Pearson Edexcel International GCSE in Mathematics (Specification A) · 4MA1 · Free · no account needed
Circles, Arcs & Sectors — exam questions
10 original Incandio exam-style questions on circles, Arcs & Sectors, 26 marks, about 31 minutes of writing. Each one carries the command word, the tariff and the specification statement it assesses, exactly as a paper presents them. This is an original Incandio practice question, written to reflect the structure and demands of the qualification. It is not an official Pearson Edexcel past-paper question.
This is the practice set for Circles, Arcs & Sectors — the module that teaches it. Read the module first if the idea is new; come here when you want to find out whether you can turn it into marks. Completely free, no account needed to read.
What these questions ask of you
6 command words run through this set, and on Pearson Edexcel International GCSE Mathematics A each one means something precise. Answering the wrong command is the commonest way a candidate who understands the module still loses the mark.
- Write down (1–2 marks)
- a value that needs no working — read off, recalled or stated
- Calculate (1–5 marks)
- a numerical answer obtained by calculation
- Work out (1–5 marks)
- a calculated result, with the working that produced it
- Explain why (1–2 marks)
- one short justification — mathematics almost never asks for extended explanation
- Find (1–5 marks)
- a value or expression obtained by a method the learner chooses
- Show that (2–5 marks)
- every step of a derivation to a value that is already printed in the question Misread as: stating the printed answer again instead of deriving it
Assessed on Paper 1 and Paper 2.
Where these sit in the specification
Pearson Edexcel International GCSE Mathematics A (4MA1) — statement 4.9. Incandio is aligned to this specification; it is not published by, endorsed by or affiliated with Pearson, and it reproduces none of Pearson's wording.
The 10 questions
Answer them on paper, then open the module's exam practice to have them marked. The mark scheme, the accepted and rejected answers and the annotated model answer are in Incandio and are not printed here — an answer beside its question is not practice.
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(1)Write down
A circle has a radius of 5 cm. Write down its circumference in terms of pi.
(Total for Question 1 = 1 mark)
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(2)Calculate
A circle has a diameter of 12 cm. Calculate its area, giving your answer to 1 decimal place.
area = ............................ cm2
(Total for Question 2 = 2 marks)
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(2)Work out
A quarter circle has a radius of 14 cm. Work out the length of its curved edge, to 1 decimal place.
length of its curved edge = ............................ cm
(Total for Question 3 = 2 marks)
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(1)Explain why
Explain why the perimeter of a sector is not the same as the length of its arc.
(Total for Question 4 = 1 mark)
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(3)Find
A sector of a circle of radius 9 cm has an angle of 72° at the centre. Find its area, to 1 decimal place.
area = ............................ cm2
(Total for Question 5 = 3 marks)
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(3)Show that
A sector has a radius of 6 cm and an angle of 60° at the centre. Show that its perimeter is (2π + 12) cm.
(Total for Question 6 = 3 marks)
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(3)Calculate
Calculate the total area of the window, to 2 decimal places.
A window is made from a rectangle of width 1.2 m and height 2 m, with a semicircle of the same width sitting on top of it.
total area of the window = ............................ m2
(Total for Question 7 = 3 marks)
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(2)Work out
A semicircular plate has a straight edge of 20 cm. Work out its area in terms of pi.
(Total for Question 8 = 2 marks)
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(4)Find
The arc of a sector is 33 cm long and the radius of the circle is 15 cm. Find the angle of the sector, to the nearest degree.
angle of the sector = ............................
(Total for Question 9 = 4 marks)
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(5)Work out
A sector of a circle has radius 9 cm and an angle of 140° at the centre. Work out the perimeter of the sector.
perimeter = ............................ cm
(Total for Question 10 = 5 marks)
Have them marked, then defend the answer
Practice tells you the mark; teaching it back tells you whether you understand it. On Incandio a topic counts as mastered only once you have taught it and defended it.
- Mark these questions — 10 questions, marked on Incandio against the authored scheme, with the mistake you actually made named.
- Teach it — explain circles, Arcs & Sectors to Ember, an AI pupil who does not have it yet and asks the awkward question.
- Defend it — argue it against Archimedes over three rounds, marked against descriptors you can read first.
Completely free. No subscriptions, no paywalls, no account needed to start.
Back to the module
- Circles, Arcs & Sectors — Circumference and area, then the fraction-of-a-circle thinking that turns arcs and sectors into one idea instead of four formulas.
- All of Incandio Mathematics · Incandio Exam Practice