sabah add math p1 & ans 2
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SULIT
3472/1
ADDITIONAL
MATHEMATICS
PAPER 1AUGUST 2008
2 HOURS
JABATAN PELAJARAN NEGERI SABAH
SIJIL PELAJARAN MALAYSIA TAHUN 2008
EXCEL 2
___________________________________________________________________________
ADDITIONAL MATHEMATICSPAPER 1 (KERTAS 1)
TWO HOURS (DUA JAM)
___________________________________________________________________________
JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU
1. Tuliskan angka giliran dan nombor kad
pengenalan anda pada ruang yangdisediakan.
2. Calon dikehendaki membaca arahan di
halaman 2 .
___________________________________________________________________________This question paper consists of 14 printed pages.
(Kertas soalan ini terdiri daripada 14 halaman bercetak.) 3472/1 [Turn over (Lihat sebelah)
NAMA : _____________________
KELAS : _____________________
NO K.P : _____________________
A. GILIRAN : _________________-
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INFORMATION FOR CANDIDATES
1. This question paper consists of 25 questions.
2. Answer all questions.
3. Give only one answer for each question.
4. Write your answers clearly in the space provided in the question paper.
5.
Show your working. It may help you to get marks.
6.
If you wish to change your answer, cross out the work that you have done. Then write
down the new answer.
7. The diagrams in the questions provided are not drawn to scale unless stated.
8.
The marks allocated for each question are shown in brackets.
9.
A list of formulae is provided on pages 3 to 5.
10.
A booklet of four-figure mathematical tables is provided.
11. You may use a non-programmable scientific calculator.
12. This question paper must be handed in at the end of the examination.
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The following formulae may be helpful in answering the questions. The symbols given are the
ones commonly used.
ALGEBRA
1.2 4
2
b b ac x
a
2. m n m na a a
3. m n m na a a
4. ( )m n mna a
5. log log loga a amn m n
6. log log loga a a
mm n
n
7. log logn
a am n m
8.log
loglog
ca
c
bb
a
9. ( 1)nT a n d
10. [2 ( 1) ]2
n
nS a n d
11. 1n
nT ar
12.( 1) (1 )
, 11 1
n n
n
a r a r S r
r r
13. , 11
aS r
r
CALCULUS
1. ,dy dv du
y uv u vdx dx dx
2.2
,
du dvv u
u dy dx dx yv dx v
3.dy dy du
dx du dx
4. Area under a curve
=b
a
y dx or
=b
a
x dy
5. Volume generated
= 2
b
a
y dx or
= 2
b
a
x dy
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STATISTICS
1.
x
x N
2. fx
x f
3.
2 2
2( ) x x x
x N N
4.
2 2
2( ) f x x fx
x f f
5.
1
2
m
N F m L c
f
6. 1 100o
Q I
Q
7.i i
i
W I I
W
8.
!
!r
nnn r P
9.
!
! !r
nnn r r C
10. P A B P A P B P A B
11. , 1n r n r
r P X r C p q p q
12. Mean, μ = np
13. npq
14. X Z
GEOMETRY
1. Distance
= 2 2
1 2 1 2 x x y y
2. Midpoint
1 2 1 2, ,2 2
x x y y x y
3. A point dividing a segment of a
line
1 2 1 2, ,nx mx ny my
x ym n m n
4. Area of triangle =
1 2 2 3 3 1 2 1 3 2 1 3
1( ) ( )
2 x y x y x y x y x y x y
5. 2 2r x y
6.2 2
ˆ xi yj
r x y
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TRIGONOMETRY
1.
Arc length, s r
2.
Area of sector, 21
2 A r
3. 2 2sin cos 1 A A
4. 2 2sec 1 tan A A
5.
2 2
cosec 1 cot A A
6. sin 2 2sin cos A A A
7. 2 2cos2 cos sin A A A
2
2
2 os 1
1 2 sin
c A
A
8. sin ( ) sin cos cos sin A B A B A B
9. cos( ) os os sin sin A B c Ac B A B
10.tan tan
tan ( )1 tan tan
A B A B
A B
11.2
2tantan 2
1 tan
A A
A
12.sin sin sin
a b c
A B C
13. 2 2 2 2 cosa b c bc A
14. Area of triangle1
sin2
ab C
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Answer all questions.
(a) State the type of relation between set P and set Q .(b) Using function notation, state the relation between set P and set Q.
[2 marks]
Answer : (a) ……………………
(b) ……………………..
