Algebra worksheet — GCSE Foundation

1.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.

2.In a shop a shirt costs £x and a pair of trousers costs £(2x + 30). Together the two items cost at least £150. Work out the lowest possible price of the shirt.

3.a = 2 and b = 5. Work out the value of a²b.

4.A gym charges a joining fee plus a monthly fee. Anna paid £100 in total after 3 months of membership. Ben paid £160 in total after 6 months of membership (same joining fee and monthly fee as Anna). Work out the monthly fee.

5.The graph of y = (x − 2)(x + 5) crosses the x-axis at two points. Work out the x-coordinates of these two points.

6.A geometric sequence starts at 4, and each term after that is found by multiplying the term before it by 3. Write down the first four terms of the sequence.

7.The graph of y = mx + 6 passes through the point (−2, 0). Work out the value of m.

8.Expand 2(x − 13)

9.Which expression means the same as a × a × a?

10.A packet contains s sweets. The sweets are shared equally between f friends. Write an expression for the number of sweets each friend receives.

11.The graph of y = x² − 7x + 2 crosses the x-axis at two points. One root, read from the graph, is approximately x = 0.30. Using the fact that the sum of the two roots of x² − 7x + 2 = 0 is 7, estimate the other root, correct to 2 decimal places.

12.Which expression is equivalent to 5x − (x + 3)?

13.Solve x² + 7x = 0.

14.Write down the gradient of the line with equation y = 7x − 2.

15.Write down the expression that means 5 more than half of n.