This Algebra course offers a comprehensive approach for learners starting from basic concepts to more advanced topics. The course is structured into multiple modules, each focusing on specific areas of algebra. Key features include:
Each module is designed to build confidence and skills, making it suitable for beginners and those looking to strengthen their algebra knowledge.
This module introduces the concept of simple algebraic equations in the form of Ax=B. Students will learn how to isolate the variable, understand the properties of equality, and solve for unknowns.
Key topics include:
Building on the previous module, this section delves into slightly more complicated equations. Students will encounter equations that require more advanced manipulation techniques.
Topics covered include:
This module focuses on equations that have variables on both sides, increasing the complexity of problem-solving. Students will learn to rearrange equations and simplify effectively.
Key learning points include:
This module covers solving linear equations that involve variable expressions in denominators. Students will learn to handle fractions and understand their role in equations.
Key areas include:
This module focuses on graphing linear equations using Cartesian coordinates. Students will learn how to plot points and draw lines based on various equations.
Topics include:
This module provides an intuitive understanding of slope and y-intercept, essential components of linear equations. Students will grasp how these concepts affect the graph of a line.
Key concepts include:
This module focuses on calculating the slope of a line given two points. Students will learn the formula for slope and practice finding it through various examples.
Key learning points include:
This module continues the exploration of slope through additional examples and problems. Students will become proficient in calculating slope in various situations.
Key areas covered include:
This module further develops the understanding of slope through advanced problems. Students will tackle challenging scenarios to enhance their skills.
Topics explored include:
This module introduces the concept of averages in algebra, providing students with a basis for solving problems that involve mean values.
Key topics include:
This module focuses on adding sums of consecutive integers. Students will explore techniques for calculating sums quickly and efficiently.
Topics covered include:
This module teaches how to take percentages of numbers, a fundamental skill in both algebra and real-world problem-solving. Students will learn the concept of percentages and practice calculations.
Key areas include:
This module focuses on growing a quantity by a percentage. Students will learn how to apply percentages to determine increased amounts in various contexts.
Key concepts include:
This module addresses a common percentage word problem: finding the original price when given a discounted price. Students will learn problem-solving techniques for these situations.
Key topics include:
This module challenges students with slightly harder percentage problems, enhancing their problem-solving skills and understanding of percentages.
Key areas covered include:
This module introduces systems of equations, where students will learn to solve multiple equations simultaneously. This is a crucial skill in algebra and problem-solving.
Key concepts include:
This module focuses on ratio problems that involve basic algebra. Students will learn to set up and solve ratio equations effectively.
Key learning points include:
This module presents more advanced ratio problems, pushing students to deepen their understanding and skills in solving ratio-related equations.
Topics covered include:
This module offers an alternate solution to the advanced ratio problem discussed previously, showcasing different methods to approach the same problem.
Key learning points include:
This module introduces basic ratio problems, ensuring that students have a solid foundation before moving on to more complex ratios and applications.
Topics covered include:
This module delves into more advanced ratio problems, building on previous knowledge to tackle more complex scenarios and calculations.
Key concepts include:
This module explores age word problems, where students will learn to set up and solve equations based on age-related scenarios.
Key topics include:
This module continues the exploration of age word problems, presenting more complex scenarios for students to tackle.
Key learning points include:
This module presents the final set of age word problems, allowing students to apply what they have learned in previous modules to solve these equations.
Key concepts include:
This module introduces the concept of multiplying expressions, starting with the multiplication of binomials. Students will learn the significance of this operation in algebra.
Key topics include:
This module focuses on solving quadratics by factoring, a crucial skill for students as they progress in algebra. Students will learn to identify and factor quadratic expressions.
Topics covered include:
This module introduces the concept of the imaginary unit 'i', explaining its significance in mathematics and how it is used in algebra.
Key areas include:
This module delves into complex numbers, teaching students how to add, subtract, and multiply them. A strong understanding of complex numbers is essential for advanced mathematics.
Key concepts include:
This module focuses on dividing complex numbers, a critical skill for students to master as they advance in algebra. Students will learn about complex conjugates and their importance in division.
Key areas covered include:
This module introduces the quadratic equation, teaching students how to use it to solve second-degree polynomials. Understanding quadratics is fundamental in algebra.
Key topics include:
This module presents additional examples of solving equations using the quadratic formula, reinforcing students' understanding and application of this important algebraic tool.
Key areas include:
This module focuses on the method of completing the square to solve quadratic equations. This technique is essential for understanding the properties of quadratics deeply.
Key concepts include:
This module covers the derivation of the quadratic formula by completing the square, providing students with a clear understanding of how this formula is formulated.
