Modul Jom Lulus Matematik
-
Upload
anonymous-7njqladn -
Category
Documents
-
view
314 -
download
8
description
Transcript of Modul Jom Lulus Matematik
![Page 1: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/1.jpg)
JOM LULUS MATEMATIK
Kaedah menyelesaikan soalan “silmultaneous linear equations” ,
2 langkah:
1) Kenal pasti anu atau huruf yang mudah diselesaikan dan darabkan mengikut nombor yang besar.
2) Kenal pasti tanda + Atau – dan pastikan tanda yang sama + dan + atau – dan - akan berlaku penolakan-tanda yang berbeza + dan – atau – dan + akan berlaku penambahan.
Contoh:
3 q + 5 r = 12q + 3 r = 4
Huruf q dipilih dan perlu didarabkan dengan nombor yang lebih besar, 33 q + 5 r = 24 ----------------1
x3 x3 x3( q + 3 r = 4 )-------------- 2
+3 q + 9 r = 12 ----------------3
Tanda sama-Penolakan - - - 3-1+3 q + 5 r = 24 ----------------1
9 r –(+5r ) = 12-24 gantikan r = -39 r – 5 r = -12 q + 3 r = 4 4 r = -12 q + 3 (-3) = 4
r = q -9 = 4
r = -3 q = 4 + 9 q = 13
Catatan- penyelesaian ini hanya untuk soalan “simultaneous linear equations” sahaja.
Tanda Penyelesaian
+ + Penolakan (-)
- - Penolakan (-)
+ - Penambahan (+)
- + Penambahan (+)
1
![Page 2: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/2.jpg)
JOM LULUS MATEMATIK 1
Section A
1. Solve the following quadratic equation:Selesaikan persamaan kuadratik berikut:
5 x2 + 5 x = 2(3 –x) [ 4 marks]
[ 4 markah]
2. Calculate the value of x and y that satisfy the following simultaneous linear equations:Hitung nilai x dan nilai yang memuaskan persamaan linear serentak berikut:
2 a – b = 9a +3 b = -6
[ 4 marks]
[ 4 markah]
2
![Page 3: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/3.jpg)
3. . On the graph provided, shade the region which satisfies the three inequalities
, ,
[ 4 marks]
[ 4 markah]
4. a) Write down two implications based on the following compound statement: Tulis dua implikasi berdasarkan pernyataan berikut:
x 3 = 64 if and only if x = 4 x 3 = 64 jika dan hanya jika x = 4
Implication 1/Implikasi 1:...............................................................................................Implication 2/Implikasi 2:...............................................................................................
[2 marks][2 markah]
b) Make a general conclusion by induction for the sequence of numbers 4, 6, 20, 58... which folloes the following pattern. Buat satu kesimpulan umum secara aruhan bagi urutan nombor 4, 6, 20, 58...yang mengikut pola berikut.
4= 3(0)3 + 56= 3(1)3 + 520= 3(2)3 + 558= 3(3)3 + 5...=...............
[2 marks][2 markah]
3
xy21
5 xy
y
x
5
5
![Page 4: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/4.jpg)
5) Write the following simultaneous linear equations as matrix equation.
Tulis persamaan linear serentak berikut dalam bentuk persamaan matriks.
3 x – 2 y = 8
6x - 5 y = 21
Hence, using matrix method, calculate the value of x and y.
Seterusnya, dengan menggunakan kaedah matriks, hitung nilai x dan nilai y.
[4 marks][4 markah]
4
![Page 5: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/5.jpg)
Section B
6 . a) Complete the table in the answer space for the equation y = 8-3x -2x2 by writing down
the values of y when x =-4 and x = 1.
Lengkapkan jadual di ruang jawapan bagi persamaan y = 8-3x -2x2 dengan menulis
nilai-nilai y apabila x =-4 dan x = 1.
[2 marks]
[2 markah]
b) By using a scale of 2 cm to 1 unit on the x –axis and 2 cm to 5 units on the y- axis, draw
the graph of y = 8-3x -2x2 for -5 ≤ x ≤ 3 and -27 ≤ y ≤ 9
Dengan menggunakan skala 2 cm kepada 1 unit pada paksi x dan 2 cm kepada 5 unit
pada paksi y,lukis graf y = 8-3x -2x2 for -5 ≤ x ≤ 3 and -27 ≤ y ≤ 9.
[4 marks]
[4 markah]
c) From your graph, find
Dari graf, cari
i) the value of y when x = -2.4nilai y apabila x = -2.4
ii) the value of x when y = -11nilai x apabila y = -11
[2 marks] [2 markah]
Answer:
a) y = 8-3x -2x2
x -5 -4 -3.5 -2 -1 0 1 2 3
y -27 -6 6 9 8 -6 -19
b) Refer graph
5
![Page 6: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/6.jpg)
c) i) y =.....................................
ii)x = ....................
