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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.
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Kertas soalan ini mengandungi 14 halaman bercetak
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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
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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'
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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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Diagram I
bDrtagamz, PQRSftI is an inegular hexagon
o
Diagram2
The value ofz is
A 36"
B 400
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7f900
cD
SULXT
1.
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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"
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cD
2s0"
26e
4.
Diagram 4
C
D
600
75"
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Diagram 4 shows a rhombus PQrRS
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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
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[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
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6
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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
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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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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
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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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A y-f*nB Y=-x"-n
c Y=g*-nD Y= -3x2 -27
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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
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A
and y > -2r+10.
Y= 10
Y - -2x +1O
f '-h+l0
DB
Diagran 8
Y ' -?-x +LO
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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
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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
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25.
2d34
63"?l'
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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
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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
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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
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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"
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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
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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]
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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
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' 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
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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
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' 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]
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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]
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MMMA2II2
Use
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. 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
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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)
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- 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
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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)
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I,,[MM424|2
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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)
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18
G) (D
Ends Of Question Paper.
(ii)
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