SPM MM2 Q&A (Johor)

8/14/2019 SPM MM2 Q&A (Johor)

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144912MatematicsKertas 2Sept. 20082 % am

Nama: ..................................................Tingkatan: 5 ..........................................

JABATAN PELAJARAN NEGERI JOHOR

PEPERIKSAAN PERCUBAAN SPM TINGKAT AN 52008

MATEMATICSKertas 2

Du a jam tiga puluh minit

JANGAN BUKA KERTAS SOALAN IN1 SEHINGGA DIBERITAHU

r Untuk Kegunaan ~en1-1 . Tzrliskan nama du n tingkutan padl1 ruangjnng disediakan.2. Kerta.s soalun ini ndalah dalanlduvihahasa.3 . Soalan dalarn bah as~r Inggeris

mendahului soalrzn yang sepadnn dularnhahasn Afelayu.

4 . C'rrlon riibennrkan menjinvirb kesellrruhanarau .sebahagiim sorrlan sam a nda dnlambahasa hle layu atau bahasa Inggeris.5 . Cmlon dikehendlzki membaca arahrrn.

Jumlah I

Bahagian Soalan Markah MarkahPenuh Di~ero leh


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Fork

11se Find the value of a and of b that satisfy the simultaneous linear equatio ns below :C'arikun nilai a dun b yang memuaskan persamaan linear serentak h erikut:

1- a - 2 b = 635 0 + 6 b = 18 [4 marks]

[4 markah]Answer i J m a p a n :

i Solve the following equation:Selesaikan per.famaa n berikut:

5 m ( m + 2) = 2m + 2 [4 marks]

[4 markah]Answer / Jawapan:


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Forexam~neri

11se In Diagram 2, straight line PQ and straight line RS re parallel.Dalam Rajah 2, garis lzrrus PQ dunRS adalah selari.

i

Diagram 2Rajah 2

FindCarikan(a) the equation of the straight line RS,persamaan garis lurus RS,(b ) the x-intercept of the straight line RS.pintasan-x bagi garis lurus RS .Answer 1Jawapan:

[3 marks][3 markah]

[2 marks][2 markah]


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6 Diagram 3 shows two arcs, PQ and R,T with a common centre, 0 . OQ isdiameter of thc semicircle with centre T. PS = SO = O R = OT = TQ = 7 cm.Given that I H O S = 90" and i P O Q = 120".Rflj!/c~lz mrnunjukknn hr u lrngkok bulatun, P Q dun k S ~ w n g erpu.rut di 0.0 Q nluh diumetcr h17gi .setrriO~~lutanerpii.sut 7: PS ==SO -- OH - OT - TQ .-crtiDiheri bah iw o L!I(US -- 90" df ln 14'OQ = 120".

Diagram 3RNjnh 3

CalculateHiturrgk(1rr( a ) perirneter o f the who lc diagram,perirneter selrlruh rqjuh,( b ) the area, in c m 2,0 f he shaded region.

l ua .~ ,luinrn cm2, km c'asnn ynrrg her lnrekAnswer I . J~rw~pnrr:


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7 (a) Co m plet e the following mathematical statem ents in the answ er space usinsymbol > o r < t o form(i) a true statemen t(ii) a false statementLengkapkan pernyataan-pernyataan ma ~e ma tik erikut d i dalurn ruanganjawapan dengan menggunakan .symbol > atau < untuk m embentuk( i ) pernyataan benar( i i j pernyuraan palsu

(b) Co mb ine the following statements to form a true com pound statement.Statement I : 3 + 6 = 10Statement 11 : 14 is an even num berGab ungk anpe rnyata an berikut unruk membentukpernyaraan gabungan ybenar. Pernyaraan 1 : 3 + 6 = I0Pernyaraan I1 : 14 udaluh nombor genap.

(c) Conclude the premises in the following argument.Premise I : If x is a factor o f 6 then x is a factor of 48Premise 2 : 3 is a factor of 6.Conclusion :

Buar k esimpu lan berdusarkan premis-premis berikut:Premis I : Jika x ialah faktor bagi 6 maka x ialah uktor bagPremis 2 : 3 ialah fakror bagi 6.Kesimpulan : [6 m[6 ma

Answer l Jmvapan :

(c) Conclusion :Kesimpulan :


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SULIT8 Diagram 4 shows 12 labelled cards in two boxes.Rajah 4 menunjukkan 12 keping kad ycmng be rlt~b el i clulam dun ko luk .