6
Graph for Question 6
![Page 7: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/7.jpg)
7) Transformation R is a 90° clockwise rotation at centre (2, 2).
Transformation T is a translation .
State the coordinate of the image for coordinate (6 , 4) under the following
transformations:
(i) R2.
(ii) TR.
Answer:
(a) (i)
(ii)
(b) Diagram 9 shows quadrilateral , ABCD, PQRS and EFGH, drawn on a
Cartesian plane.
DIAGRAM 9
PQRS is the image of ABCD under transformation S and EFGH is the image of PQRS under transformation Q. (i) Describe in full transformation :
(a)Transformation S
(b)Transformation Q
(ii) Given the area of ABCD is 64 unit2, calculate the area of shaded region.
[12 marks]
7
-12 -10 -8 -6 -4 -2 2 4 6 8 10 12F
E
GH
S
QP
DC
B A
y
xO
R
6
4
2
- 2
- 4
![Page 8: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/8.jpg)
Answer:
(b) (i) (a)
(b)
(ii)
8. The data in Diagram 5 shows the ages of members of a golf club.
45 53 48 54 46 53 55 43 47 52
63 57 50 40 52 45 49 61 54 56
51 41 56 51 61 50 53 48 51 44
57 53 47 55 46 54 42 57 58 63
42 64 50 49 52 47 55 52 45 51
Diagram 5
a) Based on the data in Diagram 5 and using a class interval of 5 years,
complete Table 4 in the answer space. [4 Marks]
b) Based on the table in a), calculate the estimated mean age of the members of the golf club. [4 Marks]
c) By using a scale of 2 cm to 5 years on the x-axis and 2 cm to 2 persons on the y-axis, draw a histogram based on the data. [4 Marks
Answer
a)
Age Frequency Midpoint
40-44
45-49
8
![Page 9: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/9.jpg)
Table
b)
c)Refer graph
9
Graph for Question 8
![Page 10: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/10.jpg)
9.
(a) Diagram 15 (i) shows a solid right prism with rectangular base ABHG on a horizontal plane. The surface
ABCDE is the uniform cross-section of the prism EA and CB are vertical edges. Rectangle EDFK and
rectangle DCJK are inclined planes. The height of D from AB is 5 cm and ED = DC.
Rajah 15 (i) menunjukkan sebuah pepejal berbentuk prisma tegak dengan tapak segiempat tepat ABHG
terletak di atas satah mengufuk. Permukaan ABCDE ialah keratan rentas seragam prisma itu. Tepi EA dan
CB adalah tegak. Segiempat tepat EDFK dan segi empat tepat DCJK ialah satah condong. Tinggi D dari AB
ialah 5 cm dan ED = DC.
Rajah 15 (i)
Lukis dengan skala penuh, pelan pepejal itu.
Sebuah pepejal lain berbentuk prisma tegak dengan trapezium PQRS sebagai ketatan rentas seragam dicantumkan kepada prisma dalam Rajah 15.1 pada satah mencancang PHTS. Gabungan pepejal adalah seperti yang ditunjukkan dalam Rajah 15.2. Tapak ABPQVHG terletak di atas satah mengufuk dan segi empat tepat SRUT ialah satah condong.
10
A
H
EC
F
K
J
7 cm
B
4 cm
D
4 cm
G
KA
H
EC
F
J
3 cm
B
4 cm
D
4 cm
G
4 cm
4 cm
4 cmT
S
PQ
U
VR
X
Y
![Page 11: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/11.jpg)
Draw to full scale,
Lukis dengan skala penuh,
(i) the elevation of the composite solid on a vertical plane parallel to AB as viewed from X,
Dongakan gabungan pepejal itu pada satah mencancang yang selari dengan AB sebagaimana dilihat dari X, [4 markah]
(ii) the elevation of the composite solid on a vertical plane parallel to QV as viewed from Y.
Dongakan gabungan pepejal itu pada satah mencancang yang selari dengan QV sebagaimana dilihat dari Y. [5 markah]
11
Diagram 15 (ii)
Rajah 15 (ii)
![Page 12: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/12.jpg)
JOM LULUS MATEMATIK 2
Section A
1. Using factorization, solve the following quadratic equation:Menggunakan pemfaktoran, selesaikan persamaan kuadratik berikut:
= m+3
[ 4 marks/4 markah]
2. Calculate the value of x and y that satisfy the following simultaneous linear equations:Hitung nilai x dan nilai yang memuaskan persamaan linear serentak berikut:
x + 2 y = -13 x – y = 11
[ 4 marks/4 markah]
12
![Page 13: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/13.jpg)
.3. On the graph in the answer space, shade the region which satisfies the three inequalities , y < x and y > 1. [3 marks]
Pada graf di ruang jawapan, lorek rantau yang memuaskan ketiga-tiga ketaksamaan , y < x and y > 2. [3 markah]
Answer/ Jawapan:
4(a) State whether the following compound statement is true or false:
13
y
y = 2
y = – x + 20
x O
![Page 14: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/14.jpg)
Nyatakan sama ada pernyataan berikut adalah benar atau palsu:
(b) Write down the converse of the following implication.
