Algebra worksheet — GCSE Foundation

1.Which expression is equivalent to 5x − (x + 3)?

2.The formula connecting speed, distance and time is v = s ÷ t. Work out v, in km/h, when s = 180 and t = 4.

3.The perimeter, P, of a rectangle with length l and width w is calculated using P = 2l + 2w. What kind of mathematical statement is P = 2l + 2w?

4.A car park charges a £4 fixed fee plus £3 for each hour. Kofi has exactly £25 to spend on parking. Using the inequality 4 + 3h ≤ 25, work out the greatest number of whole hours, h, he can park for.

5.Solve 6x − 5 = 3x + 13.

6.Solve 5x − 9 = 16

7.Write down the expression that means the same as w ÷ 6.

8.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.

9.A straight line has equation y = 4 − 3x. Work out the gradient of the line.

10.A sequence has the position-to-term rule 5n − 2, where n is the position number. Which of these is a term in the sequence?

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

12.The graph of y = x² − 7x + 2 crosses the x-axis at two points. One root, read from the graph, is approximately x = 0.30. Using the fact that the sum of the two roots of x² − 7x + 2 = 0 is 7, estimate the other root, correct to 2 decimal places.

13.Write down the gradient of the line with equation y = −x + 3.

14.A fundraising chain letter starts with 3 people taking part in round 1. Each following round has 4 times as many people taking part as the round before. Work out the number of people taking part in round 4.

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