Algebra worksheet — GCSE Foundation

1.Solve 3x − 5 = 4.

2.Which expression means the same as a × a × a?

3.A walker's distance-time graph is described as follows: she walks 3 km in the first 15 minutes at a steady speed, rests for 10 minutes, then walks a further 3 km in the next 20 minutes, also at a steady speed. Work out her speed, in km/h, during the first 15 minutes.

4.Work out the values of x and y that satisfy both x + y = 10 and x − y = 4.

5.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.

6.To solve 6x − 4 = 2x + 20, Yusuf's first step is to subtract 2x from both sides. Work out what equation this gives.

7.A ball is dropped and bounces. The height of each bounce after the first is 8 cm less than the bounce before it. The first bounce reaches 60 cm. Work out the height of the 5th bounce.

8.Solve the inequality 9 − 2x ≥ 1.

9.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.

10.The first term of an arithmetic sequence is 5, and each term after that increases by 6. Work out the 8th term of the sequence.

11.For the equation 2x + 3 = 11, and the inequality 2x + 3 > 11, which statement correctly compares their solutions?

12.A number machine adds 6 to its input. Work out the output when the input is −4.

13.Two numbers have a sum of 45. The larger number is 9 more than the smaller number. Form an equation using n for the smaller number, and solve it to find the larger number.

14.Which of these is an inequality?

15.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.