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8/12/2019 additional maths form 4,YearEnd 2013
http://slidepdf.com/reader/full/additional-maths-form-4yearend-2013 1/16
Nama : _______________________________ Ting : ______________
PEPERIKSAAN AKHIR TAHUN 2013
MATEMATIK TAMBAHAN TINGKATAN 4
KERTAS 1 / 3472/1
2 Jam
Kertas soalan ini mengandungi 17 halaman bercetak
1
SEK MEN KEB SULTAN SALAHUIN ABUL A!I! SHAH
JALAN BUNGA MA"AR 2/#$ SEKS%EN 2$ 40000 SHAH ALAM$ SELANG&R
MAKLUMAT UNTUK 'AL&N
IN(&RMATI&N (&R 'ANIATES
1. Kertas soalan ini mengandungi 25 soalan.
This question paper consists of 25 questions.
2. Jawab semua soalan
Answer all questions.
3. Tuliskan jawapan anda dalam ruangan yang disediakan di dalam kertas soalan
Write your answers in the spaces provided in this question paper.
4. Tunjukkan langkah – langkah penting dalam kerja mengira anda. ni bolehmembantu anda mendapatkan markah.
Show your working. It may help you to get marks.
5. !ajah yang mengiringi soalan tidak dilukis mengikut skala ke"ualidinyatakan.
The diagrams provided in the questions are not drawn to scale unless stated
otherwise.
#. The marks allo"ated $or ea"h %uestion are shown in bra"kets.
&arkah yang diperuntukkan bagi setiap soalan ditunjukkan
dalam kurungan.
'. ( list o$ $ormulae is pro)ided.
*atu senarai rumus ada disediakan.
+. ,ou may use a non-programmable s"ienti$i" "al"ulator.
(nda dibenarkan menggunakan kalkulator sainti$ik yang tidakoleh diprogramkan.
S)a*anMa+,a-
P.n-
Ma+,a-
i.+)*.-i
1 3
2 3
3 3
4 4
# 3
2
7 3
2
3
10 3
11 3
12 4
13 3
14 4
1# 3
1 3
17 3
1 3
1 3
20 3
21 3
22 4
23 3
24 3
2# 4
Jm*a-
8/12/2019 additional maths form 4,YearEnd 2013
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2
8/12/2019 additional maths form 4,YearEnd 2013
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Jaa5 6.ma 6)a*an
Answer all questions
0 ma+,6 8
1. !ajah 1 menunjukkan $ungsi linear f .
!iaram " shows a linear function f.
3
f
# a# $
– 4 – 5
1 5
!ajah 1 !iagram "
8/12/2019 additional maths form 4,YearEnd 2013
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a/ 0yatakan nilai a dan nilai b.
State the values of a and .
b/ ari imej bagi 2 di bawah $ungsi $.
%ind the image of 2 under the function f.
3 marks
(nswer Jawapan
a/
b/
2. amba rajah 1 menunjukkan suatu $ungsi 134 −→ # # f . ari
!iagram " shows a function 134 −→ # # f . %ind
4
f
# &# $ "
– 3 – 16
– 1 h
3 +7iagram 1
a/ nilai h
the value of h
b/ /+81− ff
8/12/2019 additional maths form 4,YearEnd 2013
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3 marks
(nswer 'awapan (
a/
b/
3. 7iberi suatu $ungsi 3' +→ # # f . ari
)iven a function 3' +→ # # f . %ind
a/ objek yang mempunyai imej 16
the o*ect that has the image "+.
b/ 9bjek yang dipetakan kepada dirinya sendiri.
The o*ect that is mapped onto itself.
3 marks
(nswer 'awapan (
a/
b/
4. 7iberi satu $ungsi ( ) # # f 32−=
dan ( ) 3
45 −=
#
# gf . ari
)iven the function ( ) # # f 32 −= and the function ( )3
45 −=
# # gf . %ind
a/ ( ) # f 1= b/ ( ) # g
4 marks
(nswer 'awapan (
a/
5
8/12/2019 additional maths form 4,YearEnd 2013
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b/
5. 7iberi ( ) #+= # #h dan $ungsi ( ) k # # # g +−= 32 : dengan keadaan k ialah pemalar. ari
)iven. ( ) #+= # #h and ( ) k # # # g +−= 32 , where k is a constant, find
a/ ( )51−h b / nilai bagi k dengan keadaan ( ) 1251=
− gh
the value of .k such that ( ) 1251=
− gh
3 marks
(nswer 'awapan (
a/
b/
#. ;entukkan persamaan kuadratik yang mempunyai pun"a5
1− dan 4.
