Algebra worksheet — GCSE Foundation

1.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.

2.Which of these statements is an equation with exactly one solution?

3.A rectangular field has length (3a + 2) metres and width (a − 1) metres. Write a simplified expression for the perimeter of the field.

4.Work out the value of 3a − 2b when a = 5 and b = 4

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

6.A sequence starts at 2. Each term after that is found using the rule "double the previous term, then add 1". Work out the 4th term of the sequence.

7.A number, n, is tripled and then 4.5 is added. The result is 22.5. Form an equation and solve it to find n.

8.y = x + 4. Work out the value of y when x = 3.

9.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.

10.A rectangular garden has width w metres and length (w + 3) metres. A gardener writes its perimeter as 2w + 3. Which statement corrects the gardener's mistake?

11.A car's fuel tank contains 50 litres when it starts a journey. After travelling for 2 hours, it contains 38 litres, and fuel is used at a constant rate. Work out the rate at which fuel is used, in litres per hour.

12.Work out the value of 4p² − 3 when p = 2.5

13.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.

14.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.

15.Given that (x − 4)(x + 9) = 0, write down the two solutions of x.