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 straight line has equation y = 4 − 3x. Work out the gradient of the line.
(a)4
(b)−4
(c)3
(d)−3
2.A taxi firm charges a fixed fee of £3.50 plus £2.20 per mile. Work out the total cost of a journey of 6 miles.
(a)£13.20
(b)£15.50
(c)£34.20
(d)£16.70
3.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.
(a)2
(b)−18
(c)−6
(d)−2
4.Two numbers have a sum of 45. The larger number is 9 more than the smaller number. Form an equation using n for the smaller number, and solve it to find the larger number.
(a)27
(b)22.5
(c)18
(d)36
5.A cyclist's speed-time graph is described as follows: speed increases steadily from 0 m/s to 8 m/s over the first 4 seconds, stays constant at 8 m/s for the next 6 seconds, then decreases steadily to 0 m/s over the final 2 seconds. Work out the total distance travelled.
(a)64 m
(b)96 m
(c)72 m
(d)24 m
6.A graph has equation y = x² − 6x + 5. A student says its turning point has x-coordinate 6, because that's the coefficient of x. Which statement corrects the student's mistake?
y = x² − 6x + 5
(a)The student is correct, because the turning point's x-coordinate always equals the coefficient of x.
(b)The turning point has x-coordinate −6, because the sign of the coefficient must be reversed.
(c)The turning point has x-coordinate 5, because that is the larger of the equation's two roots.
(d)The roots of x² − 6x + 5 = 0 are x = 1 and x = 5 (since it factorises to (x − 1)(x − 5)), so by symmetry the turning point has x-coordinate 3, not 6.
7.Tom is asked to classify the statement 5(2x − 3) = 10x − 15. Which statement about it is correct?
(a)An equation, since it has an equals sign and unknown x.
(b)An identity, since both sides are equal for every x.
(c)A formula, since it relates two different quantities.
(d)An inequality, since the sides are equal sometimes.
8.Work out the gradient of the straight line with equation 2x + y = 8.
(a)−1/2
(b)8
(c)2
(d)−2
9.An exponential model has equation y = A × bˣ, where b > 1. Its graph passes through the points (1, 135) and (2, 405). Work out the value of A.
(a)45
(b)1
(c)135
(d)3
10.Simplify fully: (x + 2)/(3x) × 6x²/(x² − 4)
(a)2/(x − 2)
(b)2x/(x + 2)
(c)2x²/(x − 2)
(d)2x/(x − 2)
11.Describe a sequence of two transformations that maps the graph of y = x² onto the graph of y = −(x − 5)².
y = x²
(a)Reflect in the y-axis, then translate +5 in x.
(b)Translate +5 in x, then reflect in the x-axis.
(c)Translate −5 in x, then reflect in the x-axis.
(d)Translate +5 in y, then reflect in the x-axis.
12.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.
(a)(3, −4)
(b)(−4, 3)
(c)(8, 3)
(d)(−4, −5)
13.A cycle route is 84 km long. Freya sets off along it at a steady 14 km/h. Write down the function for the distance y, in kilometres, that is still to be cycled after x hours.
(a)y = 84 + 14x
(b)y = 84 − 14x
(c)y = 14 − 84x
(d)y = 14x − 84
14.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
15.Expand and simplify 4(2x − 1) − 3(x + 2) − 5x
(a)−10
(b)5x − 10
(c)2
(d)−7

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