Algebra worksheet — GCSE Foundation

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

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

3.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.

4.A plant is 4 cm tall in week 1. Each week after that, its height increases by 5 cm. Work out the first week in which the plant is taller than 30 cm.

5.A rule turns each input x into an output y. The inputs are x = 1, 2, 3, 4 and the matching outputs are y = −5, −3, −1 and one missing value. Work out the missing value of y.

6.A car's speed increases steadily while it accelerates. Its speed v m/s after t seconds is given by v = u + at, where u is the starting speed in m/s and a is the acceleration in m/s². A car starts at u = 4 m/s and accelerates at a = 2 m/s² until it reaches v = 20 m/s. Work out t, the time taken in seconds.

7.Make b the subject of the formula a = 5b.

8.The point D has coordinates (3, −8). Write down the distance of D from the y-axis.

9.A point has coordinates (x, y). In which two quadrants is the product x × y positive?

10.Which of these is an expression?

11.The graph of y = 24/x is drawn for x > 0. Work out the value of y when x = 6.

12.A number machine multiplies its input by 2 and then subtracts 5. Work out the output when the input is 6.

13.A rule turns each input x into an output y. An input of 1 gives an output of 1, an input of 2 gives an output of 4 and an input of 3 gives an output of 9. Work out the rule.

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

15.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.