its area.

9.A ship sails 12 km on a bearing of 070° from a harbour to a buoy. It then sails a further 9 km, still on a bearing of 070°, from the buoy to a lighthouse. How far is the lighthouse from the harbour, in kilometres?

10.A cylinder has a volume of 942 cm³ and a height of 12 cm. Using π = 3.14, work out the radius of the cylinder.

11.To construct the perpendicular from a point P to a line l, where P is a point above l, an arc centred at P is drawn to cross l at two points, X and Y. What is the correct next step?

12.A ramp's sloped surface crosses two horizontal parallel rails. At the top rail, the angle between the ramp and the rail on the right of the ramp is (3x + 10)°. At the bottom rail, the angle between the ramp and the rail on the left of the ramp is (5x − 30)°. Work out the value of x.

13.How many faces does a cuboid have?

14.A ship's radio can be heard up to 30 km from the ship. A lighthouse's light can be seen up to 20 km from the lighthouse. The ship and the lighthouse are 40 km apart along the coast. Describe the region where BOTH the radio can be heard AND the light can be seen.

15.Work out the gradient of the line segment joining A(2, 3) and B(6, 11).