Add mth f4 final sbp 2008
-
Upload
shaila-rama -
Category
Technology
-
view
910 -
download
4
Transcript of Add mth f4 final sbp 2008
3472/1 2008 Hak Cipta SBP [Lihat sebelah SULIT
SEKOLAH BERASRAMA PENUH
BAHAGIAN PENGURUSAN SEKOLAH BERASRAMA PENUH / KLUSTER
KEMENTERIAN PELAJARAN MALAYSIA
PEPERIKSAAN AKHIR TAHUN TINGKATAN 4 2008
Kertas soalan ini mengandungi 15 halaman bercetak
For examiner’s use only
Question Total Marks Marks Obtained
1 2 2 4 3 4 4 4 5 2 6 2 7 3 8 3 9 3
10 4 11 3 12 3 13 4 14 3 15 4 16 2 17 3 18 3 19 4 20 3 21 2 22 3 23 4 24 4 25 4 TOTAL 80
ADDITIONAL MATHEMATICS
Kertas 1 Dua jam
JANGAN BUKA KERTAS SOALAN INI
SEHINGGA DIBERITAHU
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 spaces 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 and sub- part of a question are shown in brackets. 9. A list of formulae is provided on pages 2 and 3. 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.
Name : ………………..…………… Form : ………………………..……
3472/1 Additional Mathematics Kertas 1 Oktober 2008 2 Jam
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
SULIT 3472/1
3472/1 2007 Hak Cipta SBP [ Lihat sebelah SULIT
The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used.
ALGEBRA
1 2 4
2b b acx
a− ± −
=
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 nm
= log am - loga n
7 log a mn = n log a m
8 logab = ab
c
c
loglog
CALCULUS
1 y = uv , dxduv
dxdvu
dxdy
+=
2 vuy = , 2v
dxdvu
dxduv
dydx −
= ,
3 dxdu
dudy
dxdy
×=
3 A point dividing a segment of a line
( x,y) = ,21
+
+
nmmxnx
+
+
nmmyny 21
4 Area of triangle
= )()(21
312312133221 1yxyxyxyxyxyx ++−++
1 Distance = 221
221 )()( yyxx −+−
2 Midpoint
(x , y) = +
221 xx ,
+
221 yy
GEOMETRY
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
3472/1 2008 Hak Cipta SBP [ Lihat sebelah SULIT
3
STATISTIC
7 1
11
wIwI
=
1 Arc length, s = rθ
2 Area of sector , L = 212
r θ
TRIGONOMETRY
3 Cc
Bb
Aa
sinsinsin==
4 a2 = b2 + c2 - 2bc cosA
5 Area of triangle = Cabsin21
1 x = N
x
2 x =
ffx
3 σ = N
xx − 2)( =
2_2
xN
x−
4 σ =
−
fxxf 2)(
= 22
xf
fx−
5 m = Cf
FNL
m
−+ 2
1
6 1
0
100QIQ
= ×
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
3472/1 2008 Hak Cipta SBP [ Lihat sebelah SULIT
Answer all questions.
1. Diagram 1 shows the linear function f . (a) State the value of k. (b) Using function notation, write a relation between set A and set B.
[ 2 marks]
Answer : (a) ……………………..
(b) ...…………………... 2. The following information above refers to the functions f and g . (a) State the value of h. (b) Find the value of )3(1−fg .
[ 4 marks ]
Answer : (a) …………………….
(b) ..............................
4
2
2
1
For examiner’s
use only
hxx
xxf ≠+
→ ,3
4:
xxg 21: −→
1
3
5
7
3
5
k
9
x f(x)
Set A Set B
Diagram 1
f
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
3472/1 2008 Hak Cipta SBP SULIT
3. Given the function 12: −→ xxf and 16: +→ xxfg . Find (a) the function g(x) (b) the value of x when 4)( =xgf .
[ 4 marks ]
Answer : (a).........…………………
(b).....................................
4. Given that the roots of the quadratic equation kxx −=− 512 are 3 and p . Find the value of k and of p .
[4 marks]
Answer : k =.........………
p =....................
