STUDENT'S COPY MODULE 3
August 26, 2017 | Author: Jamaliah Daud | Category: N/A
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ADDITIONAL MATHEMATICS FORM 4 MODULE 3 PPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMI
QUADRATIC FUNCTIONS
MINISTRY OF EDUCATION MALAYSIA
MODULE 3: QUADRATIC FUNCTIONS Arahan: 1. Modul ini mengandungi tiga puluh lapan soalan. Semua soalan adalah dalam bahasa Inggeris. 2. Modul merangkumi lima konstruk yang diuji K3 - Memahami istilah matematik dalam bahasa Inggeris K5 - Menguasai konstruk pengetahuan K6 - Menguasai konstruk kefahaman K7 - Menguasai konstruk kemahiran K8 - Mengungkapkan idea/informasi dalam bahasa Inggeris 3. Murid hendaklah menulis maklumat diri dalam kertas jawapan objektif disediakan. Murid juga perlu memastikan maklumat konstruk, nombor soalan dan jumlah soalan seperti yang dibaca oleh guru di dalam ruangan disediakan dalam kertas jawapan objektif sebelum ujian. 4. Bagi soalan objektif, anda perlu menandakan jawapan dengan menghitamkan pilihan jawapan pada pilihan jawapan A , B , C atau D pada kertas jawapan objektif. Contoh: Antara berikut, yang manakah haiwan? A. A
Pokok
B.
B
Kambing C
C.
D
Kereta E
5. Jawab semua soalan.
Modul ini mengandungi 19 halaman bercetak
2
D.
Pe n
1.
2
What is the highest power of x for the quadratic function f ( x) A
-1
B
1
C
2
D
3
Which of the following graphs represent a quadratic function ? A .
f (x)
B .
x
0
0
f (x)
0
f (x)
C .
D .
x
Which of the following is a quadratic function ? A
f ( x) 5 x 3
B
f ( x)
1 6x x2
C
f ( x)
2 x 2 5x 9
D
f ( x)
x 3 2 x 2 10
x
f (x)
0 3
x 2 5x 4 ?
3
x
4
Diagram shows the graph of quadratic function. f (x)
y
x
a
0
x
f (x)
a
Equation x a is a vertical line passing through the turning point . What does the line known as?
5
A
x -axis
B
axis of symmetry
C
y -axis
Which of the following graphs of quadratic function has two real and equal roots?
0
C
B
f (x)
A
x
f (x)
x
0
f (x)
D
f (x)
0 0
x
4
x
6
Which of the following quadratic functions graphs has two distinct roots? f (x)
A
x
0 C
0
x
f (x)
x
0 7
f (x)
B
Which points represent the maximum point from the given quadratic function graph ?
f (x) xC Bx xD Ax
0
x axis of symmetry
5
8
Given the graph of quadratic function. f(x) 3( x 2) 2 q
g ( x)
-3
|
|
2
x
Determine the range of values of x of the shaded region.
9
A
x
3 , x
B
x {3 , 2}
C
3 x 2
D
x
2
3, 2, 1, 0, 1, 2
Graph shows the quadratic function g ( x)
3( x 2) 2 q
g (x) (2, 5) x
g ( x)
0 -7 x
3( x 2) 2 q
2
State the value of q . A
-7
B
-3
C
2
D
5
6
10
11
12
Given a function f ( x) A
-2
B
2
C
4
D
-4
2( x 2) 2 4 . State the maximum value of f (x) .
The general form of a quadratic function is written as f ( x) f ( x) 3 x 2 3 x 4 ,state the value of a , b and c . A
a
3,b
4,c
B
a
3 , b 3 , c
4
C
a
3,b
3 , c
4
D
a
3,b
4 , c 3
3
In the parabolic graph of f ( x) A
minimum point
B
maximum point
C
stationary point
ax 2 bx c .If
2 x 2 4 x 7 , what is the turning point known as?
7
13
Graph shows the function of f ( x)
2x2 7 x q .
f (x)
f ( x)
5| 1 0
| x
5 2
2x2 7 x q
x
§7 9· ¨ , ¸ ©4 8¹
Determine the value of q . 9 A 8 B
7 4
C
1
D
5
8
14
Given a quadratic function f ( x) ( x 5)( x 3) . Choose the correct position of the graph when f (x) 0 .
f (x)
A .
0
C .
15
x
D .
x
f (x)
0
The maximum point of the function f ( x) a ( x p ) 2 q is ( p, q ) . Determine the maximum point of f ( x) 3( x 2) 2 3 A
(3, 2)
B
(2, 3)
C
(2, 3)
D
(3, 3)
x
0
f (x)
0
f (x)
B .
