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.Solve 7x − 5 = 3x + 11

3.y = 5x − 1. Work out the value of y when x = 3.

4.A table shows values of y = x² − x − 6 for x from −3 to 4: at x = −3, y = 6; x = −2, y = 0; x = −1, y = −4; x = 0, y = −6; x = 1, y = −6; x = 2, y = −4; x = 3, y = 0; x = 4, y = 6. Using the table, write down the two roots of x² − x − 6 = 0.

5.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.

6.Work out the value of n² − n when n = −3

7.Make x the subject of the formula y = x/2 − 5.

8.The formula connecting speed, distance and time is v = s ÷ t. Work out v, in km/h, when s = 180 and t = 4.

9.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.

10.A sequence has the position-to-term rule n² + 1, where n is the position number. Work out how much bigger the 5th term is than the 4th term.

11.Which of these is an equation, rather than an expression, a formula or an identity?

12.Solve the inequality 3x + 6 ≤ 0.

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

14.Write down the number of terms in the expression 4x² − 7x + 3.

15.The formula for the profit, £P, made on an item is P = S − C, where S is the selling price and C is the cost price. Make S the subject of the formula.