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COURSE INTRODUCTION &

SYLLABUS (1)

Course Code: BT1093

Course Title: Matematik Perniagaan

Course Venue: BT10 Course Day/Time: Sunday/4-7PM

Course Textbook:

Haeussler Jr., E.F, Paul, R.S. & R.J. Wood(2005). Introductory Mathematical Analysis.

11th Edition. Pearson Education Inc.

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SYLLABUS (2)

Course Instructor: Cik Sharon Cheuk (Room 13, Level 3, Ext. 1581)

Blogsite: www.businessmaths.wordpress.com- course materials (lecture notes, tutorial answers)

- announcements

- suggested additional readings- your comments
http://www.businessmaths.wordpress.com/http://www.businessmaths.wordpress.com/

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SYLLABUS (3)

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SYLLABUS (4)

Course Objectives: Upon completion ofthis course, students should be able to:

Use algebra, graphs and calculus applications

to solve practical business problems Explain the meaning of compound interest,

present value, promissory, annuities, and loanamortisation

Understand the concept of probability andhow it describes a set of data

Use the results of mathematical calculationsto help evaluate various options in reaching

financial decisions, personal or business

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SYLLABUS (5)

Learning Outcomes: Obtain the skills and knowledge necessary to

succeed in math-based courses

Able to explore career options from a non-mathematician's point of viewAble to demonstrate skills in calculating

practical financial problems of a businessnature

An increased knowledge of the topics ofAlgebra, Probability and Calculus and learnhow these can be applied to solve problems

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SYLLABUS (6)

Course Syllabus (1): Week 1.......Algebra Refresher

Week 2.......Applications of Equations &Inequalities

Week 3.......Functions & graphs

Week 4.......Lines, Parabolas & Systems (Quiz 1)

Week 5.......Exponential & Logarithmic Functions Week 6.......Matrix Algebra (Quiz 2)

Week 7.......Mid-Semester Exam

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SYLLABUS (7)

Course Syllabus (2): Week 8.......Linear Programming

Week 9.......Intro to Probability & Statistics

Week 10....Limits & Continuity

Week 11....Differentiation (Quiz 3)

Week 12....Integration

Week 13....Methods & Applications ofIntegration (Quiz 4)

Week 14....Revision

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SYLLABUS (8)

Course Assessment: Individual Assignment.10%

Group Assignment15%

Quizzes..10%

Mid-Semester Exam.25%

60%

Final Exam.40%

Total.100%

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SYLLABUS (9)

Quizzes (20%): Scheduled quizzes are in Week 4, 6, 11 & 13 Quizzes will cover materials from current and

previous weeks. For e.g. Quiz in Week 4 willcover materials from Weeks 1-3

Replacement quiz is at the discretion of thelecturer

Marking will be based on completion andcorrectness of all answers

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SYLLABUS (10)

Mid-Semester Examination (20%): Mid-Sem Exam is scheduled in Week 7 Mid-Sem Exam will cover materials from

Week 1 to Week 5 Replacement of Mid-Sem Exam is at the

discretion of the lecturer

Marking will be based on completion andcorrectness of all answers

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SYLLABUS (11)

Final Examination (50%): Final Exam is scheduled to be held anytime

during the universitys examination weeks

Final Exam will cover materials from Week 1to Week 14

Replacement of Final Exam is subject to the

universitys academic rules and regulations Marking will be based on completion and

correctness of all answers

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LECTURE OUTLINE

Lecture Objectives Course Introduction & Syllabus Topic 1Sets of Real Numbers Topic 2Some Properties of Real Numbers Topic 3Exponents & Radicals Topic 4Operations with Algebraic Expressions Topic 5Factoring Topic 6Fractions Topic 7Linear Equations (Week 2) Topic 8Quadratic Equations (Week 2) Tutorial Questions

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ALGEBRA REFRESHER

Algebraic equations - its calculationinvolves formula in which variablequantities numbers are replaced with real

numbers and arithmetic operations Examples

Financial ratios (business)

Speed of car (km or mile/hour)Academic achievement GPA/CGPA(PNGS/PNGK)

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SETS OF REAL NUMBERS (1)

Set : Collection of object (also known asset element or member of the set)

Elements or members of a set can beshown in braces

E.g. A = {1,3,5,7,9}; B = {3,5,7}

In E.g. above, B is also a subsetof A

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Positive integers (or natural number) is aset of the numbers 1, 2, 3, and so on

E.g. Set of positive integers = {1,2,3,...}

Negative integers is a set of the numbers-1, -2, -3, and so on

E.g. Set of negative integers = {-1,-2,-3,...}

Set of integers: sets of positive andnegative integers E.g. Set of integers = {,3,2,1,0,-1,-2,-3,...}

