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 · Non-calculator · 15 questions

MathsUKwww.geekhero.co.uk

1.A phone company works out a monthly bill, £B, using the formula B = 18 + 0.05t, where £18 is the fixed monthly charge and t is the number of extra text messages sent beyond the free allowance, each charged at 5p. Farida's bill for one month is £24.50. Work out the number of extra text messages, t, she sent.
(a)130
(b)13
(c)65
(d)490
2.One solution of the equation x² − (k + 1)x + k = 0 is x = 3. Work out the value of k.
(a)k = 3
(b)k = −3
(c)k = 4
(d)k = 1.5
3.A rectangle is x cm wide and twice as long as it is wide, so its area A cm² is given by A = 2x². Work out A when x = 3.
(a)18 cm²
(b)6 cm²
(c)12 cm²
(d)36 cm²
4.Describe a sequence of two transformations that maps the graph of y = cos x onto the graph of y = cos(x + 90°) − 2.
y = cos(x)
(a)Translate −90° in x, then translate +2 in y.
(b)Translate −90° in x, then translate −2 in y.
(c)Reflect in the x-axis, then translate −90° in x.
(d)Translate +90° in x, then translate −2 in y.
5.A sequence has the position-to-term rule n² − 3, where n is the position number. Work out the difference between the 6th term and the 5th term.
(a)11
(b)−11
(c)1
(d)8
6.A circle has centre (0, 0) and equation x² + y² = 8. Work out the radius of the circle, giving your answer as a surd in its simplest form.
(a)√2
(b)8
(c)4
(d)2√2
7.Point P has coordinates (2, −5). P is reflected in the x-axis to point Q. Write down the coordinates of Q.
(a)(2, −5)
(b)(−2, 5)
(c)(2, 5)
(d)(−2, −5)
8.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
9.Solve the inequality 2(3x − 1) ≥ 4x + 8.
(a)x ≥ 4.5
(b)x ≥ 5
(c)x ≥ 1
(d)x ≥ 20
10.Work out the gradient of the straight line that passes through the points (−1, 5) and (3, −7).
(a)−6
(b)−3
(c)−1/3
(d)3
11.A population of bacteria doubles every 3 hours. It starts at 800. Work out the population after 9 hours.
(a)409,600
(b)8
(c)6,400
(d)3,200
12.Line L has equation y = 2x + 3. Work out the equation of the line perpendicular to L that passes through the point (4, 1), giving your answer in the form x + 2y = c.
y = 2x + 3
(a)x + 2y = 9
(b)x − 2y = 2
(c)x + 2y = 6
(d)x + 2y = −2
13.The simultaneous equations 2x + 3y = 12 and x − y = 1 are given. Work out the value of y.
(a)y = 2
(b)y = 2.2
(c)y = 3
(d)y = 10
14.Work out the value of m² + 3m when m = −2
(a)−10
(b)10
(c)−14
(d)−2
15.A curve has equation y = x³ − 4x. Work out the coordinates of the point where the curve crosses the y-axis.
y = x
(a)(0, 4)
(b)(4, 0)
(c)(0, 0)
(d)(0, −4)

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