STUDENT'S COPY MODULE 2
August 26, 2017 | Author: Jamaliah Daud | Category: N/A
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ADDITIONAL MATHEMATICS FORM 4 MODULE 2 PPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMI
QUADRATIC EQUATIONS
MINISTRY OF EDUCATION MALAYSIA
MODULE 2: QUADRATIC EQUATIONS Arahan: 1. Modul ini mengandungi tiga puluh sembilan 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. Kambing
B
C
C. Kereta D
E
5. Jawab semua soalan. Modul ini mengandungi 13 halaman bercetak
2
D. Pen
1.
2.
3.
Which of the following is the quadratic equation? A
x 2 4x 7
B
x 2 3x 2
C
x3 2x 2
D
x2
1 x
0
0
Given that ( x a )( x b) 0 where x A
variables
B
factors
C
constants
D
roots
Given that ( x 4)( x 3) 0 , then x
a or x b , therefore a and b are known as
4 or x
3.
Find the product of roots.
4.
A
43
B
4u 3
C
4y3
D
43
Quadratic equation can be formed from its roots by x 2 (sum of roots)x + (product of roots) 0 Determine the product of roots for the equation x 2 3 x 10 0 . A
-10
B
10
C
-3
D
3
3
5.
6.
Which of the following is written in general form? A
3x 2 4 x 9 x 2 0
B
2 x 2 7 x 24 0
C
x2 5 4x
D
x2
2x 10
The quadratic equation with two given roots can be obtained by x 2 (sum of roots)x + (product of roots) 0 Determine the sum of roots for the equation x 2 3x 10 0 .
7.
8.
A
10
B
10
C
-3
D
3
Determine the type of roots of quadratic equation, if b 2 4ac ! 0 A
real and distinct roots
B
equal roots
C
no real roots
D
real roots
What is the next step to find the roots of (3 x 5)( x 6) 0 ? A
3x = 5 or x = 6
B
3x 5 = 0
C
x–6=0
D
3x2 + 13x + 30 = 0
4
9.
10.
11.
12.
Which of the following is a perfect square? A
x2 p2
B
x 2 ( p q ) x pq
C
x 2 (q p ) x pq
D
x p
2
5 x n 3 x 8 0 is a quadratic equation. Determine the value of n.
A
-2
B
0
C
2
D
3
Given the general form of quadratic equation, ax 2 bx c Determine the values of a, b and c from x 2 3x 5 0 . A
a = 0, b = 3, c = 5
B
a = 0, b = 5, c = 3
C
a = 1, b = 3, c = 5
D
a = 1, b = 5, c = 3
0.
The steps of completing the square method for x 2 6x 15 are x 2 6x (3) 2 15 (3) 2 ( x p ) 2 24 Determine the value of p. A
-3
B
3
C
6
D
9
5
13.
Which is the correct quadratic formula to find the roots in quadratic equation?
A
14.
15.
16.
b r b 2 4ac 2a
B
b r b 2 4ac 2a
C
br
D
b r b 4ac 2a
b 2 4ac 2a
What is the next step to solve equation 2 x 2 x 15 by using completing the square method. A
Divide both side by 1
B
Divide both side by 2
C
Divide both side by 15
D
Divide both side by 2
Find the sum of roots if 2 and 6 are the roots of the quadratic equation. A
3
B
4
C
8
D
12
The quadratic equation does not have real roots. Which of the following is correct to determine the types of roots ? A
b 2 4ac ! 0
B
b 2 4ac 0
C
b 2 4ac
D
b 2 4ac d 0
0
6
17.
18.
19.
2 and -3 are the roots of quadratic equation ( x p )( x 3) 0 . Find the value of p A
3
B
2
C
-2
D
-3
Express 3 x 2 2
2 x in the general form
A
3x 2
B
3x 2 2 2 x
C
3x 2 2 x
D
3x 2 2 x 2 0
2x 2 0
2
Based on the general form in quadratic equation, determine the values of a, b and c for x 2 3x 5 . A
a = 1, b = 3, c = -5
B
a = 0, b = 5, c = 3
C
a = 1, b = 3, c = 5
D
a = 1, b = -5, c = 3
7
20.
Which of the following is correct to solve 4 x 2 3 x 2 0 , by using quadratic formula x
x
3 r (3) 2 4(4)(2) 2(4)
B
x
3 r (3) 2 4(2)(4) 2(3)
C
x
3 r (3) 2 4(4)(2) 2(4)
D
x
3 r (3) 2 4(2)(4) 2(3)
A
21.
22.
b r b 2 4ac 2a
From the discriminant of a quadratic equation b 2 4ac , determine the type of roots for 4 x 2 20 x 25 0 A
equal roots
B
distinct roots
C
no real roots
Find the values of a, b and c when the equation 4 x 2 px 3 x 3 is written in the general form. A
a = 1, b = p, c = 3
B
a = 1, b = p + 3, c = -3
C
a = 1, b = p + 3, c = 3
D
a = 1, b = 3, c = 3
8
23.
24.
