Algebra worksheet — GCSE Foundation

1.Solve the inequality 3x − 1 ≤ 11.

2.The graph of t = 240 ÷ s shows how the time, t hours, taken for a car journey of 240 miles depends on its average speed, s mph. Use the relationship to work out the time taken when the average speed is 48 mph.

3.A point lies on the y-axis. What can be said about the x-coordinate of that point?

4.Work out the equation of the straight line through the points (−2, 1) and (0, 7).

5.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.

6.A cinema sells adult tickets for £10 and child tickets for £6. A family group buys 9 tickets in total, spending £74. Work out how many adult tickets were bought.

7.Which expression means 'triple c, then add double d'?

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

9.For the graph of y = 1/x, where x cannot be zero, which of these statements is correct?

10.The expression 6n + 15 is written as 3(2n + 5). Which statement is correct?

11.Which of these values of x is a solution of x² + 2x − 15 = 0?

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

13.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?

14.The first four terms of a sequence are 11, 18, 25, 32. Ravi thinks the nth term is 7n. Work out the correct expression for the nth term.

15.A plumber charges a £35 call-out fee plus £20 for each hour worked, h. On a certain job the total charge was £115. Work out how many hours the plumber worked.