tutormansor.files.wordpress.com · 2012-08-29 · 144912 matematics kertas 2 sept. 2008 2% jam...

144912 Matematics Kertas 2 Sept. 2008 2% jam

Nama: ..................................................

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

JABATAN PELAJARAN NEGERI JOHOR

PEPERIKSAAN PERCUBAAN SPM TINGKATAN 5 2008

MATEMATICS

Kertas 2

Dua jam tiga puluh minit

JANGAN BUKA KERTAS SOALAN IN1 SEHINGGA DIBERITAHU

r Untuk Kegunaan ~en1-

1 . Tzrliskan nama dun tingkutan padl1 ruang jnng disediakan.

2. Kerta.s soalun ini ndalah dalanl duvihahasa.

3. Soalan dalarn bahas~r Inggeris mendahului soalrzn yang sepadnn dularn hahasn Afelayu.

4. C'rrlon riibennrkan menjinvirb kesellrruhan arau .sebahagiim sorrlan sama nda dnlam bahasa hlelayu atau bahasa Inggeris.

5 . Cmlon dikehendlzki membaca arahrrn.

Jumlah I

Bahagian

Kertas soalan ini mengandungi 29 halaman bercetak

144912 ti? HaL C'inta JPNJ 3008

Soalan

SULIT

Markah Markah Penuh Di~eroleh

SMS MUZAFFAR SYAH , MELAKAhttp://tutormansor.wordpress.com/

Section A Buhugiut~ A

[52 mcrrk.~] [52 markah]

Answer all questions in this section. Jtnrtrh semua .soalun rf(11uni huht~gic~n ini.

I 'l'hc Venn diagra~x in the answer space shows sets Y , L) and R whcre < - P u Q u R . On the diagram provided in the answer spaces, shade

G'c~rnbar rujtlh di ruangjawapan ~nrnunj~rkkun set P, Q dnr~ R di rncrna ( ~> 8d Q v R.

Di rrtang jmvupan yang di.setliczkan, lorc'kkan kawrrsun

(a) the set Q u R ser Q u R

(b) the set ( P 17 Q )' 17 R' s e t ( P r 7 L ) ) ' n R '

Answer l .Jawapc~n:

SULIT SMS MUZAFFAR SYAH , MELAKA

http://tutormansor.wordpress.com/

For examrne! k

11se Find the value of a and of b that satisfy the simultaneous linear equations below:

C'arikun nilai a dun b yang memuaskan persamaan linear serentak herikut: 1 - a - 2 b = 6 3 50 + 6 b = 18

[4 marks] [4 markah]

Answer i Jmapan:

i Solve the following equation:

Selesaikan per.famaan berikut:

5m(m + 2) = 2 m + 2


Answer / Jawapan:

SULIT


SULIT

4.

Diagram 1 Rajah 1

Diagram 1 shows a pyramid with a square base PQRS. M is the midpoint of QR. T is a vertex 12 cm above the centre 0 of the base. Calculate the angle between the plane TQR and the base PQRS. [3 marks]

Rajah 1 menunjukkan sebuah piramid dengan tapak berbentuk segiempat sama PQRS. M ialah titik tengah QR. T adalah puncak piramid tersebut yang berada betul- betul tegak di atas pusat 0 dengan ketinggian 12 cm. Kirakun sudut di antara satah TQR dun tapak PQRS. [3 markah]

Answer I Jawapan:



For exam~ner i

11se

In Diagram 2, straight line PQ and straight line RS are parallel.

Dalam Rajah 2, garis lzrrus PQ dun RS adalah selari.

i

Diagram 2 Rajah 2

Find Carikan

(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 1 Jawapan:



SULIT


6 Diagram 3 shows two arcs, PQ and R,T with a common centre, 0. OQ is diameter of thc semicircle with centre T. PS = SO = OR = OT = TQ = 7 cm. Given that IHOS = 90" and i P O Q = 120".

