Intermediate Algebra Master Class: Master the Fundamentals of Algebra
This video course will help you to learn Algebra fast and solve algebraic problems fast. Why because I try to build the foundation first. I know what are the key hurdles in understanding algebra for “most” of the students and what points need to be repeated and refreshed at what stages of learning. I gather this information from an extensive teaching and extensive reading. I do not rely just on my own experience, rather I try to find the latest research on why students struggle understanding math in general and algebra in particular. However, I have few suggestions if you want to get the most benefit out of my course:
1. You will learn much more if you start with a beginner’s mind.
2. Learn when you are not distracted.
3. Do not think that you have limited learning potential. Believe me, you can learn whatever you wish and you can learn it fast. Just put your limits aside.
3. Watch my full course, (I will be adding more deliverable material and resources).
This intermediate algebra course will help students to get a solid foundation in algebra and get ready for higher mathematics courses such as calculus.
This Algebra course is designed and structured in a way which makes it easy for students to absorb the Algebraic concepts. There are some inherent conceptual difficulties which high school students face when learning algebra. This course is designed carefully and keeping in mind all these difficulties. I tried to present critical algebraic concepts in a specific order. I am confident that this sequence will help students by making it easy for them to grasp algebraic concepts. These building blocks of algebra will not only enhance the skills of students but will motivate them to think algebraically. I have tutored high school mathematics for many years and have applied math in my engineering and research career.
To learn algebra at their best, students should start thinking algebraically. I understand that if the concepts are presented in a scientific and organized manner with the precise and clear usage of the terminology, students start to get the bigger picture and this makes them think in algebra. They start to develop critical algebra understanding and even start to talk in x and y. This is the stage where learning algebra becomes their passion. When they master the art of abstraction, they love it.
For one who has absolutely zero knowledge of algebra, there is a pre-Algebra section in this course. The students who have a strong grip on fractions and number theory may skip this section.
For Home Schooling Parents
The course could be a valuable resource for people who are homeschooling their children and want help in algebra. The quizzes are interactive and parents can sit with their children when they are solving the quiz and can see the instant result at the end. They can then select course videos in the areas of weaknesses and ask children to watch that video.
- Students of Grade 8 to 10
- Students with zero knowledge of algebra or who have knowledge gaps
- IGCSE students
- Students planning to appear in GMAT, GRE exams
- College students who think their professor is too fast while they have questions to ask.
- For students in homeschooling
What Will You Learn in This Intermediate Algebra Course:
This algebra course will lay a strong foundation for you to take advanced courses in mathematics such as calculus or planning to appear in competitive exams. At the completion of this course, students will be able to:
- Differentiate numbers and properties of numbers.
- Investigate terminating and recurring decimals
- Practice distributive law and expansion of algebraic expressions
- Recognize rational numbers and perform various operations on rational numbers.
- Differentiate exponents and radicals and perform their simplification using index laws
- Recognize algebraic expressions and like terms
- Perform Algebraic operations
- Understand Polynomials, monomials, binomials and four operations on polynomials
- Balance and reversing methods of solving algebraic equations
- Solve single variable algebraic equations
- Solve linear equations using a calculator (this will be added later at some stage)
- Sketch linear graphs using coordinates of two pints and solving linear equations
- Finding properties of straight lines using points or equations
- Draw the graphs and find out properties of straight lines
- Find out the ordered pairs from linear equations and draw graphs.
- Finding the distance between points on a Cartesian plane
- Solve problem involving parallel and perpendicular lines
- Solve two and three variables simultaneous linear equations
- Perform Factorization of polynomials
- Perform Factorization of quadratic equations(will be added soon)
- Solve Quadratic Equations using various methods and strategies (will be added soon)
Detailed Description of Each Section of this Intermediate Algebra Course
Section 1: Introduction
This is a quick introduction to the most commonly used terms and keywords in algebra. The first video of this intermediate algebra course is a general introductory video of the course. In the next few videos, you will learn what is an algebraic expression and how to make algebraic expressions from simple word problems. You will also learn the elements of an algebraic term, what are like terms, the rules of like terms and simplification. The students will learn how to use letters to signify an unknown.