5. The quadratic equation 0122 2 =+−− pxx has two distinct roots. Find the range of values of p . [2 marks]
Answer : .............………
For examiner’s
use only
4
3
4
4
2
5
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
3472/1 2008 Hak Cipta SBP [ Lihat sebelah SULIT
x
5
Diagram 2
)4,1( −+k
y
6. Diagram 2 shows the graph of the function pxy −+= 2)3( where p is a constant and )4,1( −+k is a minimum point.
Find
a) the value of k. b) the value of p.
2 marks ]
Answer : (a) ................................
(b) .................................
___________________________________________________________________________
7Find the range of values of x for which )52(3 −≤ xx . [3 marks]
Answer : ..................................
8. Solve the equation 455 12 =− ++ xx . [3 marks]
Answer : …….……………….
2
6
For examiner’s
use only
3
7
3
8
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
3472/1 2008 Hak Cipta SBP SULIT
9. Given xp =3log and yp =2log , express 12log8 in terms of x and y.
[3 marks]
Answer : ..................................
10. Solve the equation 0)1(log)23(log 33 =−−+ xx
[4 marks]
Answer : ...................................
11. The points )2,(,),( rPttA and )2,9( −−B are on a straight line. P divides AB internally in the ratio of 3 : 4 . Find the value of t and of r . [3 marks]
Answer : t = .............................. r = ..............................
3
9
For examiner’s
use only
4
10
3
11
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
3472/1 2008 Hak Cipta SBP [ Lihat sebelah SULIT
12. Diagram 3 shows a straight line PQ with equation 01234 =−+ yx .
Find (a) the value of h and of k (b) the equation of PQ in intercept form. [3 marks]
Answer : (a) ....……………...………..
(b) .........................................
13. Find the equation of the straight line that passes through a point )1,3(−P and is
perpendicular to the straight line 145=+
yx .
[4 marks]
Answer: …...…………..….......
3
12
For examiner’s
use only
4
13
P(k,0)
Q(0,h)
x
y
O
Diagram 3
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
3472/1 2008 Hak Cipta SBP SULIT
14. The coordinates of point P and Q are )1,3(− and )10,6( respectively. The point X moves such that XP : XQ = 2 : 3 . Find the equation of the locus of X . [3 marks]
Answer: …...….………..….....................
___________________________________________________________________________ 15. Table 1 shows the distribution of the weight of 40 pupils in form 4 Alpha. Table 1 (a) Find the range of the weight. (b) Without drawing an ogive, calculate the median of the distribution of weight.
[4 marks]
Answer : (a) …………………….
(b) ….……………….....
Weight (kg) Number of pupils 31 – 35 7 36 – 40 4 41 – 45 8 46 – 50 7 51 – 55 6 56 – 60 4 61 – 65 4
4
15
For examiner’s
use only
3
14
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
3472/1 2008 Hak Cipta SBP [ Lihat sebelah SULIT
16. The mean of ten numbers is m . The sum of squares of the number is k and the standard deviation is 4. Express k in terms of m .
[2 marks] Answer : .…………………
17. Diagram 4 shows a circle with centre O. The length of the minor arc AB is 3.9275 cm and the angle of the major sector AOB is 315o. Using 142.3=π , find (a) the value of θ , in radians, (Give your answer correct to four significant figures.)
(b) the length, in cm, of the radius of the circle.
[3 marks]
Answer: ……..…….…………... ___________________________________________________________________________
2
16
3
17
For examiner’s
use only
O
A
B
Diagram 4
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
3472/1 2008 Hak Cipta SBP SULIT
Diagram 5 shows a sector OTV of a circle, centre O. Find the perimeter of the shaded region.
[3 marks]
Answer: ...………………………
___________________________________________________________________________ 19. Diagram 6 shows a sector of a circle OPQ with centre O and OPR is a right angle triangle. Find the area, in cm2, of the shaded region.
