Algebra worksheet — GCSE Foundation

1.The graph of P = 480 ÷ V shows how the pressure, P pascals, of a gas depends on its volume, V cm³, at constant temperature. Use the relationship to work out the volume when the pressure is 32 pascals, and then work out by how much the volume increases when the pressure drops to 24 pascals.

2.Solve the simultaneous equations 3x + 2y = 16 and x + y = 7. Work out the value of y.

3.The first five terms of a sequence are 6, 10, 14, 18, 22. Work out an expression, in terms of n, for the nth term.

4.Work out the value of 3x² − 4x when x = −2.

5.A quadratic curve has a root at x = −2 and its turning point has x-coordinate 3. Work out the curve's other root, using the symmetry of the graph.

6.Solve the inequality 9 − 2x ≥ 1.

7.Which expression is equivalent to 3(2x − 5) + 4x?

8.A packet contains s sweets. The sweets are shared equally between f friends. Write an expression for the number of sweets each friend receives.

9.Solve the inequality 6.3x + 1.8 ≤ 40. Hence write down the greatest number with exactly one decimal place that satisfies the inequality.

10.To solve 6x − 4 = 2x + 20, Yusuf's first step is to subtract 2x from both sides. Work out what equation this gives.

11.The equation 3(2x − 1) = 4x + 9 is rearranged by expanding the brackets. Which of these is the correctly expanded equation?

12.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.

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

14.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.

15.Which expression is equivalent to 0.5(4x + 6) − x?