Hence, state whether the converse is true or false.
Tulis akas untuk implikasi berikut.
Seterusnya, nyatakan sama ada akas tersebut adalah benar atau palsu.
(c) Write down Premise 2 to complete the following argument:
Tulis Premis 2 untuk melengkapkan hujah berikut:
Premise 1: If the radius of a circle is 14 cm, then the circumference of the circle is cm.
Premis 1: Jika jejari sebuah bulatan ialah 14 cm, maka lilitan bulatan itu ialah cm.
Premise 2:/ Premis 2: ……………………………………………………………………………..
Conclusion: The radius of the circle is not 14 cm.
Kesimpulan: Jejari bulatan itu bukan 14 cm.
[4 marks]
[4 markah]
5. It is given that matrix is
Diberi bahawa matriks
(a) Find the inverse matrix of A.
Cari matriks songsang bagi A.
14
Some even numbers are divisible by 3.
Sebilangan nombor genap boleh dibahagikan dengan 3.
If x is a multiple of 12, then x is a multiple of 3.
Jika x adalah gandaan bagi 12, maka x adalah gandaan bagi 3.
![Page 15: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/15.jpg)
(b) Write the following simultaneous linear equations as matrix equation:
Tulis persamaan linear serentak berikut dalam bentuk persamaan matriks:
Section B
6 . a) Complete the table in the answer space for the equation y = 2x2 – 5x -3 by writing down
the values of y when x =-2 and x = 0.5
Lengkapkan jadual di ruang jawapan bagi persamaan y = 2x2 – 5x -3 dengan menulis
nilai-nilai y apabila x =-2 dan x = 0.5
[2 marks]
[2 markah]
b) By using a scale of 2 cm to 1 unit on the x –axis and 2 cm to 5 units on the y- axis, draw
the graph of y = 2x2 – 5x -3 for -3 ≤ x ≤ 5
Dengan menggunakan skala 2 cm kepada 1 unit pada paksi x dan 2 cm kepada 5 unit
pada paksi y,lukis graf y = 2x2 – 5x -3 for -3 ≤ x ≤ 5
[4 marks]
[4 markah}
c) From your graph, find
Dari graf, cari
iii) the value of y when x = -2.4nilai y apabila x = -2.4
iv) the value of x when y = 4nilai x apabila y = 4
[2 marks] [2 markah]
d) Answer: y = 2x2 – 5x -3
15
![Page 16: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/16.jpg)
x -3 -2 -1 0 0.5 1 2 3 4 5
y 30 4 -3 -6 -5 0 9 22
e) Refer graphf) i) y =.....................................
ii)x = ........................
16
Graph for Question 6
![Page 17: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/17.jpg)
7) Diagram 13.1 shows the point (-2, 4) and the straight line x = 1 drawn on a Cartesian plane.
Rajah 13.1 menunjukkan titik (-2, 4) dan garis lurus x = 1 dilukis pada suatu satah Cartesan.
Diagram 13.1
17
y
x– 4
– 2
2 4
2
4
– 2
– 4
O
(- 2, 4)
6 8 10
6
x = 1
![Page 18: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/18.jpg)
Rajah 13.1
(a) Transformation T is a translation
Transformation P is a reflection in the straight line x = 1.
State the coordinates of the image if point (- 2, 4) under the following transformation:
Penjelmaan T ialah translasi
Penjelmaan P ialah satu pantulan pada garis lurus x=1.
Nyatakan koordinat imej bagi titik (-2, 4) di bawah penjelmaan berikut:
(i) T
(ii) TP [4 marks/4 markah]
(b) Diagram 13.2 shows pentagons, ABCDE, JQRSU and JKLMN, drawn on a Cartesian plane.
Rajah 13.2 menunjukkan pentagon, ABCDE, JQRSU dan JKLMN, dilukis pada suatu satah Cartesan.
Diagram 13.2
Rajah 13.2
18
N
842
y
2
4
- 2
10
6
O 6 x
B
D
A
J
U
- 4
C
E
ML
K
Q
RS
- 6
![Page 19: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/19.jpg)
(i) JKLMN is the image of ABCDE under a combined transformation HG.
