Algebra worksheet — GCSE Foundation

1.Make b the subject of the formula a = 5b.

2.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.

3.A taxi charges a £3 fixed fee plus £2 for each mile travelled. Write an expression, in pounds, for the total cost of a journey of n miles.

4.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.

5.Which of these quadratic graphs does NOT cross the x-axis at all?

6.To solve 5x − 4 = 2x + 8, Chloe's working is shown. Line 1: 5x − 4 = 2x + 8. Line 2: 3x − 4 = 8. Line 3: 3x = 4. Line 4: x = 4/3. Chloe has made a mistake in her working. Which line contains the mistake?

7.Solve the simultaneous equations x + y = 15 and x − y = 3. Work out the value of x.

8.A number machine adds 6 to its input. Work out the output when the input is −4.

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

10.A scout leader is 44 years old and one of the scouts is 16 years old. Work out how many years it will be until the leader is exactly twice as old as the scout.

11.A rectangular garden has length (x + 7) m and width (x − 7) m. Work out an expression for the area of the garden, giving your answer in its simplest form.

12.A rectangular photo has length (x + 3) cm and width x cm. Its area is 40 cm². Work out the value of x.

13.Three consecutive integers add up to 72. Using n for the smallest integer, form an equation and solve it to find the smallest of the three integers.

14.Solve x² = 49.

15.A vertical line passes through the point (4, 7). Write down the equation of this line.