22 Soalan Cuti Terancang Add Maths Ting 4
-
Upload
nor-saliza-abd-sani -
Category
Documents
-
view
230 -
download
0
Transcript of 22 Soalan Cuti Terancang Add Maths Ting 4
-
7/31/2019 22 Soalan Cuti Terancang Add Maths Ting 4
1/36
SULIT 3472
3472
Matematik
Tambahan
May
2010
2 jam
SEKOLAH MENENGAH KEBANGSAAN SS17, SUBANG JAYA
PEPERIKSAAN SEMESTER 1 2010
TINGKATAN 4
MATEMATIK TAMBAHAN
JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU
INFORMATION FOR CANDIDATES
1. This question paper consists of two sections : Section A and Section B.
2. Answerall questions in Section A and Section B.
3. Answer questions from Section A in the question paper and Section B
in the test-pad.
4. Give only one answer / solution to each question.
5. Show your working. It may help you to get marks.
6. The diagrams in the questions provided are not drawn to scale unless stated.
7. The marks allocated for each question and sub-part of a question are shown in
brackets.
8. You may use a non-programmable scientific calculator.
Kertas soalan ini mengandungi 11 halaman bercetak dan 1 halaman tidak bercetak.
Dua jam tiga puluh minit
-
7/31/2019 22 Soalan Cuti Terancang Add Maths Ting 4
2/36
ADDITIONAL MATHS FORM FOUR (26 MAY 2012 TO 10 JUNE 2012)
1 Solve the simultaneous equations 2x + 3y = 5 and x2
-2xy + 3y2
= 2.
Give your answer correct to three significant figures. ( 5 marks )
2 ( a ) It is given that log 73 = k. If 73l -1
= 21, find l interms of k. ( 3 marks )
( b ) Given that 2 log 9 y - 3 log 27 x = 2, find y in terms of x. ( 5 marks )
( c ) Given that log xa = 2.32 and log xb = 2.81, find the value
of log abx . ( 2 marks )
3 The function f ( x) = x2
-6hx + 8h2
+ 1 has a minimum value of t + 2h2,
where t and h are constants.
( a ) By completing the square, show that t = 1 - 3h
2
. ( 4 marks ) ( b ) Hence, find the value of h and t if the graph of the function is
symmetrical about x = h - 1 . ( 4 marks )
4 The quadratic equation 3x2
- 2px + 9q = 0 has the roots of -5 and 2.
Find
( a ) the value of p and q . ( 4 marks )
( b ) the range of k such that 3x2
- 2px + 9q = k has no real roots. ( 4 marks )
5 The function f and its inverse function f-1
are defined by f( x) = hx ,
x - 3
x = 3, f-1
( x) = kx , x = 2 respectively, where h and k are constants.
x - 2
Another function g is defined by g( x) = 1 , x = 0.
x
( a ) Find the value of h and k . ( 3 marks )
( b ) If gf-1
( x)= -5x, find the values of x. ( 4 marks )
2
-
7/31/2019 22 Soalan Cuti Terancang Add Maths Ting 4
3/36
3
-
7/31/2019 22 Soalan Cuti Terancang Add Maths Ting 4
4/36
4
-
7/31/2019 22 Soalan Cuti Terancang Add Maths Ting 4
5/36
5
-
7/31/2019 22 Soalan Cuti Terancang Add Maths Ting 4
6/36
6
-
7/31/2019 22 Soalan Cuti Terancang Add Maths Ting 4
7/36
7
-
7/31/2019 22 Soalan Cuti Terancang Add Maths Ting 4
8/36
8
-
7/31/2019 22 Soalan Cuti Terancang Add Maths Ting 4
9/36
9
-
7/31/2019 22 Soalan Cuti Terancang Add Maths Ting 4
10/36
10
-
7/31/2019 22 Soalan Cuti Terancang Add Maths Ting 4
11/36
Prepared by, Checked by
LIANG WAI MIN CHONG KIM LIAN
LEONG YEE PING ( Head of Mths & Science Dept. )
11
-
7/31/2019 22 Soalan Cuti Terancang Add Maths Ting 4
12/36
D
6.
E F
A ( 7 - x ) cm
B C
6x cm
DIAGRAM 5
Diagram 5 shows a prism with a uniform triangular cross-section of ABC.