Describe in full the transformation:
JKLMN ialah imej bagi ABCDE di bawah gabungan penjelmaan HG.
Huraikan selengkapnya penjelmaan
(a) G,(b) H.
(ii) It is given that pentagon ABCDE represents a region of area 80 m2. Calculate the area in m2, of the region represented by the coloured region.
Diberi bahawa pentagon ABCDE mewakili luas 80 m2.
Hitung luas, dalam m2, kawasan yang diwakili oleh kawasan yang berwarna.
[8 marks/8 markah]
8. The data in Diagram 7 shows the height, in cm, of 40 students in a class
(a) Based on the data in Diagram 7, complete Table in the answer space. [3 marks]
Heights Frequency Midpoint
141-145 2
145 174 150 153 153 148 175 154
168 171 166 159 169 175 165 169
160 167 155 160 160 143 176 153
161 167 170 148 177 165 167 165
170 156 162 162 161 157 179 165
19
![Page 20: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/20.jpg)
(b) Using the completed table, in (a)
i) state the modal class
ii) estimate the mean mark [4 marks]
(c) By using the scale of 2cm to 5 cm on the x- axis and 2 cm to 1 student on the y- axis, draw a
frequency polygon for the data. [4 marks]
20
Graph for Question 8
![Page 21: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/21.jpg)
9 )Diagram 9 shows a solid right prism with rectangular base FGPN on a horizontal table . EFGHJK is
the uniform cross-section of the prism . Rectangle EKLM is an inclined plane. Rectangle JHQR is a
horizontal plane. EF , KJ and HG are vertical edges.
Draw a full plan of the solid. [3 marks]
21
F
G
P
Q
R
N
H
J
EK
LM
5 cm
7 cm 5 cm
5 cm
2 cm
2 cm
Diagram 9(i)
![Page 22: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/22.jpg)
( b ) A solid cuboid is joined to the prism in Diagram9(i) at the vertical plane PQRLMN. The
combined solid is as shown in Diagram 9(ii).The square base FGSW is a horizontal.
Draw full scale
i)the elevation of the combined solid on a vertical plane parallel to FG as viewed from C, [4 marks]
ii)the elevation of the combined solid on a vertical plane parallel to GPS as viewed from D.[5 marks]
22
F
G
P
Q
R
N
H
J
EK
LM
5 cm
7 cm 5 cm
5 cm
2 cm
2 cm
Diagram 9(ii)
SS
T
X
V U
W
7 cm
CD
2 cm
7 cm
![Page 23: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/23.jpg)
JOM LULUS MATEMATIK 3
Section A
1.Solve the following quadratic equation: Selesaikan persamaan kuadratik berikut:
x2 - 2 x + 3 = 2(x-1) [ 4 marks/4 markah]
23
![Page 24: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/24.jpg)
3. Calculate the value of x and y that satisfy the following simultaneous linear equations:Hitung nilai x dan nilai yang memuaskan persamaan linear serentak berikut:
p - q = 6
2 p +3 q = -5
[ 4 marks / 4 markah]
]
4. . On the graph provided, shade the region which satisfies the three inequalities
, ,
[ 4 marks]
[ 4 markah]
5. a) Write down two implications based on the following compound statement: Tulis dua implikasi berdasarkan pernyataan berikut:
x 3 = 64 if and only if x = 4
24
xy21
5 xy
y
x
5
5
![Page 25: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/25.jpg)
x 3 = 64 jika dan hanya jika x = 4
Implication 1/Implikasi 1:...............................................................................................Implication 2/Implikasi 2:...............................................................................................
[2 marks][2 markah]
b) Make a general conclusion by induction for the sequence of numbers 4, 6, 20, 58... which folloes the following pattern. Buat satu kesimpulan umum secara aruhan bagi urutan nombor 4, 6, 20, 58...yang mengikut pola berikut.
4= 3(0)3 + 56= 3(1)3 + 520= 3(2)3 + 558= 3(3)3 + 5...=...............
[2 marks][2 markah]
5) Write the following simultaneous linear equations as matrix equation.
Tulis persamaan linear serentak berikut dalam bentuk persamaan matriks.
4 x – 2 y = 7
2x + 5 y = -2
Hence, using matrix method, calculate the value of x and y.
Seterusnya, dengan menggunakan kaedah matriks, hitung nilai x dan nilai y.
[4 marks][4 markah]
25
![Page 26: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/26.jpg)
Section B
6 . a) Complete the table in the answer space for the equation y = 8-3x -2x2 by writing down
the values of y when x =-4 and x = 1.
Lengkapkan jadual di ruang jawapan bagi persamaan y = 8-3x -2x2 dengan menulis
nilai-nilai y apabila x =-4 dan x = 1.
