Applied Mathematics

About Course

Students interested in pursuing higher education in Business, Education, Linguistics, Social Sciences, or Arts are eligible for this course. A prerequisite is successful completion of Basic Mathematics.

A student who satisfactorily complete the course should be able to:
(a) Solve two variables linear equations and inequalities and sketch their graph
(b) Interpret a series of three simultaneous inequalities of two variables, display them graphically and determine the solution set.
(c) Demonstrate an understanding of the definition of a function and its graph.
(d) Solve quadratic, exponential, logarithmic equations, and inequalities.
(e) Solve simple real life problems involving linear, quadratic, and exponential functions graphically and algebraically.
(f) Determine the zeros and the maximum or minimum of a quadratic function, and solve related problems, including those arising from real world applications.
(g) Sketch the graphs of a quadratic, exponential, and logarithmic functions.
(h) Compare simple and compound interest and relate compound interest to exponential growth.
(i) Understand the inverse relationship between exponents and logarithms and use this relationship to solve related problems.
(j) Understand basic concepts of descriptive statistics, mean, median, mode and summarize data into tables and simple graphs (bar charts, histogram, and pie chart).
(k) Understand basic probability concepts and compute the probability of simple events using tree diagrams and formulas for permutations and combinations.

(a) Solve two variables linear equations and inequalities and sketch their graph
(b) Interpret a series of three simultaneous inequalities of two variables, display them graphically and determine the solution set.
(c) Demonstrate an understanding of the definition of a function and its graph.
(d) Solve quadratic, exponential, logarithmic equations, and inequalities.
(e) Solve simple real life problems involving linear, quadratic, and exponential functions graphically and algebraically.
(f) Determine the zeros and the maximum or minimum of a quadratic function, and solve related problems, including those arising from real world applications.
(g) Sketch the graphs of a quadratic, exponential, and logarithmic functions.
(h) Compare simple and compound interest and relate compound interest to exponential growth.
(i) Understand the inverse relationship between exponents and logarithms and use this relationship to solve related problems.
(j) Understand basic concepts of descriptive statistics, mean, median, mode and summarize data into tables and simple graphs (bar charts, histogram, and pie chart).
(k) Understand basic probability concepts and compute the probability of simple events using tree diagrams and formulas for permutations and combinations.

Course Content

Chapter 1: System of linear Equations and Inequalities
By the end of this chapter, the students will be able to: 1- Determine whether an ordered pair is a solution of a system of equations 2- Solve a system of linear equations by graphing 3- Solve a system of equations by substitution 4- Solve a system of equations by elimination 5- Solve a system of linear inequalities

Linear Equation

04:44
Linear equation (Ordered Pair)

08:15
Linear equation (Graphing)

23:58
Linear equation (Substitution)

13:33
Linear equation (Elimination)

12:49
Linear inequality (Graphing)

21:12
Assignments 1

Chapter 2: Functions and their Graphs
By the end of this chapter, the students will be able to: 1- Determine whether a relation represents a function. 2- Find the domain and range of the function. 3- Find the value of a function. 4- Determine whether a function is one-to-one. 5- Use the vertical line test to identify functions 6- Use horizontal line test to identify one-to-one function. 7- Find the inverse function and composition of functions. 8- Solve quadratic equations using the quadratic Formula. 9- Sketch the graph of linear and quadratic functions.

Functions (Part 1)

05:59
Functions (Part 2)

04:01
Functions (Part 3)

07:24
Types of Functions

04:40
Line Test for a Function

05:44
Domain of the Function

12:33
Evaluating Function at a Point

07:54
Composition of Functions

06:44
Inverse Function

11:06
Quadratic Equations

09:44
Quadratic Equations (extra)

03:05
Discriminant

03:36
Graphing Linear Function

11:14
Graphing Quadratic Function (Vertex)

13:39
Graphing Quadratic Function (Domain and Range)

04:41
Graphing Quadratic Function (Maximum and Minimum)

07:45
Graphing Quadratic Function (x and y-intercepts)

08:34
Graphing Quadratic Function (Sketch a graph)

12:56
Assignments 1
Assignments 2

Midterm Revision
Midterm Revision: A Summary of Key Topics Chapter 1: Systems of Linear Equations and Inequalities Chapter 2: Functions and Their Graphs

Chapter 3: Exponential and Logarithmic Functions
By the end of this chapter, the students will be able to: 1- Understand the concepts and properties of exponential and logarithmic functions. 2- Solve problems based on exponential and logarithmic equations.

Chapter 4: Statistics
By the end of this chapter, the students will be able to: 1- understand the basic concepts of descriptive statistics. 2- compute the basic measures of central tendency. 3- summarize a given data in to tables and graphs.

