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SULIT 3472/1
KOLEJ TUNKU KURSHIAH
KOLEJ TUNKU KURSHIAH, SEREMBANBANDAR ENSTEK, SEREMBAN
PEPERIKSAAN PERTENGAHAN TAHUN 2015 TINGKATAN 4 MATEMATIK TAMBAHAN 3472/1MASA : 2 JAM Dua jamMEI 2015
DO NOT OPEN THE QUESTION PAPER UNTIL YOU ARE TOLD TO DO SO.
For Examiner’s Use
QuestionMarks
AllocatedMarks
Obtained1 22 23 24 35 46 37 28 39 310 311 312 313 414 415 416 317 318 419 420 321 422 323 424 325 4
TOTAL MARKS
80
This question paper has 13 printed pages.
[ Lihat sebelah3472/1 SULIT
NAMA : ………………………………………………
TINGKATAN :……………
1. Write your name and class clearly in
the space provided on this page.
2. Read the information on page 13
carefully.
3. This question paper must be handedin at the end of the examination.
SULIT 3472/1
The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used.
ALGEBRA
1
2 am ¿ an = a m + n
3 am ¿ an = a m - n
4 (am) n = a nm
5 loga mn = log am + loga n
6 loga
mn = log am - loga n
7 log a mn = n log a m
8 logab =
log c b
log c a
9 Tn = a + (n-1)d
10 Sn =
n2[2 a+(n−1 )d ]
11 Tn = ar n-1
12 Sn =
a(r n−1 )r−1
=a(1−rn )
1−r , (r ¿ 1)
13 S∞= a
1−r , |r|<1
CALCULUS
1 y = uv ,
dydx
=udvdx
+vdudx
2 y=u
v ,
dxdy
=v
dudx
−udvdx
v2,
3
dydx
=dydu
×dudx
4 Area under a curve
= ∫a
b
y dx or
= ∫a
b
x dy
5 Volume generated
= ∫a
b
πy2
dx or
= ∫a
b
πx2
dy
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5 A point dividing a segment of a line
( x,y) = (
nx1+mx2
m+n,ny1+my2
m+n)
6 Area of triangle =12|(x1 y2+ x2 y3+x3 y11
)−( x2 y1+x3 y2+x1 y3 )|
1 Distance = √( x1−x2 )2+( y1− y2 )
2
2 Midpoint
(x , y) = (
x1+ x2
2 ,
y1+ y2
2)
3 |r|=√ x2+ y2
4
GEOMETRY
2
SULIT 3 3472/1
STATISTICS
[ Lihat sebelah3472/1 SULIT
1 Arc length, s = rθ
2 Area of sector , L = 3 sin 2A + cos 2A = 1
4 sec2A = 1 + tan2A
5 cosec2 A = 1 + cot2 A
6 sin 2A = 2 sinA cosA
7 cos 2A = cos2A – sin2 A = 2 cos2A - 1 = 1 - 2 sin2A
8 tan 2A =
2 tan A
1−tan2 A
TRIGONOMETRY
9 sin (A±B) = sinA cosB ± cosA sinB
10 cos (A±B) = cosA cosB ∓ sinA sinB
11 tan (A±B) =
tan A±tan B1∓tan A tan B
12
asin A
= bsin B
= csin C
13 a2 = b2 + c2 - 2bc cosA
14 Area of triangle =
12
ab sin C
1 x =
∑ x
N
2 x =
∑ fx
∑ f
3 = √∑ ( x−x )2
N = √∑ x2
N− x
¿2
4 = √∑ f ( x−x )2
∑ f = √∑ fx2
∑ f−x2
5 m = L+[ 1
2N−F
f m]C
6
7 I=
∑ w1 I 1
∑w1
8
n Pr=n!
(n−r )!
9
n C r=n !
(n−r ) !r !
10 P(A¿ B) = P(A)+P(B)- P(A¿ B)
11 P (X = r) = n C r pr qn−r
, p + q = 1
12 Mean µ = np
13 σ=√npq
14 z =
x−μσ
SULIT 3472/1Answer all questions.
1. Diagram 1 shows the relation between set M and set N.
DIAGRAM 1
State,
(a) the codomain of that relation,
(b) the type of relation
[ 2 marks ]
Answer : (a) ……………………..
(b) ……………………...
2. Given f : x→2 x−5 , Find value of q if f (q )=q
[ 2 marks]
Answer : ……………………..
3. The relation between J = {4, 6, 15, 17} and K = {2,3,5,7} is defined by the ordered
pairs of {(4,2), (6,2), (6,3), (15,3), (15,5)}. State
For examiner’s
use only
2
2
1
2
4
SULIT 3 3472/1
a) The object of 5,b) The range of the relation.
[2 marks ]
Answer :(a) ...………………………......
:(b) ...………………………......
4. Given the functions f : x → x – 1 and g : x → , find
(a) The composite function g f,(b) The value of x if g f(x) = 9.
[3 marks ]
Answer : (a).........………………… : (b) ...…………………...