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Set of rational numbers = a/b (b 0), where a, bare integers and division by 0 is not defined

Rational numbers are decimals that terminate

E.g. Set of rational numbers = {1/2 = 0.5,5/2 = 2.5,3/1 = 3}

Rational numbers are also non-terminatingrepeating decimal numbers

E.g. Set of rational numbers =

{2/3 = 0.6666., 1/15 = 0.13333.}

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Irrational numbers - non-terminating non-repeating decimals

Cannot be written as an integer divided by

another integer E.g: (pi) and 2 is not a rational number

Set of real numbers = rational + irrationalnumbers

Set of real numbers can be seen on thepoints in a line

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-4 -3 -2 -1 0 1 2 3 4 5

1/3--3.5 3 4.5

-2/3

Example of a real number (coordinate)line: (some points and coordinates)

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SOME PROPERTIES OF

REAL NUMBERS (1)

A few important properties of real numbers

The Transitive Property of Equality:

If a = b and b = c, then a = c E.g. if x = y, x = 5, then y = 5

E.g. if p = q, p = -9, then q = -9

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SOME PROPERTIES OF

REAL NUMBERS (2)

The Commutative Properties of Additionand Multiplication:

a + b = b + a and ab = ba

Two number can be added and multiplied inany order

E.g. 5 + 12 = 12 + 5

E.g. 5 12 = 12 5

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SOME PROPERTIES OF

REAL NUMBERS (3)

The Associative Properties of Addition andMultiplication:

a + (b + c) = (a + b) + c and

a(bc) = (ab)c

In addition to addition and multiplication,numbers can be grouped in any order

E.g. 3 + (5 + 7) = (3 + 5) + 7

E.g. 3 (5 7) = (3 5) 7

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SOME PROPERTIES OF

REAL NUMBERS (4)

The Inverse Properties (1):

i) For each real number a, there is a

unique real number denoteda such

that

a+(-a) = 0

also known as additive inverse or

negative of a

E.g. 5 + (-5) = 0

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SOME PROPERTIES OF

REAL NUMBERS (5)

The Inverse Properties (2):

ii) For each real number a, except 0,

there is a unique real number denoted

a-1 such that

a a-1= 1

also known as multiplicative inverse of

a

E.g. 5 (5-1) = 5 1 / 5 = 5 / 5 = 1

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SOME PROPERTIES OF

REAL NUMBERS (6)

The Distributive Properties (1):

a(b + c) = ab + ac and

(b + c)a = ba + caalso extendable to any number of

terms

a(b + c + d) = ab + ac + ad E.g. 2(3 + 5) = 2(8) = 16 is also

2(3+5) = 2(3) + 2(5) = 6 + 10 = 16

E.g. x (y + 7) = x(y) + x(7) = xy + 7x

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SOME PROPERTIES OF

REAL NUMBERS (7)


Subtraction

a

b means a + (-b) E.g. 4 - 5 = 4 + (- 5)

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SOME PROPERTIES OF

REAL NUMBERS (8)


Division

a

b , or a/b = a(b-1

)since b-1= 1/b, a/b = a(b-1) = a (1/b)

E.g. 4 5 = 4/5 is also 4 1/5

Refer to pages 7-8 of textbook forcomprehensive list of rules for realnumbers

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EXPONENTS AND RADICALS (1)

The product of x x x is abbreviated as x3

xnis the abbreviation for product of n xs,where n is a positive integer

In xn, n is the exponent and x is the base

xn= x x .. x (n factors)

x-n

= 1 / xn

= 1 / (x x .. x) (n factors) 1/x-n= xn

x0= 1 if x 0. 00is not defined.

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If rn =x, where n is a positive integer, then ris the nth root of x

E.g. 42 =16, so 4 is the square root of 16

E.g. 23 =8, so 2 is the cube root of 8

The principal nth root (n x) is positive if xis positive and negative if x is negative and

n is odd E.g. 2 4 = 2 (+ve)

E.g. 3 -27 = -3 (-ve)

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Refer to page 11 of textbook forcomprehensive list of rules for exponents

and radicals

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Exponents Prob.5 (Sec. 0.3)Simplify and express all

answers in terms of positive exponents

Answer:

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Exponents & Radicals Prob.39 (Sec. 0.3)Simplify the expressions

Answer:

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Exponents Prob.51 (Sec. 0.3)Write the expression in

terms of positive exponents only. Avoid all

radicals in the final form.

Answer:

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Exponents Prob.57 (Sec. 0.3)Write the exponential forms

involving radicals

Answer:

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Radicals Prob.71 (Sec. 0.3)Simplify the expressions.

Express all answers in terms of positive

exponents. Rationalize the denominator wherenecessary to avoid fractional exponents of

denominator.

