Pearson Edexcel International GCSE in Mathematics (Specification A) · 4MA1 · Free · no account needed
Circle Properties & Tangents — exam questions
9 original Incandio exam-style questions on circle Properties & Tangents, 21 marks, about 25 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 Circle Properties & Tangents — 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
7 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
- Give a reason for your answer (1–3 marks)
- the geometric or statistical reason NAMED precisely — the mark scheme demands the terminology Misread as: describing what you did instead of naming the property that justifies it
- 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 4.6. 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 9 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
In Figure 1 the line through T is a tangent to the circle, and O is the centre. Write down the size of angle OTP.
Diagram NOT accurately drawn
Figure 1 size of angle OTP = ............................
(Total for Question 1 = 1 mark)
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(2)Work out
In Figure 2, A and B are points on a circle with centre O. Work out the size of angle AOB.
Diagram NOT accurately drawn
Figure 2 size of angle AOB = ............................
(Total for Question 2 = 2 marks)
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(2)Calculate
In Figure 3, PT is a tangent to the circle of centre O, touching at T. Calculate the length of OP.
Diagram NOT accurately drawn
Figure 3 length of OP = ............................ cm
(Total for Question 3 = 2 marks)
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(1)Explain why
Two tangents are drawn to the same circle from a point P outside it, touching at A and at B. Explain why PA and PB must be equal in length.
(Total for Question 4 = 1 mark)
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(2)Give a reason for your answer
In Figure 4, M is the midpoint of the chord CD in a circle with centre O. State the size of angle OMD and give a reason for your answer.
Diagram NOT accurately drawn
Figure 4 (Total for Question 5 = 2 marks)
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(3)Find
A chord of length 16 cm is drawn in a circle of radius 10 cm. Find the perpendicular distance from the centre of the circle to the chord.
perpendicular distance = ............................ cm
(Total for Question 6 = 3 marks)
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(3)Show that
In Figure 5, PA and PB are tangents to the circle with centre O. Show that angle APB is 62°.
Diagram NOT accurately drawn
Figure 5 (Total for Question 7 = 3 marks)
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(3)Work out
Work out the width of the liquid surface in the tank.
A horizontal cylindrical tank has a circular cross-section of radius 25 cm. It is partly filled, and the flat surface of the liquid lies 20 cm below the centre of that circle.
width of the liquid surface = ............................ cm
(Total for Question 8 = 3 marks)
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(4)Find
In Figure 6, QS is a tangent to the circle of centre O, touching at S. Find the shortest distance from Q to the circle.
Diagram NOT accurately drawn
Figure 6 shortest distance = ............................ cm
(Total for Question 9 = 4 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 — 9 questions, marked on Incandio against the authored scheme, with the mistake you actually made named.
- Teach it — explain circle Properties & Tangents to Ember, an AI pupil who does not have it yet and asks the awkward question.
- Defend it — argue it against Ibn al-Haytham 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
- Circle Properties & Tangents — Radii, chords and tangents, and the right angles they secretly generate — the foundation the circle theorems build on.
- All of Incandio Mathematics · Incandio Exam Practice