Algebra worksheet — GCSE Foundation

1.The first five cube numbers are 1, 8, 27, 64, 125. Write down the next cube number in the sequence.

2.The simple interest, £I, earned on a savings account is given by the formula I = PRT/100, where P is the amount invested in pounds, R is the interest rate per year and T is the time in years. Rearrange the formula to make P the subject.

3.Write down the gradient of the line with equation y = −x + 3.

4.A number machine multiplies its input by 5. Work out the output when the input is −1.

5.Solve x² = 49.

6.Write down the expression that means the same as 'subtract 5 from n, then divide the result by 2'.

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

8.Here are the first four terms of an arithmetic sequence: 5, 9, 13, 17. Work out the 5th term.

9.A Fibonacci-type sequence begins 3, 5, 8, 13, ... where each term after the second is the sum of the two terms before it. Work out the 7th term of the sequence.

10.To rearrange y = 2x − 5 to make x the subject, Sam writes: 'Add 5 to both sides to get y + 5 = 2x, then divide both sides by 2 to get x = (y + 5)/2.' Which statement about Sam's method is correct?

11.The formula for the perimeter of a rectangle is P = 2(l + w). One rectangle has l = 9 cm and w = 4 cm. A second rectangle has l = 6 cm and w = 5 cm. Work out how many cm greater the perimeter of the first rectangle is than the perimeter of the second.

12.Which of these is a formula?

13.Solve x² − 5x + 6 = 0 by factorising.

14.A rule turns each input x into an output y. The inputs are x = −1, 0, 1, 2 and the matching outputs are y = 5, 3, 1, −1. Work out the rule.

15.A rectangular field has length (3a + 2) metres and width (a − 1) metres. Write a simplified expression for the perimeter of the field.