Algebra worksheet — GCSE Foundation

1.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.

2.A currency conversion graph shows that £4 is equivalent to 5 US dollars. Use this to work out how many US dollars are equivalent to £24.

3.Solve 6x + 4 = 28

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

5.A school trip costs a £15 deposit plus £9 per student for the coach. The total cost for a class is £186. Work out how many students went on the trip.

6.Which of these equations is true for every value of x, making it an identity rather than an equation with just one solution?

7.A straight line passes through the points (0, 4) and (1, 9). Write down the gradient of the line.

8.The nth term of a sequence is n² + 3. Work out the first term of the sequence that is greater than 50.

9.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.

10.A ball is dropped and bounces. The height of each bounce after the first is 8 cm less than the bounce before it. The first bounce reaches 60 cm. Work out the height of the 5th bounce.

11.Which expression is equivalent to 3(x + 4) − 2(x − 1)?

12.Write down the coefficient of p in the expression 7 − 4p + 9q.

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

14.A taxi fare in pounds is given by F = 2.50 + 1.20m, where m is the number of miles travelled. Sam takes a taxi for a journey of 6 miles. Work out the fare.

15.A candle is 30 cm tall when lit and burns at a constant rate. After burning for 5 minutes, its height is 20 cm. The height h cm after t minutes is given by h = 30 − mt. Work out the value of m.