Rflj!/c~lz 3 mrnunjukknn hru lrngkok bulatun, PQ dun k S ~ w n g herpu.rut di 0. 0 Q inluh diumetcr h17gi .setrriO~~lutan herpii.sut 7: PS == SO -- OH - OT - TQ .- 7 crti

Diheri bahiwo L!I(US -- 90" dfln 14'OQ = 120".

Diagram 3 RNjnh 3

Calculate Hiturrgk(1rr

(a) perirneter of the wholc diagram, perirneter selrlruh rqjuh,

(b ) the area, in cm2,0f the shaded region. lua.~, rluinrn cm2, kmc'asnn ynrrg herlnrek

Answer I .J~rw~pnrr:

SULIT

SMS MUZAFFAR SYAH , MELAKA


7 (a) Complete the following mathematical statements in the answer space using symbol > o r < to form (i) a true statement (ii) a false statement

Lengkapkan pernyataan-pernyataan ma~ematik berikut di dalurn ruangan jawapan dengan menggunakan .symbol > atau < untuk membentuk ( i ) pernyataan benar ( i i j pernyuraan palsu

(b) Combine the following statements to form a true compound statement. Statement I : 3 + 6 = 10 Statement 11 : 14 is an even number

Gabungkanpernyataan berikut unruk membentukpernyaraan gabungan yc; benar.

Pernyaraan 1 : 3 + 6 = I0 Pernyaraan I1 : 14 udaluh nombor genap.

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

Buar kesimpulan berdusarkan premis-premis berikut: Premis I : Jika x ialah faktor bagi 6 maka x ialah fuktor bagi Premis 2 : 3 ialah fakror bagi 6. Kesimpulan :

[6 mc [6 mar

Answer l Jmvapan :

(c) Conclusion :

Kesimpulan :



SULIT

8 Diagram 4 shows 12 labelled cards in two boxes. Rajah 4 menunjukkan 12 keping kad ycmng berlt~bel di clulam dun koluk.

Box X Kotak X

Diagram 4 Rajah 4

I I J Box Y

Kotuk Y

The cards are chosen at random. The first card is chosen at random from box X and the second card is chosen at random from box Y. Kad-kad tersebut dipilih secara rawuk. Kudpertama dipilih .recara ruwak daripada kotak X dun kad kedua dipilih secara rawak daripada kolak Y.

By listing the outcomes, find the probability that Dengan menyenaraikan 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 one card is labelled with a consonant L or H. sekurang-kurangnya sekeping kad berlabel dengan hurufkonsonan L atau H.

[ 5 murk.> [ 5 niarkuh

Answer l Jawapan :

SULIT



(a) I t is given that the inverse matrix of is[! y ] , findthe value of rn

and of n.

Diberi bahawa matriks songsang bag; (: iulah [i : 1, cari niloi rn

Jan nilai n.

(b) Using matrices, calculate the value ofx and o f y that satisfy the following matrix equation: Menggunakan kaeduh rnatriks, hitung nilai x dun nilai y yang nlernuaskan persarnaan rnatriks berikut:

Answer l Jawapan



SULIT

10. Diagram 5, shows 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 5 Rajah 5

Calculate, Hitungkan,

(a) the rate of change of speed, in ms-', during the tirst 6 seconds. I kadar perubahan laju, r n ~ - ~ , padu 6 soar pertarna.

(b) the value oft, if the total distance traveled for the period of t seconds is 270 m. I Nilai I , jiku jumlah jarak yang dilalui bagi ternpoh t saat ialah 270 m.

[5 mark.^] [ 5 markah]

Answer 1 Jawupan :

Fur exumrner k

use

SULIT



For rominer k

use 1 Diagram 6 shows a solid right prism with a half-cylinder removed from the prism.

The diameter o f the half-cylinder is 7 cm and PQ = QR = 10 cm.

