Algebra worksheet — GCSE Foundation

1.Work out the y-intercept of the graph of y = x² + 3x − 10.

2.Solve 2x − 2 = 2

3.A packet contains s sweets. The sweets are shared equally between f friends. Write an expression for the number of sweets each friend receives.

4.The diagram shows a distance–time graph for a cyclist travelling at a constant speed, for the first 6 minutes of a journey. Distance is in kilometres and time is in minutes. Work out how far the cyclist would travel in 20 minutes at the same speed.

5.Factorise fully 12x² + 18x.

6.A cycle route is 84 km long. Freya sets off along it at a steady 14 km/h. Write down the function for the distance y, in kilometres, that is still to be cycled after x hours.

7.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.

8.An arithmetic sequence has first term 40 and common difference −6. Work out the 9th term of the sequence.

9.The formula for the area of a trapezium is A = (a + b)h / 2, where a and b are the parallel side lengths and h is the height. Make h the subject of the formula.

10.A rectangle has width x cm. Its length is 3 cm more than its width. The perimeter of the rectangle is 38 cm. Form an equation and solve it to find x.

11.Which of these is an inequality?

12.Solve x/4 + 1 = 3

13.A straight line passes through the points (0, 4) and (1, 9). Write down the gradient of the line.

14.Leo is three times as old as his brother. His brother is x years old. Write down an expression for Leo's age.

15.The height, h metres, of a ball t seconds after a stopwatch is started follows h = (t − 1)(5 − t) for 1 ≤ t ≤ 5, where h = 0 means the ball is at ground level. Work out the two times at which the ball is at ground level.