9
x
16
17
Determine the minimum point of g ( x) A
(6, 4)
B
(6, 4)
C
(2, 4)
D
(2, 6)
x
2( x 6) 2 4 .
p is the equation of axis of symmetry of the function f ( x)
If f ( x ) A
x
3
B
x
3
C
3
a( x p)2 q .
4( x 3) 2 5 ,state the equation of the axis of symmetry.
D 3 18
19
The function g ( x) 3( x 5) 2 1 has a minimum value. Which of the following is referred to determine the minimum value of the function? A
–1
B
2
C
3
D
5
Given the quadratic function f ( x) x 2 mx 2 6 x 10 . If the function is written in general form, determine the value of a, b and c , A
a 1, b
6, c 10
B
a 1 m, b
C
a
D
a 1 m, b
m, b
6, c 10 6, c 10 6, c 10
10
20
Given the function f ( x) 3 x 2 5 x 2 . If
f (x) ! 0 ,
Then 3x 2 5 x 2 ! 0 Next 3 x 1 x 2 ! 0 Determine the range of values of x. A B C D
21
x >
1 , x >2 3
1 , x!2 3 1 2 x 3 1 x 2 3 x
§ b 4ac b 2 · The formula ¨ , ¸ can be used to determine the minimum point of the 4a ¹ © 2a quadratic function f ( x) 2 x 2 5 x 3 . Which of the following is correct? A.
§ (5) 4(2)(3) (5) 2 · , ¨ ¸ 4(2) © 2(2) ¹
B.
§ (5) 4(2)(3) (5) 2 · , ¨ ¸ 4(2) © 2(2) ¹
C
C.
§ (5) 4(2)(3) (5) 2 · , ¨ ¸ 4(2) © 2(2) ¹
D
D.
§ (5) 4(5)(2) (5) 2 · , ¨ ¸ 4(2) © 2(2) ¹
A B
11
22
Given f (x) = x 2)( x 5
| -2
| 5
When f (x) < 0, by using the graph sketching method, find the range of values of x.
23
A
2 d x d 5
B
2 x 5
C
x d 2, x t 5
D
x 2, x ! 5
The equation of axis of symmetry can be determined by using x Given g ( x)
2 x2 5x 7 .
Which of the following is correct? A
x
B
x
5 4
C
x
D
x
1 5
5 4
1 5
12
b . 2a
24
Given f ( x)
(2 x)(3 x) .
-2
3
When f ( x) t 0 ,by using the number line method, find the range of values of x .
25
A
x ! 3 , x 2
B
x ! 3 , x ! 2
C
x d 2 , x t 3
D
2 d x d 3
Diagram shows a quadratic function f ( x)
2( x 3) 2 7 .
f (x) 25 -
0
f ( x)
3
2( x 3) 2 7
x
What is the new function if the graph is reflected on the x -axis? A
f ( x)
2( x 3) 2 25
B
f ( x)
2( x 3) 2 25
C
f ( x)
2( x 3) 2 7
D
f ( x)
2( x 3) 2 7
13
26
Which of the following graph represent the quadratic function of f ( x) x 2 2 x 15 ? B
f (x)
A
f (x)
x
0
0 C
D
f (x)
27
x 0
x 2 5 x 4 intersect at a and b.
Diagram shows the function f ( x) f (x)
f ( x)
x 2 5x 4
40
| a
| b
x
Find the values of a and b. A
a = 4, b = 1
B
a = 1, b = 4
C
a = 4, b = 5
D
a = 5, b = 4
f (x)
x
0
x
14
28
Determine the range of values of x that satisfies the quadratic inequality (2 x 1)( x 3) d 0 . 1 x d ,x d3 2 1 x d ,x t3 2 1 d xd3 2 1 d xt3 2
A B C D 29
Diagram shows the graph of f ( x)
x 2 2qx 2q 1 .
f (x)
f ( x)
x 2 2qx 2q 1
x
0
Which of the following is correct to find the possible values of q ? A
4 q 2 8q
B
4q 2 4
C
4q 2 8q 4
D
4 q 2 8q
0 0 0
0
15
30
31
32
Determine the minimum point of quadratic function f ( x) 3 x 2 4 x 1 . A
§ 2 1· ¨ , ¸ © 3 3¹
B
§ 2 · ¨ ,5 ¸ © 3 ¹
C
§3 7· ¨ , ¸ ©2 4¹
D
§ 3 55 · ¨ , ¸ © 2 4¹
The quadratic function f ( x) mx 2 2 x 3 does not intersect the x-axis. Which of the following is correct to find the range of values of m ? A
4 + 2m < 0
B
4 + 2m > 0
C
4 + 2m = 0
D
4 12m d 0
Given 2 x 2 7 x 3 0 and m x n . Find the values of m and n . A
m
B
m
C
m
D
m
3 , n
1 2
1 , n 3 2 1 , n 3 2 1 3 , n 2
16
33
Given g ( x)
x 2 px 25 touches x - axis at (5, 0).
g (x)
g ( x)
25 -
x 2 px 25
x
0
(5,0)
x
Find the value of p.
