Algebra worksheet — GCSE Foundation

1.A number machine multiplies its input by 2 and then subtracts 5. Work out the output when the input is 6.

2.Line C passes through (0, 0) and (4, 2). Line D passes through (0, 0) and (2, 2). Write down which of the two lines is the steeper.

3.The graph of y = mx + 6 passes through the point (−2, 0). Work out the value of m.

4.A quadratic graph has roots at x = −3 and x = 5, and it crosses the y-axis at (0, −15). Work out the equation of the curve in the form y = (x − a)(x − b).

5.Make m the subject of the formula w = m − 8.

6.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.

7.Make x the subject of the formula y = x/2 − 5.

8.A table of values is being drawn for the graph of y = x³. Work out the value of y when x = −2.

9.A hiker's distance-time graph shows the following: he walks 5 km in the first 1 hour at a steady speed, rests for 1 hour, then walks a further 9 km in the next 2 hours, also at a steady speed. Work out his average speed for the whole journey, in km/h.

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

11.Look at the statement 2x + 5 = 17. Considering whether it is an expression, an equation, a formula, or an identity, which classification is correct?

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

13.Factorise x² − 64.

14.Harry will spend at most £150 on a party. The cake costs £60 and each helium balloon costs £3. Solve an inequality to find all the possible numbers of balloons, x, that he can buy.

15.Write down the first four terms of the sequence with nth term 6n − 5.