[4 marks]
Answer:………………………
For examiner’s
use only
3
18
O R Q 1 cm
5 cm
P
4
19
O
T
V 50°
7 cm
Diagram 5
Diagram 6
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
SULIT 3472/1
3472/1 2008 Hak Cipta SBP [ Lihat Sebelah SULIT
20. Evaluate the following limits,
(a) 1
1lim1 +→ xx
(b) 39lim
2
3 −
−→ x
xx
[ 3 marks ] Answer: (a) ....…………..….......
(b) .................................
___________________________________________________________________________ 21. The straight line 12 +−= xy is the tangent to the curve xxy 42 −= at the point P. Find the x-coordinate of the point P .
. [2 marks]
Answer: ……………………..
22. Given that xqpxy −= 2 and ,4
2xx
dxdy
+= where p and q are constants , find the
value of p and of q .
[3 marks]
Answer: ……………………..
2
21
3
22
For examiner’s
use only
3
20
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
SULIT 3472/1
3472/1 2008 Hak Cipta SBP SULIT
23. Given the curve 221x
xy += .
(a) Find the coordinates of the turning point.
(b) Hence, determine whether it is a maximum or a minimum point.
[4 marks]
Answer: (a)…...…………..….......
(b)....................................
___________________________________________________________________________ 24. A cylinder has a fixed height of 10 cm and a radius of 5 cm. If the radius decreases by 0.05 cm, find (in terms of π ) (a) the approximate change in the volume of the cylinder, (b) the final volume of the cylinder. [4 marks]
Answer: (a)……………………………
(b)……………………………
For examiner’s
use only
4
24
4
23
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
SULIT 3472/1
3472/1 2008 Hak Cipta SBP [ Lihat Sebelah SULIT
25. Given x
xy2)2( −
= , find the value of 2
2
dxyd when 1−=x .
[4 marks]
Answer: …...…………..….......
END OF QUESTION PAPER
4
25
For examiner’s
use only
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
2
PEPERIKSAAN AKHIR TAHUN TINGKATAN 4 2008 MARK SCHEME KERTAS 1
No. Solution and mark scheme Sub marks Full marks 1 (a) k = 7
(b) 2: +→ xxf or 2)( += xxf
1
1
2
2 (a) h = - 3 (b) - 2
B2 : 31)1(4
+−
−
B1 : 2
1)(1 xxg −=−
1
3
4
3 (a) 13)( += xxg B1 : 161)(2 +=− xxg (b) 1=x B1 : 41)12(3 =+−x
2
2
4
4 p = 2, k = 7 (both) B3 : p + 3 = 5 and 3p = k – 1 B2 : p + 3 = 5 or 3p = k – 1 B1 : 0152 =−+− kxx
4 4
5 21
>p
B1 : 0)1)(2(4)2( 2 >+−−− p
2 2
6 k = -4 p = 4
1
1
2
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
3
7 21,3 −≤≥ xx (both)
B2 : 0)3)(12( ≥−+ xx B1 : 0352 2 ≥−− xx
3 3
8 x = -1 B2 : 155 −=x B1 : 45555 12 =×−× xx
3 3
9 y
yx3
2+
B2 : 2log3
2log2log3log
p
ppp ++
B1 : 32log)223(log
p
p ××
3 3
10 23
−=x
B3 : 123 −=+ xx
B2 : 03123=
−
+
xx
B1 : 0123log3 =
−
+
xx
4 4
11 r = -1 B2 : t = 5
B1 : 7
462 t+−= or
7274 −
=tr
3 3
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
4
12 a) h = 4
k = 3
b) 143=+
yx
1
1
1
3
13 4
1945
+= xy or equivalent
B3 : )3(45)1( +=− xy
B2 : 45
2 =m
B1 : 54
1 −=m
4 4