Given that BC = 6x cm, CF = ( 7 - x ) cm and the height of the prism is 4 cm,
( a ) ( i ) show that the volume of the prism, V cm3, is given by
V = 84x - 12x2
, ( 2 marks )
( ii ) determine the maximum value of V. ( 4 marks )
( b ) A length of 40 cm wire is bent into a square. When the wire is
heated, the length expanded at a rate of 0.2 cm s -1. Find the
rate of change of the area of the square. ( p = 3.142 ) ( 4 marks )
12
-
7/31/2019 22 Soalan Cuti Terancang Add Maths Ting 4
13/36
1. V
C 77o
A 48o
B
DIAGRAM 6
Diagram 6 shows a tent VABC in the shape of a pyramid with right-angled
triangle ABC as the horizontal base. V is the vertex of the tent. The
angle between line VB and the horizontal plane is 35o
and VBA = 77o
.Given that VC = 3.6 m, calculate
( a ) the length of VB, ( 3 marks )
( b ) the length of AB if the area of the triangle ABC is 5.6 cm2
, ( 4 marks )
( c ) the area of triangle VAB. ( 3 marks )
2.
Item Weightage
A 24B
16C 28D 12E 20
TABLE 3
Table 3 shows the prices, price indices and the respective weightages of
five items.
( a ) Find the values of x, y and z . ( 3 marks )
( b ) Calculate the composite index of the items for the year 2006
based on the year 2003. ( 2 marks )
( c ) The price of item B increases by 20% from the year 2006 tothe year 2007. Find the price index of item B for the
year 2007 based on the year 2003. ( 3 marks )
( d ) The monthly expenses for the five items for the year 2006
is RM567. Find the corresponding monthly expenses
for the year 2003 ( 2 marks )
END OF QUESTION PAPER
15.00
y
14.0020.00
Answer one question from this section.
Section C
( 10 marks )
Price index for
year 2006 based
on the year 2003
20.50 x
Price in the year
2003 ( RM )
Price in the year
2006 ( RM )
z
120
110
125
130
16.50
16.50
18.2029.00
13
-
7/31/2019 22 Soalan Cuti Terancang Add Maths Ting 4
14/36
14
-
7/31/2019 22 Soalan Cuti Terancang Add Maths Ting 4
15/36
15
-
7/31/2019 22 Soalan Cuti Terancang Add Maths Ting 4
16/36
16
-
7/31/2019 22 Soalan Cuti Terancang Add Maths Ting 4
17/36
17
-
7/31/2019 22 Soalan Cuti Terancang Add Maths Ting 4
18/36
18
-
7/31/2019 22 Soalan Cuti Terancang Add Maths Ting 4
19/36
19
-
7/31/2019 22 Soalan Cuti Terancang Add Maths Ting 4
20/36
20
-
7/31/2019 22 Soalan Cuti Terancang Add Maths Ting 4
21/36
21
-
7/31/2019 22 Soalan Cuti Terancang Add Maths Ting 4
22/36
22
-
7/31/2019 22 Soalan Cuti Terancang Add Maths Ting 4
23/36
23
-
7/31/2019 22 Soalan Cuti Terancang Add Maths Ting 4
24/36
24
-
7/31/2019 22 Soalan Cuti Terancang Add Maths Ting 4
25/36
12 ( a ) Lengkapkan Jadual 1 pada ruang jawapan untuk nilai bagi y = 8 .
x
x -5 -4 -2 -1 -0.8 0.8 1 2.5 5
y -1.6 -4 -8 10 3.2 1.6
( 3 markah )
Jadual 1
( b ) Untuk ceraian soalan ini, gunakan kertas graf pada halaman 13. Anda bibenarkan
menggunakan pembaris fleksibel.
Dengan menggunakan skala 2 cm kepada 1 unit pada paksi-x dan 1 cm kepada 1 unit
pada paksi-y, lukis graf bagi y = 8 untuk nilai x dalam julat -5 < x < 5.
x ( 4 markah )
( c ) Daripada graf itu, cari
( i ) nilai y apabila x = 4.
( ii ) nilai x apabila y = 5.4. ( 2 markah )
( d ) Dengan melukis satu garis lurus yang sesuai pada graf, cari nilai-nilai x dalam julat -5 < x < 5
yang memuaskan persamaan 8 - x2
= 0. ( 3 markah )
Jawapan :
( a )
x - 4 -0.8 1
y
( b ) Rujuk graf di halaman 13.
( c ) ( i ) y =
( ii ) x = .
( d ) x = ..
Bahagian B
( 48 Markah )
Jawab empat soalan daripada bahagian ini.
25
-
7/31/2019 22 Soalan Cuti Terancang Add Maths Ting 4
26/36
26
-
7/31/2019 22 Soalan Cuti Terancang Add Maths Ting 4
27/36
13.
