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.A sequence has the position-to-term rule n² + 1, where n is the position number. Work out how much bigger the 5th term is than the 4th term.
(a)9
(b)7
(c)1
(d)11
2.A distance-time graph shows a car travelling at a constant speed, covering 90 km in 2 hours. Work out the car's speed in km/h.
(a)88 km/h
(b)180 km/h
(c)45 km/h
(d)92 km/h
3.A straight line passes through the points (2, 5) and (4, 11). Work out the gradient of the line.
(a)8/3
(b)−3
(c)3
(d)1/3
4.Write down the expression that means 5 more than half of n.
(a)(n + 5)/2
(b)5n/2
(c)2n + 5
(d)n/2 + 5
5.Work out the value of 3b − 4 when b = 6
(a)6
(b)5
(c)14
(d)18
6.The graph of y = x² − 7x + 2 crosses the x-axis at two points. One root, read from the graph, is approximately x = 0.30. Using the fact that the sum of the two roots of x² − 7x + 2 = 0 is 7, estimate the other root, correct to 2 decimal places.
y = x² − 7x + 2
(a)x ≈ 6.70
(b)x ≈ 6.30
(c)x ≈ 7.30
(d)x ≈ 0.70
7.A sequence has the position-to-term rule n² + 2, where n is the position number. Work out the 6th term.
(a)38
(b)36
(c)64
(d)14
8.The diagram shows two curves drawn on the same grid. Curve A is the graph of $y = x^{2}$ . Which equation could represent curve B?
(a) $y = (x - 3)^{2}$
(b) $y = x^{2} - 3$
(c) $y = x^{2} + 3 x$
(d) $y = x^{2} + 3$
9.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
10.Ethan is 10 years old and his father is 40 years old. Work out how many years ago Ethan's father was seven times as old as Ethan.
(a)24
(b)35
(c)5
(d)30
11.Solve x² − 100 = 0.
(a)x = 10 or x = −10
(b)x = 10
(c)x = 100 or x = −100
(d)x = 50
12.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
13.The formula for the perimeter of a rectangle is P = 2(l + w). One rectangle has l = 9 cm and w = 4 cm. A second rectangle has l = 6 cm and w = 5 cm. Work out how many cm greater the perimeter of the first rectangle is than the perimeter of the second.
(a)4
(b)26
(c)6
(d)2
14.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
15.A zip-line runs from a platform 25 m high to a landing point 5 m high, over a horizontal distance of 40 m. Work out the gradient of the zip-line.
(a)2
(b)−0.5
(c)0.5
(d)−0.8

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