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

MathsUKwww.geekhero.co.uk

1.Solve 2x − 2 = 2
(a)x = 2
(b)x = 8
(c)x = 0
(d)x = 4
2.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).
(a)(2, 7)
(b)(4, 14)
(c)(5, 2)
(d)(2, 9)
3.Which of these points lies in the first quadrant?
(a)(−1, −4)
(b)(4, −1)
(c)(−2, 3)
(d)(3, 5)
4.A rope of length L metres is cut into 6 equal pieces, and 4 metres is then removed from one piece. Write an expression, in metres, for the length of that piece after the cut.
(a)(L − 4)/6
(b)L/6 + 4
(c)4 − L/6
(d)L/6 − 4
5.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
6.Work out the value of a² − 2b when a = −3 and b = 4.
(a)1
(b)−17
(c)−11
(d)17
7.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.
(a)1
(b)−1
(c)3
(d)4
8.Factorise fully 12x² + 18x.
(a)2x(6x + 9)
(b)6(2x² + 3x)
(c)6x(2x + 3)
(d)3x(4x + 6)
9.The first four terms of a sequence are 2, 6, 10, 14. Priya says the nth term is 4n. Work out the correct expression for the nth term.
(a)2n + 2
(b)4n + 2
(c)4n − 2
(d)4n
10.A box holds n pencils. A shop has 6 full boxes and 4 loose pencils. All of these pencils are shared equally between 2 classes. Write down the expression for the number of pencils each class receives.
(a)2(6n + 4)
(b)6(n + 4)/2
(c)(6n + 4)/2
(d)6n + 4/2
11.Work out the gradient of the straight line that passes through the points (−1, 5) and (3, −7).
(a)−6
(b)−3
(c)−1/3
(d)3
12.Solve 4(x − 3) = 2x + 6.
(a)4.5
(b)−3
(c)3
(d)9
13.Tom buys 2 notebooks and 6 pencils on Monday, priced at p pence each for a notebook and q pence each for a pencil. On Tuesday he buys 3 more notebooks and 1 more pencil. Write a simplified expression, in pence, for the total amount Tom has spent on notebooks and pencils.
(a)5p + 7q
(b)5p + 6q
(c)2p + 7q
(d)12pq
14.Solve 5x² − 15x = 0.
(a)x = 0 or x = 15
(b)x = 3
(c)x = 0 or x = 3
(d)x = 5 or x = 3
15.Work out the distance of the point (−6, 4) from the x-axis.
(a)10
(b)−6
(c)4
(d)6

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