The Course
Dive into the world of variables, equations, and functions with this engaging journey through the fundamental concepts of mathematics. You’ll get to grips with everything from basic operations to complex problem-solving strategies, tackling linear equations, quadratic functions, and polynomials along the way. Whether you're deciphering coefficients or mastering the art of factoring, we'll guide you step-by-step, ensuring you build a solid foundation that’ll support all your future math adventures.
Understanding how to manipulate algebraic expressions isn't just about passing exams— it’s a skill set that will empower you in countless scenarios, from budgeting your finances to understanding the science behind the technology you use every day. You'll come to see how the patterns and principles of algebra are woven into the fabric of everyday life, and with this knowledge, you'll open doors to career opportunities, critical thinking, and a lifetime appreciation for the elegant language of numbers. Trust us, once you demystify those elusive x's and y's, the world of algebra becomes not just accessible, but downright captivating!
What you will learn
When I first crafted this course, my goal was to make the fascinating world of variables, equations, and functions as approachable and rewarding as possible. I've carefully structured our sessions to build your knowledge piece by piece, ensuring that each concept clicks into place before we move on. You'll discover that I've packed the course with supportive materials, interactive problem sets, and clear, engaging examples, all designed to help you gain confidence and mastery. As you progress, you'll see it's about developing a way of thinking that's logical, problem-solving oriented, and incredibly useful across numerous real-world scenarios.
Course Preview
In the Quadratics section, we'll work on a project to find the equation of the trajectory of a basketball ball that was shot to the rim. We clearly see that a linear equation doesn't match the curve trajectory of the ball, so we need new mathematical tools to achieve it.
Curriculum
- Exponent Rules - Study Guides
- Operations With Exponents - Example 1 (2:14)
- Operations With Exponents - Example 2 (1:41)
- Operations With Exponents - Example 3 (2:14)
- Operations With Exponents - Example 4 (1:48)
- Operations With Exponents - Example 5 (2:53)
- Rule of Exponents for Division - Example 1 (Extract From Online Class) (1:21)
- Simplifying Radicals - Example 1 (1:18)
- Simplifying Radicals - Example 2 (1:08)
- Simplifying Radicals - Example 3 (5:18)
- Simplifying Radicals - Example 4 (2:35)
- Applying the Distributive Property to Multiply Polynomials - Quick Guide
- Multiplying a Monomial by a Polynomial - Example 1 (0:54)
- Expanding The Binomial (a + b)² - Quick Guide
- Expanding The Binomial (a - b)² - Quick Guide
- Expanding The Binomial (a + b)² - Example 1 (1:32)
- Expanding The Binomial (a + b)² - Example 2 (1:52)
- Multiplying Conjugate Binomials (a + b)(a - b) - Quick Guide
- Multiplying Conjugate Binomials (a + b)(a - b) - Example 1 (1:14)
- Multiplying Binomials by FOIL - Quick Guide
- Multiplying Binomials by FOIL - Example 1 (1:55)
- Multiplying Polynomials - Example 1 (2:16)
- Factoring Polynomials by Common Factor
- Factoring Polynomials by Common Factor - Example 1 (2:26)
- Factoring Polynomials by Common Factor - Example 2 (1:33)
- Factoring Polynomials by Common Factor - Example 3 (2:20)
- Factoring Polynomials by Common Factor - Example 4 (1:34)
- Factoring Polynomials by Common Practice Exercises
- Factoring Polynomials by Grouping - Example 1 (2:37)
- Factoring Polynomials by Grouping - Practice Exercises
- Factoring a Difference of Perfect Squares a² - b² - Example 1 (1:59)
- Factoring a Difference of Perfect Squares a² - b² - Example 2 (1:49)
- Factoring a Difference of Perfect Squares a² - b² - Practice Exercises
- Factoring Trinomials: x² + bx + c
- Factoring Trinomials: x² + bx + c - Ex 1
- Factoring Trinomials: x² + bx + c - Example 1 (2:33)
- Factoring Trinomials: x² + bx + c - Practice exercises 1
- Factoring Trinomials: x² + bx + c - Practice exercises 2
- Factoring Trinomials: ax² + bx + c
- Factoring Trinomials: ax² + bx + c - Example 1 (3:57)
- Factoring Trinomials: ax² + bx + c - Practice Exercises
- Quadratic Relations (Functions) - Describing a Basketball Shot (4:37)
- The Quadratic Function and its Graphic (The Parabola) (6:10)
- First and Second Differences of the Quadratic Function - Rate of Change (2:49)
- Second Differences of the Quadratic Function (1:25)
- Transformations of the Quadratic Function - Introduction (1:16)
- Vertical Reflexion Transformation, Maximum and Minimum Value (5:15)
- Transformations - Vertical Translation (Shift) (3:27)
- Transformations - Horizontal Translation Part 1 (1:28)
- Transformations - Horizontal Translation Part 2 (4:28)
- Transformations - Vertical Stretch (3:16)
- Transformations - Vertical Compression (1:59)
- Vertex Form of the Quadratic Function (Parabola) (3:49)
- Finding the x and y-intercept of the Parabola - Introduction (2:30)
- Simplifying the Vertex Form of a Quadratic Function (4:56)
- The Standard Form of the Quadratic Function (Parabola) (2:04)
- How to Find the Y-Intercept of the Quadratic Function (Parabola) From the Standard Form (1:59)
- Cancelling the Quadratic Term in an Equation by Applying the Square Root (2:32)
- The X-Intercept Part 1 (2:53)
- The X-Intercept Part 2 - Two Points (1:52)
- The X-Intercept Part 3 - None (2:09)
- Solving a Quadratic Equation in Standard Form by Factoring
- Solving a Quadratic Equation by Factoring - Example 1 (extract from live class) (0:57)
- Solving a Quadratic Equation by Factoring - Example 2 (extract from live class) (3:53)
- Solving a Quadratic Equation by Factoring - Example 3 (extract from live class) (0:46)
- The Quadratic Formula - Quick Guide
- Optimization by Completing The Square - Example 1
- Finding The Minimum Value Of A Quadratic Function - Example 1 Part 1 (extract from live class) (5:18)
- Finding The Minimum Value Of A Quadratic Function - Example 1 Part 2 (extract from live class) (4:32)
Your instructor
As a seasoned Math and Physics tutor, I bring a wealth of knowledge from my background in Physics Engineering and Business Management to the classroom. My dedication to education extends beyond the traditional setting, as I have tailored my skills to excel in online teaching environments. Founding and directing Galvez Empower, I've harnessed my expertise to empower students by making complex concepts accessible and engaging to learners of all levels.
My passion for Mathematics and Science is reflected in my teaching philosophy; I strive to foster a deep understanding and appreciation for the subject by connecting mathematical principles to real-world applications. With years of experience guiding students through the intricacies of Algebra, I take pride in witnessing their growth and achievements. As an educator, my greatest reward is seeing my students develop the confidence and skills to tackle any mathematical challenge.
Comprehensive
Covering all the Essential Topics and Techniques in a highly structured and efficient layout
Practical
Real-World Applications and Problem-Solving Strategies
Interactive
Engaging Exercises and Collaborative Learning Experiences