14 04546210255 22 =−+++ yxyx B2 : 22 )1()3(3 −++ yx = 22 )10()6(2 −+− yx B1 : 3XP = 2XQ
3 3
15 (a) 30 (b) 46.21
B2 : m = 45.5 + 57
192
40
− (all values correct)
B1 : 45.5 ,19 , 7 , 5 (at least two are correct)
1
3
4
16 210160 mk +=
B1 : 2
1016 mk
−=
2 2
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
5
17 a) 0.7855
b) r = 5 B1 : 3.9275 = r (0.7855)
1
2
3
18 Perimeter = 12.0263 B2 : length PQ = 2r sin 25 0 = 5.9167 B1 : arc PQ = r = 7 (0.8728) = 6.1096
3
3
19 Area = 2.045
B3 : )3)(4(21)6436.0)(5(
21 2 −
B2 : = 0.6436 rad
B1 : tan = 43
4
4
20 (a)
21
(b) 6
B1 : 3
)3)(3(lim3 −
−+→ x
xxx
1
2
3
21 1=x
B1 : 42 −= xdxdy
2 2
22 21
=p and 4=q
B2 : 21
=p or 4=q
B1 : 22xqpx
dxdy
+=
3 3
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
6
23 (a)
23,1
B1 : 01 3 =− −x
(b) ,032
2
>=dx
yd minimum point
B1 : 42
2
3 −= xdx
yd
2
2
4
24 (a) π5−
B1 : )5(20π=drdV or 100π
(b) π245 B1 : ππ 5)5(10 2 −=newV
2
2
4
25 8−
B3 : 32
2
8 −= xdx
yd or 4
22 )2)(4()2(x
xxxx −−
B2 : 241 −−= xdxdy or 2
2)2()2(2x
xxx −−−
B1 : 144 −+−= xxy
4 4
END OF MARK SCHEME
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
3472/2 2008 Hak Cipta SBP [ Lihat sebelah SULIT
3472/2 Additional Mathematics Kertas 2 2 ½ jam OKT 2008
SEKTOR SEKOLAH BERASRAMA PENUH BAHAGIAN PENGURUSAN
SEKOLAH BERASRAMA PENUH / KLUSTER KEMENTERIAN PELAJARAN MALAYSIA
PEPERIKSAAN AKHIR TAHUN
TINGKATAN 4 2008
ADDITIONAL MATHEMATICS
Kertas 2
Dua jam tiga puluh minit
JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU
1. This question paper consists of three sections : Section A, Section B and Section C. 2. Answer all question in Section A , four questions from Section B and two questions from
Section C.
3. Give only one answer / solution to each question..
4. Show your working. It may help you to get marks.
5. The diagram 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 to 3.
8. A booklet of four-figure mathematical tables is provided.
9. You may use a non-programmable scientific calculator.
Kertas soalan ini mengandungi 13 halaman bercetak
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
2
3472/2 2008 Hak Cipta SBP SULIT
The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used.
ALGEBRA 1
aacbbx
242 −±−
= 5 nmmn aaa logloglog +=
2 nmnm aaa +=× 6 nm
nm
aaa logloglog −=
3 nmnm aaa −=÷ 7 mnm an
a loglog = 4 ( ) mnnm aa =
8
axx
b
ba log
loglog =
KALKULUS (CALCULUS)
STATISTIK (STATISTICS)
1 uvy = , dxduv
dxdvu
dxdy
+=
2 vuy = , 2v
dxdvu
dxduv
dxdy −
=
3 dxdu
dudy
dxdy
×=
1 Nx
x =
2 =
ffx
x
3 ( ) 222
xN
xN
xx−==
−= σ
4 ( ) 2
22
xf
fxf
xxf−=
−=
σ
6 Cf
FNLM
m
−+= 2
1
5 1000
1 ×=QQI
7 =−
i
ii
WIW
I
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
3
3472/2 2008 Hak Cipta SBP [ Lihat sebelah SULIT
GEOMETRI (GEOMETRY)
TRIGONOMETRI (TRIGONOMETRY) 1. Panjang lengkok, js =
Arc length, rs =
2. Luas Sektor, 21 2jL =
Area of sector, 21 2rA =
3. 4.
5.
