Circle theorems II Notes and examples: past paper questions

Real questions on circle theorems ii notes and examples

The newest 8 of 8 written questions. Open one to see it on the real paper.

1. 4024/11 · October/November 2024 · Q15[4]
   15 A sector of a circle with angle $60^{\circ }$ has arc length $4\pi$ cm. Find the area of the sector. Give your answer, as simply as possible, in terms of $\pi$. .................................................... ${\text{cm}}^2$See it on the paper →
2. 4024/22 · October/November 2023 · Q2b[4]
   [Diagram: A circle with centre $O$. Points $A,B,C,D$ are on the circumference. $AB$ is a diameter. Angle $BAC$ is marked as $24^{\circ }$. Lines connect $A$ to $C$, $A$ to $D$, $B$ to $C$, $C$ to $D$.] $A,B,C$ and $D$ are points on the circle, centre $O$. $AB$ is a diameter of the circle. Angle $BAC=24^{\circ }$. Find...See it on the paper →
3. 4024/11 · October/November 2022 · Q23a[3]
   [Volume of a cone = $\frac{1}{3}\pi r^{2}h$, curved surface area of a cone = $\pi rl$] [Surface area of a sphere = $4\pi r^2$] A solid cone has radius $y$ cm. The slant height of the cone is $25\%$ larger than the radius of the cone. A solid sphere has radius $R$ cm. The surface area of the sphere is equal to the **...See it on the paper →
4. 4024/12 · May/June 2022 · Q23[2]
   23 [Diagram: A major sector of a circle with centre $O$. The reflex angle at the centre is shown, with the non-reflex angle marked as $80^{\circ }$. The text "NOT TO SCALE" is present.] The diagram shows the major sector of a circle with centre $O$ and radius $3\text{ cm}$. Calculate the area of this sector. Give your an...See it on the paper →
5. 4024/12 · May/June 2021 · Q15b[1]

   1-mark question — its maths and diagrams are best seen on the paper.

   See it on the paper →
6. 4024/22 · May/June 2021 · Q10a[3]
   10 (a) [Diagram: A circle with centre $O$. Points $A$, $B$, and $C$ are on the circumference. Lines $OA$, $OB$, $AB$, $AC$, and $BC$ are drawn. A line $BD$ extends from $B$ such that $O$, $B$, and $D$ are collinear. The angle $ABD$ is marked as $130^{\circ }$. The diagram is labelled "NOT TO SCALE".] $A$, $B$ and $C$ are...See it on the paper →
7. 4024/21 · May/June 2020 · Q8a(i)[2]
   A display notice is made by removing a sector of a circle from a larger sector. Both sectors have an angle of $110^{\circ }$. The radii of the sectors are $80$ cm and $45$ cm. [Diagram: A shaded annular sector with outer radius 80, inner radius 45, and central angle 110°. The outer arc is labeled $L$.] (i) Calculate arc l...See it on the paper →
8. 4024/12 · May/June 2019 · Q23[4]

   4-mark “Find” question — its maths and diagrams are best seen on the paper.

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What examiners said

This question required candidates to use circle theorems to find an angle and to give geometrical reasons for their answer. Only a quarter of the candidates gained full marks on this question. Many candidates earned partial marks for either giving the required angle as 114° from a correct method or recognising that angle ACB was 90°. Some candidates arrived at an answer of 114° but did so by incor...

— Examiner report, October/November 2023, 4024/22 Q2(b) (Cambridge)

A few candidates were able to show the correct expression for y. A large majority were unable to 25 25 write a correct expression for the slant height of the cone. Errors included y + and y. 100 100 Some used the formula for the volume of the cone instead of the surface area of the sphere and some missed out the area of the base of the cone when writing their expression for its total surface area....

— Examiner report, October/November 2022, 4024/11 Q23(a) (Cambridge)

Many candidates knew the formula for the area of a sector. Some found the area of the minor sector using the 80° given in the question rather than subtracting this from 360° to find the major sector angle. Arithmetic errors in 360 – 80 or in cancelling the fraction were sometimes seen. Some candidates worked out the area of the whole circle and others used the formula for the arc length rather tha...

— Examiner report, May/June 2022, 4024/12 Q23 (Cambridge)