Algebra worksheet — GCSE Foundation

1.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.

2.A cinema sells adult tickets for £10 and child tickets for £6. A family group buys 9 tickets in total, spending £74. Work out how many adult tickets were bought.

3.For the graph of y = 1/x, where x cannot be zero, which of these statements is correct?

4.Line C passes through (0, 0) and (4, 2). Line D passes through (0, 0) and (2, 2). Write down which of the two lines is the steeper.

5.Solve the inequality x − 10 < −3.

6.Simplify 2b − 1 + 2b − 4 + 2b

7.The formula for the perimeter of a rectangle is P = 2(l + w). One rectangle has l = 9 cm and w = 4 cm. A second rectangle has l = 6 cm and w = 5 cm. Work out how many cm greater the perimeter of the first rectangle is than the perimeter of the second.

8.A table shows y = x² − 6x + 5 at these points (x, y): (0, 5), (1, 0), (2, −3), (3, −4), (4, −3), (5, 0), (6, 5). Using the symmetry shown, write down the x-coordinate of the turning point.

9.The nth term of a sequence is 3n + 2. Work out the 4th term of the sequence.

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

11.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?

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

13.Work out the gradient of the straight line with equation 3y = 12 − 6x.

14.Solve the simultaneous equations 2x + y = 7 and x − y = 2.

15.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.