Geometry and measures worksheet — GCSE Foundation

1.A chocolate bar is a prism. Its cross-section is a triangle with a base of 6 cm and a perpendicular height of 5 cm, and the bar is 12 cm long. Work out the volume of the bar.

2.A builder props a straight plank against a vertical wall to reach a window ledge. The foot of the plank is 2.1 m from the base of the wall, and the plank is 3.5 m long. Work out how high up the wall the plank reaches.

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.A chord is drawn across a circle, dividing the circle into two regions. Write down the name of one of these two regions.

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

6.The point (2, 5) is translated 3 units right and 4 units down. Work out the coordinates of the image point.

7.The point (5, −2) is reflected in the x-axis. Work out the coordinates of the image point.

8.A bus journey takes 2.5 hours. Work out how many minutes this is.

9.A kite string makes an angle of 30° with the ground. The kite is flying at a height of 6 m directly above a point on the ground. Using the exact value of sin 30°, work out the exact length of the kite string.

10.Write down the column vector, from the options given, that would move a point to the right and downwards.

11.A circular plate has a diameter of 20 cm. Work out the area of the plate. Use π = 3.14.

12.A designer creates a repeating tile pattern. Each tile is translated from the one before it by the column vector with top number 4.5 and bottom number −2.5 (in centimetres). The first tile has its bottom-left corner at (1.5, 3). Work out the coordinates of the bottom-left corner of the third tile.

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

14.The diagram shows a prism resting on a table. Which shape is its front elevation, the view looking at it from directly in front?

15.In triangle ABC and triangle DEF, the angle at A equals the angle at D, and AB ÷ DE = AC ÷ DF. Write down what this proves about the two triangles.