Algebra worksheet — GCSE Foundation

1.Solve 2x + 1 = 9

2.A hall is set out in rows of chairs for an assembly. Row 1 has 50 chairs, row 2 has 45 chairs, row 3 has 40 chairs, and row 4 has 35 chairs, with each row after the first having 5 fewer chairs than the one before. Work out an expression, in terms of n, for the number of chairs in row n.

3.Work out the value of 3n − 2 when n = 1

4.A ramp rises 3 m over a horizontal distance of 12 m. Work out the gradient of the ramp.

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

7.The formula for the profit, £P, made on an item is P = S − C, where S is the selling price and C is the cost price. Make S the subject of the formula.

8.A car's speed-time graph shows the following: its speed increases steadily from 0 m/s to 20 m/s over the first 10 seconds, then stays constant at 20 m/s for the next 15 seconds. Work out the total distance travelled in the first 25 seconds.

9.The area of a circle is given by the formula A = πr², where r is the radius. Rearrange the formula to make r the subject.

10.The simultaneous equations y = 3 and 4x − y = 9 are given. Work out the value of x.

11.The first four terms of a sequence are 4, 6, 8, 10. Work out an expression, in terms of n, for the nth term.

12.A box holds n pencils. A shop has 6 full boxes and 4 loose pencils. All of these pencils are shared equally between 2 classes. Write down the expression for the number of pencils each class receives.

13.Which of these quadratic graphs does NOT cross the x-axis at all?

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.A company's profit was £2000 in its first year. Each following year, the profit increases by £800. Work out the first year in which the profit is more than £7000.