Printable · GCSE Foundation · ages 14-16

Algebra worksheet — GCSE Foundation

Fifteen questions across the algebra statements at Foundation tier. Choose the non-calculator filter to rehearse Paper 1, which counts for a third of the marks.

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Algebra worksheet — GCSE Foundation

Maths · GCSE Foundation · Algebra · Non-calculator · 15 questions

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1.A student says that (x + 4)² is equivalent to x² + 16. For which value of x do the two expressions give the SAME result, making it look (misleadingly) like the student could be right?
(a)x = 4
(b)x = −4
(c)x = 0
(d)x = 8
2.A mobile phone plan charges a fixed monthly fee plus an amount for each gigabyte of data used. The total cost £C for using g gigabytes in a month is given by C = 15 + 2g. What does the number 2 represent in this formula?
(a)The cost, in pounds, for each extra 2 gigabytes of data used
(b)The fixed monthly fee, in pounds
(c)The cost, in pounds, for each extra gigabyte of data used
(d)The total number of gigabytes included in the plan
3.To solve 6x − 4 = 2x + 20, Yusuf's first step is to subtract 2x from both sides. Work out what equation this gives.
(a)4x = 20
(b)4x − 4 = 20
(c)4x − 4 = 2x + 20
(d)8x − 4 = 20
4.Write down the expression that means the same as (x + 7) ÷ 4.
(a)4(x + 7)
(b)4/(x + 7)
(c)(x + 7)/4
(d)(x + 7) − 4
5.To solve 5x − 4 = 2x + 8, Chloe's working is shown. Line 1: 5x − 4 = 2x + 8. Line 2: 3x − 4 = 8. Line 3: 3x = 4. Line 4: x = 4/3. Chloe has made a mistake in her working. Which line contains the mistake?
(a)Line 1
(b)Line 2
(c)Line 4
(d)Line 3
6.Make a the subject of the formula b = 20 − a.
(a)a = 20 − b
(b)a = b − 20
(c)a = 20 + b
(d)a = −20 − b
7.y = 5x − 1. Work out the value of y when x = 3.
y = 5x − 1
(a)14
(b)16
(c)15
(d)10
8.Here are the first five terms of an arithmetic sequence: 4, 7, 10, 13, 16. Work out the 9th term.
(a)25
(b)28
(c)27
(d)31
9.Which of these is an equation, rather than an expression, a formula or an identity?
(a)3x + 5
(b)A = πr²
(c)3x + 5 = 17
(d)3(x + 5) ≡ 3x + 15
10.A sequence has the position-to-term rule: the term is the square of the position number. Its first four terms are 1, 4, 9, 16. Work out the 10th term.
(a)20
(b)81
(c)100
(d)1000
11.A gardener charges a fixed fee of £15 plus £8 for each hour worked. The total charge, £T, for a job lasting h hours is given by T = 15 + 8h. Work out the charge for a job lasting 4 hours, and identify what kind of statement T = 15 + 8h is.
(a)£47, and T=15+8h is an equation (solved for h).
(b)£47, and T=15+8h is a formula (relates T and h).
(c)£27, and T=15+8h is a formula (relates T and h).
(d)£32, and T=15+8h is a formula (relates T and h).
12.Which of these rules generates the sequence 6, 11, 16, 21, …?
(a)6n
(b)5n − 1
(c)5n + 1
(d)n + 5
13.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.
(a)2
(b)−18
(c)−6
(d)−2
14.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.
(a)2.5
(b)0
(c)20
(d)5
15.A phone company works out a monthly bill, £B, using the formula B = 18 + 0.05t, where £18 is the fixed monthly charge and t is the number of extra text messages sent beyond the free allowance, each charged at 5p. Farida's bill for one month is £24.50. Work out the number of extra text messages, t, she sent.
(a)130
(b)13
(c)65
(d)490

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