Cc
Bb
Aa
sinsin sin ==
Abccba kos2222 −+= Abccba cos2222 −+=
12
Luas segitiga ( ) sin
Area of triangleab C=
1. Jarak (Distance) ( ) ( )221
221 yyxx −+−
2. Titik tengah (Midpoint)
++
=2
,2
),( 2121 yyxxyx
3. Titik yang membahagi suatu tembereng garis
(A point dividing a segment of a line)
+
+
+
+=
nmmyny
nmmxnxyx 2121 ,),(
4. Luas segitiga (Area of triangle) =
( ) ( )31231213322121 yxyxyxyxyxyx ++−++
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
4
3472/2 2008 Hak Cipta SBP SULIT
SECTION A
[40 marks]
Answer all questions in this section 1. Solve the simultaneous equations
425 −=+ yx 16232 =+− yxx
[5 marks]
2. Express f (x) = 1 – 6x + 2x2 in the form f (x) = m(x + n)2 + k , where m, n and k are
constants.
(a) State the values of m, n and k.
[3 marks]
(b) Find the maximum or minimum point.
[1 marks]
(c) Sketch the graph of f (x) = 1 – 6x + 2x2.
[2 marks]
3. (a) The straight line y = 1 – tx is a tangent to the curve y2 – 3y + 3x – x2 = 0.
Find the possible value of t. [3 marks]
(b) Given p and q are the roots of the quadratic equations 2x2 + 7x = m – 5, where pq = 3 and m is a constant. Calculate the values of m, p and q.
[4 marks]
4 (a) Given that 29 . 27 1x y = , find the value of x when 4y = −
[2 marks]
(b) Solve the equation 3 23 .6 18x x x−=
[2 marks]
(c) Solve the equation 2 4log ( 2) 2 2log (4 )x x− = + −
[3 marks]
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
5
3472/2 2008 Hak Cipta SBP [ Lihat sebelah SULIT
5
(a) A set of N numbers have a mean of 8 and standard deviation of 2.121. Given that the sum of the numbers, x , is 64. Find
(i) the value of N
(ii) the sum of the squares of the numbers.
[4 marks]
(b) If each of the numbers is divided by h and is added by k uniformly , the new mean
and standard deviation of the set are 5 and 1.0605 respectively.
Find the value of h and k.
[4 marks]
6. The gradient of the tangent to the curve 2qxpxy −= , where p and q are constants, at
the point (1 , 4) is 2. Find
(a) the value of p and q. [4 marks]
(b) the equation of normal to the curve at the point ( 2, 4) [3 marks]
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
6
3472/2 2008 Hak Cipta SBP SULIT
SECTION B
Answer four questions in this section
7 Diagram 1 shows function g maps x to y and function h maps z to y.
Given g (x) = mxx
≠−
,12
1 and h (z) = 1 + 4z.
(a) State the value of m. [1 marks]
(b) Find
(i) gh -1(x) (ii) h g -1(1).
[6 marks] (c) Find the value of
(i) a (ii) b
[3 marks]
Diagram 1
x y
z
g
h
a
b
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
7
3472/2 2008 Hak Cipta SBP [ Lihat sebelah SULIT
8. Diagram 2 shows a quadrilateral PQRS with vertices ( 2,5)R − and ( 1,1)S − .
Given the equation of PQ is 1474 −= xy . Find ,
(a) the equation of QR [4 marks]
(b) the coordinates of Q [2 marks]
(c) the coordinates of P [1 marks]
(d) the area of quadrilateral PQRS [3 marks]
R(−2, 5)
S(−1, 1)
P
Q
O
Diagram 2
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
8
3472/2 2008 Hak Cipta SBP SULIT
9
Table 1 shows the total time spent on watching television by 120 students for a period of 3 weeks. Calculate ,
(a) the mean, [2 marks]
(b) the standard deviation, [3 marks]
(c) the third quartile, [5 marks]
of the distribution
Total Time (hours) Number of students
5 – 14 12
15 – 24 17
25 – 34 26
35 – 44 31
45 – 54 16
55 – 64 10
65 – 74 8
Table 1
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
9
3472/2 2008 Hak Cipta SBP [ Lihat sebelah SULIT
10. Diagram 3 shows a circle ABCF with radius 6 cm and centre O.
Given that oODB 30=∠ , EBD is the tangent to the circle and OD = OE = 12 cm. Find ,
(a) the length of BD [3 marks]
(b) the area of shaded region [3 marks]
(c) the perimeter of the whole diagram [4 marks]
O
A
D
E
B
C
F
Diagram 3
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
10
3472/2 2008 Hak Cipta SBP SULIT
11
Diagram 4 shows a rectangle PQRS and a parallelogram ABCD.
