Algebra worksheet — GCSE Higher

1.A geometric sequence has first term 3 and common ratio 2. Work out the 5th term of the sequence.

2.Two numbers have a sum of 24. Their difference is 6. Work out the two numbers.

3.The table shows some values of f(x): when x = 0, f(x) = 5; when x = 1, f(x) = 8; when x = 2, f(x) = 4; when x = 3, f(x) = 1. Work out the value of f(x − 1) when x = 2.

4.Which of these equations represents the graph of y = 2ˣ translated by 3 units in the positive y-direction?

5.Solve 2(x + 3) = 10

6.The graph of y = f(x) passes through the point (0, 4). Work out the y-coordinate of the point where the graph of y = −f(x) + 5 crosses the y-axis.

7.Expand and simplify (x − 3)²

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

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

10.A rectangle has area 24x + 18. Ffion factorises the area as 6(4x + 3). Work out the value of the area when x = 2, and decide whether 6 and (4x + 3) are correctly identified as factors of 24x + 18.

11.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.

12.A graph has equation y = −2x² + 5. Which statement about its shape is correct?

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.Two brothers have ages that add up to 30. The elder brother is 6 years older than the younger brother. Work out the age of the younger brother.

15.The graph of y = f(x) has a minimum turning point at (2, −3). The graph of y = −f(x) + a has a maximum turning point at (2, 9). Work out the value of a.