Which is correct to determine the types of roots for x 2 2x 2 0 by using the discriminant b 2 4ac . A
(2)2 - 4(1)(2)
B
(1)2 - 4(2)(-2)
C
(2)2 - 4(1)(-2)
D
(1)2 - 4(-2)(2)
Determine the correct step to solve x 2 8x 2 0 by completing the square method. 2
2
A
§8· §8· x 8x ¨ ¸ ¨ ¸ 2 ©2¹ ©2¹
B
§8· §8· x 8x ¨ ¸ ¨ ¸ 2 ©2¹ ©2¹
C
§2· x 8x ¨ ¸ ©2¹
D
§2· x 8x ¨ ¸ © 2 ¹
2
2
25.
0
2
2
0
2
2
2
0 2
0
Given D and E are the roots of the quadratic equation x 2 (D E ) x DE 0 . Form a quadratic equation which has the roots 2 and 4.
26.
A
x 2 6x 8 0
B
x 2 8x 6 0
C
x 2 6x 8 0
D
x 2 8x 6 0
The value of x from ( x 3)( x 2) 0 can be determined by A
x 3 0 or x 2 0
B
x 3
C
x 3 ( x 2)
D
x2 x 6 0
x2
9
27.
28.
29.
Form a quadratic equation with roots -3 and 7. A
x 2 4x 21 0
B
x 2 4x 21 0
C
x 2 4x 21 0
D
x 2 4x 21 0
The quadratic equation x 2 4mx 2 0 has two different roots. Which of the following is correct to find the range of m? A
16 m 2 8 0
B
4m 2 8 0
C
16 m 2 8 ! 0
D
4m 2 8 ! 0
The following are the steps to solve the quadratic equation 2 x 2 8 x 7 completing the square method. x2 4x
7 2
7 2 2 2 ………………………….. (P) x 2 4 x 2
2
What is step P? 7 4 2
A
x 2 2
B
x 2
C
x 4 2
7 4 2
D
x 4
7 4 2
7 4 2
10
0 , using
30.
31.
32.
33.
Given x 1 x 4 A
1
B
-1
C
3
D
–4
px 2 3x 4 . Find the value of p .
If the quadratic equation mx 2 4x 2 0 has two equal roots, find the value of m. A
1
B
2
C
8
D
16
Given x 2 is the root of the quadratic equation x 2 2 x k Find the value of k. A
8
B
-8
C
0
D
-2
p and q are the roots for quadratic equation 2 x 2 8 x 3 Which of the following is true?
A
pq
4 and pq
3 2
B
pq
8 and pq
3
C
pq
4 and pq
2 3
D
p q 8 a n d pq
3
11
0.
0.
34.
Which is the correct step to solve the quadratic equation 3 x 2 7 x 6 completing the square method? 2
2
A
7 §7· §7· x x¨ ¸ ¨ ¸ 2 3 © 6 ¹ © 6 ¹
B
7 §7· §7· 3x x ¨ ¸ ¨ ¸ 6 3 © 6 ¹ © 6 ¹
C
x2
D
7 §7· §7· 3x x ¨ ¸ ¨ ¸ 6 3 ©6¹ ©6¹
2
2
0
2
7 §7· §7· x¨ ¸ ¨ ¸ 2 3 ©6¹ ©6¹ 2
36.
2
2
2
35.
0
0
2
2
0
Solve the quadratic equation x 2 4x 3 0 . A
4 and 3
B
1 and 3
C
- 4 and 3
D
-1 and -3
Following are the steps to solve the quadratic equation x 2 4x 5 by factorization method. Rearrange the steps. i.
Factorised completely ( x 5)( x 1)
ii.
Change to general form x 2 4x 5 0
iii.
Equalise each factor to zero
iv.
Solve x 5 0 or x 1 0
A
i, ii, iii, iv
B
ii, i, iii, iv
C
i, iii, ii, iv
D
ii, iii, i, iv
12
0 by using
37.
38.
Why is the equation x 3 x 2 x
0 not a quadratic equation?
A
The highest power of x is 1
B
The highest power of x is 2
C
The highest power of x is 3
Which of the following is the best answer to identify the quadratic equation x2 x 5 0 ? A
The highest power of x is 2.
B
The equation involves only one unknown.
C
The highest power of x is 2 and involves only one unknown.
D
The highest power of x is 2 and involves more than one unknown.
39.
0
a
b
c
4 x 2 3x 2 0
4
3
-2
ax 2 bx c
b 2 4 ac
0
41
x 0.425 or -1.175
From the table, which method is used to solve 4 x 2 3 x 2 0 A
Factorisation
B
Completing the square
C
Quadratic formula
END OF QUESTION PAPER
13
KEMENTERIAN PELAJARAN M ALAYSIA
KERTAS JAWAPAN OBJEKTIF Ujian Diagnostik
Nama Pelajar: Tahun/ Tingkatan :
4
Mata Pelajaran: MATEMATIK TAMBAHAN Modul:
Nama Sekolah:
2
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
1-7
7
2
K5
8 - 16
9
3
K6
17 - 25
9
4
K7
26 - 35
10
5
K8
36 - 39
4
8 9 10
Bilangan Soalan Gagal Dijawab
Kegunaan Guru
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