Algebra worksheet — GCSE Foundation

1.A number machine multiplies its input by 2 and then subtracts 5. Work out the output when the input is 6.

2.A delivery van's distance-time graph shows the following: it travels 9 km in the first 15 minutes at a steady speed, stops for 45 minutes to unload, then travels a further 21 km in the next 30 minutes, also at a steady speed. Work out the average speed, in km/h, for the whole journey.

3.The first four terms of a sequence are 18, 15, 12, 9. Work out an expression, in terms of n, for the nth term.

4.A point has coordinates (x, y), where x + y = 0 and x is not 0. In which two quadrants could this point lie?

5.A sequence starts at 2. Each term after that is found using the rule "double the previous term, then add 1". Work out the 4th term of the sequence.

6.A plumber charges a £35 call-out fee plus £20 for each hour worked, h. On a certain job the total charge was £115. Work out how many hours the plumber worked.

7.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.

8.Which of these is an expression?

9.Solve 2x − 2 = 2

10.In the expression 5x² − 3x + 7, which of these is a single term of the expression?

11.A formula is F = 4s. A pupil says that when s = 5 the value of F is 9, because they added 4 and 5 instead of multiplying. Work out the correct value of F when s = 5.

12.A quadratic graph has roots at x = −3 and x = 5, and it crosses the y-axis at (0, −15). Work out the equation of the curve in the form y = (x − a)(x − b).

13.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.

14.The graph of y = x² − 2x − 8 takes these values: when x = −2, y = 0; when x = −1, y = −5; when x = 0, y = −8; when x = 3, y = −5; when x = 4, y = 0. Use these values to write down the two solutions of x² − 2x − 8 = 0.

15.A plumber charges a call-out fee of £30 plus £25 for each hour worked. The total bill for a job was £130. Work out how many hours the plumber worked.