Algebra worksheet — GCSE Foundation

1.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?

2.Which of these numbers is a cube number?

3.Solve the inequality 2(x − 1) ≤ 8.

4.A sequence begins at 7. Each term after the first is found by adding 6 to the term before it. Work out the 6th term of the sequence.

5.In a sequence, each term is half the term before it. The sequence begins 100, 50, 25. Write down the next term.

6.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.

7.Oliver buys b pens. Each pen costs £2. Write down an expression for the total cost, in pounds.

8.The graph of y = x² − 2x − 8 crosses the x-axis at x = −2 and x = 4. Work out the x-coordinate of the turning point of the curve, using the symmetry of the graph.

9.The equation 3(2x − 1) = 4x + 9 is rearranged by expanding the brackets. Which of these is the correctly expanded equation?

10.A formula is F = 4s. A pupil says that when s = 5 the value of F is 9, because they added 4 and 5 instead of multiplying. Work out the correct value of F when s = 5.

11.The nth term of a sequence is 3n + 2. Work out the 4th term of the sequence.

12.A charity's fundraising total, T pounds, over d days follows T = (d − 3)(30 − d) for 3 ≤ d ≤ 30, where T = 0 marks the start and end of the campaign. Work out how many days the campaign runs for, from start to end.

13.Tom buys 2 notebooks and 6 pencils on Monday, priced at p pence each for a notebook and q pence each for a pencil. On Tuesday he buys 3 more notebooks and 1 more pencil. Write a simplified expression, in pence, for the total amount Tom has spent on notebooks and pencils.

14.A square tile has an area of 144 cm². Work out the side length of the tile.

15.Solve 2x² − 32 = 0.