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 · Calculator · 15 questions

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1.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
2.Solve 2x² − 32 = 0.
(a)x = 8
(b)x = 4
(c)x = 16
(d)x = 4 or x = −4
3.A ferry's distance-time graph is a straight line from (0 minutes, 0 km) to (25 minutes, 15 km). Work out the ferry's speed in kilometres per hour.
(a)36 km/h
(b)14.4 km/h
(c)6.25 km/h
(d)0.6 km/h
4.Amelia's mother is three times as old as Amelia. Four years ago her mother was five times as old as Amelia was then. Work out Amelia's age now.
(a)4
(b)2
(c)16
(d)8
5.Harry is 14 years old and Mia is 8 years old. Will Harry ever be exactly twice as old as Mia? Give a reason for your answer.
(a)No — it has never happened and never will
(b)Yes — when Harry is 20
(c)No — that moment has already passed
(d)Yes — when Harry is 16
6.Yuki is y years old. Her brother is 4 years younger than Yuki. Write down an expression, in terms of y, for the brother's age in 5 years' time.
(a)y + 1
(b)y − 4
(c)y − 9
(d)y + 9
7.Point R has coordinates (3, −5). Point R is reflected in the line y = 2 to point S. Write down the coordinates of S.
(a)(3, 5)
(b)(−3, 9)
(c)(3, 9)
(d)(3, 7)
8.A taxi company charges a £2.50 booking fee plus £1.80 per mile. A journey costs £15.10 in total. Work out the number of miles travelled.
(a)9.78
(b)8.39
(c)5.32
(d)7
9.Solve 5x² − 15x = 0.
(a)x = 0 or x = 15
(b)x = 3
(c)x = 0 or x = 3
(d)x = 5 or x = 3
10.A ball is thrown in the air. Its height, h metres, above the ground after t seconds is given in this table: when t = 0, h = 0; when t = 1, h = 15; when t = 2, h = 20; when t = 3, h = 15; when t = 4, h = 0. Use the table to find the two times, in seconds, at which the ball is at ground level.
(a)t = 0 or t = 4
(b)t = 2
(c)t = 0
(d)t = 1 or t = 3
11.The formula connecting speed, distance and time is v = s ÷ t. Work out v, in km/h, when s = 180 and t = 4.
(a)720
(b)184
(c)176
(d)45
12.A school trip costs a £15 deposit plus £9 per student for the coach. The total cost for a class is £186. Work out how many students went on the trip.
(a)22.33
(b)20.67
(c)19
(d)11.8
13.A quadratic graph y = ax² + bx + c has its turning point on the y-axis. Which statement about its roots must be true?
(a)The two roots must both be positive.
(b)The graph has no roots at all.
(c)The graph must touch the x-axis at exactly one point.
(d)If the graph has two real roots, they are equal and opposite in value, so they sum to zero.
14.A taxi firm charges a fixed fee of £3.50 plus £2.20 per mile. Work out the total cost of a journey of 6 miles.
(a)£13.20
(b)£15.50
(c)£34.20
(d)£16.70
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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