2. Given that : 7 4 f x x . Find the value of p if (2) 5 3 f p .
[2 marks]
Answer : p = ……………………
For Examiner’s
Use
1
2
2
2
1. In Diagram 1, set P is the domain and set Q is the codomain of a relation.
4
9
16
4
3
2
Set P Set Q
Diagram 1
2
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3. Given that 1 3: 2, and ( ) .
2 g x ax g x b x Find the values of a and b.
[3 marks]
Answer : a =………………………..
b =………………………..
4. (a) Solve the following quadratic equation:24 4 3 0 x x
(b) Given the quadratic equation 2 9 0 x px has two equal roots. Find the
values of p. [4 marks]
Answer : (a)….……………………
(b)….……………………
5. Find the range of the values of x for 2( 1) (2 3)( 1). x x x [3 marks]
Answer : ……………………………
3
3
4
4
For
Examiner’s Use
5
3
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6. The quadratic function 2( ) 3 6 5 can be expressed in the f x x x 2form 3( ) x p q , where p and q are constants. Find the values of p and q.
[3 marks]
Answer : p = ….………….……
q = ….………….……
7. Given that log 2a
p and1
log2
a q , find the value of
2
loga
p q
a.
[3 marks]
Answer : ….………….…………
8. Solve the equation1
2 1
16 4
y
y y . [3 marks ]
Answer : ….………….…………
For Examiner’s
Use
7
3
8
3
6
3
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9. An arithmetic progression has 15 as the second term and 3 as the common
difference. List the first five terms of the progression. [2 marks]
Answer : ….………………………
10. The first three terms of an arithmetic progression are 4, 3,2 2 p p p .
Find(a) the value of p,
(b) the sum of the first 8 terms of the progression. [4 marks]
Answer : (a)….……………………
(b)….……………………
11. The first term and the fourth term of a geometric progression are 16 and 2
respectively. Calculate the sum to infinity of the geometric progression.
[3 marks]
Answer : ..………………………..
9
2
For Examiner’s
Use
10
4
11
3
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(b).. ……….……………..
17. Solve the equation 3cos 2 8sin 5 for 0 360o o . [ 4 marks ]
Answer : ….………….……………
18. The curve ( ) y f x is such that2
1dy pdx x
, where p is a constant.
The gradient of the curve at 2 x is1
2 . Find the value of p. [2 marks]
Answer : ….………….……………
19. Diagram 4 shows a circle with centre O and radius 4 cm . Given that the area of the
minor sector AOB is 9 cm2, calculate the length, in cm, of the major arc AB.
[Use = 3.142] [4 marks]
Diagram 4
Answer : ….………….…………
For
Examiner’s Use
17
4
18
2
19
4
O
A
B
4 cm
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20. The curve 22 8 3 y x x has a maximum point at x = p , where p is a
constant. Find the value of p . [3 marks]
Answer : ….………………………
21. Given that3
1
( ) 6 g x dx , find
(a) the value of1
3
( ) , g x dx
(b) the value of p if3
1
[ ( )] 18 px g x dx . [4 marks]
Answer : (a) ...………………………
(b) ...………………………
22. A set of data consists of five numbers. The sum of the numbers is 175 and the
sum of the squares of the numbers is 6845. Find, for the five numbers(a) the mean,
(b) the standard deviation. [3 marks]
Answer : (a) ...………………………
(b) ...………………………
For Examiner’s
Use
22
3
21
4
20
3
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23. A badminton team that consists of 8 students is to be chosen from a group of 7male students and 6 female students . Calculate the number of different teams
that can be formed if each team must consist of(a) exactly 3 male students,
(b) not more than 2 female students. [4 marks]
Answer : (a) ………….……………
(b) ……………………….
24. In a shooting competition, the probability that Lim will strike the target is 0.75.
If Lim fires 6 shots, calculate the probability that(a) all the shots hit the target,
(b) at least one of the shots hits the target. [4 marks]
Answer : (a) ………….……………
(b) ……………………….
25. X is a random variable of a normal distribution with a mean of 75 and a standard
deviation of 3 .(a) Find the Z -score if X is 70.
(b) (72 79) P X . [4 marks]
Answer : (a) ………….……………
(b) ……………………….
