strut mnfui4z.it ltfmm.4z,ii · strut ltfmm.4z,ii lllalematik kertes 1 november 2012 l jam...

struTltfMM.4z,IIlllalematikKertes 1November2012l jam

MNfuI4z.IT

MAKTAB RENDAE SAINS MARA

PEPERIKSAAI{AKHIR SEMESTER 2 2012TINGKATAhI4

MATEMATIK

IGrtas 1

Satu jam

JANGAN B[]KA KERTAS SOAI"ANIM SEHINGGA DIBERITAIII

L. This qucstion paper consists of 30 questions.

2. Answer all quesrtons

3. Answer each question by blackening the correct spoce on the answer sheet.

4. Blacken only one space for each question.

5. If you wkh to change your onswer, erose theblackened mark that you havedone. Then blacken the space for the new answer-

6. The diagrarns it the questions provided ore not drawn to scale unless stated

7. A list of formulae is provided on page 2 and 3.

8. You may use a non-programmable sci.ertifirc calculator.

www. myschoolchildren.com

MMM42441 [Lihat sebelahSULIT

Kertas soalan ini mengandungi 14 halaman bercetak

www.myschoolchildren.commore examination papers at :

SI,'LXT 2 MMM4VIIT

TIE foiluving formulae ncy be hclpful in awwering the Etestbns. The sytbols givan are iheones connan$t used

REI,ATIONS

1. A.-- | (d -D\d-bc\-c a )

sum of dataZ. - l[treAJI =' number of data

3. Mean = Sum of (class mark x Aequency)

sum of ftequencics

4. Pythagoras Theorem, ? = a2 + f

Eihat sebelahSULIT

M,MM42A,IT


STJIIT 3

SHAPEAND SPACE

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1. Area of trapezium = I r =om of parallel sidar x height2'

Z Cirqrmference of circile = . il = 2. r

3. Area of circle = . /4. Cfrved slrrfrce ar:ea of cfliader = 2.7h

5. Surface area of sphere = 4.1

6. Vofume of right prism = ooss sectional areax length

7. Volume of cylinder = .li

8. Volume of cone =!.*n i

g. Votume of spmre = { . I3

,, ,0. Volume of right pyramid = I r base area x height

11. Sum of hterior engtes of a polygon = (n_ 2) x 1gd

- 12. arc length _ angle subtended at centre

circumferemce of circle 360'

1a areaofsector angle subtended at centre

areaofcircle 360'

pihat sebei.SU]"]

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4

Ansuter all Ercstiorc

In Iliagram I,,ABCD is a straight line.

Find the value ofp - g

ANB 300

,c 500

D7c

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[Lihat scbelahSI.]LIT

Diagram I

bDrtagamz, PQRSftI is an inegular hexagon

o

Diagram2

The value ofz is

A 36"

B 400

MMM424/1

7f900

cD

SULXT

1.


SULXT 5 MMM4z/IL

3. Diagram 3 shows a pentagon PBRSL Saaight line Pg is parallel to s[aight line tiZS

.tR

Diagram3

Eiad the value ofx + y

A 216"

B 22x

Find the value ofy

A 150

B 45"

MMM424ft

cD

2s0"

26e

4.

Diagram 4

C

D

600

75"

Eihat sebelahSI,IJT

Diagram 4 shows a rhombus PQrRS


D 3(r -3)2

- 5-m m-7o. 26

A 1-" c 2m-76-3

B 4l^ D m-43-3

4 n m'-m,, _x_ =m-t mn+ n

SULTT

5. Simotifv 6(k4,r.Y' ' 4lon -12m2

A3bl c3

4m-2

MMM42A.II

[Lihat sebelahSUIJT

3(k -3z.)2m

B

AMm-l

^mnU

BM

m+1

D m-nm+1

8. g" "-*"* area of a sphere with radius r cm is given by the forrrula A = 4trz.Therefore, r =

m+'1,

A ,:! fi21r,

s ,=IZ12, D ,= [i

{,t

^aL r=-4

MMM4zllt

6


SI,LIT MMM42I/L

9. Tabte I shows the number of goals sored by football team in a league competition

Nmber of goals 0 1 2 3 4 5

ftequency 1 3 7 x 5 4

Table I

The mode of tte number of goal scoted by the team is 2. Find the possible value olt

A6C8B7D9

10. Table 2 shows ao incomplete ptctogaph showing the number of Form 1 and Form 2students. The number of hrm 3 gful studerts is half of the total number of Form 1 and

Form 2 girl shrdents

Form 1 88 R888

Form 2 8888R

Fo,rm 3

o0 soboys

oA 50girls

TaHe 2

If the total number of Form 3 students is 350, fild the number of Form 3 boy students.

