Geometry and measures worksheet — GCSE Foundation

1.In triangle ABC the angle at A and the angle at C are equal. The side AB is extended beyond B, and the exterior angle formed at B measures 98°. Work out the size of the angle at A.

2.The point A(3, 2) is translated by the vector (−5, 4) to give point B. Work out the coordinates of B.

3.u is the column vector with top number 5 and bottom number 1. v is the column vector with top number 2 and bottom number 4. Work out u − v, giving your answer as a column vector in the form (top, bottom).

4.Two straight roads cross at a junction. The angle between them, measured with a protractor, is 118°. What is the size of the angle vertically opposite to it?

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

6.Triangle ABC is drawn. The interior angle bisectors from vertices A and B are constructed and meet at point I inside the triangle. Which statement about point I must be true?

7.Write down the exact value of sin 60°.

9.A map has a scale of 1 cm : 5 km. A road is drawn 3 cm long on the map. What is the real length of the road?

10.A model car is built to a scale of 1 : 24. The real car is 4.32 m long. Work out the length of the model, in centimetres.

11.How many vertices does a square-based pyramid have?

12.A tank holds 3.2 m³ of water. Work out this volume in litres.

13.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.

14.A circle has diameter 10 cm. Using π = 3.14, work out the circumference of the circle.

15.A recipe uses 0.75 kg of sugar. Work out how many grams of sugar this is.