For Examiner’s
Use
23
4
24
4
25
4
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END OF QUESTION PAPER
PERATURAN PEMARKAHAN EXCEL 2 PAPER 1
NO. SOLUTION AND MARK SCHEME SUBMARK
TOTALMARK
1. (a) many to one
(b) 2 2: or ( ) f x x f x x
11
2
2. P = 3
B1 : 7(2) + 4 = 5p + 3
2 2
3.a =
2, 3 [both]
3b
B2 :2 3 1 2
2 or ,3 2
b ba a
B1 : 1 2 2 2( ) or ( )
3 3
x g x b x g x
a a
3 3
4.(a)
1 3,
2 2 x (both)
B1 :24 4 4(4)( 3)
(2 1)(2 3) 0 or2(4)
x x
(b) p = 6
B1 : 2 4(1)(9) 0 p
2
2
4
5 4 < x < 1 or 1> x > 4
B2 : + +
+
4 1
B1 : ( x + 4 ) ( x – 1 ) < 0
3 3
6 p = 1 , q = 2 (both)
B2 : 3 ( x 1 ) 2 + 2
B1 : 3 ( x2
2 x + 3
5 )
3 3
73
2
1or
2
7or 3.5
B2 : 4 +2
1 1
B1: log a p2 + log a q – log a a
3 3
8 y = 4
B2 : 4( 1) 2 y y y or 3 y = 4 y – 4
3 3
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B1 :4( 1) 2
2 1
2 2
y
y y or equivalent
9 18, 15, 12, 9, 6
B1: a = 18
2 2
10 (a) p = 8
B1 : ( 4)(2 2) 2( 3) p p p or equivalent
(b) 228
B1 : S 8 =2
8[ 2 (4) + 7 ( 7) ] or equivalent
2
2
4
11 32
B2 :
)2
1(1
16
or equivalent
B1 : r =2
1
3 3
12q =
2
1 , p = 1 ( both)
B2 : 4 = 5 2q or p = 2 ( 3) + 5
B1 : x
y2
= 2 x + 5
3 3
13 5
B2 :3
m =
3
5
B1 : gradient =3
m, gradient =
3
5 (both)
3 3
14h =
5
8 , h = 1 (both)
B2 : 5h 2 + 3h – 8 = 0
B1 :
2110 2 8 2 2 10 2 8
2
4 (5 1) 4 1OR or equivalent
2 2 2 2
h h h h
h
h h
3 3
15
2
3( 5 a + 3 b )
3 3
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B2 :3
(10 6 )4
PH a b
B1 : 10 6 PT a b
16 (a)
54 or 4 i + 5 j
B1 :
3
2
2
2 or 2 i + 3 j ( 2 i 2 j )
(b)2
1( i + j ) or
2
1
1
1 or equivalent
B1 : 44 Or 8 Or 2 2
2
2
4
17 41.81, 138.19
B3 : sin =3
2 , sin = 2 ( both)
B2 : (3 sin 2) (4 sin +2) = 0
B1 :3 ( 1 – 2 sin 2 ) = 8 sin 5
4 4
18 p = 2
B1 : 2
1
2 1( 2)
p
2 2
19 s = 20.64 cmB3 : s = 4 (5.159) rad
B2 : major AOB = (2−8
9) rad or 5.159 rad
B1 : 9 =21 ( 4) 2
4 4
20 p = 2
B2 : x – 2 = 0 or 4 p + 8 = 0
B1 : 2 [ ( x 2 )2
( 2)2
+ 2
3
] or 4 8
dy
xdx
3 3
21 (a) 6
(b) p = 6
B2 :2 2(3) 1
( ) 6 18 or equivalent2 2
p
B1 :
32
1
6 182
px
1
3
4
22 (a) mean = 35 1 3
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(b) 12
B1: 26845(35)
5 or equivalent
2
23 (a) 210B1 : 7 C 3 x 6 C 5
(b) 111
B1 : 7 C 7 x 6 C1 + 7 C 6 x 6 C
2
2
2
4
24 (a) 0.1780
B1 : 6 C 6 ( 0.75) 6 (0.25) 0 or equivalent
(b) 0.9998
B1 : 1 P( x = 0)
2
2
4
25 (a) Z = 1.667
B1 :3
7570 or equivalent
(b) 0.7449 – 0.7501
B1 : 1 – P( x 1) – P( x 1.333) or equivalent
2
2
4
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CO-ORDINATOR
JUDY LIAN YEE LING
SEKTOR PENGURUSAN AKADEMIK
LIST OF PANEL MEMBERS
1. Shirney Chua (Leader) SMK Kolombong, Inanam
2. Phoon Chiew Fun SMK Chung Hwa, Tenom
3. Seak Sain Yon SMK Konven St. Ursula, Tawau
4. Aileen Beh Chik Heang SMK Datuk Peter Mojuntin, Penampang
5. Sudirman Darise SMK Bongawan, Papar
6. Surianih Sewan SMK Sri Nangka, Tuaran
7. Ting Kai Chu SMK St. Michael, Penampang
8. Farah Ibrahim SMK Agama, Kota Kinabalu
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