Algebra worksheet — GCSE Foundation

1.Which expression is equivalent to 4(x − 2) + 10?

2.The area of a triangle is given by the formula A = bh/2, where b is the base and h is the height. Make h the subject of the formula.

3.A ball's height, h metres, t seconds after being thrown follows h = (t − 1)(9 − t). Given that the ball is at ground level at t = 1 and t = 9, work out at what time t the ball reaches its maximum height, using symmetry.

4.The point C is 6 units to the right of the origin and 0 units up. Write down the coordinates of C.

5.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.

6.Expand 7(a + 8)

7.The graph of t = 240 ÷ s shows how the time, t hours, taken for a car journey of 240 miles depends on its average speed, s mph. Use the relationship to work out the time taken when the average speed is 48 mph.

8.Simplify (5x² + 3x − 2) − (2x² − x + 5)

9.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?

10.A rectangle is x cm wide and twice as long as it is wide, so its area A cm² is given by A = 2x². Work out A when x = 3.

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

12.Which expression is equivalent to 6x − (2x − 5)?

13.Solve the inequality 4x + 1 > 2x + 9.

14.A quadratic graph has equation y = (x − 4)². A student says this graph crosses the x-axis at two different points. Explain why the student is wrong.

15.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.