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 · 15 questions

MathsUKwww.geekhero.co.uk

1.A box contains 6 chocolates. Write down an expression for the total number of chocolates in c boxes.
(a)6c
(b)6 + c
(c)c ÷ 6
(d)c − 6
2.Solve the simultaneous equations 2x + y = 7 and x + 2y = 8.
(a)x = 2, y = 5
(b)x = 3, y = 2
(c)x = 2, y = 3
(d)x = −2, y = 11
3.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).
4.An equation has exactly one value of x that makes it true, but an identity is true for every value of x. Which of these best explains why 3x + 5 = 20 is an equation rather than an identity?
(a)It has an = sign, and equations always use =.
(b)3x + 5 cannot be simplified, so it must be an equation.
(c)Only x = 5 satisfies 3x + 5 = 20, not every value of x.
(d)A number on the right-hand side makes it an equation.
5.A scout leader is 44 years old and one of the scouts is 16 years old. Work out how many years it will be until the leader is exactly twice as old as the scout.
(a)6 years
(b)12 years
(c)14 years
(d)28 years
6.Work out the value of 2(x + 2) when x = −5
(a)−3
(b)−1
(c)−6
(d)−8
7.Two numbers have a sum of 50. The larger number is twice the smaller number. Work out the smaller number.
(a)100/3
(b)25
(c)24
(d)50/3
8.Write down the coordinates of the point where the line y = 2x + 4 crosses the y-axis.
y = 2x + 4
(a)(4, 0)
(b)(−2, 0)
(c)(0, 2)
(d)(0, 4)
9.Two numbers have a sum of 24. Their difference is 6. Work out the two numbers.
(a)15 and 6
(b)15 and 21
(c)15 and 9
(d)18 and 6
10.Solve the simultaneous equations 3x + 2y = 16 and x + y = 7. Work out the value of y.
(a)2
(b)5
(c)9
(d)−5
11.The first five square numbers are 1, 4, 9, 16, 25. Write down the next square number in the sequence.
(a)36
(b)30
(c)35
(d)49
12.The nth term of a sequence is 2n − 1. Work out the 6th term of the sequence.
(a)11
(b)7
(c)9
(d)12
13.Solve x² + 7x = 0.
(a)x = 0 or x = 7
(b)x = 0 or x = −14
(c)x = 0 or x = −7
(d)x = −7
14.The diagram shows the graph of $y = x^{2} - x - 2$ , together with the horizontal line $y = 3$ . Use the graphs to estimate, to 1 decimal place, the two solutions of $x^{2} - x - 2 = 3$ .
(a)x = −1.8 and x = 2.8
(b)x = −3.0 and x = 4.0
(c)x = 1.8 and x = 2.8
(d)x = −1.0 and x = 2.0
15.Solve the inequality x + 5 < 12.
(a)x < 7
(b)x < 17
(c)x > 7
(d)x < −7

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