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.Simplify 5x + 3y − 2x + y.
(a)3x + 2y
(b)7x + 4y
(c)3x + 4y
(d)6xy
2.The first five square numbers are 1, 4, 9, 16, 25. Write down the next square number in the sequence.
(a)36
(b)30
(c)35
(d)49
3.A graph shows the total monthly cost of a mobile phone tariff against the number of minutes of calls. The line starts at £12 and stays level until 200 minutes, then rises by 5p for each further minute of calls. Use the graph to work out the total cost of a month in which 250 minutes of calls are made.
(a)£14.50
(b)£13.50
(c)£12.50
(d)£24.50
4.The graph of y = x² + 2x − 15 crosses the x-axis at two points. By factorising, work out the x-coordinates of these two points.
y = x² + 2x − 15
(a)x = −3 and x = 5
(b)x = 5 and x = 3
(c)x = 3 and x = −5
(d)x = −15 and x = 1
5.A sequence has nth term 3n + 4. Two terms are missing from the list of its first five terms: 7, 10, _, 16, _. Work out the missing 3rd and 5th terms added together.
(a)28
(b)38
(c)32
(d)33
6.A ball is dropped and bounces. The height of each bounce after the first is 8 cm less than the bounce before it. The first bounce reaches 60 cm. Work out the height of the 5th bounce.
(a)40
(b)92
(c)20
(d)28
7.Solve x − 4 = −9
(a)x = 13
(b)x = −13
(c)x = −5
(d)x = 5
8.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
9.A sequence has the position-to-term rule: the term is the position number multiplied by itself. Its first five terms are 1, 4, 9, 16, 25. Work out the 8th term.
(a)8
(b)64
(c)16
(d)81
10.Which of these is an equation, rather than an expression, a formula or an identity?
(a)3x + 5
(b)A = πr²
(c)3x + 5 = 17
(d)3(x + 5) ≡ 3x + 15
11.Two expressions are 4(x + 3) and 4x + 3. A student checks whether they are equivalent by substituting x = 2. Which statement correctly interprets the result?
(a)4(x + 3) = 20 and 4x + 3 = 11 when x = 2, so the two expressions are not equivalent, because the bracket means the 3 must be added before multiplying by 4.
(b)4(x + 3) = 11 and 4x + 3 = 11 when x = 2, since the bracket has no effect on the multiplication, so the two expressions are equivalent.
(c)4(x + 3) = 20 and 4x + 3 = 11 when x = 2, but the two expressions are equivalent because both involve the same terms, 4x and 3.
(d)4(x + 3) = 20 and 4x + 3 = 11 when x = 2, so the two expressions are not equivalent, but they would become equal for some larger value of x.
12.A straight line has equation 4y = 12x + 20. Work out the gradient of the line.
y = 12x + 20
(a)12
(b)3
(c)20
(d)5
13.The diagram shows a distance–time graph for a cyclist travelling at a constant speed, for the first 6 minutes of a journey. Distance is in kilometres and time is in minutes. Work out how far the cyclist would travel in 20 minutes at the same speed.
(a)20 km
(b)10 km
(c)40 km
(d)3 km
14.Work out the value of 3a − 2b when a = 5 and b = 4
(a)52
(b)−7
(c)23
(d)7
15.The graph of y = 20/x is drawn for x > 0. As the value of x increases, what happens to the value of y?
(a)y stays the same however large x becomes
(b)y decreases towards zero but never reaches it
(c)y increases towards a limit but never reaches it
(d)y decreases at a steady rate and reaches zero

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