Geometry and measures worksheet — GCSE Foundation

1.A rectangle has vertices A(1, 1), B(4, 1), C(4, 5) and D(1, 5). Work out the perimeter of the rectangle.

2.Two straight lines PQ and RS cross at point O. Angle POR = 52°. Work out angle QOS.

3.A polygon has 12 straight sides. What is the mathematical name for this polygon?

4.Two triangles are similar. The sides of the first triangle are 3 cm, 4 cm and 5 cm. The shortest side of the second triangle is 9 cm. Work out the scale factor from the first triangle to the second.

5.Two triangles are proved congruent using the ASA condition. What can be concluded about the two remaining pairs of corresponding sides that were not part of the original ASA facts?

6.Work out the exact value of (sin 30°)² + (cos 30°)².

7.A recipe uses 1.25 kg of flour. Work out how many grams of flour this is.

8.Compasses are opened to exactly half the length of AB, and arcs are drawn centred at A and at B, to construct the perpendicular bisector of AB. Why does this fail?

9.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?

10.The bearing of a harbour B from a ferry's position A is 260°. What is the bearing of A from B?

11.Work out the y-coordinate of the midpoint of the line segment joining (2, 4) and (8, 10).

12.A shop stacks identical storage crates in a display. The diagram shows the plan of the floor positions used, with one corner position marked. Every floor position is filled with crates stacked 3 high, except the marked corner position, which is left completely empty. Work out how many crates are used in total.

13.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.

14.A solid has 5 faces, 9 edges and 6 vertices. Two of its faces are triangles and the other three are rectangles. Which solid is it?

15.A gardener wants to plant a tree so that it is the same distance from two straight garden walls that meet at a corner, and also the same distance from two ornamental posts standing 4 m apart. Which construction locates this point?