This module provides a proof of the hyperbola foci formula. Understanding this proof will deepen your knowledge of hyperbola properties and enhance your ability to apply these concepts in algebra.
This module introduces basic algebraic equations, focusing on the structure and solving methods for equations of the form Ax = B. You'll learn how to isolate the variable and understand the balance in equations.
In this module, we delve into slightly more complicated equations, building on the foundation established in the first module. You'll learn to tackle equations that involve additional operations and how to manipulate them effectively.
This module covers equations where the variable appears on both sides. You'll learn techniques to simplify and solve these types of equations, enhancing your algebraic skills and confidence.
In this module, we focus on solving linear equations that include variable expressions in the denominators of fractions. You'll learn critical methods for isolating the variable while managing fractions.
This module teaches you how to graph linear equations, a fundamental skill in algebra. You'll learn to create graphs from equations and understand the relationship between algebraic expressions and their graphical representations.
This module focuses on understanding slope and y-intercept, key components of linear equations. You will gain intuition about how these elements influence the graph of a line and what they signify in practical scenarios.
In this module, you will learn how to calculate the slope of a line using various methods. Understanding slope is crucial for interpreting and analyzing linear relationships in algebra.
This module continues exploring slope, providing further examples and methods for determining the slope of various lines. You'll gain confidence in calculating and interpreting slope in different contexts.
This module wraps up the discussion on slope with additional techniques and real-world applications. You will learn to apply slope concepts to solve practical problems, reinforcing your learning through practice.
In this module, you'll learn how to add sums of consecutive integers, a fundamental skill in algebra. You'll explore various techniques and applications of integer sums in real-world scenarios.
This module focuses on the concept of percentages. You will learn how to calculate percentages of numbers and apply this knowledge to solve various algebraic problems involving percentages.
This module explores how to grow a quantity by a percentage. Understanding this concept is essential for solving problems related to growth, such as interest and population changes.
In this module, you'll learn to find the original price of an item when you know the discounted price. This skill is particularly useful for real-life applications in shopping and finance.
This module covers more complex percentage problems that require deeper understanding and application of percentage calculations. You'll practice solving these problems with various examples.
This module introduces systems of equations, focusing on methods to solve multiple equations simultaneously. You'll learn different techniques, including substitution and elimination, to find solutions.
This module presents a ratio problem involving basic algebra concepts. You'll learn to set up and solve ratio problems, enhancing your problem-solving skills in algebra.
This module advances the discussion on ratios, tackling more complex problems. You'll learn strategies for solving advanced ratio problems and applying these skills to various scenarios.
This module offers an alternate solution to the advanced ratio problem discussed previously. You'll explore different methods to arrive at the same solution, reinforcing the versatility of algebraic techniques.
This module introduces basic ratio problems, focusing on understanding the concept of ratios and their applications in algebra. You'll learn how to solve simple ratio equations step-by-step.
This module delves into more advanced ratio problems, requiring a deeper understanding of ratios and their relationships. You'll tackle complex scenarios and learn to apply algebraic methods to solve them.
This module covers age word problems, where you'll learn to set up equations based on age-related scenarios. These problems help strengthen your algebra skills by applying them to real-life situations.
Building on the previous module, this session introduces a second set of age word problems, providing further practice in setting up and solving equations based on age-related contexts.
This module presents a third part of the age word problems, introducing more complex scenarios. You'll learn to navigate these problems, enhancing your ability to apply algebra in various contexts.
This module covers level 1 multiplying expressions, focusing on expanding the product of two binomials. You'll learn the distributive property and how to combine like terms effectively.
In this module, we explore the method of solving quadratics by factoring. You'll learn to identify factors and apply this technique to find the roots of quadratic equations.
This module introduces the imaginary unit 'i' and how to work with imaginary numbers. You will learn how to raise 'i' to various powers and understand its significance in algebra.
In this module, we delve deeper into complex numbers, focusing on addition, subtraction, and multiplication. You will learn the rules governing complex numbers and how to manipulate them effectively.
This module focuses on dividing complex numbers and introduces the concept of complex conjugates. You'll learn how to simplify expressions involving complex numbers through division.
This module introduces the quadratic equation and its use in solving second-degree polynomials. You'll learn the standard form of a quadratic equation and how to apply it to find solutions.
In this module, you'll see more examples of solving equations using the quadratic equation. You'll practice applying the quadratic formula to various problems to reinforce your understanding.
This module covers the method of completing the square to solve quadratics. You'll learn how to transform quadratic equations into a form that makes finding solutions easier.
In this module, we derive the quadratic formula by completing the square. You'll see how this formula can be used to find the roots of any quadratic equation systematically.
