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 theatre's front row has 18 seats. Each row behind has 4 more seats than the row in front. Which row has exactly 62 seats?
(a)11
(b)48
(c)15.5
(d)12
2.A walker's distance-time graph is described as follows: she walks 3 km in the first 15 minutes at a steady speed, rests for 10 minutes, then walks a further 3 km in the next 20 minutes, also at a steady speed. Work out her speed, in km/h, during the first 15 minutes.
(a)12 km/h
(b)9 km/h
(c)8 km/h
(d)0.2 km/h
3.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
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.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.
(a)y = x + 2
(b)y = 2x − 1
(c)y = 2x + 1
(d)y = 2x + 3
6.Simplify 5a/6 − a/3
(a)7a/6
(b)2a/3
(c)4a/3
(d)a/2
7.The diagram shows the graph of a quadratic function. Write down the values of x where the graph crosses the x-axis.
(a)−2 and 2
(b)0 and 2
(c)−4 and 4
(d)−2 and 3
8.A quadratic graph has equation y = (x − 4)². A student says this graph crosses the x-axis at two different points. Explain why the student is wrong.
(a)It touches the x-axis once, only at x = 4.
(b)It never touches the x-axis at all.
(c)It crosses twice, at x = 4 and x = −4.
(d)It crosses twice, at x = 2 and x = −2.
9.Solve the inequality x − 10 < −3.
(a)x < 13
(b)x > 7
(c)x < −13
(d)x < 7
10.Write down the y-intercept of the line with equation y = 3x + 8.
y = 3x + 8
(a)−8
(b)11
(c)3
(d)8
11.The point A lies on the x-axis. Which statement about A must be true?
(a)y = 0
(b)x = 0
(c)x > 0
(d)x = y
12.Make x the subject of the formula y = x/2 − 5.
y = x
(a)x = (y + 5)/2
(b)x = 2y − 10
(c)x = 2y + 10
(d)x = 2y + 5
13.A number machine multiplies its input by 2 and then subtracts 5. Work out the output when the input is 6.
(a)7
(b)17
(c)12
(d)2
14.A rectangle has area 24x + 18. Ffion factorises the area as 6(4x + 3). Work out the value of the area when x = 2, and decide whether 6 and (4x + 3) are correctly identified as factors of 24x + 18.
(a)11 — 6 and (4x + 3) are correct factors of 24x + 18.
(b)66 — 6 and (4x + 3) are not correct factors of 24x + 18.
(c)84 — 6 and (4x + 3) are correct factors of 24x + 18.
(d)66 — 6 and (4x + 3) are correct factors of 24x + 18.
15.The simultaneous equations y = 3 and 4x − y = 9 are given. Work out the value of x.
(a)1.5
(b)8
(c)3
(d)12

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