Algebra worksheet — GCSE Foundation

1.Grace has t books. Noah has 1 book fewer than Grace. Write down an expression for the number of books Noah has.

2.A straight line has gradient 3 and passes through the point (1, 4). Work out the equation of the line.

3.Solve the inequality 2(x − 1) ≤ 8.

4.A ribbon of length L metres is cut into 5 equal pieces, and then 3 metres is removed from one piece. Write down an expression, in metres, for the length of that piece after 3 metres is removed.

5.Work out the coordinates of the point halfway between (−9, −2) and (−1, −2).

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

7.A rectangular garden has length (x + 7) m and width (x − 7) m. Work out an expression for the area of the garden, giving your answer in its simplest form.

8.Expand and simplify 4(2x − 1) − 3(x + 2) − 5x

9.A walker's distance-time graph is described as follows: she walks 3 km in the first 15 minutes at a steady speed, rests for 10 minutes, then walks a further 3 km in the next 20 minutes, also at a steady speed. Work out her speed, in km/h, during the first 15 minutes.

10.The first four terms of a sequence are 11, 18, 25, 32. Ravi thinks the nth term is 7n. Work out the correct expression for the nth term.

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

12.The diagram shows the graph of a quadratic function. Write down the values of x where the graph crosses the x-axis.

13.The first five terms of a quadratic sequence are 2, 5, 10, 17, 26. Work out the next term in the sequence.

14.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.

15.Given that (x − 4)(x + 9) = 0, write down the two solutions of x.