Algebra worksheet — GCSE Foundation

1.Factorise x² − 3x − 10.

2.The graph of y = (x − 4)(x + 1) crosses the x-axis. Which pair gives the correct roots and reasoning?

3.Yusuf has £40 saved and adds £6 each week. His sister Aisha has £10 saved and adds £11 each week. After how many weeks will they have saved the same amount?

4.Write down the first four terms of the sequence with nth term 6n − 5.

5.Which of these is a factor of 15x + 20?

6.A point has coordinates (−6, 9). Work out the sum of the x-coordinate and the y-coordinate.

7.Which of these is a formula, rather than an expression, an equation, or an identity?

8.y = x + 10. Work out the value of y when x = 0.

9.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.

10.A rectangle has area 24x + 18. Ffion factorises the area as 6(4x + 3). Work out the value of the area when x = 2, and decide whether 6 and (4x + 3) are correctly identified as factors of 24x + 18.

11.Which of these is an equation, rather than an expression, a formula or an identity?

12.Oliver buys b pens. Each pen costs £2. Write down an expression for the total cost, in pounds.

13.Noah says that y = 3 is the solution of the equation y + 10 = 12. Noah is wrong. Work out the correct value of y.

14.A candle is 30 cm tall when lit and burns at a constant rate. After burning for 5 minutes, its height is 20 cm. The height h cm after t minutes is given by h = 30 − mt. Work out the value of m.

15.Write down the coordinates of the point that is 4 units to the left of the origin and 7 units up.