Algebra worksheet — GCSE Foundation

1.Solve 2x + 1 = 9

2.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.

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

4.Which expression is equivalent to 6x − (2x − 5)?

5.A cinema sells adult tickets and child tickets. On one evening, 40 tickets are sold in total. There are 8 more adult tickets sold than child tickets. Work out the number of child tickets sold.

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

7.A plant is 4 cm tall in week 1. Each week after that, its height increases by 5 cm. Work out the first week in which the plant is taller than 30 cm.

8.A sequence has the position-to-term rule: the nth term is 3n. Write down the first four terms of the sequence.

9.Ben writes n + 4 ≤ 9. Which statement describes what Ben has written? Give a reason for your answer.

10.A caterer uses the formula C = 6p + 20 to work out the total cost, £C, of a buffet for p people, where £20 covers fixed costs. A customer is charged £92. Work out how many people, p, the buffet was for.

11.Write down the first four terms of the sequence with nth term 6n − 5.

12.The expression 6n + 15 is written as 3(2n + 5). Which statement is correct?

13.Work out the gradient of the straight line with equation 3y = 12 − 6x.

14.The first four terms of a sequence are 4, 6, 8, 10. Work out an expression, in terms of n, for the nth term.

15.Rosie is asked whether 4(x + 3) = 4x + 12 is an equation or an identity. Which statement is correct? Give a reason for your answer.