[2 marks]
[2 markah]
b) By using a scale of 2 cm to 1 unit on the x –axis and 2 cm to 5 units on the y- axis, draw
the graph of y = 8-3x -2x2 for -5 ≤ x ≤ 3 and -27 ≤ y ≤ 9
Dengan menggunakan skala 2 cm kepada 1 unit pada paksi x dan 2 cm kepada 5 unit
pada paksi y,lukis graf y = 8-3x -2x2 for -5 ≤ x ≤ 3 and -27 ≤ y ≤ 9.
[4 marks]
[4 markah]
26
![Page 27: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/27.jpg)
c) From your graph, find
Dari graf, cari
v) the value of y when x = -2.4nilai y apabila x = -2.4
vi) the value of x when y = -11nilai x apabila y = -11
[2 marks]
[2 markah]
Answer:
g) y = 8-3x -2x2
x -5 -4 -3.5 -2 -1 0 1 2 3
y -27 -6 6 9 8 -6 -19
h) Refer graphi) i) y =.....................................
ii)x = ......................
27
Graph for Question 6
![Page 28: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/28.jpg)
7) Transformation R is a 90° clockwise rotation at centre (2, 2).
Transformation T is a translation .
State the coordinate of the image for coordinate (6 , 4) under the following
transformations:
(i) R2.
(ii) TR.
Answer:
(a) (i)
(ii)
(b) Diagram 9 shows quadrilateral , ABCD, PQRS and EFGH, drawn on a
Cartesian plane.
28 -12 -10 -8 -6 -4 -2 2 4 6 8 10 12F
E
GH
S
QP
DC
B A
y
xO
R
6
4
2
- 2
- 4
![Page 29: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/29.jpg)
DIAGRAM 9
PQRS is the image of ABCD under transformation S and EFGH is the image of PQRS under transformation Q.
(i) Describe in full transformation :
(a)Transformation S
(b)Transformation Q
(ii) Given the area of ABCD is 64 unit2, calculate the area of shaded region.
[12 marks]
Answer:(b) (i) (a)
(b (ii)
8. The data in Diagram 5 shows the ages of members of a golf club.
45 53 48 54 46 53 55 43 47 52
63 57 50 40 52 45 49 61 54 56
51 41 56 51 61 50 53 48 51 44
57 53 47 55 46 54 42 57 58 63
42 64 50 49 52 47 55 52 45 51
Diagram 5
a) Based on the data in Diagram 5 and using a class interval of 5 years,
complete Table 4 in the answer space. [4 Marks]
29
![Page 30: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/30.jpg)
d) Based on the table in a), calculate the estimated mean age of the members of the golf club. [4 Marks]
e) By using a scale of 2 cm to 5 years on the x-axis and 2 cm to 2 persons on the y-axis, draw a histogram based on the data. [4 Marks]
Answer
a)
Age Frequency Midpoint
40-44
45-49
Table
30
Graph for Question 8
![Page 31: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/31.jpg)
JOM LULUS MATEMATIK 4
Section A
6. Solve the following quadratic equation:Selesaikan persamaan kuadratik berikut:
5 x2 + 4 x = 2(3 –x) [ 4 marks]
[ 4 markah]
31
![Page 32: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/32.jpg)
7. Calculate the value of x and y that satisfy the following simultaneous linear equations:Hitung nilai x dan nilai yang memuaskan persamaan linear serentak berikut:
2 a – b = 6a +3 b = -6
[ 4 marks]
[ 4 markah]
8. . On the graph provided, shade the region which satisfies the three inequalities
, ,
[ 4 marks]
[ 4 markah]
32
xy21
5 xy
y
x
5
5
![Page 33: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/33.jpg)
9. a) Write down two implications based on the following compound statement: Tulis dua implikasi berdasarkan pernyataan berikut:
x 3 = 64 if and only if x = 4 x 3 = 64 jika dan hanya jika x = 4
Implication 1/Implikasi 1:...............................................................................................Implication 2/Implikasi 2:...............................................................................................
[2 marks][2 markah]
b) Make a general conclusion by induction for the sequence of numbers 4, 6, 20, 58... which folloes the following pattern. Buat satu kesimpulan umum secara aruhan bagi urutan nombor 4, 6, 20, 58...yang mengikut pola berikut.
4= 3(0)3 + 56= 3(1)3 + 520= 3(2)3 + 558= 3(3)3 + 5...=...............
[2 marks][2 markah]
5) Write the following simultaneous linear equations as matrix equation.
Tulis persamaan linear serentak berikut dalam bentuk persamaan matriks.
4 x – 2 y = 7
2x + 5 y = -2
Hence, using matrix method, calculate the value of x and y.
Seterusnya, dengan menggunakan kaedah matriks, hitung nilai x dan nilai y.