Rajah 6 menunjukkan sebuah pepejal prisma tegak dengun sebuah separuh silinder yang telah dikeluarkan daripada prisma itu. Diameter separuh silinder itu iuluh 7 cm dun P Q = QR = 10 cm.

Diagram 6 Rajah 6

Calculate the volume, in cm3' of the solid. Kira isipadu bongkah tersebut, dalam cm3.

Use I Guna ~r = - 7 ,,I

Answer I Jawapan :


SULIT



SULIT

Section B Bahagian B


Answer four questions in this section. Jawab empat soalan dulum buhugiun ini.

12 (a) Complete Table 1 in the answer space for the equation y = 14 + 3x - 2x2 by writing down the values ofy when x = -3 and x = 3. [2 marks]

Lengkapkan Jadual 1 di ruang jawapan bag; persamaan y = 14 + 3x - 2x2 dengan menu1i.s nilai-nilai y apabila x = -3 dun x = 3. [2 markuh]

(b) For this part of the question, use the graph paper provided on page 19. You may use a flexible curve ruler.

Untuk ceraian soalan ini, gunakan kertas grafyang di.sediakanpada halaman 19. 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 they- axis, draw the graph ofy = 14 + 3x - 2x2 for -3 5 x 1 4. [4 murky]

Dengan menggunakan skala 2 cm kepada 1 unitpada paksi-x dan 2 crn kepada 5 unit pada paksi-y, lukis grafy = 14 + 3x - 2x2 bugi nilai x dalam julat -3 5 x 5 4. [4 markah]

(c) From your graph, find Daripada graf anda, cari

(i) the value of x when y = -8.

nilai x apabila y = -8.

(ii) the value ofy when x = 1.9. I nilai y apabila x = 1.9.

[ 2 marks] [2 markah]

(d) Draw a suitable line on your graph to find the values ofx which satisfy the equation 1 1 - x - 2x2 = 0 for -3 5 x 1 4 . [4 marks]

Lukis salu garis lurus yang srsuai pada graf anda untuk mencnri nilai-nilai x yang memuaskan persamaan 1 1 - x - 2x2 = 0 bagi -3 i x i 4. [4 markuh]

SULIT


3 You are not allowed to use graph paper to answer this question . Anda tidak dibenar rnenggunakan kertas graf untuk menjawab soalan ini

Diagram 7(i) shows a solid right prism with a rectangular base ABCD. ABMKGF is the uniform cross-section of the prism. Rectangle GHJK is an inclined plane. EFGH and JKMN is a horizontal plane. 'The edges AF, BM, CN and DE are verticals. BM=CN=2cm,AF=DE=4cm,AB=C1)=7cm,KM=JN=5cmand F G = E H = 3 c m

Rajah 7(i) menunjukkan sebuah pepejal berbentuk prisrna tegak dengan tapak segi empat tepat ABCD. Permukaan ABMKGF ialah keratan rentas seragamnya. Segiernpat tepat GHJK ialah satah condong. . EFGH dun JKMN ialah satah rnengufuk. Tepi AF, BM, CN dun DE adalah regak. B M = C N = 2 c m , A F = D E = 4 c m , A B = C D = 7 c m , K M = J N = 5 c m d a n F G = E H = 3 c m -

Diagram 7(i) Rajah 7(i)

a) Draw to full scale, the elevation of the solid on a vertical plane parallel to AB as viewed from X. [3 marks]

Lukiskan dengan skala penuh, dongakan pepejal iru pada sarah rnencancang yang selari dengan AB sebagaimana dilihat dari X. [3 markah]

Answer I Jawapan:

SULIT

(b:

SULIT SULIT



SULIT 21

(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 PQR and 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) pada satah fegak CDEHJN . Pepejal gabungan adalah seperti ditunjukkan dalam rajah 7(ii). Segitiga tepat PQR dun DSC adalah keratan rentas bagiprisma tegak tersebut. LQPR = LSDC = 90°, DP = CR = SQ = 6 cm dun PQ = 3 cm.

