Algebra worksheet — GCSE Foundation

1.Expand 4(2x − 3).

2.Work out the coordinates of the reflection of (6, −3) in the y-axis.

3.A taxi firm charges a fixed fee of £3.50 plus £2.20 per mile. Work out the total cost of a journey of 6 miles.

4.The first five terms of a quadratic sequence are 2, 5, 10, 17, 26. Work out the next term in the sequence.

5.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.

6.Solve 3x − 1 = 8

7.A point has coordinates (−6, 9). Work out the sum of the x-coordinate and the y-coordinate.

8.A sequence has the position-to-term rule n² + 1, where n is the position number. Work out how much bigger the 5th term is than the 4th term.

9.A student says that 5(x + 2) is equivalent to 5x + 2. Which statement explains why the student is wrong?

10.Solve the simultaneous equations 2x + y = 7 and x − y = 2.

11.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.

12.Work out the value of (x − 4)/2 + 3 when x = 10

13.Noah says that y = 3 is the solution of the equation y + 10 = 12. Noah is wrong. Work out the correct value of y.

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

15.A tank already contains some water and is then filled at a constant rate. After 2 minutes it contains 50 litres in total; after 7 minutes it contains 150 litres in total. Work out the rate at which water is added, in litres per minute.