Algebra worksheet — GCSE Foundation

1.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.

2.A number machine multiplies its input by 3. The output is 15. Work out the input.

3.Solve the simultaneous equations x + y = 1 and 2x + y = 5.

4.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.

5.Point P has coordinates (2, −5). P is reflected in the x-axis to point Q. Write down the coordinates of Q.

6.Here are the first five terms of an arithmetic sequence: 2, 5, 8, 11, 14. Work out the 8th term.

7.Solve 5x² − 15x = 0.

8.Expand 2(x + 12)

9.A sequence has the position-to-term rule n² + 2, where n is the position number. Work out the 6th term.

10.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.

11.A pizza shop charges a fixed delivery fee of £3, plus £9 for each pizza ordered. Write down the function for the total cost y, in pounds, of ordering x pizzas.

12.A ribbon of length L metres is cut into 5 equal pieces, and then 3 metres is removed from one piece. Write down an expression, in metres, for the length of that piece after 3 metres is removed.

13.The formula for the area of a trapezium is A = (a + b)h / 2, where a and b are the parallel side lengths and h is the height. Make h the subject of the formula.

14.The first four terms of a sequence are 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.

15.A taxi charges a fixed fee of £3 plus £2 for every mile travelled. The journey is m miles. Write down an expression for the total cost, in pounds.