Diagram 7(ii) Rajah 7(ii)

Draw to full scale,

Lukis dengan skalapenuh,

(i) the elevation of the combined solid on a vertical plane parallel to BC as viewed from Y. [4 marks]

dongakan gabunganpepejal itu pada satah mencancang yang selari dengan BC sebagaimana dilihat dari Y. [4 markah]

(ii) the plan of the combined solid,

pelan gabungnn pepejal iru

[ 5 marks)

[ 5 markah]

For eruttlrner 'S

.IISt'

SULIT



SULIT

14. Diagram 8 shows four points P. Q, R and Ton the surface of the earth. P lies on the longitude 80" E, QR is the diameter of the parallel of latitude 52" N. T lies 5880 nautical miles due south ot'P. Rujuh 8 menzinjukkun empat titik P, Q, R clan T di utas perrnukann hutni. P herada puda longifud 80°T, QR ialah diam~rer hngi selnricin Icititud 52" U. T bercrdu 5880 hutu t7autikn ke ~elararr P.

N l (/

Diagram 8 Rajah 8

(a) Find the location of Q. Cnri kc>htclukan Q.

12 n~urk., j [ 2 marknh]

(b) Calculate the shortest distance in nautical nliles from Q to K, measured along the surface of the earth. [2 t n t ~ r h ] Hlrung jarak rerciekar dalam haru nuutlka dari Q ke R, ~iizlkur .sepatvang permtrkaan htcmr [ 2 rntlrkah]

(c) Find the latitude of I: Cari latitzld hagi T.

id) An aeroplane took off from R and flew due west to P along the parallel of latitude 52"N and then flew due south to Twith an average speed of 600 knots. Sebunh kapal rerbang berlepas ciari R dun rerbang arch barar kc R .sepcitQutzg sel~rrian larirud 52'11 dan ke~nudian terbang arah selatan ke Tdengun purtltcr Iqjtc 600 knot.

Calculate Hirung

(i) the distance. in nautical mile, taken by the aeroplane from K to P measured along the comlnon parallel of latitude, [ 3 tncirk.sJ ,juruk, dalatn haru naurika, yang dilaltli oleh kcipal rerbung itu dc~t-i R ke P clizrkur sepanjang selarinn lari~udsccpunya. [3 murkuh]

(ii) the total time, in hours, taken for the whole flight. 12 marks] ,jutnlrrh masa, rkllam jom, yang diamhil bagi seluruh perjalanan itu.

12 mcrrkah]

SU LIT


SLILIT 2 5

15 Diagram 9 hhows trapeziums .-llj('D, EFGH and L,/liL drawn on a C<+rtcs~an planc

Diagrani 9 Rnjnlt 9

(a) Transfor~natio~r T i s a translation (-6,). Tranrfonnetiun Xis ii reflection in {lr

Perljclniuan T ialalt rransltlsr . Penjeltnaun ,Y ialcrh pnntzllan puc l~~ guris [:,I State the coordinates of the image of point (2, 5 ) under each of the Sollowing transformations: ( i) 1' ( i i ) XT

Nyuruktrn koorclincr~ i r m j bagi tiiik (2. 5 ) cli bcrruc~h .scti~ll~ per~jrlinucxrr brriklrf: (1) T fii) .IT

[3 rnc1rk.l [3 ~norkal



1449L2 Matematics Kertas 2 Sept. 2008

JABATAN PELAJARAN NEGERI JOHOR

PEPERIKSAAN PERCUBAAN SPM TAHUN 2008

SKEMA PEMARKAHAN

MATEMATICS

Kertas 2

Dua jam tiga puluh minit

144912 0 Hak Cipta JPNJ 2008 SULIT


4 Ildentify LTMO or LOMT

/tar O = 12 or equivalent 4 -


SULIT 3

-- -- -

r ~ o a l a n Peraturan Pernarkahan r w - - - - - I -

I .- I 8 I (a) I { (E , 4 9 (A, A) 1

(b) ' 3 + 6 = 10 or 1 4 is an even number

SULIT

(c) 3 is a factor of 48


SUL IT 4

SULIT

Peraturan Pernarkahan - 1

rn= - i 2 I

'Note:

[ ' 2 ) o r -'),awardPl

I

10

,--- 1 '

' 4 1 - 2 1 - 1 4 I

(1 n = 2 P 1

iNotes : 1 I .

