Algebra worksheet — GCSE Foundation

1.Work out the value of 3b − 4 when b = 6

2.Simplify 2b − 1 + 2b − 4 + 2b

3.Solve 5x − 9 = 16

4.Solve (2x + 1)/3 = 5

5.The braking distance of a car, in metres, is estimated using the formula d = 0.4v² + 6, where v is the speed in mph. A car travelling at 35 mph brakes. Work out the estimated braking distance.

6.A taxi charges a £3 fixed fee plus £2 for each mile travelled. Write an expression, in pounds, for the total cost of a journey of n miles.

7.Which expression means 'y squared, multiplied by 3'?

8.Work out the coordinates of the point where the graph of y = 2x − 6 crosses the x-axis.

9.A delivery van's distance-time graph shows the following: it travels 9 km in the first 15 minutes at a steady speed, stops for 45 minutes to unload, then travels a further 21 km in the next 30 minutes, also at a steady speed. Work out the average speed, in km/h, for the whole journey.

10.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.

11.Work out the value of 3x² − 4x when x = −2.

12.Solve 6x + 4 = 28

13.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?

14.A student says that (x + 4)² is equivalent to x² + 16. For which value of x do the two expressions give the SAME result, making it look (misleadingly) like the student could be right?

15.A parcel delivery company's cost graph shows the following: the cost is a flat £5 for parcels weighing up to 2 kg, and then rises by £2 for each additional kg above 2 kg. Use the graph to work out the weight of a parcel that costs £17.