Algebra worksheet — GCSE Foundation

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

2.Which of these is an inequality?

3.A rectangular garden has width w metres and length (w + 3) metres. A gardener writes its perimeter as 2w + 3. Which statement corrects the gardener's mistake?

4.The nth term of a sequence is 4n + 2. A term in the sequence has value 30. Work out its position, n, in the sequence.

5.The line y = 3x + 6 meets the x-axis at one point. Work out the coordinates of that point.

6.A plumber charges a £40 call-out fee plus £25 for each hour worked. The total charge, £C, for a job lasting h hours is given by C = 40 + 25h. Work out the charge for a job lasting 3 hours, and name what kind of statement C = 40 + 25h is.

7.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.

8.Three consecutive integers add up to 72. Using n for the smallest integer, form an equation and solve it to find the smallest of the three integers.

9.Solve x² − 100 = 0.

10.Work out the value of 3a − 2b when a = 5 and b = 4

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

12.A straight line has equation y = 2x − 7. Write down the coordinates of the point where the line crosses the y-axis.

13.Solve 2x − 2 = 2

14.A table shows values of y = x² − x − 6 for x from −3 to 4: at x = −3, y = 6; x = −2, y = 0; x = −1, y = −4; x = 0, y = −6; x = 1, y = −6; x = 2, y = −4; x = 3, y = 0; x = 4, y = 6. Using the table, write down the two roots of x² − x − 6 = 0.

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