Algebra worksheet — GCSE Foundation

1.The graph of W = 840 ÷ L shows how the width, W metres, of a rectangular field of area 840 m² depends on its length, L metres. Use the relationship to work out the width when the length is 35 m, and hence the perimeter of the field.

2.A sequence begins at 60, and each term after that is found by subtracting 7 from the term before it. Work out the 5th term of the sequence.

3.The formula for the perimeter of a rectangle is P = 2(l + w). One rectangle has l = 9 cm and w = 4 cm. A second rectangle has l = 6 cm and w = 5 cm. Work out how many cm greater the perimeter of the first rectangle is than the perimeter of the second.

4.Work out the gradient of the straight line with equation 2x + y = 8.

5.Work out the value of (x − 4)/2 + 3 when x = 10

6.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.

7.Solve 4x² − 9 = 0.

8.y = 5 − 2x. Work out the value of x when y = 11.

9.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.

10.The first five terms of a quadratic sequence are 2, 5, 10, 17, 26. Work out the next term in the sequence.

11.A stack of firewood has 3 logs in the top layer. Each layer below has 4 more logs than the layer above it. Work out the number of logs in the 6th layer from the top.

12.A theatre's front row has 18 seats. Each row behind has 4 more seats than the row in front. Which row has exactly 62 seats?

13.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.

14.Solve 2(x + 3) = 10

15.Work out the value of 3x² − 4x when x = −2.