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 car's speed-time graph shows the following: its speed increases steadily from 0 m/s to 20 m/s over the first 10 seconds, then stays constant at 20 m/s for the next 15 seconds. Work out the total distance travelled in the first 25 seconds.

3.A quadratic graph has roots at x = −3 and x = 5, and it crosses the y-axis at (0, −15). Work out the equation of the curve in the form y = (x − a)(x − b).

4.The point P has coordinates (0, 12). Write down the axis that P lies on and the y-coordinate of P.

5.The first five cube numbers are 1, 8, 27, 64, 125. Write down the next cube number in the sequence.

6.A rule turns each input x into an output y. The inputs are x = −1, 0, 1, 2 and the matching outputs are y = 5, 3, 1, −1. Work out the rule.

7.Which of these statements is an identity?

8.A vertical line passes through the point (4, 7). Write down the equation of this line.

9.A formula is F = 4s. A pupil says that when s = 5 the value of F is 9, because they added 4 and 5 instead of multiplying. Work out the correct value of F when s = 5.

10.Solve the inequality 5 − x ≤ 2.

11.Make x the subject of the formula y = 2x − 9.

12.The formula for the circumference of a circle is C = 2πr, where r is the radius. Make r the subject of the formula.

13.The triangular numbers begin 1, 3, 6, 10, 15, ... Work out the next term in the sequence.

14.Solve the inequality x + 5 < 12.

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