Measure of Central Tendency

04:51
Mean (Average) – Ungrouped Data

11:10
Mean (Average) – Grouped Data

06:58
Median (Ungrouped Data)

06:03
Mode (Ungrouped Data)

01:57
Example (Mean, Mode and Median)

04:06
Frequency Distributions

04:20
Relative Frequency (fraction or proportion)

05:26
Cumulative Relative Frequency

05:02
Summarising Data Using Tables and Graphs

02:54
Representing Data Using Tables (Ungrouped Data)

05:33
Representing Data Using Tables (Grouped Data)

05:54
Bar Charts

05:15
Pie Charts

05:15
Histogram

04:03

Chapter 5: Probability
By the end of this chapter, the students will be able to: 1- Understand the basic concepts of mathematical probability. 2- Compute the probability of simple events. 3- Compute probability using tree diagrams and permutations and combinations.

Basic Concepts of Probability

09:25
“OR” and “AND” events and complement of event

09:19
Basic Concepts of Probability (Examples 1)

10:25
Basic Concepts of Probability (Example 2)

10:35
Basic Rules of Probability

07:17
Basic Rules of Probability (Examples)

14:07
Tree Diagrams

06:05
Tree Diagrams (Examples)

16:50
Introduction to Permutations and Combinations

02:39
Permutations

12:36
Combinations

00:00
Probability Using Permutations and Combinations

00:00

Chapter 6: Mathematics of Finance
By the end of this chapter, the students will be able to: 1- Solve financial problems that involve simple interest and compound interest. 2- Find the future value of an annuity, and the amount of payments to a sinking fund. 3- Solve problems involving perpetuity, depletion, and capital cost. 4- Solve problems involving stocks and bonds.

Final Exam Revision

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About Course

What Will You Learn?

Course Content

Linear Equation

Linear equation (Ordered Pair)

Linear equation (Graphing)

Linear equation (Substitution)

Linear equation (Elimination)

Linear inequality (Graphing)

Assignments 1

Functions (Part 1)

Functions (Part 2)

Functions (Part 3)

Types of Functions

Line Test for a Function

Domain of the Function

Evaluating Function at a Point

Composition of Functions

Inverse Function

Quadratic Equations

Quadratic Equations (extra)

Discriminant

Graphing Linear Function

Graphing Quadratic Function (Vertex)

Graphing Quadratic Function (Domain and Range)

Graphing Quadratic Function (Maximum and Minimum)

Graphing Quadratic Function (x and y-intercepts)

Graphing Quadratic Function (Sketch a graph)

Assignments 1

Assignments 2

Midterm Revision Midterm Revision: A Summary of Key Topics Chapter 1: Systems of Linear Equations and Inequalities Chapter 2: Functions and Their Graphs

Assignments 1 Solution

Assignments 2.1 Solution

Assignments 2.2 Solution

Midterm Revision

Midterm Revision Solution

Chapter 3: Exponential and Logarithmic Functions By the end of this chapter, the students will be able to: 1- Understand the concepts and properties of exponential and logarithmic functions. 2- Solve problems based on exponential and logarithmic equations.

Exponential Function

Solving Exponential Function

Graphing Exponential Functions

Logarithmic Functions

Convert between Logarithms and exponentials

Solving Logarithmic Functions

Graphing Logarithmic Functions

Application of Exponential Functions

Chapter 4: Statistics By the end of this chapter, the students will be able to: 1- understand the basic concepts of descriptive statistics. 2- compute the basic measures of central tendency. 3- summarize a given data in to tables and graphs.

Measure of Central Tendency

Mean (Average) – Ungrouped Data

Mean (Average) – Grouped Data

Median (Ungrouped Data)

Mode (Ungrouped Data)

Example (Mean, Mode and Median)

Frequency Distributions

Relative Frequency (fraction or proportion)

Cumulative Relative Frequency

Summarising Data Using Tables and Graphs

Representing Data Using Tables (Ungrouped Data)

Representing Data Using Tables (Grouped Data)

Bar Charts

Pie Charts

Histogram

Chapter 5: Probability By the end of this chapter, the students will be able to: 1- Understand the basic concepts of mathematical probability. 2- Compute the probability of simple events. 3- Compute probability using tree diagrams and permutations and combinations.

Basic Concepts of Probability

“OR” and “AND” events and complement of event

Basic Concepts of Probability (Examples 1)

Basic Concepts of Probability (Example 2)

Basic Rules of Probability

Basic Rules of Probability (Examples)

Tree Diagrams

Tree Diagrams (Examples)

Introduction to Permutations and Combinations

Permutations

Combinations

Probability Using Permutations and Combinations

Simple Interest

Discounts and Proceeds