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 circle has centre (0, 0) and equation x² + y² = 50. Work out the radius of the circle, giving your answer as a surd in its simplest form.
(a)50
(b)25
(c)25√2
(d)5√2
2.Which expression is equivalent to 3(2x − 5) + 4x?
(a)10x + 15
(b)6x − 15
(c)10x − 15
(d)10x − 5
3.Solve 2x² = 18.
(a)x = 9 or x = −9
(b)x = 4 or x = −4
(c)x = 6 or x = −6
(d)x = 3 or x = −3
4.Solve (2x + 1)/3 = 5
(a)7
(b)14
(c)8
(d)2
5.The area under a speed-time graph between t = 0 and t = 6 seconds is estimated using three strips of equal width, using the speeds, in m/s, at t = 0, 2, 4 and 6: 0, 5, 9 and 12. Using the trapezium rule with these three trapezia, estimate the distance travelled.
(a)28 m
(b)80 m
(c)52 m
(d)40 m
6.Expand and simplify 4(2x − 1) − 3(x + 2) − 5x
(a)−10
(b)5x − 10
(c)2
(d)−7
7.Isla says that the lines y = 2x + 1 and y = −2x + 3 are parallel. Write down the statement that gives the correct answer for the correct reason.
y = 2x + 1y = -2x + 3
(a)Yes, because the gradients 2 and −2 add to 0
(b)No, because their gradients are 2 and −2
(c)Yes, because both gradients have size 2
(d)No, because their y-intercepts are 1 and 3
8.A company's cost, in £, for producing x items is shown on a graph. The tangent to the curve at x = 50 passes through (30, 400) and (70, 800). Interpret the gradient of this tangent in the context of the company's costs.
(a)The cost decreases by about £10 per extra item
(b)The cost increases by about £400 per extra item
(c)The cost increases by about £0.10 per extra item
(d)The cost increases by about £10 per extra item
9.A car park charges a £4 fixed fee plus £3 for each hour. Kofi has exactly £25 to spend on parking. Using the inequality 4 + 3h ≤ 25, work out the greatest number of whole hours, h, he can park for.
(a)7
(b)8
(c)6
(d)9
10.The solution set of a quadratic inequality is {x : x ≤ −3} ∪ {x : x ≥ 5}. Which of these inequalities has this solution set?
(a)x² − 8x + 15 ≥ 0
(b)x² + 2x − 15 ≥ 0
(c)x² − 2x − 15 ≥ 0
(d)x² − 2x − 15 ≤ 0
11.A rope of length L metres is cut into 6 equal pieces, and 4 metres is then removed from one piece. Write an expression, in metres, for the length of that piece after the cut.
(a)(L − 4)/6
(b)L/6 + 4
(c)4 − L/6
(d)L/6 − 4
12.By completing the square, find the turning point of the curve y = x² − 10x + 30.
y = x² − 10x + 30
(a)x = 10, y = −70
(b)x = 5, y = −5
(c)x = 5, y = 5
(d)x = −5, y = 5
13.A tap fills a tank at a varying rate. A graph shows the rate of flow, in litres per minute, against time, in minutes. What does the area under this graph represent?
(a)The rate at which the flow rate changes, in litres/min².
(b)The total volume of water, in litres, that has flowed in.
(c)The average rate of flow, in litres per minute.
(d)The total time taken to fill the tank, in minutes.
14.a = 2 and b = 5. Work out the value of a²b.
(a)9
(b)20
(c)100
(d)50
15.A student is asked whether the lines y = (2/5)x − 1 and 5y = −2x + 15 are perpendicular. The student answers: "Yes, because when I rearrange the second equation I get y = −(2/5)x + 3, and 2/5 times −2/5 is negative." Which of these is a correct comment on the student's reasoning?
y = -2x + 15
(a)Wrong — the rearrangement is incorrect.
(b)Right — 2/5 and −2/5 are negatives of each other.
(c)Wrong — the product is −4/25, not −1.
(d)Right — a negative product always means perpendicular.

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