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.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
2.The graph of y = f(x) has x-intercepts at x = −2 and x = 6 and crosses the y-axis at (0, −12). Work out the x-intercepts and the y-intercept of y = −f(x).
(a)x = 2, x = −6; y-intercept (0, 12)
(b)x = 2, x = −6; y-intercept (0, −12)
(c)x = −2, x = 6; y-intercept (0, −12)
(d)x = −2, x = 6; y-intercept (0, 12)
3.Write down the coordinates of the point where the line y = 2x + 4 crosses the y-axis.
y = 2x + 4
(a)(4, 0)
(b)(−2, 0)
(c)(0, 2)
(d)(0, 4)
4.Line L has equation y = 3x + 1. Which of these lines is perpendicular to L?
y = 3x + 1
(a)y = (1/3)x + 2
(b)y = −(1/3)x + 2
(c)y = −3x + 2
(d)y = 3x − 4
5.The graph of y = sin x is reflected in the x-axis to give the graph of y = g(x). Work out the value of g(90), where x is measured in degrees.
y = sin(x)
(a)−1
(b)1
(c)−0.5
(d)0
6.A tram sets off from a stop. Its velocity-time graph rises in a straight line from 0 m/s to 12 m/s over the first 8 seconds, then stays constant at 12 m/s for a further 10 seconds. Work out the total distance the tram travels in these 18 seconds, using the area under the graph.
(a)120 m
(b)216 m
(c)108 m
(d)168 m
7.The nth term of a sequence is n² + 4n. Work out the term number, n, for which the term equals 45.
(a)11
(b)5
(c)7
(d)9
8.Make x the subject of the formula y = 2x − 9.
y = 2x − 9
(a)x = (y + 9) / 2
(b)x = (y − 9) / 2
(c)x = 2(y + 9)
(d)x = y / 2 + 9
9.A graph passes through the point (0, 1). As x increases through positive values, the graph rises more and more steeply, and as x decreases through negative values, the graph gets closer and closer to the x-axis without ever reaching it. Which of these could be the equation of the graph?
(a)y = 2ˣ
(b)y = x² + 1
(c)y = x³ + 1
(d)y = 1 − x²
10.A student claims: 'For every positive integer n, n² + n + 1 is a prime number.' Which value of n shows that this claim is false?
(a)n = 3
(b)n = 1
(c)n = 4
(d)n = 2
11.A circle has centre (0, 0) and equation x² + y² = 3721. The point (11, 60) lies on the circle. One of these is the gradient of the tangent to the circle at (11, 60). Work out which one.
(a)11/60
(b)−60/11
(c)60/11
(d)−11/60
12.Two students each use the trapezium rule to estimate the area under the same curve between x = 0 and x = 8. Student A uses 4 strips of width 2. Student B uses 8 strips of width 1. Which estimate is more likely to be closer to the true area, and why?
(a)Student A's — fewer strips means fewer rounding errors.
(b)Student B's — narrower strips fit the curve more closely.
(c)They are always the same; the trapezium rule is exact.
(d)Student A's — wider strips give a better average height.
13.The area of a circle is given by the formula A = πr², where r is the radius. Rearrange the formula to make r the subject.
(a)r = A/π
(b)r = √A/π
(c)r = √(A/π)
(d)r = (A/π)²
14.Work out the coordinates of the point where the graph of y = 2x − 6 crosses the x-axis.
y = 2x − 6
(a)(−3, 0)
(b)(6, 0)
(c)(0, −6)
(d)(3, 0)
15.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.
(a)5n + 2
(b)5n + 12
(c)5n + 7
(d)7n + 5

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