(a) If L 2cm is the area of the parallelogram,
(i) Show that 22 16L x x= − +
(ii) Find the value of x when L is maximum.
(iii) Find the maximum area of the parallelogram ABCD. [7 marks]
(b)
Given that the rate of change of x is -10.1 cms , find the rate of change of L , in -1cms , when x is 2 cm.
[3 marks]
B P Q
A
S D
C
R
x cm
x cm
x cm
x cm
10 cm
6 cm
Diagram 4
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
11
3472/2 2008 Hak Cipta SBP [ Lihat sebelah SULIT
SECTION C Answer two questions in this section
12. Diagram 5 shows two triangles ABC and ACD . BCD is a straight line.
Find ,
(a) ADC∠ [3 marks]
(b) the length of CD [3 marks]
(c) the area of triangle ABD [4 marks]
13
Diagram 6 shows two triangles ABE and BCF , where ABC is a straight line. Given that AE = 5 cm, BE = 7 cm, BC = 8 cm, CF = 9 cm, 050=∠BAE , 0104EBF∠ = and .1000=∠BCF Calculate
(a) AEB∠ , [3 marks]
(b) the length of BF. [3 marks]
(c) if point E joint with F, find the area of the quadrilateral ACFE. [4 marks]
A
D C B 55o
8 cm 8 cm 9 cm
Diagram 5
50o 1040 100o
A B C
E F
Diagram 6
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
12
3472/2 2008 Hak Cipta SBP SULIT
14 Table 2 shows the prices and the price indices of five types of food, H, I, J, K and L
represented the cost of food. Diagram 7 shows a percentage according to the food’s pyramid.
Types of food
Price (RM) for the year Price index for the year 2008
based on the year 2006 2006 2008
H 2.20 2.75 125 I m 2.20 110 J 5.00 7.50 150 K 3.00 2.70 n
L 2.00 2.80 140
(a) Find the value of m and of n. [3 marks]
(b) Calculate the composite index for the cost of food in the year 2008 based on the year 2006.
[3 marks] (c) The price of each food increases by 30% from the year 2008 to the year 2009.
Given that the cost of food in the year 2006 is RM80, calculate the corresponding cost in the year 2009.
[4 marks]
L I
10 %
K 20 %
J
25 % H 40 %
Table 2
Diagram 7
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
13
3472/2 2008 Hak Cipta SBP [ Lihat sebelah SULIT
15
Table 3 shows the price indices and percentage of usage of four items, J, K, L and M, which are the main ingredients in the production of a brand of cake.
(a) Calculate (i) the price of item M in the year 2003 if its price in the year 2005
was RM2.50.
(ii) the price index of item J for the year 2005 based on the year 2001 if its price index for the year 2003 based on the year 2001 is 108.
[5 marks]
(b) The composite index of the cost of cake production for the year 2005 based on the year 2003 is 113. Calculate ,
(i) the value of t
(ii) the price of a cake in the year 2003 if its corresponding price in the year 2005 was RM 25,
[ 5 marks ]
END OF THE QUESTIONS
Item Price Index for the year 2005 Based on the year 2003 Percentage of usage (%)
J 118 22
K t 12
L 108 31
M 113 35
Table 3
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
2
SKEMA PERMARKAHAN MATEMATIK TAMBAHAN KERTAS 2
PEPERIKSAAN DIAGNOSTIK TINGKATAN 4, 2008
Number Solution and mark scheme Sub Marks Full Marks 1 4 5 4 2@
2 5x yy x− − − −
= =
2
2
4 53 2 162
4 2 4 2@ 3 2 165 5
xx x
y y y
− − − + =
− − − − − + =
( )( ) ( )( )10 2 0@ 27 3 0x x y y− + = + − = 10, 2 and 27,3x y= − = −
P1 K1 K1 N1, N1 5
5 2
(a)
23 7
22 2
x − −
m = 2 , n = – 32
and k = – 72
K1 N 0, 1, 2 3
6
(b)
72
3( , )2
−
N1 1
(c)
Shape Minimum point and y-intercept
P1 P1 2
y
( 32
,– 72
) •
o x
1
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
3
Number Solution and mark scheme Sub Marks Full Marks 3
(a)
(1 – tx)2 – 3(1 – tx) + 3x – x2 = 0 (t2 – 1)x2 + (t + 3)x – 2 = 0 (t + 3)2 – 4(t2 – 1)(–2) = 0 (3t + 1) (3t + 1) = 0
.31
−=t
K1 K1 N1 3
7
(b)
SOR or POR pq or p + q POR: pq = 3
5 32
1..
