Exponential and logarithmic functions

Integer  exponents

Definition    If  a  is a real number and n is a positive integer then        

   

 

 

  

 

 

a is the base and n is the exponent.

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Laws of Integral Indices

If a and b are real numbers, and m,n are integers, then the following hold.

 

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Example 1 : Multiplying and dividing integer exponents.

Solution

 

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    Example 2 : Simplify the following and express answers  with positive indices.

 

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Exercise 1

Determine whether each of the following is true or false.

 

 

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Exercise 2

Simplify the following and express your answers with positive indices.

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Properties of nth roots

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Exercise 4

From the following equation, find the values of n.

Consider the following examples :

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Adding and Subtracting nth roots

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Consider the following examples :

Multiplying and Dividing nth roots

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Exercise 6

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Consider the following examples :

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Consider the following exampls :

Exponential Functions

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 Solve the equation of the following :

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Logarithmic Functions

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Preparation for PAT 1 Test.
PAT 1 Test (2553)

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Solve the following logarithmic equations.

Exercise 15

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Preparation for ONET Test.
Math O-NET Test (2548)

Exercise 17

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Consider the following examples :

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Math is Fun.com [cited 2016].Available from : http://www.mathsisfun.com/index.htm
Keith Taylor and Holly Fraser. EMR  [cited 2002]. Available from :
http://math.usask.ca/mrc-cgi-bin/emr/first_page.cgi
Purplemath.com [cited 2016 May 19]. Available from :
http://www.purplemath.com/modules/graphexp.htm
Mathematics Core Course Textbook 11th Grade Exponential and Logarithmic Functions
by The Institute for the Promotion of Teaching Science and Technology Ministry of Education.
Chow Wai Keung and Li Kam Yuk. (2009) Discovering Mathematic 4B. Pub,Inc. Hong Kong.

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History of trigonometry

Trigonometric functions

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Sine and Cosine Functions

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Exercise 2

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Exercise 3

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  Constructing angles of the following.

Exercise 5

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Preparation for O-NET Test.
Math O-NET Test (2551)

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The six trigonometric functions

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Math is Fun [cited 2014].Available from :
https://www.mathsisfun.com/algebra/trig-four-quadrants.html
Purplemath. [cited 2016 May 19]. Available from :
http://www.purplemath.com/modules/radians.htm
Regentsprep.org [cited 1998-2012]. Available from :
http://www.regentsprep.org/regents/math/algtrig/att14/formulalesson.htm
Syvum.com [cited 1999-2016]. Available from :
http://www.syvum.com/cgi/online/serve.cgi/math/trigo/trig3.html?question_hide
Mathematics Core Course Textbook 11th Grade Exponential and Logarithmic Functions
by The Institute for the Promotion of Teaching Science and Technology Ministry of Education
Chow Wai Keung and Li Kam Yuk. (2009) Discovering Mathematic 4B. Pub,Inc. Hong Kong.

Thank you for the information

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Heights and distances  of trigonometry

144

Exercise 29

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Preparation for O-NET Test.

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The law of sines

138

Exercise 28

137

Preparation for O-NET Test.

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The law of cosines

The laws of cosines and sines

132

Exercise 27

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Preparation for O-NET Test.

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Consider the following examples :

Trigonometric equations

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Exercise 26

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Preparation for O-NET Test.

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Trigonometric Identities

Trigonometric Identities and Equations

123

Exercise 25

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Preparation for ONET Test.

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Exercise 24

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Preparation for O-NET Test.

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Inverse tangent

114

Exercise 23

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Preparation for O-NET Test.

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Inverse cosine

110

Exercise 22

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Preparation for O-NET Test.

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Inverse sine

Inverse trigonometric functions

106

Exercise 21

105

Preparation for O-NET Test.

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102

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Preparation for O-NET Test.

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Consider the following examples.

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Sum and difference  formulas in trigonometry

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Exercise 20

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Exercise 19

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Exercise 18

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Exercise 17

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            Consider the following examples :

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Graphs of trigonometric functions

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Exercise 16

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Preparation for O-NET Test.