Key topics include:
This module introduces quadratic inequalities, teaching students how to solve these inequalities using techniques such as factoring and graphing.
Key concepts include:
This module serves as an introduction to functions, where students will learn the definition of a function and its fundamental characteristics.
Key topics include:
This module continues the exploration of functions with more examples, allowing students to practice solving function problems and understanding their applications.
Key areas covered include:
This module provides even more examples of function exercises, allowing students to deepen their understanding and application of functions in various scenarios.
Key topics include:
This module presents a function problem submitted by a viewer, providing students with a practical example to solve and analyze.
Key concepts include:
This module focuses on figuring out the domain of a function, a key aspect of understanding how functions operate and their limitations.
Key topics include:
This module presents a proof of the logarithmic property: log a + log b = log ab, helping students understand the foundational rules of logarithms.
Key concepts include:
This module covers proofs of additional logarithmic properties, including A(log B) = log (B^A) and log A - log B = log (A/B), essential skills for algebra students.
Key areas include:
This module presents proof of the logarithm property log_a (B) = (log_x (B))/(log_x (A)), deepening students' understanding of logarithmic properties across different bases.
Key concepts include:
This module introduces polynomial long division, a technique necessary for dividing one polynomial by another. Students will learn the steps involved in this process.
Key topics include:
This module serves as an introduction to conic sections, explaining what conic sections are and their significance in mathematics and geometry.
Key concepts include:
This module provides an introduction to circles, one of the primary conic sections. Students will learn the properties and equations associated with circles.
Key topics include:
This module introduces ellipses as another conic section, explaining their properties and equations. Students will learn to identify and work with ellipses.
Key concepts include:
This module focuses on hyperbolas, introducing students to their properties and equations as another important conic section.
Key areas covered include:
This module continues the exploration of hyperbolas, diving deeper into their properties and various applications in mathematics and real life.
Key topics include:
This module presents the final part of the hyperbola series, focusing on advanced concepts and problem-solving techniques related to hyperbolas.
Key areas covered include:
This module focuses on identifying conic sections, helping students understand how to recognize and differentiate between different types of conics.
Key concepts include:
This module continues the identification of conic sections, providing students with more examples and practice in recognizing different types of conics.
Key areas covered include:
This module provides further practice in identifying conic sections, allowing students to apply their knowledge and skills to more complex scenarios.
Key concepts include:
This module focuses on calculating the foci of an ellipse, an important aspect of understanding this conic section.
Key topics include:
This module introduces the concept of foci in hyperbolas, teaching students how to calculate the foci and understand their significance.
Key areas covered include:
This module provides a proof of the hyperbola foci formula, solidifying students' understanding of this important concept in geometry.
Key concepts include:
This module introduces partial fraction expansion, a technique used to simplify rational expressions. Students will learn the importance of this method in algebra.
Key topics include:
This module continues the study of partial fraction expansion with more complex problems. Students will practice applying techniques learned in the previous module.
Key concepts include:
This module addresses partial fraction expansion dealing with repeated factors. Students will learn advanced techniques for simplifying these expressions.
Key topics include:
This module focuses on the concept of parabolas as the locus of all points equidistant from a point and a line. Students will learn the properties of parabolas.
Key topics include:
This module continues the study of parabolas, focusing on how to find the focus and directrix. Students will engage in practical examples to solidify their understanding.
Key concepts include:
This module presents a fun algebra word problem involving two bicycles passing each other. Students will apply their problem-solving skills to find the solution.
Key areas covered include:
This module presents a fun algebra word problem involving a train passing a bike. Students will learn to set up equations and solve the scenario effectively.
Key concepts include:
This module addresses a scenario involving trains passing at different rates. Students will learn to set up and solve equations based on the situation.
Key topics include:
This module presents a word problem involving three people overtaking each other at different rates. Students will analyze the problem and solve the equations.
Key concepts include:
This module explores a fun word problem that is almost a brain teaser involving trains. Students will need to apply their problem-solving skills effectively.
Key areas covered include:
This module presents a fun scenario involving an officer on horseback, providing students with a unique word problem to solve.
Key concepts include:
This module introduces rational inequalities, teaching students two methods for solving these types of inequalities effectively.
Key topics include:
This module continues the exploration of rational inequalities, presenting slightly harder problems for students to tackle and solve.
Key concepts include:
This module presents an interesting polynomial problem where students will find the coefficients of a third-degree polynomial given two roots and the y-intercept.
Key topics include:
This module focuses on geometric series and their sums, specifically teaching students how to figure out the formula for fixed mortgage payments.
Key concepts include: