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.There are 30 students in a Year 10 maths class. There are 2 more boys than girls. Work out the number of boys and the number of girls.
(a)15 boys and 15 girls
(b)17 boys and 13 girls
(c)14 boys and 16 girls
(d)16 boys and 14 girls
2.f(x) = x + 3 and g(x) = 2x. Work out fg(x).
y = x + 3
(a)2x² + 6x
(b)2x + 3
(c)3x + 3
(d)2x + 6
3.f(x) = x² − 1 and g(x) = 3x. Work out fg(4).
y = x² − 1
(a)36
(b)143
(c)11
(d)45
4.A proof that the product of two consecutive even numbers is always a multiple of 8 begins: Let the two consecutive even numbers be 2n and 2n + 2, so their product is 2n(2n + 2) = 4n(n + 1). Which line correctly completes the proof?
(a)4n(n + 1) is a multiple of 4, and because n and n + 1 are consecutive integers, it must be a multiple of 8.
(b)Expanding gives 4n(n + 1) = 4n² + 4n, which is clearly a multiple of 8.
(c)4n is always a multiple of 4 for any integer n, so 4n(n + 1) is a multiple of 4 as well, which means it is a multiple of 8.
(d)n and n + 1 are consecutive integers, so one of them must be even; this makes n(n + 1) even, so 4n(n + 1) is 4 × an even number, which is a multiple of 8.
5.The first five terms of a quadratic sequence are 6, 11, 18, 27, 38. Work out an expression, in terms of n, for the nth term.
(a)2n² + 2n + 3
(b)n² + 2n + 3
(c)n² + 3
(d)n² + 2n
6.For 0 ≤ x ≤ 360, the equation sin x = 0.5 has two solutions. What are they?
(a)30° and 120°
(b)30° and 210°
(c)45° and 135°
(d)30° and 150°
7.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
8.The diagram shows the graph of the cost, in pounds, of a taxi journey plotted against the distance travelled, in miles, for journeys of up to 4 miles. The same fixed charge and the same cost per mile apply to longer journeys. Work out the cost of a 6-mile journey.
(a)£24
(b)£14
(c)£12
(d)£8
9.A hiker's distance-time graph shows the following: he walks 5 km in the first 1 hour at a steady speed, rests for 1 hour, then walks a further 9 km in the next 2 hours, also at a steady speed. Work out his average speed for the whole journey, in km/h.
(a)3.5 km/h
(b)4.75 km/h
(c)4.67 km/h
(d)2.25 km/h
10.An exponential graph y = A × rˣ passes through the points (0, 8) and (2, 18). Work out the value of r, correct to 2 decimal places.
(a)1.13
(b)1.50
(c)0.44
(d)2.25
11.The point A(−6, 8) lies on the circle x² + y² = 100, whose centre is the origin O. The tangent to the circle at A crosses the y-axis at the point B. Work out the length of OB.
(a)12.5
(b)8
(c)10
(d)3.5
12.The graph of y = x³ − 5x is reflected in the y-axis. Work out the equation of the image.
y = x
(a)y = −x³ + 5x
(b)y = x³ − 5x
(c)y = x³ + 5x
(d)y = −x³ − 5x
13.A circle has centre (0, 0) and equation x² + y² = 25. Work out the x-coordinates of the two points where the circle crosses the line y = 3.
(a)x = 3 and x = −3
(b)x = 4
(c)x = 5 and x = −5
(d)x = 4 and x = −4
14.Two numbers have a sum of 24. Their difference is 6. Work out the two numbers.
(a)15 and 6
(b)15 and 21
(c)15 and 9
(d)18 and 6
15.The nth term of a sequence is n² − 2n + 5. Work out the 10th term.
(a)68
(b)85
(c)80
(d)125

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