Algebra worksheet — GCSE Foundation

1.A sequence begins at 7. Each term after the first is found by adding 6 to the term before it. Work out the 6th term of the sequence.

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

3.A sequence has the position-to-term rule: the term is the position number multiplied by itself. Its first five terms are 1, 4, 9, 16, 25. Work out the 8th term.

4.Solve x² − 2x − 24 = 0.

5.The simultaneous equations 2x + 3y = 12 and x − y = 1 are given. Work out the value of y.

6.A car's fuel tank contains 50 litres when it starts a journey. After travelling for 2 hours, it contains 38 litres, and fuel is used at a constant rate. Work out the rate at which fuel is used, in litres per hour.

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

8.Solve the simultaneous equations x + y = 15 and x − y = 3. Work out the value of x.

9.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.

10.A square tile has an area of 144 cm². Work out the side length of the tile.

11.Solve the inequality 5x − 3 > 2x + 9.

12.A rectangle has length k cm and width 5 cm less than its length. Write down an expression for the width of the rectangle, in cm.

13.Write down the gradient of the line with equation y = −x + 3.

14.Water is poured into a container at a constant rate. A graph of the depth of the water, in cm, against the time since pouring began, in minutes, is a straight line through the origin, and it passes through the point (3, 12). Use the graph to work out the depth of the water after 7 minutes.

15.Which of these statements is an equation with exactly one solution?