%orm the quadratic equation which has the roots5
1− and -.
2 marks
(nswer 'awapan (
#
8/12/2019 additional maths form 4,YearEnd 2013
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'. 7iberi pun"a – pun"a persamaan ( )( ) 652 =−+ # # adalah α dan . ;entukkan suatu persamaan
dengan
pun"a - pun"aα
1 and
β
1.
)iven the roots of the quadratic equation ( )( ) 652 =−+ # # are α and . %orm an equation with
roots
α
1
and β
1
.
3 marks
(nswer 'awapan (
+. 7iberi bahawa 2− ialah satu daripada pun"a – pun"a persamaan kuadratik 652=−+ p# # .
ari nilai p.
)iven that 2− is one of the roots of the quadratic equation 652=−+ p# # . %ind the value of
p.
2 marks
(nswer 'awapan (
'
8/12/2019 additional maths form 4,YearEnd 2013
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<. ra$ 1 menunjukkan gra$ bagi $ungsi kuadratik ( ) ( ) <5 2+−= #a # f yang mempunyai satu titik
maksimum di =. 0yatakan
)raph " shows the graph of a quadratic function ( ) ( ) <5 2+−= #a # f has a ma#imum point
at .
State a/nilai maksimum bagi $ungsi itu.
the ma#imum value of the function. f/#0
b/ persamaan paksi simetrinya
the equation of the a#is of symmetry.
( ) ( ) <5 2+−= #a # f
(nswer 'awapan (
a/
b/ ra$ 1
3 marks
16. >ersamaan kuadratik ( ) 6132 2=+− #k # tidak mempunyai pun"a nyata. ari julat nilai k.
The quadratic equation ( ) 6132 2=+− #k # has no real roots. %ind the range of the values of
k.
3
marks
(nswer 'awapan (
+
.
8/12/2019 additional maths form 4,YearEnd 2013
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11. *atu daripada pun"a persamaan 6+2
=++ k# # adalah dua kali pun"a yang satu lagi.
ari nilai – nilai k.
1ne of the roots of the equation 6+2
=++ k# # is two times the other root. %ind the values of
k.
(nswer 'awapan (
3 marks
12. !ajah di bawah menunjukkan gra$ $ungsi /8 # f y = . 7iberi $ungsi /8 # f ialah( ) nm # # f ++=
2/8 .
Titik &inimum lengkungan itu ialah 8 4: -1 / . ari nilai – nilai bagi m: n dan k
The diagram shows the graph of a quadratic function /8 # f y = . The function /8 # f is
given y
( ) nm # # f ++= 2
/8 . The minimum point on the curve is / -, $ " 0 . %ind the values of m, n
and k.
.
3 marks
(nswer 'awapan (
<
#
y
/ + , k 0
/ - , $ " 0
y f/#0
.
8/12/2019 additional maths form 4,YearEnd 2013
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13. ari julat nilai ? bagi # # 1#312 2
−≥
%ind the range of values of # for which # # 1#312 2
−≥
(nswer 'awapan (
3 marks
14. ari julat nilai # bagi # # 5'2 2 ≤− %ind the range of values of # for which # # 5'2 2
≤−
(nswer 'awapan (
3 marks
16
8/12/2019 additional maths form 4,YearEnd 2013
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15. *elesaikan persamaan 11 <2' −+
= # #
Solve the equation 11 <2' −+
= # #
(nswer 'awapan (
3 marks
1#. >ermudahkan persamaan logarithms 1#log4log22log5 p p p
+− sebagai logarithms tuggal.
Simplify the logharithmic e#pression 1#log4log22log5 p p p
+− as a single logarithms
(nswer 'awapan ( 3
marks
1'. *elesaikan persamaan ( ) 314log2log ++ =−− # #
Solve the equation ( )3
14log2log ++ =−− # #
3 marks
(nswer Jawapan
11
8/12/2019 additional maths form 4,YearEnd 2013
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1+. 7iberi hm =3
log dan k n =3log : ungkapkann
m 2
3log dalam sebutan h dan k .
