O-LevelMathematicsGeometry4024/22 · Oct/Nov 2022 · Q1010 Marks
(a) [Figure with points A, B, C, D on a circle. AC is diameter. Angles ACD and CAB are 40 degrees] A, B, C and D are points on a circle. AC is a diameter of the circle. ACD = CÂB = 40°.
- (a)(i)Show that triangle ABC is congruent to triangle CDA. Give a reason for each statement you make.[3]
- (a)(ii)Explain why ABCD is a rectangle.[2]
- (b)[Figure with points E, F, G, H on a circle with centre O. Angles EHO = 30 and EFG = 116] E, F, G and H are points on a circle with centre O and radius 6 cm. EHO = 30° and EFG = 116° . Calculate the shaded area.[5]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.
- [3] B2 for two pairs of equal sides/angles with correct reasons or B1 for ∠ABC=∠CDA angle in semicircle or AC is common or for two appropriate pairs with no/incorrect reasons
- [2] M1 for ∠ACB = ∠CAD =50° since ∠ABC = ∠CDA = 90° angle in semicircle OR AB parallel to DC since ∠ACD and ∠CAB are alternate angles A1 for Rectangle because ∠DAB=∠BCD=∠ABC=∠CDA= 90° OR Rectangle because perpendicular parallel sides
- [5] B2 for ∠HOG = 112° soi or B1FT for ∠OHG = 34° soi or ∠HOG = 180 - 2 × their ∠OHG M1 for (their112/360) × π × 6² oe M1 for 1/2 × 6² × sin(their112) oe
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →