Algebra worksheet — GCSE Foundation

1.In a shop a shirt costs £x and a pair of trousers costs £(2x + 30). Together the two items cost at least £150. Work out the lowest possible price of the shirt.

2.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.

3.Simplify 2a + 3b − a + 2b − b

4.The diagram shows the graph of a straight line, drawn on a grid numbered from −5 to 5 on both axes. Which equation could represent the line?

5.A photo printing service has two adverts for its price. Advert A: cost in pounds = 3(2n + 4) for n photos. Advert B: cost in pounds = 6n + 12. A customer says the two adverts always charge the same amount. Is the customer correct?

6.A table of values is being drawn for the graph of y = x³. Work out the value of y when x = −2.

7.Solve 3(2x − 1) = 27

8.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.

9.Write down the expression that means the same as p + p + p + q.

10.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.

11.Which of these is an expression?

12.The first four terms of a sequence are 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.

13.In a sequence, each term is half the term before it. The sequence begins 100, 50, 25. Write down the next term.

14.Write down the expression that means the same as m × m × m × n.

15.y = 3x − 2. Work out the value of y when x = 4.