Algebra worksheet — GCSE Foundation

1.p = 4. Work out the value of 2p³.

2.A lift has a weight limit: it must carry no more than 630 kg. Let w be the total weight, in kg, carried by the lift. Which inequality describes this?

3.Simplify x + x + 4

4.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.

5.A Fibonacci-type sequence begins 3, 5, 8, 13, ... where each term after the second is the sum of the two terms before it. Work out the 7th term of the sequence.

6.The nth term of a sequence is 2n² + 1. Work out the 4th term of the sequence.

7.Solve 2x² − 32 = 0.

8.The simultaneous equations 2x + 3y = 12 and x − y = 1 are given. Work out the value of y.

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

10.The graph of y = x² − 2x − 8 takes these values: when x = −2, y = 0; when x = −1, y = −5; when x = 0, y = −8; when x = 3, y = −5; when x = 4, y = 0. Use these values to write down the two solutions of x² − 2x − 8 = 0.

11.Jack is x years old. His brother Kwame is 3 years older than Jack. Write down an expression for Kwame's age.

12.Work out the value of 3n − 2 when n = 1

13.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).

14.y = 5x − 1. Work out the value of y when x = 3.

15.Solve x² = 49.