Printable · GCSE Higher · ages 14-16

Algebra worksheet — GCSE Higher

Fifteen questions across the algebra statements at Higher 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 Higher

Maths · GCSE Higher · Algebra · 15 questions

MathsUKwww.geekhero.co.uk

1.A quadratic graph has equation y = (x − 4)². A student says this graph crosses the x-axis at two different points. Explain why the student is wrong.
(a)It touches the x-axis once, only at x = 4.
(b)It never touches the x-axis at all.
(c)It crosses twice, at x = 4 and x = −4.
(d)It crosses twice, at x = 2 and x = −2.
2.A van's value depreciates by 18% each year. After 2 years it is worth £5,379.20. Work out its value when it was new, correct to the nearest pound.
(a)£6,560
(b)£3,617
(c)£8,000
(d)£8,405
3.x = 5. Work out the value of 3x² − 4.
(a)221
(b)75
(c)71
(d)3
4.f(x) = 2x² + 1 and g(x) = x − 1. Work out fg(x), giving your answer in expanded form.
y = 2x² + 1
(a)2x² − 4x + 2
(b)2x² − 1
(c)2x²
(d)2x² − 4x + 3
5.A car's journey is represented by a velocity-time graph. The total distance travelled, found from the area under the graph, is 350 metres, and the total time for the journey is 25 seconds. Work out the car's average speed for the whole journey, in m/s.
(a)375 m/s
(b)14 m/s
(c)8750 m/s
(d)0.07 m/s
6.The nth term of a sequence is 4n + 2. A term in the sequence has value 30. Work out its position, n, in the sequence.
(a)5
(b)8
(c)7
(d)28
7.The graph of y = f(x) has a maximum turning point at (−1, 6). Write down the coordinates of the maximum turning point of the graph of y = f(x − 3).
(a)(−1, 9)
(b)(2, 6)
(c)(−1, 3)
(d)(−4, 6)
8.a = 2 and b = 5. Work out the value of a²b.
(a)9
(b)20
(c)100
(d)50
9.Solve the inequality x² − 5x + 6 < 0.
(a)−3 < x < −2
(b)x < 2 or x > 3
(c)2 < x < 3
(d)2 ≤ x ≤ 3
10.A tree is 2 metres tall. Each year its height increases by 10% of its height at the start of that year. Work out the height of the tree after 3 years, giving your answer to 1 decimal place.
(a)2.6
(b)2.9
(c)2.4
(d)2.7
11.By completing the square, find the turning point of the curve y = 3x² + 12x + 7.
y = 3x² + 12x + 7
(a)x = −2, y = 5
(b)x = −4, y = −41
(c)x = 2, y = −5
(d)x = −2, y = −5
12.The graph of y = x² − 2x − 8 takes these values: when x = −2, y = 0; when x = −1, y = −5; when x = 0, y = −8; when x = 3, y = −5; when x = 4, y = 0. Use these values to write down the two solutions of x² − 2x − 8 = 0.
y = x² − 2x − 8
(a)x = −2
(b)x = −1 or x = 3
(c)x = −2 or x = 4
(d)x = 0 or x = −8
13.For the graph of y = 1/x, where x cannot be zero, which of these statements is correct?
(a)The graph has only one branch, in quadrant 1
(b)The graph passes through the origin, (0, 0)
(c)The graph crosses the y-axis but never the x-axis
(d)The graph never crosses either axis
14.To solve 5x − 4 = 2x + 8, Chloe's working is shown. Line 1: 5x − 4 = 2x + 8. Line 2: 3x − 4 = 8. Line 3: 3x = 4. Line 4: x = 4/3. Chloe has made a mistake in her working. Which line contains the mistake?
(a)Line 1
(b)Line 2
(c)Line 4
(d)Line 3
15.Simplify (2x² + 7x + 3) ÷ (x² − 9), giving your answer as a single fraction.
(a)(2x + 1)/(x + 3)
(b)(2x + 1)/(x − 3)
(c)2x + 1
(d)(2x + 3)/(x − 3)

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