Rajah 7
Graf dalam Rajah 7 menunjukkan sisi empat ABCD, sisi empat AGFE, dan sisi empat HJKE.
( a ) Penjelmaan T mewakili translasi 2 . Penjelmaan P mewakili putaran ikut arah jam
-3
melalui 90O
pada titik D. Nyatakan koordinat imej bagi titik E di bawah penjelmaan berikut.( i ) T
( ii ) P
( iii ) TP ( 4 markah )
( b ) Sisi empat AGFE ialah imej bagi sisi empat ABCD di bawah satu penjelmaan V dan sisi
empat HJKE ialah imej bagi sisi empat AGFE di bawah satu penjelmaan W. Huraikan selengkapnya
( i ) penjelmaan V,
( ii ) penjelmaan W. ( 6 markah )
( c ) Diberi bahawa luas sisi empat ABCD ialah 12.5 unit2, hitung luas sisi empat BCDEFG.
( 2 markah )Jawapan :
( a ) ( i )
( ii )
( iii )
( b ) ( i )
( ii )
( c )
27
-
7/31/2019 22 Soalan Cuti Terancang Add Maths Ting 4
28/36
14.
Rajah 8
Poligon kekerapan dalam Rajah 8 menunjukkan elaun harian bagi sekumpulan 100 pekerja
sambilan di Ekspo Perdagangan.
( a ) Berdasarkan poligon kekerapan itu, salin dan lengkapkan jadual di bawah.
Elaun ( RM ) Titik tengah Sempadan Atas Kekerapan Kekerapan longgokan
15 - 19 19.5
20 - 24
25 - 29
30 - 34
35 - 39
40 - 44
45 - 49
50 - 54
55 - 59 100
( 5 markah )
( b ) Dengan menggunakan jadual yang dibina di ( a ),
( i ) nyatakan kelas mod,
( ii ) hitungkan min anggaran. ( 3 markah )
( c ) Untuk ceraian soalan ini, gunakan kertas graf pada halaman 17.
( i ) Dengan menggunakan skala 2 cm kepada RM5 pada paksi-x dan 2 cm kepada 10
orang pekerja sambilan pada paksi-y, binakan satu ogif berdasarkan jadual yang di ( a ).
( ii ) Daripada ogif itu, nyatakan kuartil ketiga.
( 4 markah )
28
-
7/31/2019 22 Soalan Cuti Terancang Add Maths Ting 4
29/36
Jawapan :
( a )
Elaun ( RM ) Titik tengah Sempadan Atas Kekerapan Kekerapan longgokan
15 - 19 19.5
20 - 24
25 - 29
30 - 34
35 - 39
40 - 44
45 - 49
50 - 54
55 - 59 100
( b ) ( i )
( ii )
( c ) ( i ) Rujuk graf di halaman 17.
( ii )
29
-
7/31/2019 22 Soalan Cuti Terancang Add Maths Ting 4
30/36
30
-
7/31/2019 22 Soalan Cuti Terancang Add Maths Ting 4
31/36
15.
U
V
T
S
P 34O
R
Q
Rajah 9
( a ) Dalam Rajah 9, PQR ialah tangen kepada bulatan SQVUT di Q. O ialah pusat bulatan dan
PSOV ialah garis lurus. Diberi SPQ = 34O
dan UV = VQ. Hitung
( i ) OVQ,
( ii ) QUV,
( iii ) STU. ( 6 markah )
( b ) ( i ) Cari nilai-nilai bagi x jika 0O
< x < 360O
bagi tan x = 1.25.
( ii ) Cari nilai bagi kos 246O25'.
( iii )
U T
xO
10 cm
S
yO
P Q 5 cm R
Rajah 10
Dalam Rajah 10, PQR dan USR ialah garis lurus. Diberi kos UST = 3 dan S
ialah titik tengah UR. Cari kos xO
dan tan yO. 5
( 6 markah )
O
31
-
7/31/2019 22 Soalan Cuti Terancang Add Maths Ting 4
32/36
Jawapan :
( a ) ( i )
( ii )
( iii )
( b ) ( i )
( ii )
( iii ) kos xO
=
tan yO
= .
KERTAS SOALAN TAMAT
32
-
7/31/2019 22 Soalan Cuti Terancang Add Maths Ting 4
33/36
KERTAS SOALAN TAMAT
33
-
7/31/2019 22 Soalan Cuti Terancang Add Maths Ting 4
34/36
34
-
7/31/2019 22 Soalan Cuti Terancang Add Maths Ting 4
35/36
35
-
7/31/2019 22 Soalan Cuti Terancang Add Maths Ting 4
36/36
KERTAS SOALAN TAMAT