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Find the values of trigonometric function with tables

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Exercise 15

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Exercise 14

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Preparation for O-NET Test.

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Consider the following example :

An Angle in a Right Angled Triangle

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Exercise 13

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Preparation for O-NET Test.

Math is Fun

66

Converting from degrees to radians and radians to degrees.

65

I have a couple of questions for you.

64

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Measure of an angle

Trigonometric function of an angles

61

Exercise 12

60

Preparation for O-NET Test.

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Consider the following examples:

The six trigonometric functions

57

Exercise 11

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Preparation for O-NET Test.

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Reciprocal Functions of Trigonometry

54

Reciprocal Functions of Trigonometry

53

 The figure below, find the value of the six trigonometric functions .

Exercise 10

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Preparation for O-NET Test.

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Consider the following example :

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A right triangle

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Exercise 9

47

Preparation for O-NET Test.
Math O-NET Test (2552)

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Trick for trig

45

Preparation for O-NET Test.
Math O-NET Test (2550)

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                      Consider the following example :

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Unit circle hand trick

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Exercise 8

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37

36

35

Consider the following examples :

Find the value of Sine and Cosine Functions

34

Exercise 7

33

Preparation for O-NET Test.
Math O-NET Test (2548)

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Consider the following example:

30

Find the value  of sine and cosine function of angles  and

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Is this statement true or false?

Exercise 6

Preparation for O-NET Test.
Math O-NET Test (2549)

28

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27

Find quadrant is angles ,and in

26

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Consider the following examples.

Find the value of Sine and Cosine Functions

Is this statement true or false?

Exercise 4

Preparation for O-NET Test

 Math O-NET Test (2548)

I have a couple of questions for you.

Unit Circle and Reference Angles

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Find the value of the following.

Preparation for O-NET Test.

Math O-NET Test (2551)

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Preparation for O-NET Test.

Math O-NET Test (2551)

Fill in the blank .

Math is Fun

Four Quadrants

I have a couple of questions for you

Exercise 1

Preparation for O-NET Test

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I have 3 questions for you.

Thank you for the information

Exercise 21

Preparation for O-NET Test.
Math O-NET Test (2551)

Consider the following examples :
Applications of Exponential and Logarithmic Functions

Exercise 20

Preparation for O-NET Test.
Math O-NET Test (2549)

Exercise 19

Preparation for O-NET Test.
Math O-NET Test (2553)

Applications of Exponential and Logarithmic Functions

Exercise 18

Preparation for O-NET Test.
Math O-NET Test (2548)

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Consider the following examples  :

70

Changing the base of a logarithm

Preparation for PAT 1 Test.
PAT 1 Test (2551)

Math is Fun : “Antilogarithm”

Consider the followng example :

Find the value of logarithm

Draw the graph of the following.

Exercise 16

Preparation for O-NET Test.
Math O-NET Test (2555)

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Graph of logarithmic functions

Solution

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53

Consider the following examples :
Writing in Logarithmic and Exponential form.

Exercise 14

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Consider the following examples :
Draw the graph of the following.

Exercise 13

Preparation for GAT/PAT Test.
PAT 1 (2555)

Write the equation of the following exponential function.

Exercise 12

Preparation for O-NET Test.
Math O-NET Test (2553)

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Graph of exponential functions

 

Solve the following exponential equations.

Exercise 11

Preparation for O-NET Test.
Math O-NET Test (2550)

Math is Fun : “The Exponent”
Fill in the blank , Base or Exponent equal to:

 

Consider the following examples :

The following is true or false.

Exercise 10

Preparation for O-NET Test.
Math O-NET Test (2549)

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Exercise 9

Exercise 8

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Math O-NET Test (2549)

Exercise 7

 

Preparation for O-NET Test.
Math O-NET Test (2550)

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Rational indices

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Dividing nth roots

Exercise 5

Find the value of the following.

Preparation for O-NET Test

Math O-NET Test (2552)

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nth root of a Real Number
Math Cross Puzzle

Exercise 3

Simplify the following and express your answers with positive indices.

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