STUDENT'S COPY MODULE 4

PPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMI

ADDITIONAL MATHEMATICS FORM 4 MODULE 4 PPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMI

INDICES & LOGARITHMS

MINISTRY OF EDUCATION MALAYSIA

MODULE 4: INDICES & LOGARITHMS Arahan: 1 Modul ini mengandungi empat puluh lima 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

D.

Pe n

E

5 Untuk soalan subjektif, jawapan hendaklah ditulis pada kertas berasingan yang disediakan oleh guru. 6 Jawab semua soalan.

Modul ini mengandungi 15 halaman bercetak

2

1

2

53 is known as _________, A

Index number

B

logarithm

C

indices

D

base

Which of the following represent a fractional index ? A

1 2 (5) 3

B

53

C

1 54

D

3 ( )2 2

2

3

4

What is zero index ? A

a0 = 1, a z 0

B

a0 = 1, a = 0

C

a1 = 0, a z 0

D

a1 = 0, a = 0

What does a n mean if n is a positive integer ? A

a multiply by n .

B

n multiply by a .

C

a multiplies itself for n times.

D

n multiply itself for a times.

3

5

6

7

8

9

What does number 5 represent in 5 n ? A

index

B

base

C

logarithm

D

antilogarithm

What is common logarithm ? A

A log with base 10

B

A log with index 10

C

A log with base 2

D

A log with index 2

In what form 103 = 1000 is written? A

index form.

B

indices form.

C

logarithmic form

D

general form

What does y represent in the equation log y N x ? A

base.

B

factor.

C

integer.

D

index.

What does number 5 represent in 25 A

base.

B

indices.

C

integer.

D

index.

32

4

10

11

12

13

Determine the base in log q p A

p

B

q

C

r

r

Which of the following represent a common log ? A

log 2 10

B

log 4 10

C

log8 10

D

log10 10

Change log4 7 from the base 4 to the base 10. A

log10 4 log10 7

B

log 10

C

log10 7 log10 4

D

log 10

4 7

7 4 2 3

Rewrite 125 as cube root of 125. A B

3 2

2 3

125

125

C

2

1253

D

3

125 2

5

14

15

0

Find the value of 8 . A

0

B

1

C

8

D

80

Change 5-2 to the fractional form. A B C D

16

17

1 25 1 2 -5 1 5 -2 1 52

Express

1 in index notation. 1000

A

10

4

B

10

-4

C

10 3

D

10 -3

Find the simplest form for 7n + 1 x 72n A

7 3 n 1

B

7 2 n ( n 1)

C

72n

D

7 n 1 2 n

2

1

6

18

19

20

21

If log a N x then N a x Change log q p r into index form. A

p

rq

B

p

qr

C

r

qp

D

r

pq

Find the value of log A

0

B

1

C

10

D

100

10

10 .

Find the value of log 2 - 8 . A

zero

B

negative

C

undefined

D

unknown

Which of the following is true ? 2 3

A

2

B

2 2 = 0.25

C

23 = 6

D

2

1 2

= 2.67

=2

7

22

4

5 2

i.

is equal to § 21 · 5 ¨4 ¸ ¨ ¸ © ¹ 1 2

ii.

4

iii.

§ 51 · ¨4 ¸ ¨ ¸ © ¹

iv.

4

5

2

2

1 5

Which of the following is the correct answer?

23

24

A

i and ii

B

i and iii

C

ii and iv

D

iii and i

Express log a 2 + log a 5 as a single logarithm. A

log a 7

B

log a 10

C

log 10 7

D

log 10 10

Simplify 5 1 y 5 2 . A

53

B

52

C

52

D

5 1

1

8

25

Rewrite 8

A B C D 26

27



2 3

1

u 16 2

2

(4 ) 3

(2 )





(8

2

(2

-3

2 3

2 3

in index form with the same base. 1 4 2

u (4 )

1 4 2

u (2 ) 1 3

2

) u (8 )

1 2

2 3

) u ( 2 4 ) -1

Change log5 8 from base 5 to other base. A

log10 5 log10 8

B

1 log8 5

C

log 5 8 log8 5

D

1 log 5 8

Change

log 2 45 using laws of logarithms.