)iven hm =3log and k n =3log , e#press n
m 2
3log in term of h and k.
(nswer 'awapan
3 marks
1<. !ajah di bawah menunjukkan garis lurus yang merentasi garis & 8 4 : 6 / dan 0 8 6 : – 4 /.
The diagram elow shows a straight line passing through 3 / - , + 0 and 4 / + , $ - 0.
a/ Tuliskan persamaan garis lurus &0 dalam bentuk 1=+
y
a
#.
Write down the equation of the straight line 34 in the form of 1=+
y
a
#
b/ *atu titik !8 # , y / bergerak dalam keadaan 2!& @ !0. ari persamaan lokus !.
A point /# , y 0 moves such that 23 4. %ind the equation of the locus of .
4 marks
(nswer 'awapan (
12
.
.
y
#
& 8 4 : 6 /
0 8 6 : – 4 /.
8/12/2019 additional maths form 4,YearEnd 2013
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26. ;u"u – bu"u satu segitiga >84:2/: =83:#/ and !8h: – 3/. 7iberi luas segitiga tersebut 1.5 unit2:
"ari nilai – nilai h.
The vertices of a triangle are 6/-,20, /&,70 and /h, $ &0. )iven that the area of the triangle is
".5 unit 2 , find the values of h.
3 marks
(nswer 'awapan (
21. !ajah di bawah menunjukkan satu garis lurus (. Titik ; terletak di atas garisan ( dengan
keadaan (; ; @ 2 1. ari koordinat ;. The diagram elow shows a straight line A8. The point 9 lies on A8 such that A9 ( 98 2 ( ".
%ind the coordinate of 9.
13
.
y
( 8 $ 4 : 5 /
; 8 # ,y /.
#
8#:6/
.
.
8/12/2019 additional maths form 4,YearEnd 2013
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3 marks
(nswer 'awapan (
22. &arkah bagi 4 pelajar dalam satu ujian ialah masing – masing 35: 4#: 5# dan '2.
The marks of - students otained in a test are &5, -7, 57 and :2 respectively.
a/ ari nilai markah min.
8alculate the mean mark.
b/ &arkah tambahan bonus sebanyak 3 ditambah kepada setiap pelajar tersebut. ari nilai min
yang baru.
;#traonus marks of & are added to each of the students, calculate the new mean mark.
3 marks
(nswer 'awapan (
23.
S9)+. (+..n9;
15 – 1< 1
26 – 24 +
25 – 2< #
36 – 34 5
35 – 3< 4
;erdasarkan jadual di atas: kirakan
9ased on the aove tale, calculate
a/ )arian b/ sisihan piawai
the variance, the standard deviation
14
8/12/2019 additional maths form 4,YearEnd 2013
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3 marks
(nswer 'awapan (
24. !ajah di bawah menunjukkan sektor 9>= berpusat di 9 dan berjejari 4 "m. 7iberi luas sektor
itu
ialah 12"m2.
The diagram elow shows a sector 16 with centre 1 and a radius of -cm. )iven the area of
the
sector is "2cm2.
a/ ari nilai : θ dalam radian.
%ind the value of θ in radian.
b/ ari perimeter dalam "m: sektor itu.
%ind the perimeter , in cm of the sector.
3 marks
(nswer 'awapan (
15
>
9 θ rad
4"m
=
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25. !ajah di bawah menunjukkan sebuah semibulatan berpusat 9. 7iberi panjang lengkok (; adalah sama
dengan perimeter se"tor 9;. ari nilai θ dalam darjah dan minit.
The diagram elow shows a semicircle with centre 1. )iven the length of arc A9 is equal to the perimeter
of
sector 198. %ind the value of θ in degrees and minutes. [ Guna / Use π=3.142]
3 marks
(nswer 'awapan (
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7isediakan oleh 7isemak oleh 7isahkan oleh
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8 >n &aslihah ;t Cashim / 8 >n !oslinda ;t (bu 0aim / 8 >n *aDadiah ;t ,uso$ /
1#
;
θ
( 9