Box XKotak XDiagram 4Rajah 4

I I JBox YKotuk Y

Th e card s are chosen at random. The first card is chosen at random from box X andthe second card is chosen at random from box Y.Ka d-ka d tersebut dipilih secara rawuk. K ud pe rta ma dipilih .recara ruwak daripadakotak X dun kad kedua dipilih secara rawak d aripada kolak Y.By listing the outcomes, find the probability thatDenga n menye naraikan kesuduhan , cari kebartmngkuliun ~ L I ~ U W L I(a ) both cards have the same letters,kedua-dua kad mempunyai hurzrfyang soma,(b) at least on e card is labelled with a consonant L or H.

sekurang-kurangnya sekeping kad berlabel dengan huru fkons ona n L atau H.[ 5 murk.>[ 5 niarkuhAnswer l Jawapan :

SULITSMS MUZAFFAR SYAH , MELAKA


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(a) I t is given that the inverse matrix of is[! y ] , indthe value of rnand o f n .Diberi bahawa m atriks songsang bag; (: iulah [i:,cari niloi rnJan nilai n.

(b) Using matrices, calculate the value o f x and o f y that satisfy the followingmatrix equation:Menggunakan kaeduh rnatriks, hitung nilai x dun n ilai y yang nlernuaskanpersarnaan rnatriks berikut:

Answer l Jawapan


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. Diagram 5, sho ws the speed-time graph of an object over a period of t seconds.Rajah 5, rnenunjukkan graf laju-masa bagi suatu objek dalarn tempoh t saat.

Speed (ms-')

Time (s)Masa (s)Diagram 5Rajah 5Calculate,

Hitungkan,(a) the rate of change of speed, in ms-', during the tirst 6 seconds. I

kadar perubahan laju, r n ~ - ~ ,adu 6 soar pertarna.(b) the value oft, f the total distance traveled for the period o f t seconds is 270 m. INilai I , jiku jumlah jarak yang dilalui bagi ternpoh t saat ialah 270 m.[5 mark.^]

[ 5 markah]Answer 1Jawupan :

Furexumrner k

use


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k

1 Diagram 6 shows a solid right prism with a half-cylinder removed from the prism.Th e diameter o f the half-cylinder is 7 cm and P Q = QR = 10 cm .Rajah 6 menunjukkan sebuah pepejal prisma tegak dengun sebuah separuh silinderyang telah dikeluarkan daripada prisma itu. Diam eter separuh silinder itu iuluh 7 cmdun P Q = Q R = 10 cm.

Diagram 6Rajah 6

Calculate the vo lume , in cm3'of the solid.Kira isipadu bongkah tersebut, dalam cm3.Use I Guna ~r-Answer I Jawapan :

[4 marks][4 markah]


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Section BBahagian B[48 marks][48 markah]Answer fo ur questions in this section.Jawab empat soalan dulum buhugiun ini.

(a) Complete Table 1 in the answer space for the equation y = 14 + 3x - 2x2 bywriting down the values o f y when x = -3 and x = 3. [2 marks]Lengkapkan Jadual 1 di ruang jawapan bag; persamaan y = 14 + 3x - 2x2dengan menu1i.s nilai-nilaiy apabila x = -3 dun x = 3 . [2 markuh]

(b ) For this part of the question, use the graph paper provided on page 19. Youmay use a flexible curve ruler.Untuk ceraian soalan ini, gunakan kertas grafy an g di.sediakanpada halaman19. Anda boleh menggunakan pembarisjlexibel.By using a scale of 2 cm to 1 unit on the x-axis and 2 crn to 5 units on th ey -axis, draw the graph ofy = 14 + 3x - 2x2 for -3 5 x 1 . [ 4 murky]Dengan menggunakan skala 2 cm kepada 1 unitpada paksi-x dan 2 crnkepada 5 unit pada paksi-y, lukis gra fy = 14 + 3x - 2x2 bugi nilai x dalamjulat - 3 5 x 5 4. [4 markah]

(c) From your graph, findDaripada graf anda, cari(i ) the value of x when y = -8.

nilai x apabila y = -8.(ii) the value o f y when x = 1.9. Inilai y apabila x = 1.9.

[ 2 marks][2 markah]

(d) Draw a suitable line on your graph to find the values o f x which satisfy theequation 1 1 - - 2x2= 0 for -3 5 x 1 4 . [4 marks]Lukis salu garis lurus yang srsuai pada graf anda untuk mencnri nilai-nilai xyang memuaskan persamaan 1 1 - x - 2x2 = 0 bagi -3 i i . [4 markuh]


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(b) A prism is joined to the solid in Diagram 7(i) at the vertical plane CDEHJN.The combined solid is as shown in Diagram 7(ii). Right angle triangle PQRand DSC is the uniform cross-section of the prism. LQPR = LSDC = 90"DP=CR=SQ=6cmandPQ=3cm.Sebuah prisma tegak dicantumkan kepada pepejal dalam rajah 7(i)padasatah fegak CDEHJN . Pepejal gabungan adalah seperti ditunju kkan dalamrajah 7(ii). Segitiga tepat PQR dun DSC adalah keratan rentas ba gip rism ategak tersebut. LQPR = LSDC = 90, DP = CR = SQ = 6 cm dunPQ = 3 cm.

