Worked solutions for all 28 questions by Acer Academy's Maths team. Answers to 3 s.f., angles to 1 d.p., as the paper instructs.
28 questions · 90 marksUpdated Working is in red; the final answer sits on the answer line, with the marks in brackets.
1
(a)
Simplify the expression.
= 6a − 10a + 15
= −4a + 15
Answer−4a + 15[1]
(b)
Factorise the expression.
c(d − 1) + 1(d − 1)
= (d − 1)(c + 1)
Answer(d − 1)(c + 1)[2]
2
(a)
Express 120 as a product of prime factors, in index form.
Answer2³ × 3 × 5[1]
(b)(i)
Find the HCF of A and B in terms of p, q and r.
A = p × q² × r⁴
B = p² × q × r³
HCF = lowest power of each common prime = p × q × r³
Answerp × q × r³[1]
(ii)
Given that the HCF is 120, find A.
p × q × r³ = 120 = 2³ × 3 × 5
so r = 2
p > q, so p = 5 and q = 3
A = p × q² × r⁴ = 5 × 3² × 2⁴ = 720
Answer A =720[2]
(iii)
Find the LCM of A and B as a product of prime factors.
LCM = highest power of each prime = p² × q² × r⁴ = 5² × 3² × 2⁴
Answer5² × 3² × 2⁴[1]
3
(a)
Find angle BOC, giving a reason.
△OCA is isosceles (OC = OA are radii)
∠AOC = 180° − 16° − 16° = 148°
∠BOC = 148° − 44° = 104°
Angle BOC =104°because
△OCA is isosceles, so ∠AOC = 148°. Hence ∠BOC = 148° − 44° = 104°.
[2]
(b)
Find angle BAC, giving a reason.
△OBA is isosceles (OB = OA are radii)
∠OAB = (180° − 44°) ÷ 2 = 68°
∠BAC = 68° − 16° = 52°
Angle BAC =52°because
△OBA is isosceles, so ∠OAB = 68°. Hence ∠BAC = 68° − 16° = 52°.
[2]
4
Show that the expression has the same value for all x and y.
Answer
= 21x + 14y6x + 4y
= 7(3x + 2y)2(3x + 2y)
= 72
The result is a constant, so the values of x and y do not affect the expression.
[2]
5
Find the two integers added to the list.
There are now 8 integers, so the median is the mean of the 4th and 5th values.
Median = 9 = 9 + 92, so the other new integer is 9.
Range = 7 = 12 − x, so x = 5.
Answer5and9[2]
6
(a)(i)
Write an expression in x for the total time from A to C.
Total time = x18 + x12 = 5x36
Answer5x36hours[1]
(ii)
Find the average speed from A to C.
Average speed = total distancetotal time
= 2x ÷ 5x36
= 14.4
Answer14.4km/h[2]
(b)
Convert 12 km/h to metres per second.
12 km/h = 12 × 1000 m60 × 60 s = 103 m/s
Answer103m/s[1]
7
Find the obtuse angle x.
sin−1(0.9867) = 80.6°
x is obtuse, so x = 180° − 80.6° = 99.4°
Answer x =99.4[1]
8
(a)
Find x, the number of adults who visited both.
n(T ∪ C) = 72 − 12 = 60
Theatre only = x − 4, cinema only = x + 10
60 = (x − 4) + x + (x + 10)
60 = 3x + 6
x = 543 = 18
Answer x =18[2]
(b)
Find n((T ∩ C) ∪ (T ∪ C)′).
n(T ∩ C) = x = 18, n((T ∪ C)′) = 12
18 + 12 = 30
Answer30[1]
(c)
Find the probability that a theatre-goer also visited a cinema.
Visited a theatre = x + (x − 4) = 32
Also visited a cinema = x = 18
P = 1832 = 916
Answer916[1]
Topic and marks for each. The full working is in the PDF.
- Q9Standard form[3]
- Q10Statistics[2]
- Q11Ratio[3]
- Q12Box-and-whisker plots[3]
- Q13Inequalities[3]
- Q14Coordinate geometry and vectors[6]
- Q15Simultaneous equations[3]
- Q16Algebraic fractions[2]
- Q17Percentages and exchange rates[3]
- Q18Circles and Pythagoras[2]
- Q19Probability[3]
- Q20Bearings and trigonometry[5]
- Q21Factorisation[3]
- Q22Equations with fractions[3]
- Q23Indices[3]
- Q24Similar triangles[5]
- Q25Arc length and cones[6]
- Q26Mean and standard deviation[1]
- Q27Variation[3]
- Q28Quadratic graphs[3]
Unlock Q9–28 with full working
All 28 questions with full working, emailed to you as a PDF.
Are these the official SEAB answers?
No. These are Acer Academy's own worked solutions; SEAB does not publish answer keys.
How were the answers rounded?
To 3 significant figures, with angles to 1 decimal place, as the paper instructs.
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Questions from the 2026 GCE O-Level Elementary Mathematics Paper 1 © SEAB / Cambridge. Worked solutions and diagrams: Acer Academy.
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