Algebra worksheet — GCSE Foundation

1.n = 3. Work out the value of (2n)².

2.Work out the value of a² − 2b when a = −3 and b = 4.

3.Solve 3x − 1 = 8

4.A charity's fundraising total, T pounds, over d days follows T = (d − 3)(30 − d) for 3 ≤ d ≤ 30, where T = 0 marks the start and end of the campaign. Work out how many days the campaign runs for, from start to end.

5.An arithmetic sequence has first term 40 and common difference −6. Work out the 9th term of the sequence.

6.Expand and simplify 4(2x − 1) − 3(x + 2) − 5x

7.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.

8.A taxi fare in pounds is given by F = 2.50 + 1.20m, where m is the number of miles travelled. Sam takes a taxi for a journey of 6 miles. Work out the fare.

9.Expand 4(2x − 3).

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

11.Kai writes the expression 8 − 3x + 5x² and says it has three terms. Ryan says it only has two terms because a number on its own is not a term. Work out the correct number of terms in the expression.

12.Which of these equations is equivalent to 5x − 2 = 3x + 8?

13.A recipe gives the cooking time, in minutes, for a chicken as T = 40m + 20, where m is the mass in kg. A chicken has a mass of 1.8 kg. Work out the cooking time in hours and minutes.

14.Solve the simultaneous equations 4x + 3y = 25 and 4x − y = 1. Work out the value of y.

15.A geometric sequence starts at 4, and each term after that is found by multiplying the term before it by 3. Write down the first four terms of the sequence.