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SULIT 1 34723472MatematikTambahanSEPT 20072 jam
SEKOLAH MENENGAH KEBANGSAAN SEKSYEN 18
SHAH ALAM
PEPERIKSAAN AKHIR TAHUN 2007
TINGKATAN 4
MATEMATIK TAMBAHAN
KERTAS 1
Dua jam
JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU
1. Kertas soalan ini mengandungi 25 soalan.
2. Jawab semuasoalan.
3. Bagi setiap soalan berikan SATU jawapan / penyelesaian sahaja
4. Tunjukkan langkah-langkah penting dalam kerja mengira anda. Ini boleh membantuanda untuk mendapatkan markah
5. Rajah yang mengiringi soalan tidak dilukiskan mengikut skala kecuali dinyatakan
6. Markah yang diperuntukan bagi setiap soalan atau ceraian soalan ditunjukkandalam kurungan
7. Satu senarai rumus disediakan di halaman 2 hingga 3
8. Penggunaan kalkulator saintifik yangtidak boleh diprogramkan adalah dibenarkan
Disediakan oleh Disemak oleh Disahkan oleh
_______________ ___________________ __________________
(Ms Liew Hui Kin) (Pn Norizan Kasim) (Pn Rosnah Abd Rahman)
Kertas soalan ini mengandungi 14 halaman bercetak
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SULIT 3472
Following formulae may be helpful in answering the questions. The symbols given are theones commonly used.
ALGEBRA
1 x =a
acbb2
4
2
2 am an = a m + n
3 am an = a m - n
4 (am) n = a nm
5 logamn = log am + logan
6 loga
n
m= log am - logan
7 log amn = n log am
8 logab =a
b
c
c
log
log
9 Tn = a + (n-1)d
10 Sn = ])1(2[2
dnan
+
11 Tn = arn-1
12 Sn =r
ra
r
ra nn
=
1
)1(
1
)1(, (r 1)
13r
aS = 1 , r
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SULIT 3472
STATISTIC
1 Arc length,s = r
2 Area of a sector , A = 2
2
1r
3 sin 2A + cos 2A = 1
4 sek2A = 1 + tan2A
5 cosek2 A = 1 + kot2 A
6 sin2A = 2 sinAcosA
7 cos 2A = cos2A sin2 A
= 2 cos2A-1
= 1- 2 sin2A
8 tan2A =A
A2tan1
tan2
TRIGONOMETRY
9 sin (A B) = sinAcosB cosAsinB
10 cos (A B) = cosAcosB sinAsinB
11 tan (A B) =BA
BA
tantan1
tantan
12C
c
B
b
A
a
sinsinsin==
13 a2 = b2 +c2 - 2bccosA
14 Area of triangle = Cabsin2
1
1 x =N
x
2 x =
f
fx
3 =N
xx 2)( =2_2
xN
x
4 =
f
xxf 2)(=
22
xf
fx
5 M = Cf
FN
Lm
+ 2
1
6 1000
1 =P
PI
71
11
w
IwI
=
8)!(
!rn
nPrn
=
9!)!(
!
rrn
nCr
n
=
10 P(A B)=P(A)+P(B)-P(A B)
11 p (X=r) =rnr
r
n qpC , p + q = 1
12 Min(mean) = np
13 npq=
14 z =
x
3
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P Q
1
2
4
5
a
3
7
9
Answer all questions .
1 Diagram 1 represents a functionf that maps elements in setPto elements in set Q. Each
objects in setPis multiplied by two then minus by 1.
State the
(a) value of a
(b) functionf in the form of function notation[2 marks]
Answer: (a) ....
(b)
____________________________________________________________________________________
2 Given ,3
23)(
1 =x
xh find the value of
(a) h(4)
(b) m such that 32)3(1 = mmh
[4 marks]
Answer: (a)
(b)
4
Untuk
Kegunaan
Pemeriksa
Diagram 1
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SULIT 5
3 The roots for quadratic equation 033102 =+ kxx are in the ratio 2 : 3.
Find the,
(a) roots,
(b) value ofk.
[4 marks]
Answer: (a)
(b)....
______________________________________________________________________________
4 Given 2)1()( += pxxpxxf . Find the range of values ofp iff(x) is always positive.
[3 marks]
Answer:
______________________________________________________________________________
5 A function g and its inverse are defined as g: x3
+x
bax, x 3 and g-1: x
2
23
x
x, x
respectively.
Finda) Values of a and b
b) Value of x such that g(x) = 3
[4 marks]
Answer: (a)
(b)
3472/1 SULI
Untuk
Kegunaan
Pemeriksa
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UntukKegunaan
Pemeriksa
6 Solve 2422 2343 = ++ xx .[4 marks]
Answer:
____________________________________________________________________________________
7 Given ym =27log and xn =3log . Express 349log nm in terms ofx andy.[4 marks]
Answer:
____________________________________________________________________________________
8 Find the roots of the following quadratic equation
a) x (2x - 3) = 5
[2 marks]
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SULIT 7
Answer: (a)
9 Diagram 2 shows a straight line 63 += xy that is perpendicular to a straight line that connects
pointA (2, 3) andB(s, t).
Express tin terms of s. [4 marks]
Answer: __________________________________________________________________________________
10 Given = -3 and = 4. Form a quadratic equation that has 2 + 5 and 3 7 as the roots.
[3 marks]
Answer:
3472/1 SULI
y
B(s, t)
A(2 , 3)x
Diagram 2
Untuk
Kegunaan
Pemeriksa
y=3x+6
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(b)..
16 Express each of the following in terms of log axandlog a y.
a) 2
5
logyxa
b) 37log yx
aa
[4 marks]
Answer: (a)
(b)..____________________________________________________________________________________
17 N is a point that lies on the straight line that connects Q (-1,-3) and R (4, 1) such thatQN = 4NR. Find the coordinate of point N.
[2 mark
Untuk
Kegunaan
Pemeriksa
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SULIT 11
Answer:
3472/1 SULI
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18 Calculates the mean, standard deviation and variance for 14, 16, 20 ,23 ,30.[4 marks]
Answer:
____________________________________________________________________________________
19 Find the median for 4, 7, 3, 7, 2, 5, 3 and 7.
[2 marks]
Answer:
Untuk
Kegunaan
Pemeriksa
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SULIT 13
20 The mean and standard deviation for the set of number x1, x2, x3,.., xn are 6 and 2 respectively.
Find the mean and standard deviation set for 5x1 + 2, 5x2 + 2, 5x3 + 2, , 5xn + 2
[4 marks]
Answer: (a)
(b) ..
____________________________________________________________________________________21
Diagram 4
Diagram 4 shows a sector with radius of 6 cm. The arc AB is 4 cm. Find
a) Angle AOB
b) Area of the shaded region [3 marks]
[3 march]
3472/1 SULI
Untuk
Kegunaan
Pemeriksa
6 cm 4 cm
A
B
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Answer: (a)
(b) .
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Answer:
24 Given y = 15x ( 3 - x ), calculate thea) value of x when y is maximum
b) maximum value of y
[3 marks]
Answer:(a).
(b).........................................
______________________________________________________________________
25 Given y = x2 + 3x, find the small changes in y when x increases from 2 to 2.01.
[3 marks]
Answer: ..
Untukegunaan
meriksa
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SULIT 17
KERTAS SOALAN TAMAT
3472/1 SULIT