Algebra worksheet — GCSE Foundation

1.Factorise fully 56x − 24

2.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.

3.A sequence starts at 2. Each term after that is found using the rule "double the previous term, then add 1". Work out the 4th term of the sequence.

4.A ribbon of length L metres is cut into 5 equal pieces, and then 3 metres is removed from one piece. Write down an expression, in metres, for the length of that piece after 3 metres is removed.

5.The volume of a cuboid is given by the formula V = lwh. Work out V, in cm³, when l = 2, w = 3 and h = 6.

6.Solve 3(2x − 1) = 27

7.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.

8.A zip-line runs from a platform 25 m high to a landing point 5 m high, over a horizontal distance of 40 m. Work out the gradient of the zip-line.

9.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.

10.Which expression is equivalent to 4(x − 2) + 10?

11.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.

12.Explain why the equation 4x + 3 = 4x + 10 has no solution for x.

13.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.

14.Work out the value of 3a − 2b when a = 5 and b = 4

15.The nth term of a sequence is 2n² + 1. Work out the 4th term of the sequence.