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Either paper 1 mark
Here is a circle with centre \(O\).
State the mathematical name of the line \(OA\).
Show answer
radiusIt is radius, because it runs from the centre to the circumference.
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Either paper 1 mark
A circular clock face on a station wall has a diameter of \(48\) cm.
Work out the radius of the clock face.
Show answer
\(24\ \text{cm}\)The diameter goes right across the circle through the centre, so it is twice the radius.
\(\text{radius} = 48 \div 2 = 24\) cm
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Either paper 1 mark
Nadia measures the circular trampoline in her garden. The distance from the centre \(O\) to the edge is \(11\) cm.
Find the diameter of the trampoline.
Show answer
\(22\ \text{cm}\)\(OA\) runs from the centre to the circumference, so it is a radius.
The diameter is made of two radii laid end to end:
\(\text{diameter} = 2 \times 11 = 22\) cm
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Either paper 2 marks
Here is a description of one part of a circle.
> The part that goes touching the circle at exactly one point.
Write down its mathematical name, and explain how it differs from a chord.
Show answer
tangent — a chord cuts across and meets the circle twiceThe part that goes touching the circle at exactly one point is the tangent.
It is not a chord because a chord cuts across and meets the circle twice.
- B1the part is the tangent
- C1explanation: a chord cuts across and meets the circle twice
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Either paper 3 marksHere is a circle with centre \(C\). \(W\), \(X\) and \(Y\) are points on the circle. \(WY\) is a straight line. Tick one box for each statement.
True False \(WY\) is a diameter. \(WX\) is a chord. The shaded section is a sector. Arc \(XY\) is part of the circumference. Show answer
WY is a diameter: True; WX is a chord: True; the shaded section is a sector: True; arc XY is part of the circumference: True\(WY\) is a diameter: True. A diameter must pass through the centre, and it passes through the centre C.
\(WX\) is a chord: True. W and X both lie on the circle, so WX is a chord.
The shaded section is a sector: True. The shaded region is bounded by two radii and an arc, so it is a sector, so the statement is true.
Arc \(XY\) is part of the circumference: True. An arc is any part of the way round the edge.
- B1at least two of the four rows ticked correctly
- B1at least three of the four rows ticked correctly
- B1all four verdicts correct: True, True, True, True
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Either paper 1 mark
Which of these parts of a circle is a curve?
Circle your answer.
diameter centre arc radius
Show answer
arcThe arc is a curve: it is a piece of the edge of the circle.
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Either paper 1 markIsla adds labels to this diagram of a circle with centre \(O\).
Explain why one of the labels is wrong.Line Isla's label \(AB\) diameter \(OC\) chord \(DE\) chord the line touching the circle at \(F\) tangent Show answer
The line \(OC\) is labelled "chord" but it starts at the centre O; a chord has both ends on the circumference.A radius joins the centre to a point on the circumference. A diameter joins two points on the circumference and passes through the centre. A chord joins two points on the circumference. A tangent touches the circle at exactly one point.
Checking each line in the diagram against these: \(AB\) has both ends on the circle and passes through \(O\), so it is a diameter. \(OC\) runs from the centre \(O\) to the circle, so it is a radius. \(DE\) has both ends on the circle and misses \(O\), so it is a chord. The line at \(F\) meets the circle at one point only, so it is a tangent.
Comparing these with the table, Isla's label for \(OC\) is the one that does not match: it is a radius, not a chord.
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Either paper 2 marks
Here is a circle with centre \(O\). The shaded region is bounded by two radii and the arc between them.
The angle at the centre is \(135^\circ\).
What fraction of the whole circle is shaded? Give your answer in its simplest form.
Show answer
\(\frac{3}{8}\)The shaded region is a sector — bounded by two radii and an arc.
A full turn is \(360^\circ\), so the sector is
\(\dfrac{ 135 }{360} = \frac{3}{8}\)
of the whole circle.
- M1sector angle over a full turn, \(\dfrac{ 135 }{360}\)
- A1simplified to \(\frac{3}{8}\)
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Either paper 3 marks
\(A\) and \(B\) are points on a circle with centre \(C\).
\(B\) could be in any other position on the circle that still makes a triangle \(ABC\). For each statement, tick one box: definitely true, might be true or cannot be true.
(a)Triangle ABC is equilateral.
(b)AB is longer than the radius of the circle.
(c)Triangle ABC has a right angle.
Show answer
(a) Might be true
(b) Might be true
(c) Might be trueMight be true, because CA = CB always, but AB = CA only for two positions of B (one each side of A, where the angle at C is 60 degrees), so it can happen but need not.
Might be true, because AB is shorter than the radius when B is close to A and longer when B is far from A.
Might be true, because the angle at C is 90 degrees for two positions of B (one each side of A), but B can be elsewhere.
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Either paper 1 mark
An arc is drawn on a circle. Which statement is correct?
Tick one box.
☐ The arc must be longer than the radius.
☐ The arc must be equal in length to the radius.
☐ The arc must be shorter than the radius.
☐ The arc could be longer than, equal in length to or shorter than the radius.
Show answer
The arc could be longer than, equal in length to or shorter than the radius.Picture the extreme cases and test each statement against them.
A very short arc is shorter than the radius, and an arc that goes most of the way round is much longer than the radius, so the arc can be shorter than, equal to or longer than it.
So the correct statement is: The arc could be longer than, equal in length to or shorter than the radius.