bt1093 week1 plums
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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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COURSE INTRODUCTION &
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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COURSE INTRODUCTION &
SYLLABUS (3)
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COURSE INTRODUCTION &
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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COURSE INTRODUCTION &
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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COURSE INTRODUCTION &
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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COURSE INTRODUCTION &
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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COURSE INTRODUCTION &
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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COURSE INTRODUCTION &
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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COURSE INTRODUCTION &
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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COURSE INTRODUCTION &
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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SETS OF REAL NUMBERS (2)
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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SETS OF REAL NUMBERS (3)
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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SETS OF REAL NUMBERS (4)
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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SETS OF REAL NUMBERS (5)
-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)
The Distributive Properties (2):
Subtraction
a
b means a + (-b) E.g. 4 - 5 = 4 + (- 5)
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SOME PROPERTIES OF
REAL NUMBERS (8)
The Distributive Properties (3):
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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EXPONENTS AND RADICALS (2)
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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EXPONENTS AND RADICALS (3)
Refer to page 11 of textbook forcomprehensive list of rules for exponents
and radicals
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EXPONENTS AND RADICALS (4)
Exponents Prob.5 (Sec. 0.3)Simplify and express all
answers in terms of positive exponents
Answer:
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EXPONENTS AND RADICALS (5)
Exponents & Radicals Prob.39 (Sec. 0.3)Simplify the expressions
Answer:
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EXPONENTS AND RADICALS (7)
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 AND RADICALS (8)
Exponents Prob.57 (Sec. 0.3)Write the exponential forms
involving radicals
Answer:
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EXPONENTS AND RADICALS (9)
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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EXPONENTS AND RADICALS (10)
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 (2)
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
ALGEBRAIC EXPRESSIONS (3)
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
ALGEBRAIC EXPRESSIONS (4)
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
ALGEBRAIC EXPRESSIONS (6)
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
ALGEBRAIC EXPRESSIONS (7)
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
ALGEBRAIC EXPRESSIONS (9)
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
expressions completely
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
expressions completely
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