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 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.
(a)6n + 1
(b)7n
(c)7n − 1
(d)7n + 6
2.Which of these is a term, rather than a whole expression, an equation, or a formula?
(a)A = 5x²
(b)5x² + 3x
(c)5x² = 20
(d)5x²
3.Solve 6x − 5 = 3x + 13.
(a)18
(b)2
(c)2.67
(d)6
4.Expand 7(a + 8)
(a)a + 56
(b)7a + 15
(c)7a + 8
(d)7a + 56
5.Solve the simultaneous equations 3x + y = 14 and x + y = 6. Work out the value of x.
(a)4.67
(b)−4
(c)2
(d)4
6.A straight line has gradient −2 and passes through the point (3, 1). Work out the equation of the line.
(a)y = −2x + 7
(b)y = −2x − 5
(c)y = 2x + 7
(d)y = −2x + 1
7.A photo printing service has two adverts for its price. Advert A: cost in pounds = 3(2n + 4) for n photos. Advert B: cost in pounds = 6n + 12. A customer says the two adverts always charge the same amount. Is the customer correct?
(a)They always charge the same, since 3(2n + 4) = 6n + 12.
(b)It depends on the value of n, so it cannot be decided.
(c)Advert A is cheaper, since 3(2n + 4) = 6n + 4.
(d)Advert A is cheaper, since 3(2n + 4) = 2n + 7.
8.Solve the simultaneous equations 4x + 3y = 25 and 4x − y = 1. Work out the value of y.
(a)6
(b)4
(c)12
(d)−6
9.Point P has coordinates (2, −5). P is reflected in the x-axis to point Q. Write down the coordinates of Q.
(a)(2, −5)
(b)(−2, 5)
(c)(2, 5)
(d)(−2, −5)
10.The formula for the volume of a cuboid is V = lwh, where l is the length, w is the width and h is the height. Make h the subject of the formula.
(a)h = Vlw
(b)h = V − lw
(c)h = V / (lw)
(d)h = lw / V
11.Work out the coordinates of the point halfway between (−9, −2) and (−1, −2).
(a)(−10, −2)
(b)(−5, −2)
(c)(−4, −2)
(d)(5, −2)
12.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?
(a)An identity, true for every value of x
(b)A formula, relating two expressions
(c)An equation, because it has an equals sign
(d)An equation, solved by one value of x
13.Jack is x years old. His brother Kwame is 3 years older than Jack. Write down an expression for Kwame's age.
(a)x + 3
(b)3 − x
(c)x − 3
(d)3x
14.A rectangular garden has width w metres and length (w + 3) metres. A gardener writes its perimeter as 2w + 3. Which statement corrects the gardener's mistake?
(a)It is 2(w + (w + 3)) = 4w + 6, not 2w + 3.
(b)It is 3w + 6, since the length doubles but not the width.
(c)It is w + (w + 3) = 2w + 3, matching the gardener.
(d)It is 4(w + 3) = 4w + 12, treating it as a square.
15.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

Build your own mix at the worksheet builder.