11 (a) Q P NOT TO SCALE x° O 3 In the circle, centre O, the length of the minor arc PQis of the length of the major arc PQ. 7 Show that x = 108. [3] (cid:300)(cid:209)(cid:265)(cid:191)(cid:288)(cid:179)(cid:237)(cid:203)(cid:241)(cid:209)(cid:257)(cid:205)(cid:290)(cid:211)(cid:270)(cid:197)(cid:290)(cid:215) © UCLES 2024 (cid:300)(cid:282)(cid:278)(cid:226)(cid:204)(cid:288)(cid:208)(cid:270)(cid:231)(cid:253)(cid:262)(cid:194)(cid:278)(cid:212)(cid:185)(cid:266)(cid:208)(cid:258) 0580/43/M/J/24 (cid:293)(cid:229)(cid:245)(cid:277)(cid:245)(cid:213)(cid:261)(cid:245)(cid:213)(cid:245)(cid:261)(cid:213)(cid:245)(cid:261)(cid:293)(cid:213)(cid:277)(cid:213) M SIHT NI ETIRW TON OD NIGRAM SIHT NI ETIRW TON OD NIGRAM SIHT NI ETIRW TON OD NIGRAM SIHT NI ETIRW TON OD NIGRAM SIHT NI ETIRW TON OD * 0019655323423 * 23 (cid:44)(cid:1)(cid:1)(cid:2)(cid:10)(cid:7)(cid:6)(cid:6)(cid:4)(cid:3)(cid:4)(cid:5)(cid:3)(cid:4)(cid:44) (b) A NOT TO SCALE r y° B O The diagram shows a sector , OAB, of a circle with centre O and radius r. The area of triangle OAB is half the area of the sector . Angle AOB = y° and is obtuse. (i) Show that 360siny = ry . [2] (ii) Complete the table, giving your answers correct to two decimal places. y 360siny ry 108.4 341.60 340.55 108.5 341.40 340.86 108.6 341.20 108.7 [3] (iii) Complete the statement. The value of y, correct to one decimal place, that satisfies the equation 360siny = ry is ....................................... . [1] (cid:300)(cid:211)(cid:265)(cid:191)(cid:288)(cid:179)(cid:237)(cid:203)(cid:241)(cid:209)(cid:257)(cid:205)(cid:290)(cid:211)(cid:272)(cid:197)(cid:290)(cid:215) © UCLES 2024 (cid:300)(cid:282)(cid:277)(cid:225)(cid:196)(cid:298)(cid:212)(cid:286)(cid:210)(cid:251)(cid:251)(cid:263)(cid:194)(cid:236)(cid:285)(cid:266)(cid:224)(cid:258) 0580/43/M/J/24 (cid:293)(cid:229)(cid:261)(cid:213)(cid:181)(cid:181)(cid:293)(cid:277)(cid:197)(cid:261)(cid:213)(cid:213)(cid:245)(cid:293)(cid:261)(cid:277)(cid:261)(cid:213) NIGRAM SIHT NI ETIRW TON OD NIGRAM SIHT NI ETIRW TON OD NIGRAM SIHT NI ETIRW TON OD NIGRAM SIHT NI ETIRW TON OD NIGRAM SIHT NI ETIRW TON OD * 0019655323424 * 24 (cid:44)(cid:1)(cid:1)(cid:2)(cid:10)(cid:7)(cid:6)(cid:6)(cid:4)(cid:3)(cid:4)(cid:5)(cid:3)(cid:5)(cid:44) BLANK PAGE Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. Cambridge Assessment International Education is part of Cambridge Assessment. Cambridge Assessment is the brand name of the University of Cambridge Local Examinations Syndicate (UCLES), which is a department of the University of Cambridge. (cid:300)(cid:209)(cid:265)(cid:191)(cid:288)(cid:179)(cid:237)(cid:203)(cid:241)(cid:209)(cid:257)(cid:205)(cid:290)(cid:209)(cid:270)(cid:197)(cid:292)(cid:215) © UCLES 2024 (cid:300)(cid:282)(cid:277)(cid:228)(cid:196)(cid:292)(cid:226)(cid:299)(cid:229)(cid:245)(cid:244)(cid:256)(cid:292)(cid:264)(cid:191)(cid:282)(cid:216)(cid:258) 0580/43/M/J/24 (cid:293)(cid:277)(cid:213)(cid:213)(cid:245)(cid:181)(cid:293)(cid:181)(cid:229)(cid:229)(cid:229)(cid:213)(cid:181)(cid:293)(cid:229)(cid:277)(cid:277)(cid:213) NIGRAM SIHT NI ETIRW TON OD NIGRAM SIHT NI ETIRW TON OD NIGRAM SIHT NI ETIRW TON OD NIGRAM SIHT NI ETIRW TON OD NIGRAM SIHT NI ETIRW TON OD