Algebra worksheet — GCSE Foundation

1.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.

2.A recipe gives the cooking time, in minutes, for a chicken as T = 40m + 20, where m is the mass in kg. A chicken has a mass of 1.8 kg. Work out the cooking time in hours and minutes.

3.Make a the subject of the formula b = 20 − a.

4.A rectangular sheep pen has perimeter P, length l and width w, connected by the formula P = 2l + 2w. A farmer has 60 m of fencing for the perimeter and sets the width at 8 m. Work out the length of the pen.

5.Write down the expression that means the same as m × m × m × n.

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

7.Write down the coordinates of the point that is 4 units to the left of the origin and 7 units up.

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

9.Which expression means 'y squared, multiplied by 3'?

10.Work out the coordinates of the reflection of (6, −3) in the y-axis.

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

12.The graph of P = 480 ÷ V shows how the pressure, P pascals, of a gas depends on its volume, V cm³, at constant temperature. Use the relationship to work out the volume when the pressure is 32 pascals, and then work out by how much the volume increases when the pressure drops to 24 pascals.

13.Solve the inequality 2(3x − 1) ≥ 4x + 8.

14.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.

15.A company's profit was £2000 in its first year. Each following year, the profit increases by £800. Work out the first year in which the profit is more than £7000.