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.Expand and simplify 2(a + 6) − 2(a − 7)
(a)13
(b)4a − 2
(c)−2
(d)26
2.A geometric sequence has first term 5, and each term after that is 3 times the term before it. Work out the first term of the sequence that is greater than 1000.
(a)405
(b)1215
(c)2187
(d)3645
3.The graph of y = f(x) has a minimum point at (4, −1). Write down the coordinates of the corresponding turning point on the graph of y = −f(x).
(a)(4, 1)
(b)(4, −1)
(c)(−4, 1)
(d)(−4, −1)
4.A plumber charges a call-out fee of £30 plus £25 per hour worked. Work out the total charge for a job that takes 3 hours.
(a)£165
(b)£105
(c)£75
(d)£90
5.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.
(a)7n
(b)12n + 7
(c)7n + 12
(d)7n + 5
6.f(x) = (x + 1)/2. Find f⁻¹(x).
(a)2x − 1
(b)(x − 1)/2
(c)x/2 − 1
(d)2x + 1
7.A region S consists of every point that lies on or above the line y = 2, on or below the line y = x, and on or to the left of the line x = 6. Which of these is the system of inequalities that defines S?
y = x
(a)y ≥ 2, y ≥ x, x ≤ 6
(b)y ≥ 2, y ≤ x, x ≤ 6
(c)y ≤ 2, y ≤ x, x ≤ 6
(d)y ≥ 2, y ≤ x, x ≥ 6
8.Work out the value of 2(x + 2) when x = −5
(a)−3
(b)−1
(c)−6
(d)−8
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.A tank already contains some water and is then filled at a constant rate. After 2 minutes it contains 50 litres in total; after 7 minutes it contains 150 litres in total. Work out the rate at which water is added, in litres per minute.
(a)0.05
(b)20
(c)100
(d)25
11.A car's speed-time graph shows the following: its speed increases steadily from 0 m/s to 20 m/s over the first 10 seconds, then stays constant at 20 m/s for the next 15 seconds. Work out the total distance travelled in the first 25 seconds.
(a)500 m
(b)300 m
(c)200 m
(d)400 m
12.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
13.The simultaneous equations kx + 2y = 4 and 3x + y = 5 have no solution. Work out the value of k.
(a)k = −6
(b)k = 6
(c)k = 2/3
(d)k = 3
14.Solve the inequality 3x + 6 ≤ 0.
(a)x ≤ 2
(b)x ≤ −2
(c)x ≥ −2
(d)x ≤ −18
15.Factorise fully 5x + 5y − 5
(a)5(xy − 1)
(b)5(x + y + 1)
(c)5(x + y − 1)
(d)5(x + y − 5)

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