5. Given the functions f : x → 5x+3 and g : x → x+ 1, find the value of f−1(g). [ Lihat sebelah
3472/1 SULIT
For examiner’s
use only
3
2
4
3
SULIT 3472/1
[4 marks]
Answer : ……........................
6. A rock falls from a height of 64 metres above the ground. It’s height, H (in metres) after t seconds is given by H (t )=64−16 t2 .a) What is the height of the rock when t=1.5 seconds?b) When does the rock strike the ground? [3 marks]
Answer : a)…...…………..……..b) …...…………..……..
7. It is given that x = is one of the roots of the quadratic equation 2x2 – 3x + 1 = 0. Find the value of another root.
[2 marks]
Answer : …...…………..……..…...
5
4
7
2
6
3
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use only
6
SULIT 3 3472/1
8. Given that α and β are the roots of quadratic equation 2 x2+5 x−3=0,
form a quadratic equation which has roots 1
2 α and
12 β
.
[3 marks ]
Answer : ...………………………...
9. The quadratic equation 4x + c = 16 – (2 – x)2 has two equal roots. Find the value of c
[3 marks ]
Answer : .........…………………
10. The roots of the equations 2 x2−5 x+4+k=0are h and k , Find the value of k and h[3 marks ]
Answer : .........………………
11. The quadratic function f ( x )=p (x+q)2=r, where p ,q , r are constants, has minimum value of -4. The equation of the axis symmetry is x=3. State
a) The ranges of values of p[ Lihat sebelah
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8
3
9
3
10
3
SULIT 3472/1 b) The values of q c) The value of r
[3 marks]
Answer : a) .........………………… b) .........………………… c) .........…………………
12 Find the range of x for3 x2−5 x−16 ≤ x (2 x+1). [3 marks]
Answer : …...…………..……..…...
13. Solve the simultaneous y=4 x−1 and (x+1)( y+2)=0.[4 marks]
Answer : …...…………..……..…...14. Pak Hassan has a rectangular plot of land. Given that the perimeter and area of the land
are 150m and 1250 m2 respectively. Find the length and width of the land.
[4 marks]
11
3
13
2
12
3
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use only
8
SULIT 3 3472/1
Answer : ...………………………......
15. Solve the simultaneous equations x – y = –1 and x2 + y2 = 25.
[4 marks ]
Answer : .........…………………
16. Sketch the graph for the quadratic function f ( x )=2(x−1)2−5.
[3 marks]
Answer : .........…………………
17. Solve the equation 4 x−1=8x +3
[3 marks]
[ Lihat sebelah3472/1 SULIT
14
3
15
4
16
3
SULIT 3472/1
Answer : ……........................
18. Solve the equation 23 x=8+23x−1
[4 marks]
Answer : …...…………..……..…...
19. Given that log 2 x=hand log 2 y=k , express log 2x3
y in terms of h and k .
[4 marks]
Answer : …...…………..……..…...
20. Solve the equation log3 2+ log3( x−4)=1 [3 marks]
17
3
19
4
18
4
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use only
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3
10
SULIT 3 3472/1
Answer : ...………………………......
21. Given that log10 x y2=1 and log10 x2 y=−1. Find the values of x andy.
[4 marks ]
Answer : .........…………………
22. Given the points A(4,6) and B(-1,3), a point P divides AB in the ratio 3:1, find coordinates of the point P.
[3 marks]
Answer : .........…………………
23. The distance between points (4,2) and (a,3) is √17 units. Find the possible values of a.
[4 marks]
[ Lihat sebelah3472/1 SULIT
21
4
22
3
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Answer : ……........................
24. Points A(2,3) , B(-2h, 4) and C(5h,1) are collinear. Find the value of h.
[3 marks]
Answer : …...…………..……..…...
25. Find the equation of the straight line that passes through point (-3,6) and is parallel to the straight line 2 x−4 y+3=0.
[4 marks]
Answer : …...…………..……..…...
END OF THE QUESTION PAPER
INFORMATION FOR CANDIDATES
1 This question paper consists of 25 questions.
2 Answer all questions.
3 Write you answer clearly on the answer spaces provided in the question paper.
4 Show your working. It may help you to get marks.
23
4
25
4
24
3
12
SULIT 3 3472/1
5 The diagrams in the questions provided are not drawn to scale unless stated.
6 The marks allocated for each question and sub-part of a question are shown in
brackets.
7 A list of formulae is provided on pages 2 and 3.
8 You may use a non-programmable scientific calculator.
9 This question paper must be handed in at the end of the examination
Prepared by, Checked by,
………………………………….(Pn. Maisarah Abdul Manas)
………………………………….( Pn. Norlida Binti Ahmad )
Additional Mathematic’s Teacher Head of Additional Mathematic’s Panel.
Approved by,
………………………………….(Cik Rahmah Binti Kasmuni)
Head of Vocational and Technic’s Department
[ Lihat sebelah3472/1 SULIT