33
![Page 34: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/34.jpg)
[4 marks][4 markah]
Section B
6 . a) Complete the table in the answer space for the equation y = 8-3x -2x2 by writing down
the values of y when x =-4 and x = 1.
Lengkapkan jadual di ruang jawapan bagi persamaan y = 8-3x -2x2 dengan menulis
nilai-nilai y apabila x =-4 dan x = 1.
[2 marks]
[2 markah]
b) By using a scale of 2 cm to 1 unit on the x –axis and 2 cm to 5 units on the y- axis, draw
the graph of y = 8-3x -2x2 for -5 ≤ x ≤ 3 and -27 ≤ y ≤ 9
Dengan menggunakan skala 2 cm kepada 1 unit pada paksi x dan 2 cm kepada 5 unit
pada paksi y,lukis graf y = 8-3x -2x2 for -5 ≤ x ≤ 3 and -27 ≤ y ≤ 9.
[4 marks]
[4 markah]
c) From your graph, find
Dari graf, cari
vii) the value of y when x = -2.4nilai y apabila x = -2.4
viii) the value of x when y = -11nilai x apabila y = -11
34
![Page 35: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/35.jpg)
[2 marks]
[2 markah]
Answer:
j) y = 8-3x -2x2
x -5 -4 -3.5 -2 -1 0 1 2 3
y -27 -6 6 9 8 -6 -19
k) Refer graphl) i) y =.....................................
ii)x = ........................
35
Graph for Question 6
![Page 36: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/36.jpg)
7) Transformation R is a 90° clockwise rotation at centre (2, 2).
Transformation T is a translation .
State the coordinate of the image for coordinate (6 , 4) under the following
transformations:
(i) R2.
(ii) TR.
Answer:
36
![Page 37: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/37.jpg)
(a) (i)
(ii)
(b) Diagram 9 shows quadrilateral , ABCD, PQRS and EFGH, drawn on a
Cartesian plane.
PQRS is the image of ABCD under transformation S and EFGH is the image of PQRS under transformation Q.
(i) Describe in full transformation :
(a)Transformation S
(b)Transformation Q
(ii) Given the area of ABCD is 64 unit2, calculate the area of shaded region.
[12 marks
Answer:
(b) (i) (a)
(b) (ii)
8. The data in Diagram 5 shows the ages of members of a golf club.
45 53 48 54 46 53 55 43 47 52
63 57 50 40 52 45 49 61 54 56
51 41 56 51 61 50 53 48 51 44
57 53 47 55 46 54 42 57 58 63
42 64 50 49 52 47 55 52 45 51
37
-12 -10 -8 -6 -4 -2 2 4 6 8 10 12F
E
GH
S
QP
DC
B A
y
xO
R
6
4
2
- 2
- 4
![Page 38: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/38.jpg)
Diagram 5
a) Based on the data in Diagram 5 and using a class interval of 5 years,
complete Table 4 in the answer space. [4 Marks]
f) Based on the table in a), calculate the estimated mean age of the members of the golf club. [4 Marks]
g) By using a scale of 2 cm to 5 years on the x-axis and 2 cm to 2 persons on the y-axis, draw a histogram based on the data. [4 Marks]
Answer
a)
Age Frequency Midpoint
40-44
45-49
b)
38
Graph for Question 8
![Page 39: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/39.jpg)
9.
JOM LULUS MATEMATIK 5
Section A
10. Solve the following quadratic equation:Selesaikan persamaan kuadratik berikut:
39
![Page 40: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/40.jpg)
5 x2 + 4 x = 2(3 –x) [ 4 marks]
[ 4 markah]
11. Calculate the value of x and y that satisfy the following simultaneous linear equations:Hitung nilai x dan nilai yang memuaskan persamaan linear serentak berikut:
2 a – b = 6a +3 b = -6
[ 4 marks]
[ 4 markah]
12. . On the graph provided, shade the region which satisfies the three inequalities
, ,
[ 4 marks]
[ 4 markah]
40
xy21
5 xy
y
x
5
5
![Page 41: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/41.jpg)
13. a) Write down two implications based on the following compound statement: Tulis dua implikasi berdasarkan pernyataan berikut:
x 3 = 64 if and only if x = 4 x 3 = 64 jika dan hanya jika x = 4
Implication 1/Implikasi 1:...............................................................................................Implication 2/Implikasi 2:...............................................................................................
[2 marks][2 markah]
b) Make a general conclusion by induction for the sequence of numbers 4, 6, 20, 58... which folloes the following pattern. Buat satu kesimpulan umum secara aruhan bagi urutan nombor 4, 6, 20, 58...yang mengikut pola berikut.
