Algebra worksheet — GCSE Foundation

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

2.Solve x − 4 = −9

3.A parcel delivery company's cost graph shows the following: the cost is a flat £5 for parcels weighing up to 2 kg, and then rises by £2 for each additional kg above 2 kg. Use the graph to work out the weight of a parcel that costs £17.

4.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.

5.A caterer uses the formula C = 6p + 20 to work out the total cost, £C, of a buffet for p people, where £20 covers fixed costs. A customer is charged £92. Work out how many people, p, the buffet was for.

6.The simultaneous equations 2x + 3y = 12 and x − y = 1 are given. Work out the value of y.

7.Water is poured into a container at a constant rate. A graph of the depth of the water, in cm, against the time since pouring began, in minutes, is a straight line through the origin, and it passes through the point (3, 12). Use the graph to work out the depth of the water after 7 minutes.

8.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.

9.A point has coordinates (x, y). In which two quadrants is the product x × y positive?

10.The first four terms of a sequence are 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.

11.Expand 2(x + 12)

12.The nth term of a sequence is 2n² + 1. Work out the 4th term of the sequence.

13.A number, n, is doubled and then 7 is subtracted. The result is 15. Form an equation and solve it to find n.

14.The formula for the volume of a cuboid is V = lwh, where l is the length, w is the width and h is the height. Make h the subject of the formula.

15.The formula for the perimeter of a square is P = 4s, where s is the side length. Make s the subject of the formula.