Algebra worksheet — GCSE Foundation

1.The formula connecting speed, distance and time is v = s ÷ t. Work out v, in km/h, when s = 180 and t = 4.

2.A number machine adds 1 to its input. Isla says that an input of 5 gives an output of 6. Which statement is correct?

3.A company's profit is £500 in its first year. Each year after that, the profit is £300 more than the year before. Work out the profit in the company's 6th year.

4.A sequence has the position-to-term rule n² + 1, where n is the position number. Work out how much bigger the 5th term is than the 4th term.

5.Solve x² − 2x − 24 = 0.

6.Solve the inequality x + 5 < 12.

7.A plumber charges a call-out fee plus an hourly rate for a job. The total cost, £C, for a job lasting h hours is given by the formula C = 40 + 25h. What does the number 40 represent in this formula?

8.A table of values is being drawn for the graph of y = x³. Work out the value of y when x = −2.

9.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.

10.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.

11.Sophie's mother is 34 years old. In x years' time she will be 50 years old. Work out the value of x.

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

13.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.

14.Solve the simultaneous equations x + y = 15 and x − y = 3. Work out the value of x.

15.Factorise x² − 3x − 10.