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.For the equation 2x + 3 = 11, and the inequality 2x + 3 > 11, which statement correctly compares their solutions?
(a)The equation has one solution; the inequality has many.
(b)Both have exactly one solution.
(c)Both have many solutions.
(d)The equation has many solutions; the inequality has one.
2.A taxi charges a £3 fixed fee plus £2 for each mile travelled. Write an expression, in pounds, for the total cost of a journey of n miles.
(a)3n + 2
(b)2n + 3
(c)2n − 3
(d)5n
3.Work out the value of m² + 3m when m = −2
(a)−10
(b)10
(c)−14
(d)−2
4.The first five terms of a sequence are 6, 10, 14, 18, 22. Work out an expression, in terms of n, for the nth term.
(a)6n + 4
(b)4n + 6
(c)4n − 2
(d)4n + 2
5.A square has sides of length y cm. Write down an expression for the perimeter of the square.
(a)2y
(b)y + 4
(c)y²
(d)4y
6.A cinema sells adult tickets and child tickets. On one evening, 40 tickets are sold in total. There are 8 more adult tickets sold than child tickets. Work out the number of child tickets sold.
(a)20
(b)32
(c)16
(d)24
7.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
8.Factorise fully 56x − 24
(a)8(7x − 16)
(b)8(56x − 3)
(c)8(7x + 3)
(d)8(7x − 3)
9.A delivery van's distance-time graph shows the following: it travels 9 km in the first 15 minutes at a steady speed, stops for 45 minutes to unload, then travels a further 21 km in the next 30 minutes, also at a steady speed. Work out the average speed, in km/h, for the whole journey.
(a)36 km/h
(b)39 km/h
(c)40 km/h
(d)20 km/h
10.Which of these equations gives a straight-line graph when plotted?
(a)y = 3/x
(b)y = 2x − 3
(c)y = x³ − 3
(d)y = x² − 3
11.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
12.To rearrange the formula y = 3x − 8 to make x the subject, Priya writes: 'Add 8 to both sides to get y + 8 = 3x, then divide both sides by 3 to get x = y + 8 ÷ 3.' Work out the correct expression for x.
y = 3x − 8
(a)x = 3(y + 8)
(b)x = (y − 8) / 3
(c)x = y + 8 / 3
(d)x = (y + 8) / 3
13.A rectangle has length k cm and width 5 cm less than its length. Write down an expression for the width of the rectangle, in cm.
(a)k + 5
(b)k − 5
(c)5k
(d)5 − k
14.Solve 3x + 14 = 8x − 6
(a)x = 15
(b)x = 2.5
(c)x = 4
(d)x = −1.6
15.Solve 3x − 5 = 4.
(a)9
(b)−1/3
(c)6
(d)3

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