Algebra worksheet — GCSE Foundation

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

2.Write down the expression that means the same as m² × m × 3.

3.The graph of y = x² − 2x − 8 crosses the x-axis at x = −2 and x = 4. Work out the x-coordinate of the turning point of the curve, using the symmetry of the graph.

4.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.

5.Work out the value of 5a + 2 when a = 3

6.For the graph of y = 1/x, where x cannot be zero, which of these statements is correct?

7.The diagram shows the graph of the cost, in pounds, of a taxi journey plotted against the distance travelled, in miles, for journeys of up to 4 miles. The same fixed charge and the same cost per mile apply to longer journeys. Work out the cost of a 6-mile journey.

8.Solve the inequality 6x ≥ 18.

9.Write down the gradient of the line with equation y = 6 + 4x.

10.A car passes the 15 km marker on a road and passes the 195 km marker 3 hours later. Work out the gradient of the distance-time graph, that is the rate of change of distance with time.

11.Solve the inequality 9 − 2x ≥ 1.

12.The diagram shows the graph of a quadratic function. Write down the values of x where the graph crosses the x-axis.

13.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.

14.The simple interest, £I, earned on a savings account is given by the formula I = PRT/100, where P is the amount invested in pounds, R is the interest rate per year and T is the time in years. Rearrange the formula to make P the subject.

15.Write down the expression that means the same as 3 × y × y.