Algebra worksheet — GCSE Foundation

1.A runner's journey is shown on a distance-time graph: she runs 8 km in the first hour, rests for 30 minutes with no distance gained, then runs a further 4 km in the next 30 minutes. Work out her average speed for the whole journey, in kilometres per hour.

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

3.The simple interest, £I, earned on a savings account is given by the formula I = PRT/100, where P is the amount invested in pounds, R is the interest rate per year and T is the time in years. Rearrange the formula to make P the subject.

4.Expand 4(2x − 3).

5.A rectangular garden has width w metres and length (w + 3) metres. A gardener writes its perimeter as 2w + 3. Which statement corrects the gardener's mistake?

6.The graph of y = x² − 2x − 8 takes these values: when x = −2, y = 0; when x = −1, y = −5; when x = 0, y = −8; when x = 3, y = −5; when x = 4, y = 0. Use these values to write down the two solutions of x² − 2x − 8 = 0.

7.Jack is x years old. His brother Kwame is 3 years older than Jack. Write down an expression for Kwame's age.

8.The formula for the perimeter of a square is P = 4s, where s is the side length. Make s the subject of the formula.

9.A theatre's front row has 18 seats. Each row behind has 4 more seats than the row in front. Which row has exactly 62 seats?

10.A recipe gives the cooking time, in minutes, for a chicken as T = 40m + 20, where m is the mass in kg. A chicken has a mass of 1.8 kg. Work out the cooking time in hours and minutes.

11.Simplify p + p + p.

12.Solve 6x + 4 = 28

13.A company's profit was £2000 in its first year. Each following year, the profit increases by £800. Work out the first year in which the profit is more than £7000.

14.Given that (x + 2)(x − 7) = 0, write down the two solutions of x.

15.Solve x/4 + 1 = 3