Algebra worksheet — GCSE Foundation

1.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.

2.Solve 5(x + 3) = 40

3.Kai writes the expression 8 − 3x + 5x² and says it has three terms. Ryan says it only has two terms because a number on its own is not a term. Work out the correct number of terms in the expression.

4.A straight line passes through the points (0, 4) and (1, 9). Write down the gradient of the line.

5.Oliver has m stickers and gives 5 of them away. The number he has left is L = m − 5. Work out L when m = 8.

6.Look at the statement 2x + 5 = 17. Considering whether it is an expression, an equation, a formula, or an identity, which classification is correct?

7.Solve x² − x − 12 = 0.

8.Work out the value of 3b − 4 when b = 6

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

10.A water tank empties according to y = −5x + 200, where y is the number of litres left after x minutes. Work out the coordinates of the point where this graph crosses the x-axis.

11.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.

12.Two numbers have a sum of 50. The larger number is twice the smaller number. Work out the smaller number.

13.Write down the coefficient of p in the expression 7 − 4p + 9q.

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

15.A line segment has one endpoint at (−6, 2) and its midpoint at (−1, 5). Work out the coordinates of the other endpoint.