Algebra worksheet — GCSE Foundation

1.Simplify (5x² + 3x − 2) − (2x² − x + 5)

2.A conversion graph shows that 5 miles is equivalent to 8 kilometres. Use this to work out how many kilometres are equivalent to 20 miles.

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.A rectangle has area 24x + 18. Ffion factorises the area as 6(4x + 3). Work out the value of the area when x = 2, and decide whether 6 and (4x + 3) are correctly identified as factors of 24x + 18.

5.A sequence has nth term 3n + 4. Two terms are missing from the list of its first five terms: 7, 10, _, 16, _. Work out the missing 3rd and 5th terms added together.

6.Which expression is equivalent to 5x − (x + 3)?

7.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.

8.Solve the inequality 6x ≥ 18.

9.Work out the value of 3a − 2b when a = 5 and b = 4

10.Leo is three times as old as his brother. His brother is x years old. Write down an expression for Leo's age.

12.a = 2 and b = 5. Work out the value of ab².

13.Expand 2(x + 12)

14.A car's speed-time graph shows the following: its speed increases steadily from 0 m/s to 20 m/s over the first 10 seconds, then stays constant at 20 m/s for the next 15 seconds. Work out the total distance travelled in the first 25 seconds.

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