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.Write down the coefficient of p in the expression 7 − 4p + 9q.
(a)7
(b)4
(c)9
(d)−4
2.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
3.A curve has equation y = x² − 9. Which statement about its graph is correct?
y = x² − 9
(a)It crosses the x-axis only once, at x = 9.
(b)It does not cross the x-axis, since −9 is negative.
(c)It crosses the x-axis at x = 9 and x = −9.
(d)It crosses the x-axis at x = 3 and x = −3.
4.Three consecutive integers add up to 72. Using n for the smallest integer, form an equation and solve it to find the smallest of the three integers.
(a)25
(b)24
(c)21
(d)23
5.Write down the number of terms in the expression 4x² − 7x + 3.
(a)2
(b)5
(c)4
(d)3
6.A plumber charges a call-out fee plus an hourly rate for a job. The total cost, £C, for a job lasting h hours is given by the formula C = 40 + 25h. What does the number 40 represent in this formula?
(a)The total cost for a job lasting 1 hour.
(b)The hourly rate the plumber charges.
(c)The number of hours worked before charging starts.
(d)The fixed call-out fee, charged before the hourly rate.
7.The nth term of a sequence is 2n² + 1. Work out the 4th term of the sequence.
(a)33
(b)65
(c)32
(d)17
8.Ben writes n + 4 ≤ 9. Which statement describes what Ben has written? Give a reason for your answer.
(a)An equation, because solving it gives the value of n
(b)An identity, because it is true for many values of n
(c)A formula, because it works out n from 9
(d)An inequality, because ≤ compares the two sides
9.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
10.Solve the inequality 9 − 2x ≥ 1.
(a)x ≤ 5
(b)x ≥ 4
(c)x ≤ 4
(d)x ≤ −4
11.The graph of y = (x − 2)(x + 5) crosses the x-axis at two points. Work out the x-coordinates of these two points.
(a)x = −2 and x = −5
(b)x = 2 and x = −5
(c)x = −2 and x = 5
(d)x = 2 and x = 5
12.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
13.Priya has a budget of £50 for a school trip. The coach costs £14 and each student ticket costs £4. Using the inequality 14 + 4s ≤ 50, work out the greatest number of student tickets, s, she can buy.
(a)16
(b)9
(c)8
(d)12
14.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
15.The nth term of a sequence is n² + 3. Work out the first term of the sequence that is greater than 50.
(a)52
(b)67
(c)39
(d)17

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