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 pattern is made from tiles. Pattern 1 uses 4 tiles, pattern 2 uses 7 tiles, pattern 3 uses 10 tiles and pattern 4 uses 13 tiles, with each pattern using 3 more tiles than the one before. Work out an expression, in terms of n, for the number of tiles used in pattern n.
(a)3n − 2
(b)3n + 1
(c)3n + 4
(d)n + 3
2.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.
(a)9n + 6
(b)6n
(c)6n + 9
(d)6n + 3
3.A fundraising chain letter starts with 3 people taking part in round 1. Each following round has 4 times as many people taking part as the round before. Work out the number of people taking part in round 4.
(a)39
(b)192
(c)768
(d)256
4.A tank already contains some water and is then filled at a constant rate. After 2 minutes it contains 50 litres in total; after 7 minutes it contains 150 litres in total. Work out the rate at which water is added, in litres per minute.
(a)0.05
(b)20
(c)100
(d)25
5.Write down the coordinates of the point that is 4 units to the left of the origin and 7 units up.
(a)(−4, −7)
(b)(7, −4)
(c)(−4, 7)
(d)(4, 7)
6.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
7.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.
8.Noah says that y = 3 is the solution of the equation y + 10 = 12. Noah is wrong. Work out the correct value of y.
(a)y = 22
(b)y = −2
(c)y = 2
(d)y = 12
9.The area of a triangle is given by the formula A = bh/2, where b is the base and h is the height. Make h the subject of the formula.
(a)h = b/(2A)
(b)h = 2A/b
(c)h = A/(2b)
(d)h = 2Ab
10.A car's fuel tank contains 50 litres when it starts a journey. After travelling for 2 hours, it contains 38 litres, and fuel is used at a constant rate. Work out the rate at which fuel is used, in litres per hour.
(a)44
(b)19
(c)6
(d)12
11.A printer starts a job with 480 sheets of paper loaded and prints at a steady rate. The number of sheets left, S, after t minutes is given by S = 480 − 24t. Work out how many minutes it takes for the paper to run out completely.
(a)20
(b)456
(c)0.05
(d)480
12.Which expression is equivalent to 4(x − 2) + 10?
(a)4x + 2
(b)4x + 8
(c)4x − 8
(d)4x + 18
13.Solve x² = 49.
(a)x = 7
(b)x = 24.5
(c)x = −7
(d)x = 7 or x = −7
14.Which of these quadratic graphs does NOT cross the x-axis at all?
(a)y = (x − 2)² + 3
(b)y = (x + 4)(x − 1)
(c)y = (x − 2)(x + 3)
(d)y = x² − 9
15.Solve 4x² − 9 = 0.
(a)x = 3/2 or x = −3/2
(b)x = 3/2 only
(c)x = 3 or x = −3
(d)x = 9/4 or x = −9/4

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