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.

VersionsA only A + B A + B + Csame questions, different order

AnswersQuestions only With answer key Key only

CalculatorMixed Non-calculator (Paper 1)Calculator (Papers 2 and 3)

New sheet

Algebra worksheet — GCSE Foundation

Maths · GCSE Foundation · Algebra · 15 questions

MathsUKwww.geekhero.co.uk

1.Solve x² − 2x − 24 = 0.
(a)x = 6 or x = −4
(b)x = −6 or x = 4
(c)x = −8 or x = 3
(d)x = −6 or x = −4
2.A phone plan costs a fixed £15 per month plus 8p per minute of calls. In one month, Jamal's bill was £23.80. Form an equation using m for the number of minutes, and solve it to find how many minutes Jamal used that month.
(a)485
(b)1.1
(c)297.5
(d)110
3.A car's fuel tank contains 50 litres when it starts a journey. After travelling for 2 hours, it contains 38 litres, and fuel is used at a constant rate. Work out the rate at which fuel is used, in litres per hour.
(a)44
(b)19
(c)6
(d)12
4.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.
(a)9 m
(b)18 m
(c)37 m
(d)16 m
5.Expand 4(2x − 3).
(a)2x + 1
(b)8x + 12
(c)8x − 12
(d)8x − 3
6.Which of these equations describes a vertical line?
(a)y = 5x
(b)x = y
(c)x = 5
(d)y = 5
7.Write down the expression that means the same as p + p + p + q.
(a)3p + q
(b)3(p + q)
(c)p³ + q
(d)3pq
8.a = 2 and b = 5. Work out the value of ab².
(a)50
(b)10
(c)20
(d)100
9.Solve the inequality 5 − x ≤ 2.
(a)x ≤ −3
(b)x ≥ −3
(c)x ≥ 3
(d)x ≤ 3
10.A student is asked whether 3(x − 4) = 3x − 4 is an identity. Which statement gives the correct verdict and reason?
(a)It is an identity, because both sides begin with the term 3x, so they must be equivalent.
(b)It is not even an ordinary equation with a solution: expanding the left-hand side gives 3x − 12, and 3x − 12 = 3x − 4 would require −12 = −4, which is never true.
(c)It is not an identity, because the student forgot to multiply the 4 by 3 on both sides of the equation.
(d)It is not an identity, because the student needs to substitute a specific value of x before comparing the two sides.
11.Make x the subject of the formula y = 4x − 3.
y = 4x − 3
(a)x = 4(y + 3)
(b)x = y/4 + 3
(c)x = (y − 3)/4
(d)x = (y + 3)/4
12.Solve 4(x − 3) = 2x + 6.
(a)4.5
(b)−3
(c)3
(d)9
13.The nth term of a sequence is 4n + 2. A term in the sequence has value 30. Work out its position, n, in the sequence.
(a)5
(b)8
(c)7
(d)28
14.Make m the subject of the formula w = m − 8.
(a)m = 8 − w
(b)m = w + 8
(c)m = w/8
(d)m = w − 8
15.Solve the inequality 5x − 3 > 2x + 9.
(a)x > 4
(b)x > 2
(c)x < 4
(d)x > 36

Build your own mix at the worksheet builder.