Pearson Edexcel International GCSE in Mathematics (Specification A) · 4MA1 · Free · no account needed
Polygons — exam questions
10 original Incandio exam-style questions on polygons, 27 marks, about 33 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 Polygons — 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
- Work out (1–5 marks)
- a calculated result, with the working that produced it
- Calculate (1–5 marks)
- a numerical answer obtained by calculation
- Explain why (1–2 marks)
- one short justification — mathematics almost never asks for extended explanation
- 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
- Find (1–5 marks)
- a value or expression obtained by a method the learner chooses
Assessed on Paper 1 and Paper 2.
Where these sit in the specification
Pearson Edexcel International GCSE Mathematics A (4MA1) — statement 4.2. 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
Write down the sum of the exterior angles of any polygon.
(Total for Question 1 = 1 mark)
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(2)Work out
Work out the size of each exterior angle of a regular decagon.
(Total for Question 2 = 2 marks)
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(2)Calculate
Calculate the sum of the interior angles of a hexagon.
(Total for Question 3 = 2 marks)
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(1)Explain why
Explain why a regular polygon cannot have an exterior angle of 50°.
(Total for Question 4 = 1 mark)
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(3)Work out
Each interior angle of a regular polygon is 156°. Work out how many sides it has.
(Total for Question 5 = 3 marks)
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(3)Show that
Show that each interior angle of a regular octagon is 135°.
(Total for Question 6 = 3 marks)
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(3)Find
Four of the five interior angles of a pentagon are 100°, 115°, 96° and 121°. Find the fifth angle.
fifth angle = ............................
(Total for Question 7 = 3 marks)
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(3)Work out
The four interior angles of a quadrilateral are in the ratio 2 : 3 : 4 : 6. Work out the largest angle.
largest angle = ............................
(Total for Question 8 = 3 marks)
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(4)Find
A regular hexagon and a regular polygon with n sides sit side by side against a straight line, with one vertex of each meeting the line at the same point. The two interior angles at that point add to 240°. Find n.
(Total for Question 9 = 4 marks)
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(5)Work out
The interior angle of a regular polygon is 156°. Work out the number of sides, and the sum of the interior angles of that polygon.
number of sides and angle sum = ............................
(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 polygons to Ember, an AI pupil who does not have it yet and asks the awkward question.
- Defend it — argue it against Johannes Kepler 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
- Polygons — Interior and exterior angles of any polygon — driven by the one unbreakable fact that exterior angles always total 360°.
- All of Incandio Mathematics · Incandio Exam Practice