Diagram 7(ii)Rajah 7(ii)Draw to full scale,Lukis dengan skalapenu h,( i) the elevation of the combined solid on a vertical plane parallel to BC asviewed from Y. [4 marks]

donga kan gabunganp epejal itu pada satah mencancang yang selaridengan BC sebagaimana dilihat dari Y. [4 markah]

(ii) the plan of the combined solid,pelan gabung nn pepejal iru

[ 5 marks )[ 5 markah]

Fo rerutt l rner 'S

.IISt'


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Diagram 9 hhows trapeziums .-llj('D, EFGH and L,/liL drawn on a C


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1449L2MatematicsKertas 2Sept. 2008

JABATAN PELAJARAN NEGERI JOHOR

PEPERIKSAAN PERCUBAAN SPM TAHUN 2008

SKEMAPEMARKAHANMATEMATICS

Kertas 2Du a jam tiga puluh minit


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4 Ildentify L TMO or LOMT

/tar O = 12 or equivalent4 -


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3-- - -~ o a l a n Peraturan Pernarkahan-

I .-8 I (a) I { ( E ,4 (A, A) 1

(b) ' 3+ 6 = 10 or 1 4 is an even number(c) 3 is a factor of 48


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SU L IT 4

Peraturan Pernarkahan-rn= -2'Note:

[ ' 2 ) o r - ') ,aw ardP l

10

,--- 1 '' 4 1 2 1 - 4 I(1n = 2 P 1

iNo t e s :1 I . = [-23) as a fin d answer, award N l2. Do not accept any solutions solved not using m atrices

(a) ! 2 4 - 1 2' 0 -6I

-2I I( 2 4 + 1 2 ) x 6 + - ( 1 2 + 1 8 ) x 6 + - ~ ( t - 1 2 ) x 2 4=2702 2

j Note : Any two areas correct, award K1t = 20 seconds

K2

N 1 5


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SULIT 5

p a i n~

1 I

correctly without any straight segment in the range of -3 5 x 5 4 ,Ignore that are o ut of the range.

-eraturan PernarkahanI- ~ 1 0 x 1 0 ~ 1 53

K 1K 1

I1; = 4 x + 3 K 1The straight line y = 4x + 3 drawn correctly. K I( Judgement: straight line that passes 2 points marks correctly )Values of x = -2.6 f .1 N 1

x=2.1 +0.1 N1II

(b)GraphTh e axes drawn in the right direction with a uniform scale for K 1-3 5 x 5 46 points and *2 oints plotted correctly or the curve passe s through the K28 points in the range of - 3 I x I 3.5.Note: If 7 points are plotted correc tly, entitle K 1If 6 points o r less are plotted correctly, assign KOSmoo th and con tinuous curve that passes through all the 8 points K 1


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SMS MUZAFFAR SYAH , MELAKA


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SULlT 7 . .

1 Soalan i Peraturau PernarkahanI I

ICor rect shape

Accurate measurement (k0.2 cm), all right angles - 90" k 1 ",

Correct shapeBC=GH= SQ=CR> BG=C I ; I > B IW=CNAccurate measurement (k 0.2 em ), all right angles = 90" 7 f i l o .

3 cm

N / J

R / P2 cm

G / F 6 cm HIE2 cmM / k '2 em

-


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SULIT 8

Correct shapeI K J dotted lineF Q > ~ M > ~ ~ = ~ ~ = ~ = ~ ~ > ~ ~Accurate measurement (k0.2 cm), all right angle s = 90" f ".


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SULIT 9 .

SoalanTq 52ON, 55"W) Peraturan Pernarkahan Markp 2 1I II Note : If 52"N or 55" W used co rrectly award 1 mark.

(180" - 25") x 60 x cos 52"Note: If ~l se d 1 80"- 25") or co s 52" correctly

1 9.34 or 19 hours 20 minutes

m :/ 1 . P2 : Rotation 90" anticlockw ise or rotation centre (5, 3)'2 . P1 : Rotation

(b)(i) Rotation 90" anticlockwise centre (5, 3)orEnlargement centre (2, 0) with scale factor 3

1. P2 : Enlargement centre (6, 0) or enlargemerit scale factor 3 IPI : Enlargement

(b)(ji)

Note :

Enlargemen t centre (6, 0) with scale factor 3orRotation 90" anticlockw ise centre (7, 5)

P l P l P l

P l P l P l


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LIT 10

Mark : ( I l l to V111)Frequency : ( I to VIII)Midpoint : (1 to VIII)iNote : Allow o ne mistake in frequency for 1 mark

I

I11111Ivvv 1VIIVlII

(a) 1 Murkah Kekerupan

Axes drawn in correct direction, uniform and correct scales for3 4 . 5 5 x 57 4 . 5 a n d O S y 5 1 0 .

Titikidpointenguh I

* 7 bar correctly drawnNote : 6 or *5 bar correctly drawn, award 1 mark(Smoothand continuous bar using a given scale.iI students have marks between 55-59(Award 1mark for any true statement)l o


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SPM MM2 Q&A (Johor)

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