4= 3(0)3 + 56= 3(1)3 + 520= 3(2)3 + 558= 3(3)3 + 5...=...............
[2 marks][2 markah]
5) Write the following simultaneous linear equations as matrix equation.
Tulis persamaan linear serentak berikut dalam bentuk persamaan matriks.
4 x – 2 y = 7
41
![Page 42: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/42.jpg)
2x + 5 y = -2
Hence, using matrix method, calculate the value of x and y.
Seterusnya, dengan menggunakan kaedah matriks, hitung nilai x dan nilai y.
[4 marks][4 markah]
Section B
6 . a) Complete the table in the answer space for the equation y = 8-3x -2x2 by writing down
the values of y when x =-4 and x = 1.
Lengkapkan jadual di ruang jawapan bagi persamaan y = 8-3x -2x2 dengan menulis
nilai-nilai y apabila x =-4 dan x = 1.
[2 marks]
[2 markah]
b) By using a scale of 2 cm to 1 unit on the x –axis and 2 cm to 5 units on the y- axis, draw
the graph of y = 8-3x -2x2 for -5 ≤ x ≤ 3 and -27 ≤ y ≤ 9
Dengan menggunakan skala 2 cm kepada 1 unit pada paksi x dan 2 cm kepada 5 unit
pada paksi y,lukis graf y = 8-3x -2x2 for -5 ≤ x ≤ 3 and -27 ≤ y ≤ 9.
[4 marks]
[4 markah]
c) From your graph, find
Dari graf, cari
42
![Page 43: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/43.jpg)
ix) the value of y when x = -2.4nilai y apabila x = -2.4
x) the value of x when y = -11nilai x apabila y = -11
[2 marks]
[2 markah]
Answer:
m) y = 8-3x -2x2
x -5 -4 -3.5 -2 -1 0 1 2 3
y -27 -6 6 9 8 -6 -19
n) Refer grapho) i) y =.....................................
ii)x = ........................
43
Graph for Question 6
![Page 44: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/44.jpg)
7) Transformation R is a 90° clockwise rotation at centre (2, 2).
Transformation T is a translation .
44
![Page 45: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/45.jpg)
State the coordinate of the image for coordinate (6 , 4) under the following
transformations:
(i) R2.
(ii) TR.
Answer:
(a) (i)
(ii)
(b) Diagram 9 shows quadrilateral , ABCD, PQRS and EFGH, drawn on a
Cartesian plane.
DIAGRAM 9
PQRS is the image of ABCD under transformation S and EFGH is the image of PQRS under transformation Q.
(i) Describe in full transformation :
(a)Transformation S
(b)Transformation Q
(ii) Given the area of ABCD is 64 unit2, calculate the area of shaded region.
[12 marks]
Answer:
(b) (i) (a)
45
-12 -10 -8 -6 -4 -2 2 4 6 8 10 12F
E
GH
S
QP
DC
B A
y
xO
R
6
4
2
- 2
- 4
![Page 46: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/46.jpg)
(b)
(ii)
8. The data in Diagram 5 shows the ages of members of a golf club.
45 53 48 54 46 53 55 43 47 52
63 57 50 40 52 45 49 61 54 56
51 41 56 51 61 50 53 48 51 44
57 53 47 55 46 54 42 57 58 63
42 64 50 49 52 47 55 52 45 51
Diagram 5
a) Based on the data in Diagram 5 and using a class interval of 5 years,
complete Table 4 in the answer space. [4 Marks]
h) Based on the table in a), calculate the estimated mean age of the members of the golf club. [4 Marks]
i) By using a scale of 2 cm to 5 years on the x-axis and 2 cm to 2 persons on the y-axis, draw a histogram based on the data. [4 Marks]
Answer
a)
Age Frequency Midpoint
46
![Page 47: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/47.jpg)
40-44
45-49
Table
b)
c)Refer graph
47
Graph for Question 8
![Page 48: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/48.jpg)
9.
48
![Page 49: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/49.jpg)
49
![Page 50: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/50.jpg)
JOM LULUS MATEMATIK 6
Section A
14. Solve the following quadratic equation:Selesaikan persamaan kuadratik berikut:
5 x2 + 4 x = 2(3 –x)
50
![Page 51: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/51.jpg)
[ 4 marks]
[ 4 markah]
15. Calculate the value of x and y that satisfy the following simultaneous linear equations:Hitung nilai x dan nilai yang memuaskan persamaan linear serentak berikut:
2 a – b = 6a +3 b = -6
[ 4 marks]
[ 4 markah]
16. . On the graph provided, shade the region which satisfies the three inequalities
, ,
[ 4 marks]
[ 4 markah]
51
xy21
5 xy
y
x
5
5
![Page 52: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/52.jpg)
17. a) Write down two implications based on the following compound statement: Tulis dua implikasi berdasarkan pernyataan berikut:
x 3 = 64 if and only if x = 4 x 3 = 64 jika dan hanya jika x = 4
Implication 1/Implikasi 1:...............................................................................................Implication 2/Implikasi 2:...............................................................................................