Answer:

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Radicals Prob.75 (Sec. 0.3)Simplify the expressions.

Express all answers in terms of positive

exponents. Rationalize the denominator wherenecessary to avoid fractional exponents of

denominator.

Answer:

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OPERATIONS WITH

ALGEBRAIC EXPRESSIONS (1)

Algebraic expressions are numbersrepresented by symbols which are

combined by any or all of the arithmetic

operations such as addition, subtraction,multiplication and division as well as

exponentiation and extraction of roots.

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OPERATIONS WITH


Algebraic expressions with exactly one term : monomials

with exactly two terms: binomials

with exactly three terms: trinomials

with more than one term: multinomials

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OPERATIONS WITH


Adding Algebraic ExpressionProb.7 (Sec. 0.4)Perform the indicatedoperations and simplify

(6x2 + 10xy + 2) (2zxy + 4)

Answer: (6x2 + 10xy + 2) (2zxy + 4)

= 6x2 + 10xy + 2 2z + xy - 4= 6x2 + 10xy + xy - 2z + 2 4

= 6x2 + 11xy - 2z + 2 4

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OPERATIONS WITH


Subtracting Algebraic ExpressionProb.13 (Sec. 0.4)Perform the indicatedoperations and simplify

3(x2 + y2)x(y + 2x) + 2y(x + 3y)

Answer: 3x2 + 3y2xy - 2x2 + 2xy+ 6y2

= 3x2 - 2x2 + 3y2+ 6y2xy + 2xy= x2 + 9y2 + xy

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OPERATIONS WITH


Special Products

Refer to page 18 of textbook for list ofrules for special products

Prob.19 (Sec. 0.4)Perform the indicatedoperations and simplify

(x+ 4)(x + 5)

Answer: (x+4)(x + 5) = x2 + 5x + 4x + 20

= x2 + 9x + 20

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OPERATIONS WITH


Multiplying MultinomialsProb.35 (Sec. 0.4)Perform the indicatedoperations and simplify

(x2 - 4)(3x2+ 2x - 1)

Answer: x2(3x2 + 2x1)4(3x2 + 2x1)

= 3x4 + 2x3- x2 - 12x2- 8x+ 4= 3x4 + 2x3- 13x2- 8x+ 4

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OPERATIONS WITH


Long Division Prob.51 (Sec. 0.4)

Perform the indicated

operations and simplify(3x3-2x2+x3)(x + 2)

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FACTORING (1)

Factoring is rewriting expression as aproduct of 2 or more factors

E.g. If c = ab, then a and b are factors of c

Refer to page 21 of textbook for list ofrules for factoring

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FACTORING (2)

Common Factors Prob.5 (Sec. 0.5)Factor the following

expressions completely

8a3bc - 12ab3cd + 4b4c2d2

Answer:

4bc(2a3 - 3ab2d + b3cd2)

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FACTORING (3)

Factoring Trinomials Prob.9 (Sec. 0.5)Factor the following


p2+ 4p + 3

Answer:

(p+1)(p+3)

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FRACTIONS (1)

Algebraic expressions which arefractions can be simplified multiplying

and dividing both numerator and

denominator of a fraction by the same

non-zero quantity

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FRACTIONS (3)

Multiplying and Dividing Fractions Rule for multiplying with is

Rule for dividing with where c 0 is

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FRACTIONS (4)

Multiplying and Dividing Fractions Prob.11 (Sec. 0.6)Simplify the expressions

Answer:

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FRACTIONS (5)

Rationalizing the Denominator Prob.53 (Sec. 0.6)Simplify and express your

answer in a form that is free of radicals in the

denominator

Answer:

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FRACTIONS (6)

Addition and Subtraction of Fractions Prob.29 (Sec. 0.6)Perform the operations and

simplify as much as possible

Answer:

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FRACTIONS (7)

Addition andSubtraction of

Fractions

Prob.39 (Sec. 0.6)Perform the operations

and simplify as much

as possible

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FRACTIONS (8)

Addition and Subtraction of Fractions Prob.47 (Sec. 0.6)Factor the following


Answer:

TUTORIAL QUESTIONS

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TUTORIAL QUESTIONS

- CHAPTER 0 (1)

Sec. 0.14, 5, 7, 8

Sec. 0.23, 4, 10, 22

Sec. 0.355, 58, 65, 85, 90

Sec. 0.418, 37, 39, 50 Sec. 0.538, 40, 46, 50

Sec. 0.610, 34, 46, 59

Sec. 0.730, 37, 46, 59, 71, 75, 85, 92, 105 Sec. 0.825, 32, 40, 47, 54, 74, 84

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Bt1093 Week1 Plums