Section 2: Pre-Algebra Rational Numbers and Operations on Rational Numbers
In this section, you will first learn the types of numbers and the properties of numbers. These properties are the math principle which we will be using during this algebra course. After that, the focus in this section will be on rational numbers (fractions). You will the types of fractions and mathematical operations on fractions. You will be able to find the equivalent fractions and compare various fractions in ascending order. You will also master the divisibility rules and will be able to figure out whether any large number is divisible by 2, 3, 4, 5, 6 or not. Using these divisibility rules, you will be able to simplify any fraction containing large numbers. At the end of the section you will learn the factorization of numbers, what are prime factors and how to find the prime factors of large numbers.
Section-3: Exponents and Radicals
In algebra, you must know how to handle numbers and variables with exponents and radicals. This is the first skill you will be mastering after the pre-algebra section of the course. You will learn the exponent rules, also called index laws. These rules explain how the value of exponent changes when we multiply or divide two or more numbers with exponents. You will also learn exponents of exponents and their operations. You will also learn about the algebraic expressions that include radicals and how to work with radicals. You will be able to understand the radical, variable and coefficients. Also, you will master your skills of converting a radical notation into exponent form or vice versa. You will do operations of multiplication and division on algebraic terms that include radicals.
Section-4: Introduction to Solving Algebraic Equations
The algebra lessons in this section are the starting point for you to solving the equations in algebra. First, two basic methods of solving algebraic equations are explained. These methods are the balance method and the reversing method. I explained why reversing method can save us some time once we are comfortable with solving algebraic equations. This is followed by many examples of solving algebraic equations.
Section-5: Advanced Linear Equations in One Variable
The algebra lesson in this section of this online intermediate algebra course is on solving advanced algebraic equations. We tackle the solution of algebraic equations with grouping signs, with radicals and the ones which have fractions. The tips and tricks for solving these types of equations are explained with many examples.
Section-6: Polynomials and Factorization of Polynomials
In the first algebra lessons in this section are about the terminology used in polynomials and the basis of classification of polynomials. Then we do four operations (subtraction, addition, multiplication, and division) of polynomials.
Section-7: Methods of Solving Quadratic Equations
Once we know how to factorize, we can now solve the quadratic polynomials. This is one of the core topics of algebra and the one where students struggle the most. In this section, many methods of solving the quadratic equations are explained. The algebra lessons in this section describe factorization method of solving quadratic equations, the completing the square method of solving quadratic equations and the quadratic formula. You will see me over the shoulder, solving many examples of all of these methods.
Section-8: Solving Multi-variable Simultaneous Linear Equations
In this section of this online algebra course, we solve the sets of equations. These are two or three variable linear equations which we solve using the solution methods of simultaneous linear equations.
section-9: Functions and their Graphs
In this section of the algebra course, students will be introduced to the concepts of functions and graphs. We will explain the ordered pairs and the Cartesian coordinate system. Then there are video lectures about functions, about straight lines and their graphs. Perpendicular and parallel lines. Students will learn the properties of these types of lines such as slope and intercept. Student will also learn how to draw the graphs of straight lines and find their intersection. Also the distance formula will also be introduced in this section of this online algebra course.
About Course Resources:
You will love the quizzes of this intermediate algebra course. The quizzes are downloadable interactive files. You take a pen and paper and start answering the questions. At the end you press end quiz button and you will see your score. If you want to know the correct answers, you can then press the “correct” button and it will show you the correct answers and your answers whether correct or wrong. You can then see your weaknesses and watch the lecture videos once again. The quizzes are challenging and you will be tested from various angles of the same question. This will help you for competitive exams where the simple question is phrased in a complex way. I have put a lot of effort and time in quizzes and I would like to have your feedback and review because I am always looking for ways to improve my course.
Homework questions is an important source for questions. Top students always want more work to sharpen their skills. I make these questions in such a manner which will give you a full chance to master your algebra skills. Homework questions in this algebra course are full of variety and different level of difficulty from beginner to intermediate to advanced. But if you think there is a question which I have not covered in the video lecture of this algebra course, please feel free to contact me and I will cover that topic with an additional lecture video.
Future Plans for the Curriculum:
My plan is to present the fullest possible curriculum for students of grade 8 to 10. The contents of this course will increase over time because I will be adding more video lectures and resources such as homework and quizzes. In the beginning, I will add one quiz for each section of the course but later my plan is to add more topic-based quizzes. The objectives of every section will be added clearly at the beginning of each section so that you know what skills you must learn during that section of this intermediate algebra course.