Algebra worksheet — GCSE Foundation

1.Write down the expression that means the same as w ÷ 6.

2.Solve the inequality 9 − 2x ≥ 1.

3.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.

4.Solve x² − 6x = 0.

5.A mobile phone tariff charges a fixed £15 plus 20p for every minute of calls made, so the total monthly charge, £C, for m minutes of calls is given by C = 15 + 0.2m. In a month where Ali's charge was £46.60, work out how many minutes of calls he made.

6.Which of these equations is equivalent to 5x − 2 = 3x + 8?

7.A packet contains s sweets. The sweets are shared equally between f friends. Write an expression for the number of sweets each friend receives.

8.A hall is set out in rows of chairs for an assembly. Row 1 has 50 chairs, row 2 has 45 chairs, row 3 has 40 chairs, and row 4 has 35 chairs, with each row after the first having 5 fewer chairs than the one before. Work out an expression, in terms of n, for the number of chairs in row n.

9.Simplify 2b − 1 + 2b − 4 + 2b

10.Solve 2x² − 32 = 0.

11.Grace says that 2(x + 1) and 2x + 2 always have the same value. Work out the value of both expressions when x = 3.

12.A sequence has the position-to-term rule 5n − 2, where n is the position number. Which of these is a term in the sequence?

13.Two expressions are 6(x − 1) and 6x − 6. A student says these are equivalent for every value of x. Is the student correct?

14.The graph of t = 240 ÷ s shows how the time, t hours, taken for a car journey of 240 miles depends on its average speed, s mph. Use the relationship to work out the time taken when the average speed is 48 mph.

15.Point R has coordinates (3, −5). Point R is reflected in the line y = 2 to point S. Write down the coordinates of S.