[2 marks][2 markah]
b) Make a general conclusion by induction for the sequence of numbers 4, 6, 20, 58... which folloes the following pattern. Buat satu kesimpulan umum secara aruhan bagi urutan nombor 4, 6, 20, 58...yang mengikut pola berikut.
4= 3(0)3 + 56= 3(1)3 + 520= 3(2)3 + 558= 3(3)3 + 5...=...............
[2 marks][2 markah]
5) Write the following simultaneous linear equations as matrix equation.
Tulis persamaan linear serentak berikut dalam bentuk persamaan matriks.
4 x – 2 y = 7
2x + 5 y = -2
Hence, using matrix method, calculate the value of x and y.
Seterusnya, dengan menggunakan kaedah matriks, hitung nilai x dan nilai y.
52
![Page 53: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/53.jpg)
[4 marks][4 markah]
Section B
6 . a) Complete the table in the answer space for the equation y = 8-3x -2x2 by writing down
the values of y when x =-4 and x = 1.
Lengkapkan jadual di ruang jawapan bagi persamaan y = 8-3x -2x2 dengan menulis
nilai-nilai y apabila x =-4 dan x = 1.
[2 marks]
[2 markah]
b) By using a scale of 2 cm to 1 unit on the x –axis and 2 cm to 5 units on the y- axis, draw
the graph of y = 8-3x -2x2 for -5 ≤ x ≤ 3 and -27 ≤ y ≤ 9
Dengan menggunakan skala 2 cm kepada 1 unit pada paksi x dan 2 cm kepada 5 unit
pada paksi y,lukis graf y = 8-3x -2x2 for -5 ≤ x ≤ 3 and -27 ≤ y ≤ 9.
[4 marks]
[4 markah]
c) From your graph, find
Dari graf, cari
xi) the value of y when x = -2.4nilai y apabila x = -2.4
xii) the value of x when y = -11nilai x apabila y = -11
[2 marks]
[2 markah]
Answer:
p) y = 8-3x -2x2
53
![Page 54: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/54.jpg)
x -5 -4 -3.5 -2 -1 0 1 2 3
y -27 -6 6 9 8 -6 -19
q) Refer graphr) i) y =.....................................
ii)x = ........................
54
Graph for Question 6
![Page 55: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/55.jpg)
7) Transformation R is a 90° clockwise rotation at centre (2, 2).
Transformation T is a translation .
State the coordinate of the image for coordinate (6 , 4) under the following
transformations:
(i) R2.
(ii) TR.
Answer:
(a) (i)
55
![Page 56: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/56.jpg)
(ii)
(b) Diagram 9 shows quadrilateral , ABCD, PQRS and EFGH, drawn on a
Cartesian plane.
DIAGRAM 9
PQRS is the image of ABCD under transformation S and EFGH is the image of PQRS under transformation Q.
(i) Describe in full transformation :
(a)Transformation S
(b)Transformation Q
(ii) Given the area of ABCD is 64 unit2, calculate the area of shaded region.
[12 marks]
Answer:
(b) (i) (a)
(b)
(ii)
8. The data in Diagram 5 shows the ages of members of a golf club.
56
-12 -10 -8 -6 -4 -2 2 4 6 8 10 12F
E
GH
S
QP
DC
B A
y
xO
R
6
4
2
- 2
- 4
![Page 57: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/57.jpg)
45 53 48 54 46 53 55 43 47 52
63 57 50 40 52 45 49 61 54 56
51 41 56 51 61 50 53 48 51 44
57 53 47 55 46 54 42 57 58 63
42 64 50 49 52 47 55 52 45 51
Diagram 5
a) Based on the data in Diagram 5 and using a class interval of 5 years,
complete Table 4 in the answer space. [4 Marks]
j) Based on the table in a), calculate the estimated mean age of the members of the golf club. [4 Marks]
k) By using a scale of 2 cm to 5 years on the x-axis and 2 cm to 2 persons on the y-axis, draw a histogram based on the data. [4 Marks]
Answer
a)
Age Frequency Midpoint
40-44
45-49
57
![Page 58: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/58.jpg)
Table
b)
c)Refer graph
58
Graph for Question 8
![Page 59: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/59.jpg)
9.
59
![Page 60: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/60.jpg)
60
![Page 61: Modul Jom Lulus Matematik](https://reader033.fdokumen.site/reader033/viewer/2022061501/577c7f381a28abe054a3b83f/html5/thumbnails/61.jpg)
61