A2WB 125

c 150

D 100

MMll'd.A4L tUhat sebelahsllrT


SI.'LIT

11. Table 3 shows the scores obtained by a group of students in a competition

Sore 3 4 ) 6 7

Nuobet ofstudens 5 11 12 3 0

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tlihat sebelahSULXT

Tabh3

Tte median score is

A5B 4.5

In Diagram 5, P@R is a tangent to the circle with centle O . PTU is a straight line.

Diagran5

Eind the value of 'x.

A7eB 6Cf

cD

4

3.5

4A

3tr

C

D

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13, In Diegram 6, O is the cenhe of the cirde. POR is a tangent to a circle at Q.

Find the value ofx.

A5tr

;14. Diagram 7 shows ABC aud,4D are tangents to the circle, with centre O, at B atd Drespectively.

c 64"

t7a

Find the value ofx.

A3sB 44"

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Diagram 7

c5tD6f

[Uhat sebelai

suu


st txT

15. Table 4 shows the frequency of the nass of fish caught by 20 fishermen.

Mass of Esh Caug[t @) trYequency

11 -13 8

74-16 4

t7 -t9 1

m-22 2

B-25 5

Table 4

Based on the frequency in the Table d the modal class is

10 MMnn4jzqL

A 10.5 - 13.5

B 17 -79

c 16.5 - 19.5

D 11 -13

16. The mean of 10 numbers is 60. Fourof the numbersare takeo out, and its mean is 75. Themean of six numbers left is

L7. Which of the following graphs represents ! - -x2 + 6 .

[I ihat sebelahSULIT

c

u.85

C

D

50

15

AB

A

DB

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SI,IIJT

A y-f*nB Y=-x"-n

c Y=g*-nD Y= -3x2 -27

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fi.ihat sebelahsurxr

11

18. IXagram E shows a graph on a Cartesian plane.

v

Which of the following is the equation of the graph?

19. Which of the following shaded region rcpresents by x <5, y sll

lgY

.y=10

Y = -2x +LO

y=10

MMM4Z.Il

A

and y > -2r+10.

Y= 10

Y - -2x +1O

f '-h+l0

DB

Diagran 8

Y ' -?-x +LO


StIIf,T t2 MMM424lt

[ihat sebelahs(ruT

Z). Which of the statements catr be generalized to cover all cases using the quantifier 'all'?

A Multiples of 6 are multiples of 8.

B Factors of6 are factors of 24,

C Prime numbers are odd numbers,

D Factors of 6 are factors of9.

. 21. Which of the follouring is a Eue statement?

A l+2>3 or 1+3>5B 121 is the multiple of 11 and 13

c 2 e {1,,2} ailt {1} € {1,2JD (32)a = 3s or1.47 = 4.7 x,:0-t

22. Premise 1 : lfZx-5=7,thenx=6Premise 2 : ... ... ...Conclusion : ?*-5 *7Based on the argument, which is the Bost likely Premise 2?

A x:6 C x*6B x>6 D bL12

23. Given a sequence of numbers 2,5, 10, 17, ... which follows the following pattern2 = 1+72

5 -7+2210:1+32

- L7 -l+ 42

Make a general conclusion for the above nunber pattern,

A 1+(z+l)'?,n=112,3,.....

B 7+ (n -l)z , n =\ 2,3,.....

C l- n2 , n = 0,1, 2, 3,.....

D 1+ n2, n -L,2,3,,,...

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E

MMM42A,II

2a. nfiagrarmg shows a right prism with recianglefiLM as its horizontal base. P and @ are themidpoints ofXZ and Jitl, rcspectively.

Diagram 9

Name the angle betw'een the planeKLE and the plane.trZF.

13

cD

AB

LEPF

LEPO

LPEF

LPES

Question 25 and 26 based on the Diagram 10.

P 16cm A

Iliagram 10

Identify the angle between the line RT and the plane TUQP.

A LTRP C LQRT

B I.RTS D LQTR

Given that I!r7 = 7O an,TP = 8 cm and Pp = 16 cm, calculate the ange between the plane

PSRQ and the plane RQW.

a 3d52 C

B 53"E D

MMI0//424ll

25.

2d34

63"?l'

pihat sebelahSIJLIT

W 10cm

s !_____-__:

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l,x:. r"""*, (_lr) is a matrix rz x z. rhevalues ofn and z are.

A m=l,n=3B m=3,n=LC m=3,n=2D m=2,n3

?a. ci,e" (3 or) - , (!, il = (? !) , noa vaues orp ana e .

