Algebra worksheet — GCSE Foundation

1.A gardener charges a fixed fee of £15 plus £8 for each hour worked. The total charge, £T, for a job lasting h hours is given by T = 15 + 8h. Work out the charge for a job lasting 4 hours, and identify what kind of statement T = 15 + 8h is.

2.Solve the simultaneous equations x + y = 1 and 2x + y = 5.

3.The first four terms of a sequence are 18, 15, 12, 9. Work out an expression, in terms of n, for the nth term.

4.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.

5.Write down the y-intercept of the line with equation y = 3x + 8.

6.A sequence has the position-to-term rule: the nth term is 3n. Write down the first four terms of the sequence.

7.The first term of an arithmetic sequence is 5, and each term after that increases by 6. Work out the 8th term of the sequence.

8.A quadratic curve has a minimum turning point at (3, −4). Which of these statements about the curve must be true?

9.The diagram shows the graph of a straight line, drawn on a grid numbered from −5 to 5 on both axes. Which equation could represent the line?

10.A tree is 2 metres tall. Each year its height increases by 10% of its height at the start of that year. Work out the height of the tree after 3 years, giving your answer to 1 decimal place.

11.A car's speed-time graph shows the following: its speed increases steadily from 0 m/s to 20 m/s over the first 10 seconds, then stays constant at 20 m/s for the next 15 seconds. Work out the total distance travelled in the first 25 seconds.

12.Simplify 5x + 3y − 2x + y.

13.A number, w, satisfies the statement "three times w, minus 5, is at least 16". Which of these is the correct inequality for w?

14.Make x the subject of the formula y = 4x − 3.

15.A ferry's distance-time graph is a straight line from (0 minutes, 0 km) to (25 minutes, 15 km). Work out the ferry's speed in kilometres per hour.