Algebra worksheet — GCSE Foundation

1.The formula for converting a distance in miles, m, to kilometres, k, is k = 8m ÷ 5. Work out k when m = 10.

2.The graph of y = 24/x is drawn for x > 0. Work out the value of y when x = 6.

3.A pattern is made from tiles. Pattern 1 uses 4 tiles, pattern 2 uses 7 tiles, pattern 3 uses 10 tiles and pattern 4 uses 13 tiles, with each pattern using 3 more tiles than the one before. Work out an expression, in terms of n, for the number of tiles used in pattern n.

4.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).

5.A number, n, is doubled and then 7 is subtracted. The result is 15. Form an equation and solve it to find n.

6.A tank already contains some water and is then filled at a constant rate. After 2 minutes it contains 50 litres in total; after 7 minutes it contains 150 litres in total. Work out the rate at which water is added, in litres per minute.

7.A geometric sequence starts at 3, and each term after that is found by multiplying the term before it by 2. Write down the first four terms.

8.Two numbers have a sum of 24. Their difference is 6. Work out the two numbers.

9.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.

10.Oliver has m stickers and gives 5 of them away. The number he has left is L = m − 5. Work out L when m = 8.

11.Isla says that the lines y = 2x + 1 and y = −2x + 3 are parallel. Write down the statement that gives the correct answer for the correct reason.

12.Factorise x² − 64.

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

14.Which of these is a formula?

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