ECZ 2013 · O-Level Paper 2 · Question 2 — Circle Theorems
Question from ECZ 2013 · O-Level Paper 2 · Question 2
(a) In the diagram below, a circle with centre O passes through the points P, Q, R and S. MRN is a tangent to the circle at R. PR = RQ, PS = SR and PR = 5 cm. Find
(a(i)) angle PRQ,[1]
Verified working — step 1
PQ passes through the centre O, so PQ is a diameter.(a(ii)) angle RSP,[1]
Verified working — step 1
PR = RQ gives arc PR = arc RQ = 90°, and PS = SR gives arc PS = arc SR = 45°.(a(iii)) angle QRM,[1]
Verified working — step 1
MRN is a tangent and RQ a chord.(a(iv)) angle SRN,[2]
Verified working — step 1
MRN is a tangent and SR a chord.(a(v)) the length of PQ correct to 3 decimal places.[2]
Verified working — step 1
Triangle PRQ is right-angled at R with PR = RQ = 5 cm.(b) Express 2ax - 1 - ax - 2 as a single fraction in its simplest form.[3]
Verified working — step 1
Common denominator (x - 1)(x - 2).The full step-by-step working and final answer are included with Premium — checked against ECZ marking standards.
Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.
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