Algebra worksheet — GCSE Foundation

1.Simplify 2b − 1 + 2b − 4 + 2b

2.A regular hexagon has sides of length (x + 2) cm. Write down an expression, in terms of x, for the perimeter of the hexagon.

3.A sequence has the position-to-term rule: the term is the square of the position number. Its first four terms are 1, 4, 9, 16. Work out the 10th term.

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

5.A formula is F = 4s. A pupil says that when s = 5 the value of F is 9, because they added 4 and 5 instead of multiplying. Work out the correct value of F when s = 5.

6.The graph of y = x² − 5x + 6 crosses the x-axis at two points. By factorising, work out the x-coordinates of these two points.

7.A car park charges a £4 fixed fee plus £3 for each hour. Kofi has exactly £25 to spend on parking. Using the inequality 4 + 3h ≤ 25, work out the greatest number of whole hours, h, he can park for.

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

9.A square has sides of length y cm. Write down an expression for the perimeter of the square.

10.Work out the coordinates of the point where the graph of y = 2x − 6 crosses the x-axis.

11.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.

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

13.A speed-time graph for a car shows the speed increasing steadily from 5 m/s to 17 m/s over 6 seconds. Work out the acceleration of the car, in m/s².

14.A number, n, is doubled and then 7 is subtracted. The result is 15. Form an equation and solve it to find n.

15.Which expression means 'add 3 to n, then multiply the result by 4'?