Algebra worksheet — GCSE Higher

1.Make x the subject of the formula y = 5x + 3.

2.A ferry's distance-time graph is a straight line from (0 minutes, 0 km) to (25 minutes, 15 km). Work out the ferry's speed in kilometres per hour.

3.Work out the coordinates of the reflection of (6, −3) in the y-axis.

4.A student claims: 'For every positive integer n, n² + n + 1 is a prime number.' Which value of n shows that this claim is false?

5.Solve x² − 8x + 3 = 0 by completing the square. Give your answers in surd form.

6.Simplify (x² − 9) ÷ (x² + 5x + 6).

7.On Monday, a runner covers 15 km in 2.5 hours. On Tuesday, she covers 12 km in 1.5 hours. Using the formula speed = distance ÷ time, work out on which day she ran faster, and by how much.

8.A delivery van's distance-time graph shows the following: it travels 9 km in the first 15 minutes at a steady speed, stops for 45 minutes to unload, then travels a further 21 km in the next 30 minutes, also at a steady speed. Work out the average speed, in km/h, for the whole journey.

9.Line L has equation y = 3x + 1. Which of these lines is perpendicular to L?

10.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).

11.A straight line has gradient −3 and passes through the point (0, 1). Work out the value of y when x = 2.

12.Which of these statements is an equation with exactly one solution?

13.A taxi fare in pounds is given by F = 2.50 + 1.20m, where m is the number of miles travelled. Sam takes a taxi for a journey of 6 miles. Work out the fare.

14.The graph of y = f(x) passes through the point (2, 5). Write down the coordinates of the corresponding point on the graph of y = f(x − 4) + 1.

15.Four sequences are shown below. Sequence P: 4, 8, 16, 32, ... Sequence Q: 4, 8, 12, 16, ... Sequence R: 4, 7, 12, 19, ... Sequence S: 4, 9, 16, 25, ... Work out which of the sequences P, Q, R and S is geometric.