= [-23) as a find answer, award N l

2. Do not accept any solutions solved not using matrices

(a) !24-12 ' 0 - 6

I

-2

I I ( 2 4 + 1 2 ) x 6 + - ( 1 2 + 1 8 ) x 6 + - ~ ( t - 1 2 ) x 2 4 =270

2 2 j

Note : Any two areas correct, award K1

t = 20 seconds

K2

N 1 5


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 out of the range.

- Peraturan Pernarkahan I - ~ 1 0 x 1 0 ~ 1 5 3

K1 K 1

I

1; = 4 x + 3 K 1

The straight line y = 4x + 3 drawn correctly. KI

( Judgement: straight line that passes 2 points marks correctly ) Values of x = -2.6 f 0.1

N1

x=2.1 +0.1 N1 I I

(b)

SULIT

Graph The axes drawn in the right direction with a uniform scale for K1

-3 5 x 5 4 6 points and *2 points plotted correctly or the curve passes through the K2 8 points in the range of - 3 I x I 3.5. Note: If 7 points are plotted correctly, entitle K1

If 6 points or less are plotted correctly, assign KO Smooth and continuous curve that passes through all the 8 points K1


SULlT 7 . .

1 Soalan i Peraturau Pernarkahan I I

I Correct shape

Accurate measurement (k 0.2 cm), all right angles - 90" k 1 ",

Correct shape

BC=GH=SQ=CR>BG=CI;I>BIW=CN

Accurate measurement (k 0.2 em), all right angles = 90" 7 f i lo .

3 cm

144912 SULIT

N / J

R / P

2 cm

G / F 6 cm H I E

2 cm

M / k '

2 em

-


SULIT 8

Correct shape

I K J dotted line

F Q > ~ M > ~ ~ = ~ ~ = ~ = ~ ~ > ~ ~ = ~ ~ > ~ ~ = ~ ~ = ~ ~

Accurate measurement (k 0.2 cm), all right angles = 90" f 1 ".



SULIT 9.

Soalan Tq ( 52ON, 55"W) Peraturan Pernarkahan Mark

p 2 1 I I

I Note : If 52"N or 55" W used correctly award 1 mark.

(180" - 25") x 60 x cos 52" Note: If ~lsed (1 80"- 25") or cos 52" correctly

1 9.34 or 19 hours 20 minutes

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

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

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

(b)(ji)

Note: iAny correct centre of enlargement corresponding to centre of rotation be awarded marks.

Enlargement centre (6, 0) with scale factor 3 or Rotation 90" anticlockwise centre (7, 5)

P lP lP l

P l P l P l

SULIT


SU LIT 10

Mark : ( Ill to V111) Frequency : ( I to VIII) Midpoint : (1 to VIII) iNote : Allow one mistake in frequency for 1 mark

I

I 11 111 I v v v 1 VII VlII

(a) 1 ; Murkah Kekerupan

Axes drawn in correct direction, uniform and correct scales for 34 .55x574 .5and O S y 510 .

Titik Midpoint Tenguh I

* 7 bar correctly drawn Note : 6 or *5 bar correctly drawn, award 1 mark

(Smooth and continuous bar using a given scale. i I I students have marks between 55-59

(Award 1 mark for any true statement) l o



SULIT 1 1

Frequency / Kekerapan

144912 SULIT


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