Algebra worksheet — GCSE Foundation

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

2.Expand and simplify (x − 3)²

3.Write down the expression that means the same as (x + 7) ÷ 4.

4.The line y = 3x + 6 meets the x-axis at one point. Work out the coordinates of that point.

5.The point P has coordinates (0, 12). Write down the axis that P lies on and the y-coordinate of P.

6.A student solves the simultaneous equations 2x + y = 11 and x − y = 1 by elimination, adding the two equations together. Which of these is the correct result of that step?

7.Factorise fully 5x + 5y − 5

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

9.A company's profit is £500 in its first year. Each year after that, the profit is £300 more than the year before. Work out the profit in the company's 6th year.

10.A school trip costs a £15 deposit plus £9 per student for the coach. The total cost for a class is £186. Work out how many students went on the trip.

11.A plumber charges a call-out fee of £30 plus £25 for each hour worked. The total bill for a job was £130. Work out how many hours the plumber worked.

12.A water butt holds 200 litres and is being drained at a steady 8 litres per minute. Write down the function for the amount of water y, in litres, left after x minutes.

13.Simplify k + k + k + k + k.

14.A walker's distance-time graph is described as follows: she walks 3 km in the first 15 minutes at a steady speed, rests for 10 minutes, then walks a further 3 km in the next 20 minutes, also at a steady speed. Work out her speed, in km/h, during the first 15 minutes.

15.A number, n, is doubled and then 7 is subtracted. The result is 15. Form an equation and solve it to find n.