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.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
2.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)
3.A circle has centre (0, 0) and equation x² + y² = 64. Write down the radius of the circle.
(a)64
(b)8
(c)16
(d)32
4.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
5.There are 50 adults on a coach to the Lake District. Every adult is either a man or a woman. There are 10 more men than women. Work out the number of men.
(a)20
(b)40
(c)35
(d)30
6.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.
(a)8n − 1
(b)8n + 15
(c)8n + 7
(d)7n + 8
7.The 2nd term of a geometric sequence is 6 and the 4th term is 24. Given that all the terms of the sequence are positive, work out the common ratio.
(a)−2
(b)18
(c)2
(d)4
8.The solution set of an inequality is described as: x is less than −3, or x is greater than or equal to 1. Write this solution set using set notation.
(a){x : x < −3} ∪ {x : x ≥ 1}
(b){x : −3 < x ≤ 1}
(c){x : x > −3} ∪ {x : x ≤ 1}
(d){x : x ≤ −3} ∪ {x : x > 1}
9.x = 5. Work out the value of 3x² − 4.
(a)221
(b)75
(c)71
(d)3
10.The area of a triangle is given by the formula A = bh/2, where b is the base and h is the height. Make h the subject of the formula.
(a)h = b/(2A)
(b)h = 2A/b
(c)h = A/(2b)
(d)h = 2Ab
11.Work out the coordinates of the reflection of (6, −3) in the y-axis.
(a)(−6, −3)
(b)(6, −3)
(c)(−6, 3)
(d)(6, 3)
12.A plumber charges a £40 call-out fee plus £25 for each hour worked. The total charge, £C, for a job lasting h hours is given by C = 40 + 25h. Work out the charge for a job lasting 3 hours, and name what kind of statement C = 40 + 25h is.
(a)£65, and C = 40 + 25h is an expression
(b)£115, and C = 40 + 25h is a formula
(c)£195, and C = 40 + 25h is a formula
(d)£115, and C = 40 + 25h is an expression
13.A ribbon of length L metres is cut into 5 equal pieces, and then 3 metres is removed from one piece. Write down an expression, in metres, for the length of that piece after 3 metres is removed.
(a)5/L − 3
(b)(L − 3)/5
(c)L/5 − 3
(d)L − 3/5
14.A student is asked whether 3(x − 4) = 3x − 4 is an identity. Which statement gives the correct verdict and reason?
(a)It is an identity, because both sides begin with the term 3x, so they must be equivalent.
(b)It is not even an ordinary equation with a solution: expanding the left-hand side gives 3x − 12, and 3x − 12 = 3x − 4 would require −12 = −4, which is never true.
(c)It is not an identity, because the student forgot to multiply the 4 by 3 on both sides of the equation.
(d)It is not an identity, because the student needs to substitute a specific value of x before comparing the two sides.
15.The first five terms of a quadratic sequence are 5, 8, 13, 20, 29. Work out the next term in the sequence.
(a)38
(b)40
(c)32
(d)39

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