SMKA NAIM LILBANAT KOTA BHARU KELANTAN. SEKOLAH BERPRESTASI TINGGI. Kertas soalan ini mengandungi 7 halaman bercetak.
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1 Name : Frm :. SMKA NAIM LILBANAT 55 KOTA BHARU KELANTAN. SEKOLAH BERPRESTASI TINGGI PEPERIKSAAN PERCUBAAN SPM / ADDITIONAL MATHEMATICS Keras ½ Jam ½ Jam Unuk Kegunaan Pemeriksa Arahan:. This quesin paper cnsiss f hree secins: Secin A, Secin B and Secin C. Salan Markah Penuh JUMLAH A. Answer all quesins in Secin A, an fur quesins frm Secin B and an w quesins frm Secin C.. Wrie ur answers n he paper shees prvided. B C Keras salan ini mengandungi halaman berceak. / / hp:// Markah Diperleh
2 Secin A [ marks] (Answer all quesins. Slve he simulaneus equains and Give ur answers crrec hree decimal places. [5 marks]. (a Skach he graph f sin fr [ marks] B using he same aes, skech a suiable sraigh line find he number f he sluins f he equain sin. [ marks] 9. A curve has a gradien funcin k p wih urning pins (, and (,, where k and p are cnsans. Find (a he value f k and f p, [ marks] equain f curve. [ marks]. Diagram shws f n siries f circle. The al f perimeer f all circle is cm. Given he radius f smalles circle is cm and radius f he bigges circle is cm. The arrangemen f circles frm a arihmeic prgressin. cm cm Find (a he value f n, Diagram [ marks] perimeer f he sih circle in erm f. [ marks] / al perimeer fr he firs si circles in erm f π hp:// [ marks]
3 5. Diagram 5 shws w riangles ABC and ABD. Pin E lies n he sraigh line AD. C E D I is given ha (a A AC Diagram 5, BD Epress in erms f and (i (ii AD BC I is given ha (i (ii m, and k, and m AD and AE and AB k BC EC Hence, find he value f m and f k. B, Epress AEin erms f [ marks] [ marks] [ marks]. The mean f se numbers k, (k+, (k-, and (k+ is. (a Find he value f k Each number in he se is divided b and hen added i. Find (i new mean (ii he new sandard deviain. [ marks] [ marks] / hp://
4 Secin B [ marks] (Answer an fur quesins frm his secin. Use graph paper answer his quesin. Table shws he values f w variables, and, bained frm an eperimen. I is knwn k p ha and are relaed b he equain, where p and k are cnsans Table (a Pl agains b using a scale cm. unis n -ais and cm uni n - ais. Hence, draw he line f bes fi. Use he graph in (a find he value f (i k and p. (ii when =.. [ marks] [ marks]. Diagram shws a par f curve which passes hrugh A (-, ( A (-, ( Diagram - - (a Find he equain f angen a pin A. [ marks] The shaded regin is baunded b -ais, sraigh line and. (i Find he area f he shaded regin.. (ii Find he vlume revluin, in erm f π, when he shaded regin is raed hrugh abu he - ais [ marks] O / hp://
5 9. Sluin b scale drawing is n acceped. Diagram 9 shws a rapeziuem ABCD. Given he equain f sraigh line DC is C(, 9 D O B(k, A(, - Diagram 9 Find, (a (d he value f k he equain f sraigh line AD. crdinaes f D equain f he perpendicular bisecr f AC. [ marks] [ marks] [ marks] [ marks] / hp://
6 . In diagram, OKLM is a secr f circle wih cenre O and radius cm. L 5 M S cm cm K O Rajah Calculae (a MOK, in radian he perimeer, in cm, f he shaded regin. he area, in cm, f he shaded regin. [ marks] [ marks] [ marks]. (a The resul f a surve in an urban area shws he he prbabili f a suden having a mbile phne is k. The mean and variance f n sudens chsen a randm having a mbile phne are and recpecivel. Find he value f n and f k. [5 marks] A grup f wrker are given medical check up. The bld pressure f he wrkers have a nrmal disribuin wih a mean f mmhg.and a sandard deviain f mmhg. Bld pressure ha is mre han 5 mmhg is classified as high bld presure (i A wrker is chsen a randm frm he grup. Calculae he prbabili ha he wrker has a bld pressure beween 5 mmhg and 5 mmhg. (ii I is fund ha wrkers have high bld pressure. Find he al number f wrkers in he grup. [5 marks] / hp://
