Algebra worksheet — GCSE Foundation

1.A printer starts a job with 480 sheets of paper loaded and prints at a steady rate. The number of sheets left, S, after t minutes is given by S = 480 − 24t. Work out how many minutes it takes for the paper to run out completely.

2.The formula for converting a temperature from degrees Celsius, C, to degrees Fahrenheit, F, is F = 1.8C + 32. Work out F when C = 20, and identify what kind of mathematical statement F = 1.8C + 32 is.

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

4.The solution to an inequality is n ≤ 5. Write down the largest integer value of n that satisfies this inequality.

5.The first four terms of a sequence are 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.

6.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.

7.Solve the simultaneous equations x + y = 1 and 2x + y = 5.

8.Simplify k + k + k + k + k.

9.A sequence has the position-to-term rule: the nth term is 3n. Write down the first four terms of the sequence.

10.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.

11.A ball is thrown in the air. Its height, h metres, above the ground after t seconds is given in this table: when t = 0, h = 0; when t = 1, h = 15; when t = 2, h = 20; when t = 3, h = 15; when t = 4, h = 0. Use the table to find the two times, in seconds, at which the ball is at ground level.

12.A rectangle is x cm wide and twice as long as it is wide, so its area A cm² is given by A = 2x². Work out A when x = 3.

13.Harry is 14 years old and Mia is 8 years old. Will Harry ever be exactly twice as old as Mia? Give a reason for your answer.

14.Which expression is equivalent to 3(2x − 5) + 4x?

15.Work out the gradient of the straight line with equation 2x + y = 8.