Algebra worksheet — GCSE Foundation

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

2.Write down the expression that means 5 more than half of n.

3.A vertical line passes through the point (4, 7). Write down the equation of this line.

4.Solve the simultaneous equations 3x + 2y = 16 and x + y = 7. Work out the value of y.

5.Solve 5x − 9 = 16

6.Work out the value of m² + 3m when m = −2

7.A gym charges a joining fee plus a monthly fee. Anna paid £100 in total after 3 months of membership. Ben paid £160 in total after 6 months of membership (same joining fee and monthly fee as Anna). Work out the monthly fee.

8.Write down the expression that means the same as m² × m × 3.

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

10.Solve 2x² = 18.

11.Solve 2x − 2 = 2

12.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.

13.Work out the gradient of the straight line with equation 2x + y = 8.

14.A student is asked whether 3(x − 4) = 3x − 4 is an identity. Which statement gives the correct verdict and reason?

15.A charity's fundraising total, T pounds, over d days follows T = (d − 3)(30 − d) for 3 ≤ d ≤ 30, where T = 0 marks the start and end of the campaign. Work out how many days the campaign runs for, from start to end.