Algebra worksheet — GCSE Foundation

1.There are 50 adults on a coach to the Lake District. Every adult is either a man or a woman. There are 10 more men than women. Work out the number of men.

2.Which of these equations gives a straight-line graph when plotted?

3.The cost, in pounds, of hiring a van for d days is given by the formula C = 25 + 18d. A customer's hire cost £133. Work out how many days, d, they hired the van for, by first rearranging the formula to make d the subject.

4.A ball's height, h metres, t seconds after being thrown follows h = (t − 1)(9 − t). Given that the ball is at ground level at t = 1 and t = 9, work out at what time t the ball reaches its maximum height, using symmetry.

5.Priya buys b balloons for a party. Each balloon costs 15p. Write down an expression for the total cost, in pence.

6.A printer starts a job with 480 sheets of paper loaded and prints at a steady rate. The number of sheets left, S, after t minutes is given by S = 480 − 24t. Work out how many minutes it takes for the paper to run out completely.

7.Factorise fully 56x − 24

8.Expand and simplify 2(a + 6) − 2(a − 7)

9.A ribbon of length L metres is cut into 5 equal pieces, and then 3 metres is removed from one piece. Write down an expression, in metres, for the length of that piece after 3 metres is removed.

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

11.Simplify 2b − 1 + 2b − 4 + 2b

12.A pattern is made from tiles. Pattern 1 has 7 tiles, pattern 2 has 11 tiles, pattern 3 has 15 tiles, and pattern 4 has 19 tiles, with each new pattern having 4 more tiles than the one before it. Work out an expression, in terms of n, for the number of tiles in pattern n.

13.Solve the inequality 2(x − 1) ≤ 8.

14.Work out the value of 2x² when x = −3

15.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.