Algebra worksheet — GCSE Foundation

1.Grace says that 2(x + 1) and 2x + 2 always have the same value. Work out the value of both expressions when x = 3.

2.Solve the inequality x − 10 < −3.

3.A candle is 30 cm tall and burns down at a steady rate of 1 cm per hour. Write down the function for the height of the candle y, in centimetres, after x hours.

4.The line y = 3x + 6 meets the x-axis at one point. Work out the coordinates of that point.

5.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.

6.A curve has equation y = x³ − 4x. Work out the coordinates of the point where the curve crosses the y-axis.

7.Solve 6x + 4 = 28

8.Work out the gradient of the straight line with equation y = (2x/5) − 3.

9.Write down the expression that means the same as (x + 7) ÷ 4.

10.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.

11.Work out the value of n² − n when n = −3

12.A sequence has the position-to-term rule: the term is the position number multiplied by itself. Its first five terms are 1, 4, 9, 16, 25. Work out the 8th term.

13.The area of a circle is given by the formula A = πr², where r is the radius. Rearrange the formula to make r the subject.

14.Yuki is y years old. Her brother is 4 years younger than Yuki. Write down an expression, in terms of y, for the brother's age in 5 years' time.

15.Solve the inequality 6x ≥ 18.