Algebra worksheet — GCSE Foundation

1.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.

2.The expression 6n + 15 is written as 3(2n + 5). Which statement is correct?

3.x = 5. Work out the value of 3x² − 4.

4.Solve x² − 6x = 0.

5.The first four terms of a sequence are 18, 15, 12, 9. Work out an expression, in terms of n, for the nth term.

6.Solve the inequality x + 5 < 12.

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

8.A rectangular photo has length (x + 3) cm and width x cm. Its area is 40 cm². Work out the value of x.

9.Work out the gradient of the straight line with equation y = (2x/5) − 3.

10.The formula for converting a temperature in Fahrenheit, F, to Celsius, C, is C = 5(F − 32) ÷ 9. Work out C, to 1 decimal place, when F = 98.6.

11.A square has vertices at (−2, 3), (−2, −3) and (4, −3). Write down the coordinates of the fourth vertex.

12.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?

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

14.A phone plan costs a fixed £15 per month plus 8p per minute of calls. In one month, Jamal's bill was £23.80. Form an equation using m for the number of minutes, and solve it to find how many minutes Jamal used that month.

15.Solve the inequality 3x + 6 ≤ 0.