Algebra worksheet — GCSE Foundation

1.A taxi fare, in pounds, for a journey of m miles is given by the formula F = 3 + 2.5m. A journey costs £15.50. Work out the distance travelled, m, by first rearranging the formula to make m the subject, then substituting F = 15.50.

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

3.Matchsticks are laid out as a row of squares, with each new square sharing a side with the square before it. The first square uses 4 matchsticks and every extra square uses 3 more. Work out how many matchsticks a row of 4 squares uses.

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

5.Make c the subject of the formula k = 6c.

6.A speed-time graph for a car shows the speed increasing steadily from 5 m/s to 17 m/s over 6 seconds. Work out the acceleration of the car, in m/s².

7.Solve the inequality 3x − 1 ≤ 11.

8.The first term of an arithmetic sequence is 5, and each term after that increases by 6. Work out the 8th term of the sequence.

9.Solve 6x + 4 = 28

10.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.

11.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.

12.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.

13.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.

14.Solve the inequality 2(x − 1) ≤ 8.

15.Factorise fully 5x + 5y − 5