7 SECTION C [ marks] (Answer an w quesins frm his secin. Diagram shws a quadrilaeral PQRS. cm S R.cm P 5. cm Q Diagram (a Calculae (i he lengh, in cm, f QS (ii PQS Pin Q lies n he QS such ha (i Skech a riangle Q RS (ii Calculae he area, in Q R QR cm, f riangle Q RS [ marks] [ marks]. Table shws he price f fur iems P, Q, R and S in he ear and ear 5. Price inde and weighage fr he ear 5 based n he ear. (a Iems Price n (RM Price n 5 (RM Price inde fr he ear 5 based weighage P.. Q 5.5. R 5. 5 S.. Table Find he value f (i (ii [ marks] Calculae he cmpsie inde f he price f hse iems fr he ear 5 based n he ear. [ marks] / hp://
8 (d The al cs f all iems in he ear is RM 9. Calculae he crrespnding cs f iems in he ear 5. [ marks] The price f iems P and Q are increase b % and he price f iems R and S are increase b 5% fm he ear 5 he ear. Find he cmpsie inde fr he ear based n he ear. [ marks]. Use graph paper answer his quesin. The member f a Naim s Teacher Club plan rganise a picnic. The agree ren bus and van. The renal f a bus is RM 9 and he renal f a van is RM. The renal f he vehicles fr he rip is based n he fllwing cnsrains. I : The al number f vehicles be rened is n mre han 9. II : The number f bus is a ms wice he number f vans. III : The minimum allcain fr he renal f he vehicles are RM (a Wrie hree inequaliies, her han and, which saisf all he abve cnsrain. [ marks] Using a scale f cm vehicle n bh aes, cnsruck and shade he regin R which saisfies all he abve cnsrains. [ marks] Using he graph cnsruced in, find (i he maimum number f van rened if buses are rened. (ii he maimum number f members ha can be accmmdaed in he rened vehicles if a bus can accmmdae 5 passengers and a van can accmmdae passengers. [ marks] 5. A paricle mves in a sraigh line and passes hrugh a fied pin O. Is accelerain, a ms -, given b a, where is he ime, in s, afer passing hrugh O. The iniial velci is ms -. Find (a he minimum velci, in ms -, f he paricle. he ime, in s, a which he paricle in insananeusl a res. he al disance, in m, ravelled b he paricle in he firs secnds. [ marks] [ marks] [ marks] / hp://
9 SEK. MEN. KEB. AGAMA NAIM LILBANAT PEPERIKSAAN PERCUBAAN SPM SKEMA PERMARKAHAN MATEMATIK TAMBAHAN KERTAS NO. SOLUTIONS MARKS TOTAL P = + r -( + (++= r + = r = (( ( r ( ( (( ( =.,. (bh =.,. (bh (a shape f sine curve P ccle fr P maimum = 5 and minimum = - P sraigh line N. f sluins = (a / d k p d hp://
10 9 /, : ( p k : 9, ( p k p and k d ( c : 9, (, ( r ganian (a ( ( l a r n n S n d d T 5( T 5( ( S P 5(a (i BD AB AD (ii AC BA BC hp://
11 5. (i AE mad m m P (ii EC kbc EA AC k BC EA k k AE k ( k m k m k r m k 5 m 5 n (a k k k k k (i New mean (ii, 5,, Sandard deviain. 5 (. New sandard deviain. / hp://
12 (a Bh aes crrec (a leas pling pin Pling all pins crrec line f he bes fi - crrec. (i k k p p gradien.. P (ii., (a ( d d ( d A (, ; d Equain f angen : ( (i Area f he shaded regin: Inegrae ( d ( ( ( ( 5 5 / hp://
13 / (ii Vlume: Inegrae = π ( d = ( =. r. r uni 5 9 (a (d k k m m AB DC ( : AD f equain m AD...( (... D(, Mid-pin AC, 9, Equain bisecr AC: ( P hp://
14 / (a rad MOK MOK MOK cs cm Perimer.5 (. ( sin(.55 ( (. ( Area (a nkq nk and.. k q q 5. n nk (i.9 ( z P z P (ii 5/ ( N N z P z P ii P hp://
15 / (a (ii cm QS i.9.95 ((. cs(5. ( /..9 sin.9 sin 5 PQS sin ( PQS PQS ii (i.9 sin. sin QSR QSR SQR and ( QRQ. 9...(. sin sin 9 cm ( - (. (. ( A Q RS reaf Q R S. cm Q hp://
16 5 (a Q Use I Q, I 5/ ( ( 5( (.5 P5.5 9 P RM95 5 (d I / w P.= Q.=5 R 5.5=.5 S.5=5.5 P I / (a 9 r ` 9 r 9 Draw crrecl all hree sraigh line which invlves and. Regin shaded crrecl (i, 5 (ii Use 5 fr pin in he shaded regin (, : 5( ( / hp://
17 / 5(a d v V minimum, a = min ( ( ms V res, v =, ( ( d s m vd vd disance al hp://
18 / hp://
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