Algebra worksheet — GCSE Foundation

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

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

3.Solve 2x + 1 = 9

4.Write down the number of terms in the expression 4x² − 7x + 3.

5.Work out the value of 2x² when x = −3

6.Solve 3x − 1 = 8

7.Solve 2x² − 32 = 0.

8.A car park charges a £4 fixed fee plus £3 for each hour. Kofi has exactly £25 to spend on parking. Using the inequality 4 + 3h ≤ 25, work out the greatest number of whole hours, h, he can park for.

9.Make p the subject of the formula n = p/3.

10.A printer starts a job with 480 sheets of paper loaded and prints at a steady rate. The number of sheets left, S, after t minutes is given by S = 480 − 24t. Work out how many minutes it takes for the paper to run out completely.

11.A straight line has equation 4y = 12x + 20. Work out the gradient of the line.

12.Work out the coordinates of the point where the graph of y = 2x − 6 crosses the x-axis.

13.The area of a circle is given by the formula A = πr², where r is the radius. Rearrange the formula to make r the subject.

14.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.

15.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.