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

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1.A sequence begins at 60, and each term after that is found by subtracting 7 from the term before it. Work out the 5th term of the sequence.
(a)88
(b)39
(c)32
(d)25
2.Write down the gradient of the line with equation y = 6 + 4x.
(a)6
(b)24
(c)10
(d)4
3.Solve 4(x − 3) = 2x + 6.
(a)4.5
(b)−3
(c)3
(d)9
4.Solve the inequality 2(3x − 1) ≥ 4x + 8.
(a)x ≥ 4.5
(b)x ≥ 5
(c)x ≥ 1
(d)x ≥ 20
5.A geometric sequence starts at 3, and each term after that is found by multiplying the term before it by 2. Write down the first four terms.
(a)6, 12, 24, 48
(b)3, 5, 7, 9
(c)3, 9, 27, 81
(d)3, 6, 12, 24
6.The formula for converting a temperature from degrees Celsius, C, to degrees Fahrenheit, F, is F = 1.8C + 32. Work out F when C = 20, and identify what kind of mathematical statement F = 1.8C + 32 is.
(a)68, and it is an equation
(b)36, and it is a formula
(c)52, and it is a formula
(d)68, and it is a formula
7.Solve x² − 100 = 0.
(a)x = 10 or x = −10
(b)x = 10
(c)x = 100 or x = −100
(d)x = 50
8.Simplify 2a + 3b − a + 2b − b
(a)a + 4b
(b)a + 6b
(c)5ab
(d)3a + 4b
9.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
10.A rectangular photo has length (x + 3) cm and width x cm. Its area is 40 cm². Work out the value of x.
(a)x = −8
(b)x = 5
(c)x = 5 or x = −8
(d)x = 4
11.Work out the gradient of the straight line with equation 3y = 12 − 6x.
(a)2
(b)4
(c)−2
(d)−6
12.Which expression means the same as a × a × a?
(a)a²
(b)3a
(c)a³
(d)3 + a
13.The solution set of x ≥ −1 is drawn on a number line. Which description of that number line is correct?
(a)An open circle at −1 with the arrow pointing right
(b)An open circle at −1 with the arrow pointing left
(c)A solid circle at −1 with the arrow pointing right
(d)A solid circle at −1 with the arrow pointing left
14.A stack of firewood has 3 logs in the top layer. Each layer below has 4 more logs than the layer above it. Work out the number of logs in the 6th layer from the top.
(a)23
(b)27
(c)24
(d)20
15.Which expression is equivalent to 5x − (x + 3)?
(a)4x + 3
(b)6x − 3
(c)4x − 3
(d)5x − 3

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