Algebra worksheet — GCSE Foundation

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

2.A sequence begins at 7. Each term after the first is found by adding 6 to the term before it. Work out the 6th term of the sequence.

3.Solve the inequality 6x ≥ 18.

4.A cyclist's distance-time graph shows the following: she travels 12 km in the first 30 minutes at a steady speed, then rests for 30 minutes, then travels a further 8 km in the next 15 minutes. Work out her average speed, in km/h, for the whole journey.

5.Solve the inequality 9 − 2x ≥ 1.

6.Solve 5x − 9 = 16

7.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.

8.There are 30 students in a Year 10 maths class. There are 2 more boys than girls. Work out the number of boys and the number of girls.

9.The solution to an inequality is n ≤ 5. Write down the largest integer value of n that satisfies this inequality.

10.A mobile phone tariff charges a fixed £15 plus 20p for every minute of calls made, so the total monthly charge, £C, for m minutes of calls is given by C = 15 + 0.2m. In a month where Ali's charge was £46.60, work out how many minutes of calls he made.

11.Solve 2x² − 32 = 0.

12.Make a the subject of the formula b = 20 − a.

13.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.

14.Work out the gradient of the straight line with equation 2x + y = 8.

15.Point P has coordinates (5, 2). Point P is rotated 180° about the origin to point Q. Write down the coordinates of Q.