Geometry and measures worksheet — GCSE Foundation

1.A plumber charges a £45 call-out fee, plus £28 for each hour worked. She works on a job for 3 hours 30 minutes, and her hours are billed by rounding up to the next whole hour. Work out the total amount she charges.

2.A bead starts at position (2, −1) on a grid, in centimetres. It is moved by the column vector u, with top number 3 and bottom number 5, and then moved by the column vector v, with top number −7 and bottom number 2. Work out the coordinates of the bead's final position.

3.A straight transversal crosses a pair of parallel lines. At one crossing point, the angle between the transversal and a parallel line is 118°. Work out the size of the co-interior (allied) angle at the other crossing point.

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

5.Four angles meet at a point. Three of them measure 82°, 105° and 96°. Work out the size of the fourth angle.

6.A triangle has vertices X, Y and Z, with a right angle at Y. Side XY is twice as long as side YZ. Which of the following correctly describes this triangle?

7.A diameter divides a circle into two equal halves. Write down the special name given to each of these two halves.

8.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?

9.Rectangle ABCD has vertices A(−1, 2), B(4, 2), C(4, 5) and D(−1, 5). The rectangle is translated so that C moves to (0, −1). Write down the coordinates of the image of A.

10.A translation moves the point (1, 1) to the point (9, 4). Write down the column vector of this translation.

12.Point M lies exactly halfway between point A and point B, with A, M and B all on the same straight line. Which term correctly describes point M?

13.A circular coin has a diameter of 3 cm. Work out the circumference of the coin. Give your answer in terms of π.

14.Two similar hexagonal tiles have lengths in the ratio 4 : 7. A side of the smaller tile is 8.4 cm long. Work out the length of the corresponding side of the larger tile.

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