m
m
−=
= −
7:2
3 22
322
.
SOR p q
q or
p or
+ = −
= − −
= − −
K1 N1 N1 N1 4
4
(a)
3034
3)3()3( 0322
=
=+
=⋅
xyx
yx
K1 N1 2
7
(b)
3 218 183 21
x x
x xx
−=
= −
=
K1 N1 2
(c)
4log)4(log22)2(log
2
22
xx −+=−
Change base
)4(log4log)2(log 222 xx −+=−
( 2) 4(4 )3.6
x xx
− = −
=
K1 K1 N1 3
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
4
Number Solution and mark scheme Sub Marks Full Marks 5
(a)
i) 648
8N
N
=
=
ii)
=
−=
99.547
88
121.2
2
22
x
x
K1 N1 K1 N1 4
8
(b)
New mean = 58=+ k
h
or
New Stnd. Deviation = 0605.1121.2=
h
h = 2
8 52
1
k
k
+ =
=
K1 N1 K1 N1 4
6
(a)
)1(22
2
qp
qxpdxdy
−=
−= ……………
Substitute ( 1, 4 ) in 2qxpxy −= 4 = p – q ………… – ; q = 2 and p = 6
K1 K1 K1 N1 4
7
(b) x = 2, )2(46 −=
dxdy
21
2
2
1
=
−=∴
m
m
3
21
)2(214
+=
−=−
xy
xy
K1 K1 N1 3
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
5
Number Solution and mark scheme Sub Marks Full Marks
7
(a)
.
21
=m P1 1
10
(b)
(i) 4
1)(1 −=− zzh
1
412
1)(1
−
−
=−
xxgh
.3,3
2≠
−= x
x (ii) 1 = g(x)
1
1
112 11
(1) (1) 1 4(1)(1) 5
xx
hg hhg
−
−
=−
=
= = +
=
K1 K1 N1 K1 K1 N1 6
(c) (i)
1( )41
12( ) 14
2
a g
a
a
=
=−
= −
(ii)
( )1 4 2
34
h b ab
b
=
+ = −
= −
K1 N1 N1 3
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
6
Number Solution and mark scheme Sub Marks Full Marks 8
(a)
4RSM = − 14QRM =
( )15 24
y x− = + or other suitable method
4 22y x= + or equivalent
P1
P1
K1
N1 4
10
(b)
Solve simultaneous equation 22 7 14x x+ = − (6,7)Q
K1 N1 2
(c)
(2, 0)P
N1 1
(d) Area of quadrilateral PQRS 2 6 2 1 210 7 5 1 02
1 [2(7) 6(5) ( 2)(1) ( 1)(0)] [6(0) ( 2)7 ( 1)5 2(1)]229.5
− −=
= + + − + − − + − + − +
=
K1 K1 N1 3
9
(a)
12(9.5) 17(19.5) 26(29.5) 31(39.5) 16(49.5) 10(59.5) 8(69.5)120
x + + + + + +=
= 36.5
K1 N1 2
10
(b)
2222
)5.36(120
)5.69(8...)5.19(17)5.9(12−
+++=σ
= 266 = 16.31
K1 K1 N1 3
(c)
L = 44.5 ; F = 86
3
3 (120) 86444.5 10
16Q
− = +
K1 lower boundry 44.5
K1 using formula = 44.5 + 2.5 = 47
P1, P1 K1 K1 N1 5
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
7
Number Solution and mark scheme Sub Marks Full Marks
10
(a)
060 60
12DBDOB or Sin∠ = = °
0tan 606
10.3923
DB
DB
=
=
P1 K1 N1 3
10
(b)
2 10.392320.7846
DE = ×
=
Area of shaded region
( ) ( ) ( )( )21 120.7846 6 2.0944 62 224.6546
= −
=
N1 K1 N1 3
(c)
0240 or 4.1888 radMajor AOC∠ =