A

log 2 3 u log 2 3 u log 2 5

B

log 10 3  log10 3  log10 5

C

log 2 3  log 2 3  log 2 5

D

log 10 3 u log10 3 u log 10 5

9

28

29

30

31

Without using a scientific calculator, calculate the value of log 5 A

3

B

3

C

1 3

D



1 . 125

1 3

Calculate the value of log 3 0.0562 by using a scientific calculator. A

 3.260

B

 1.250

C

 2.620

D

 0.3816

Given log10 2 0.3010 and log10 3 the value of log106 A

0.1761

B

0.1436

C

0.7782

D

0.7781

0.4771, without using scientific calculator, find

§ 4 · ¸¸ . © 3p ¹

Using the laws of logarithm, simplify log 2 ¨¨ A

log 2 4  log 2 3  log 2 p

B

log 2 4  log 2 3 - log 2 p

C

log 2 4 - log 2 3  log 2 p

D

log 2 4 - log 2 3 - log 2 p

10

32

33

34

35

Given log 5 M A

3

B

5

C

6

D

9

2 log 5 3 , find the value of M .

Without using a scientific calculator, calculate the value of log 2 2 4 . A

8

B

4

C

4

D

8

Simplify log a p 2  2 log a pq  log a q 2 using laws of logarithms. A

§ p 2q 2 · ¸ log a ¨¨ 2 ¸ p q © ¹

B

§ p 2q 2 · ¸¸ log a ¨¨ © 2 pq ¹

C

§ p2  q2 · ¸ log a ¨¨ 2 ¸ © ( pq ) ¹

D

§ p2q2 log a ¨¨ 2 © ( pq )

· ¸¸ ¹

Without using a calculator, evaluate 2 log10 5 + log10 4 A

2

B

10

C

40

D

100

11

36

37

Without using the scientific calculator, evaluate A

3

B

1 3

C

2 3

D

3 2

Given

log b

= =

log b b N

1 2

§1· b - log a ¨ ¸ ©a¹

- log a 1  log a a

Determine the value of N ?

A



B

3 2

C



D

1 2

3 2 1 2

12

log 9 27 .

38

x

5

logM x

N

Given

logM x

1 log 5 9 2

log5 9

x

1 2

3

From the given steps in solving

39

M=9,N=

B

M=

C

M = 5, N =

D

M = 10, N =

x

3 uP 3

log 5 9

1 ,N= 2

x

x

3 (9 - 1)

1 log 5 9 2

log 5 9

3x  2 - 3x 216

216

can be solve as below:

216

(3x )8

216 Q

3x x

3

33

What is P and Q ? A

3 and 24 x

B

3 and 3 x

C

3 2 and 24 x

D

3 2 and 3 x

, find M and N.

1 log 5 9 2

A

The equation

5

1 log 5 9 2

216 27 216 27 13

40

The logarithmic equation log 2 (2 x  1)  log 2 ( x  5) following steps:

log 2 (2 x  1)  log 2 ( x  5)

§ 2x 1 · log 2 ¨ ¸ © x 5 ¹

3 can be solved by the

3

3

K

2 x  1 8( x  5) 2 x  1 8 x  40

: : :

x =L Find K and L .

41

A

2x  1 x -5

2 3 and 41

B

2x  1 x -5

2 3 and - 41

C

2x  1 x -5

3 2 and 41

D

2x  1 x -5

3 2 and - 41

Given log 27 n

6

6

6

6

2 . How can we find the value of n ? 3

A

Change the logarithm equation to index equation.

B

Change the index equation to logarithm equation.

C

Use the laws of logarithm.

D

Use the laws of indices.

14

42

43

44

45

How to solve the equation 3 x

2 ?

A

Use indices on both sides.

B

Use indices on one side only.

C

Use logarithm on both sides.

D

Use logarithm on one side only.

Which of the following is the best way to solve 2 x

64 ?

A

Change the base.

B

Divide 64 both side by 2 and simplify .

C

Square root of 64 .

D

Express in the same base and compare the indices.

How to read loga x completely? A

log of x to the base of a

B

log of a to the base of x

C

log x .

D

log a

How to read a x ? A B C D

x to the power of a a to the power of x x index a a index x

END OF QUESTIONS PAPER

15

KEMENTERIAN PELAJARAN M ALAYSIA

KERTAS JAWAPAN OBJEKTIF Ujian Diagnostik

Nama Pelajar: Tahun/ Tingkatan :

4

Mata Pelajaran: MATEMATIK TAMBAHAN Modul:

Nama Sekolah:

4

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

1-6

6

2

K5

7 - 20

14

3

K6

21 - 33

13

4

K7

34 - 40

7

5

K8

41 - 45

5

8 9 10

Bilangan Soalan Gagal Dijawab

Kegunaan Guru