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.

Non-calculator

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 · Non-calculator · 15 questions

MathsUKwww.geekhero.co.uk

1.The first four terms of a sequence are 4, 6, 8, 10. Work out an expression, in terms of n, for the nth term.
(a)2n + 4
(b)2n
(c)2n + 2
(d)2n − 2
2.The equation 3(2x − 1) = 4x + 9 is rearranged by expanding the brackets. Which of these is the correctly expanded equation?
(a)5x − 3 = 4x + 9
(b)6x − 3 = 4x + 9
(c)6x − 1 = 4x + 9
(d)6x − 4 = 4x + 9
3.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.
(a)34
(b)68
(c)55
(d)47
4.Rosie is asked whether 4(x + 3) = 4x + 12 is an equation or an identity. Which statement is correct? Give a reason for your answer.
(a)An identity, because it is true for every value of x
(b)An identity, because the brackets can be expanded
(c)An equation, because solving it gives x = 3
(d)A formula, because it works out 4x + 12 from x
5.The graph of t = 240 ÷ s shows how the time, t hours, taken for a car journey of 240 miles depends on its average speed, s mph. Use the relationship to work out the time taken when the average speed is 48 mph.
(a)0.2 hours
(b)10 hours
(c)5 hours
(d)4.8 hours
6.Which of these points lies in the first quadrant?
(a)(−1, −4)
(b)(4, −1)
(c)(−2, 3)
(d)(3, 5)
7.Which expression means the same as a × a × a?
(a)a²
(b)3a
(c)a³
(d)3 + a
8.Amelia is buying books. Each book costs £5 and she has at most £30 to spend. Write down an inequality for x, the number of books she can buy.
(a)5x ≥ 30
(b)x + 5 ≤ 30
(c)5x < 30
(d)5x ≤ 30
9.The expression 6n + 15 is written as 3(2n + 5). Which statement is correct?
(a)3 and 2n + 5 are the two terms of 6n + 15
(b)6n and 15 are the factors of 6n + 15
(c)3 and 2n + 5 are both factors of 6n + 15
(d)3 is the only factor of 6n + 15
10.Write down the gradient of the line with equation y = 6 + 4x.
(a)6
(b)24
(c)10
(d)4
11.Which expression is equivalent to 2(x + 6)?
(a)2x + 8
(b)x + 12
(c)2x + 12
(d)2x + 6
12.Solve (3x + 2)/5 = (x + 4)/3
(a)x = 3.5
(b)x = 4.5
(c)x = 10
(d)x = 1
13.The point D has coordinates (3, −8). Write down the distance of D from the y-axis.
(a)8
(b)3
(c)11
(d)−8
14.A rectangle is x cm wide and twice as long as it is wide, so its area A cm² is given by A = 2x². Work out A when x = 3.
(a)18 cm²
(b)6 cm²
(c)12 cm²
(d)36 cm²
15.The graph of y = (x − 4)(x + 1) crosses the x-axis. Which pair gives the correct roots and reasoning?
(a)x = −4 and x = −1, because the roots are always the negative of the numbers shown in the brackets.
(b)x = 4 and x = 1, because both brackets must be positive at the roots.
(c)x = 4 and x = −1, because the graph crosses the x-axis where x − 4 = 0 or x + 1 = 0.
(d)x = −4 and x = 1, because the signs inside the brackets must be reversed to solve them.

Build your own mix at the worksheet builder.