( ) 6 4.188825.13228
AFCS =
=
Perimeter 25.1328 6 6 20.784657.9174
AFCS AD CE DE= + + +
= + + +
=
P1 N1 K1 N1 4
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
8
Number Solution and mark scheme Sub Marks Full Marks
11
(a)
(i)
−−−
−= )6)(10(212
212)6(10 2 xxxL
= xx 162 2 +− (ii)
164 +−= xdxdL
,0=dxdL 0164 =+− x
x = 4
(iii) 2
max 2(4) 16(4)32
L = − +
=
K1 N1 K1 K1 N1 K1 N1 7
10
(b)
0.1dxdt=
( 4(2) 16) 0.1dLdt
= − + ×
= 0.8
P1 K1 N1 3
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
9
Number Solution and mark scheme Sub Marks Full Marks
12
(a)
5589
SinBCASin=
∠
0 0112 51' or 67 9 'BCA ACD∠ = ∠ =
067 9 ' 67.15ADC or∠ = °
K1 N1 N1 3
10
(b)
0
0
180 2(67 9')45 42 ' 45.7
CADor
∠ = −
= °
2 2 2 08 8 2(8)(8)cos45 42 '6.213
CDCD
= + −
=
K1 K1 N1 3
(c)
0 0 0
0
180 55 112 51'12 9 '
CAB∠ = − −
=
( )( ) ( )( )0 01 1Area 9 8 sin12 9 ' 8 8 sin 45 42 '2 230.48
= +
=
N1 K1, K1 N1 4
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
10
Number Solution and mark scheme Sub Marks Full Marks
13
(a)
5 750SinB Sin
=°
33.17 33 10' ABE or∠ = ° °
180 50 33.17AEB∠ = − − °
= 96.83º or 96º 50’
K1 K1 N1 3
10
(b)
42.83 42 50' CBF or∠ = ° °
9sin100 sin 42.83
BF=
° °
BF = 13.04 cm OR equivalent
P1 K1 N1 3
(c)
Area AEB = 1 5 7sin 96.832× × ° or equivalent
= 17.38
Area BCF = 1 8 9sin1002× × °
or equivalent
= 35.45
Area BEF = 1 7 13.04sin1042× × °
= 44.28 Area of quadrilateral ACFE = 100.08
K1 K1 K1 N1 4
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
11
Number Solution and mark scheme Sub Marks Full Marks
14
(a)
2.20 100 110
2.002.70 1003.00
90
mm
n
n
× =
=
× =
=
K1 N1 N1 3
10
(b)
(125 40) (110 10) (150 25) (90 20) (140 5)
10012350100
123.5
IWW
× + × + × + × + ×=
=
=
K1 K1 N1 3
(c)
080906
08
130 123.5 100 100 123.5100 100 80160.55 98.80
QI OR
Q RM
= × × × =
= =
0909
09
160.55 80 100 130100 98.80
128.44. 128.44
QQ RM
RM Q RM
= × × =
= =
K1 K1 K1 N1 4
MOZ@C
SMS MUZAFFAR SYAH , MELAKA
12
END OF MARK SCHEME
Number Solution and marking scheme Sub Marks Full Marks
15
(a)
(i)
11310050.203
=×P
21.203 RMP = (ii)
10810001
03 =×PP 118100
03
05 =×PP
44.127100100108
100118
=×
K1 N1 K1, K1 N1 5
10
(b)
(i) 113100
)35(113)31(108)12()22(118=
+++=
− tI
t = 116.75
(ii) 1131002503
=×P
12.2203 RMP =
K1, K1 N1 K1 N1 5
MOZ@C
SMS MUZAFFAR SYAH , MELAKA