34
A
10
B
-10
C
100
D
-100
Given f ( x) 16 x 2 1 . Find the range of values x if f (x) is positive. A B C D
1 1 x 4 4 1 1 x , x ! 4 4 1 1 x! , x! 4 4 1 1 !x! 4 4
17
35
Given the function g ( x) 4 x 2 8 x 9 . Express g (x) in the form of a ( x p ) 2 q where a, p and q are constants. 5 4 2 4( x 1) 5 5 ( x 1) 2 4 2 (x 1) 5 4( x 1) 2
A B C D 36
Diagram shows the graph of quadratic function. y
y
f (x)
c a
b
x
Which of the following is true to describe the graph ? A
The functions has no real roots
B
The function has two distinct roots
C
The function has two equal roots.
D
The function touches x -axis at one point .
18
37
Given f ( x)
x 2 x hx 4 and f (x) has two distinct roots.
I.
Determine the values of a, b and c .
II.
Use the discriminant b 2 4ac ! 0
III.
Factorise and determine the range
IV .
Write in general form ax 2 bx c
0
Which of the arrangement is correct to find the range of values of x ?
38
A
III, II, IV, I
B
II, I, III, IV
C
I, II, IV , III
D
IV , I, II, III
y
mx c is a tangent to the graph y
f (x)
y
f (x) .
f (x) y
mx c
x 0
x
Which of the following statements is correct about f ( x) A
The equation has one solution
B
The equation has two solutions
C
The equation has no solution
END OF QUESTION PAPER
19
mx c ?
KEMENTERIAN PELAJARAN M ALAYSIA
KERTAS JAWAPAN OBJEKTIF Ujian Diagnostik
Nama Pelajar: Tahun/ Tingkatan :
4
Mata Pelajaran: MATEMATIK TAMBAHAN Modul:
Nama Sekolah:
3
GUNAKAN PENSIL 2B ATAU BB SAHAJA. TENTUKAN TIAP-TIAP TANDA ITU HITAM DAN MEMENUHI KESELURUHAN RUANG.
PADAMKAN HINGGA HABIS MANA-MANA TANDA YANG ANDA UBAH
SILA HITAMKAN JAWAPAN DI BAWAH MENGIKUT HURUF JAWAPAN YANG ANDA PILIH 1
A
2
A
E
31
A
D
E
32
A
B
C
3
A
B
C
B
C
D
E
33
A
B
C
4
A
B
C
D
E
34
A
B
5
A
B
C
D
E
35
A
6
A
B
C
D
E
36
A
7
A
B
C
D
E
37
8
A
B
C
D
E
9
A
B
C
D
E
B
C
D
10
A
B
C
D
E
11
A
B
C
D
E
E
46
A
B
C
D
E
D
E
47
A
B
C
D
E
D
E
48
A
B
C
D
E
C
D
E
49
A
B
C
D
E
B
C
D
E
50
A
B
C
D
E
B
C
D
E
51
A
B
C
D
E
38
A
B
C
D
39
A
B
C
40
A
B
C
41
B
C
D
A
1 52
B
C
D
E
A
B
C
D
E
E
53
A
B
C
D
E
D
E
54
A
B
C
D
E
D
E
55
A
B
C
D
E
A
B
C
D
E
56
A
B
C
D
E
A
B
C
D
E
57
A
B
C
D
E
12
A
B
C
D
E
1 42
13
A
B
C
D
E
43
A
B
C
D
E
58
A
B
C
D
E
14
A
B
C
D
E
44
A
B
C
D
E
59
A
B
C
D
E
15
A
B
C
D
E
45
A
B
C
D
E
60
A
B
C
D
E
16
A
B
C
D
E
17
A
B
C
D
E
18
A
B
C
D
E
19
A
B
C
D
E
20
A
B
C
D
E
21
A
B
C
D
E
22
A
B
C
D
E
23
A
B
C
D
E
24
A
B
C
D
E
25
A
B
C
D
E
6
26
A
B
C
D
E
7
27
A
B
C
D
E
28
A
B
C
D
E
29
A
B
C
D
E
30
A
B
C
D
E
Konstruk
No. Soalan
Jumlah Soalan
1
K3
1-8
8
2
K5
9 - 16
8
3
K6
17 - 25
9
4
K7
26 - 35
10
5
K8
36 - 38
3
8 9 10
Bilangan Soalan Gagal Dijawab
Kegunaan Guru
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