A P=4 'q=2B P=2 'q=4C p=2 ,q=-1D P=-1 'q=-2

29. Giventhat <z D(!+)= (12),findthevalueofy

AzB-2

30. (;4) Q -e= -

A (-11)

B (-8 -3)c (_31

D (? _*r)

Ends Of Question Paper

c-6D6

MMMA24/lSI,ILIT


Name:

MMM4UNIlrabmrtikKertrs 2Novembermtllthjam

Class :

MAKTAB RENI}AII SAINS MARA

PEPERIKSAAI{ AKEIR SEMESTftJR 2 2012TINGKATAN4

MATEMATIK

Icrtas 2

Satu jam tig'a puluh minit

JANGAN BUKA IGRTAS SOAI,AIIT II\u SEHINGGA DIBERITAHL

1. This question paper @Dsist of twolsection : Section A and section B.

2. Answer all quesion in Section A andthree guestions from Secrion B.

3, Write your alswer in the sPaccprovidedjn the questiotr paper.

4. Show your working. It may help youto get marlis.

5. The diag'ams in the questionsprovided are trot &awn to scale unlessstaEd.

6. A list of formulae is provided on Page2and3.

7. You may use a non-Programmablescientific calculator.

8. Iland in this question PaPer toinvigilator at the end ofglaminatiOn.

Bahagian SoalanMarkahPenuh

MarkahDiperoleh

A

1 3

2 4

3 5

4 3

5 5

6 4

B

7 t2

8 t2

9 12

10 t2

Jumlah

thethe

MMM424|2

Kertas soalan ini mengandungi 18 halaman bercetak-

[Lihet sebelah$ruT


2

lte fotlotei;ng fqrnnae may be hetpful in answering tle Etestions. The symbob givan are the

ones comnonl! used

REIATIONS

r. A-r- | (d -D)ad-bc\-c a )

Mean=sum of data

;- mrmbetof data

Mean=sum of Aequencies

Pythagoras Theorem,} =t +8

3.

4.

ll-ihat sebelahSULIT

NIMM424I2


3

SEAPEANDSPA(D

11. Area of tapezium = ix sum of parallel sides x height

2. Circumference of circle = .d =2.r

3. Area of circle = . I

4. Glrved surface area of cylinder = 2. rft

5. Surface area of sphere =4.1

6. Volume of right prism = cross sectional area x length

7. Volume of cylinder = . llr1^8. Vohrme of oone = ! .lh

9. Volume of sphere = | . y'3

1

; 10. Volune of right pyramid = ,: x base area x heiSht

11. SuE of interior angles of a polygon = (n- 2) x 180'

arcleugth anglesubtended at cenre -circumference of circle 360'

area of sector "ng!e

subtended at centre

arca of circle 360"

fi.ihat sebelai,SULIT

MMM424(2


4

Section AWnarksl

Atrswer all questions in this section.

In Iliagran 1, TP ail TQU ae two tangmts to the circle with cenre O ilP and Qreqrcctively.

Diagram I

(ir)

Calculate the value ofi)xii) viii) z

Answer t

(D

Itnarklll narklIt markl

lLihat sebelahSUI,IT

I0"'fMl|,.4?AI2

ForExnmbUse


5

2, In Diagram 1 TA nd 7C are two tangents to the ckde with cenne O ^l

A ar.d Brespectively.

ForExaniner'sUse

Diagam2

Given that /JBC -12f afiTA=10cm. Calctlate the '

i) major sec'tor of /,AOC,D /Arc,iii) radius of the circle.

[1 mark]

[1 mark][2 marks]

fi,ihat sebekr.sr&r


6

Table I shows the frequency distribution of the ages of 88 workers in a fuctory'

Agc (years) Ilequency

26-yJ 3

3t-3s 9

36-40 n4t-45 3L

46-50 11

51- 55 5

56-60 2

Table I

i) Calculate the estimated mean of the age of a worker.

D Eind the range for the data.

Answer :

(r)

(ir)

[3 marks]

[2 marks]

E ihat sebelahsuurMMM4AI2

ForExanher'Use


' ForEmmiwr's

. Use

7

On the graph in the answer space, shade the rcgion which satisfy the three inequalitiesy<-x+8, y <x rtd y>2.

[3 marks]

MMMAAI2 ll,ihat sebelahST'LIT

a

r+8

a 1

\

o


I

5. G) State whether each of the following statemeDts is &ue or false.

(r) ?x+x-?*2 or ?,x+x=k(ii) 3 is an odd nitmber and a prime number

O) State the oonverse of the fotlowing statement and hence determine whether itscowerse is true or false.

"If 10 is a multiple of 5, then 5 is a factor of 1(I'[1 mar$

(c) I\tlake a general conclusion by induction for the sequence of numbers

\n,79,190, ... which follows the pattern:

[2 marb]

[2 marts]

t = 3of-222 = 38\-279 = 3Qy-2t90= 3@f -2

Arutwer i

(a) (r) ....-.-.-................'.'...'..

(iD............

ForExt niner'Use

Eihat sebelahSI,LIT

NIMM424I2


' ForEtaminer's

- Use

9

Diagram 3 shows a right prism with a horizoatal rectangular basn ABCD. EFGH is asquare. lAe plare, AEHD is vertical and the uniform clqsssection of the prism is [email protected].

Diagram3

Calculate the argls $stwssa th6 planeAHGB arrd the planeABFE.

Answer :

[4 marks]

MMM424|2 lUhat sebelahSI]LIT


10

Section B[36matk]

Answer any thrte questions from this section.

7. Table 2(a) shows the frequency distribution of the masses, in kg of a group of 80students.

Mass (ldl trhequency

30-34 5

35 -39 8

40 -44 11

45-49 2l

50-54 22

55-59 10

@-il 3

Table 2(a).

G) State the modal class. [1 mark]

O) Calculate the estimated mean of the mass of a studint.[3 marks]

(c) Based on Table 2ta), complete Table 2(b) in the answer space to show thecumulative Aequency on the masses.

[2 marks]

(d) For this part of the question, use the graph paper.

By using a scale of 2 cm to 5 kg on the horizontal axis and 2 cm to 10 studenB onthe vertical axis, draw an ogive for the data.

[4 marks]

(e) Using your ogive or otherwise, calculate the interquartile range.

[2 marks]

[lihat sebelahSI'LIT

MMMA2II2

Use


. ForEmmitur'sUse

11

Answer t

G)

o)

(c)

(O Refer graph on page 12.

fiJhat sebela':

flil"

Upper Boundary (kg) Grmulative Frirquency

29.5 '0

34.5

Tabte 2(b)

MMM AI2


ForExamher'sUse

13

8. (a) Complete Table 3 in the answer space for the equation y = x3 - 2 by writing downthe values ofy whetx = -1.5 atdx = 2.

l2lrlr,rksl

(b) By using a scale of 2 cm o 1 uoit on the x-axis and 2 cm to 5 units on they'axis,

draw the graph of y-f -2for-3=xs3.14narlcsl

(c) From your gra.ph, findi) tbe value of .r wheny = Z),ii) the valuE of y when.r = 2.5.

l2narksl

(O Draw a suitable staight line on your graph to find the values ofr which satisfy the

equation -l +9x+2-O for -3(.r-<3.14 marksl

Answer :

(a)

Table 3

Refer graph on page 74.

(r) x=

(b)

G)

x -3 -2 .-1.5 o 7 2 3

v -29 -10 -2 -1 25

(d)

(ii)

[lhat sebelahSTJLIT

NIMM424D


- ForEtaniner'sUse

15

9. (a) Wrib down two implication based on the follouri4g statemert(2r-5[x-1)-0 if ad only{ ?*2 -7x+5-O

12narltsl

b) Complete the premise in the fiollowing argunetrt :

Premise 1 : If r is a multiple of 6, then it is a multiple of 3.Premise 2:Conclusion : 42 is a multiple of 3.

Urnarkl

c) Oomplete each of the followiag statemenB with the quautifier ..all,'or .someo so thatit will become a tue stateDe .

pentagOns bave five sides.

[2 marks]

d) IV{n}e a general conclusion by induction for the sequence of numben 7, 14, Zl, ...which follows the following pattern . i

7 -z(2)1 +1

14-3(2)2 +2

z7 -3(2)' +3

12 narkst

e) Complete the following statements using the word .or, or .and, to make thestatement Eue

(ii)

[2turk\

ll markj

ll marV,

lt.ihat sebelabsulxt

(ii) -3<-1 l--_-l -3<o

(D State whether the sentence below a statement or a non-statement.

A factor of Z) is 6

G) State whether the following statement is Eue or false.

Some fractions have Dumetabr smaller than denominator

MMM4AI2


16

For a regular polygon with z sides, the size of the exterior angte is !99. Ua;fe onen

conclusion by deduction on the size of the exterior angfe of a regular octagon-

fl tturksl

Implication 1 :

Implication 2 :

Premise 2 :

Angter :

(a)

(b)

(c)

ExamherUse

(e) (D

(ii)

(D

G)

(h)

fl,ihat sebelehSI'IJT

I,,[MM424|2


ForExaniner's

- Use

L7

12narksl

b) lt i,s eiven .,1 = (f fili) End the value of r if Ahasnoinverse.ii) If , = 3 , find the determinant of matrixA

[4nurksl

c) rheinverseor(i _il--;(_i ) ,

i) Find the value ofd and eii) using mahices , calc,late the value of x and y that satisfy both of the following

equations2x-Y=713x-4Y=9

[6markslAnstq:.

(a)

(b) (D

[Lihat sebelalSULTi

(ii)

MMM424l2


18

G) (D

Ends Of Question Paper.

(ii)

MMM4AI2$ruT

ForExtmiaqUse


strut mnfui4z.it ltfmm.4z,ii · strut ltfmm.4z,ii lllalematik kertes 1 november 2012 l jam...

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