This module focuses on solving quadratic inequalities using factoring methods. You'll learn to identify solution intervals and express your answers in a clear and concise manner.
This module introduces functions, explaining their definitions and characteristics. You'll learn how to identify functions, understand their notation, and explore their mappings between sets.
In this module, we provide more examples of function problems. You'll practice solving various types of function exercises, deepening your understanding of function applications in algebra.
This module continues with additional examples of function exercises. You'll encounter various functions and their properties, enhancing your ability to work with and analyze functions.
In this module, you'll see a specific function problem submitted by a viewer. You'll learn how to approach unique function problems and apply algebraic concepts to find solutions.
This module focuses on determining the domain of a function. You'll learn how to identify valid input values for functions and the importance of domain in function analysis.
This module provides a proof of the logarithm property: log a + log b = log ab. You'll learn the steps involved in this proof and its significance in algebra.
In this module, we prove two logarithm properties: A(log B) = log (B^A) and log A - log B = log (A/B). Understanding these properties is essential for manipulating logarithmic expressions in algebra.
This module provides a proof of the logarithm property: log_a (B) = (log_x (B))/(log_x (A)). You'll learn the derivation and importance of this property in algebraic manipulations.
This module introduces algebraic long division, a technique for dividing one polynomial by another. You'll learn the steps involved in polynomial long division and how to apply them effectively.
This module introduces conic sections, explaining what they are and their significance in mathematics. You'll learn about different types of conic sections and their properties.
In this module, we focus on circles, one of the primary conic sections. You'll learn the standard form of the circle's equation and its graphical representation.
This module introduces ellipses, another type of conic section. You'll learn their characteristics, equations, and how to graph them effectively in the Cartesian plane.
This module introduces hyperbolas, a unique conic section. You'll explore their properties, standard equations, and how to graph hyperbolas in the Cartesian coordinate system.
This module continues the discussion on hyperbolas, providing further insights and examples on their properties and graphing methods. You'll learn to identify hyperbolas and analyze their behavior.
In this module, we take a closer look at hyperbolas, focusing on their unique features and how to represent them graphically. You'll practice identifying and graphing hyperbolas based on their equations.
This module focuses on identifying conics through their equations and graphs. You'll learn to classify conic sections based on their equations and how to graph them accurately.
Continuing with conics identification, this module provides further practice in classifying and graphing various conic sections. You'll solidify your understanding of how to distinguish between them.
This module concludes the identification of conics, providing additional examples to reinforce your skills. You'll work on various problems to ensure a thorough understanding of conic sections.
This module focuses on calculating the foci of an ellipse. You'll learn the significance of foci in understanding ellipse properties and how to calculate their locations using standard formulas.
This module introduces the foci of hyperbolas, explaining their importance in hyperbola geometry. You'll learn how to calculate the foci and analyze their role in the properties of hyperbolas.
This module provides a proof of the hyperbola foci formula. Understanding this proof will deepen your knowledge of hyperbola properties and enhance your ability to apply these concepts in algebra.
This module introduces partial fraction expansion, a technique used to simplify rational functions. You'll learn the steps involved in breaking down complex fractions into simpler components.
In this module, we tackle a more complex problem involving partial fraction expansion. You'll practice applying the techniques learned in the previous module to more challenging fractions.
This module deals with repeated factors in partial fraction expansion. You'll learn how to handle these cases and apply the appropriate techniques to simplify complex rational expressions.
This module explores the concept of parabolas as the locus of points equidistant from a point and a line. You'll learn the geometric definition and implications of this concept for algebraic applications.
In this module, we focus on finding the focus and directrix of a parabola. You'll learn how these elements relate to the parabola's properties and how to calculate them using algebraic methods.
This module features an algebra word problem involving two bicycles passing each other. You'll apply your algebra skills to set up and solve the problem, reinforcing your learning through practical application.
This module presents a fun algebra word problem involving a train passing a bike. You'll learn to set up the problem using algebraic expressions and find solutions through calculations.
This module focuses on trains passing each other at different rates. You'll learn to set up equations based on relative speeds and distances, enhancing your algebra skills through practical application.
This module covers an overtaking word problem involving three people at different rates. You'll learn to frame the problem using algebraic expressions and solve it step-by-step.
In this module, we explore an early train word problem that poses a fun challenge. You'll apply your algebraic skills to unravel the problem and find the solution through logical reasoning.
This module features a problem involving an officer on horseback. You'll apply your algebra skills to analyze the situation and derive a solution using mathematical reasoning.
This module introduces rational inequalities, focusing on two methods to solve them. You'll learn how to analyze inequalities involving fractional expressions and apply these techniques in various contexts.
This module presents a slightly harder rational inequality problem. You'll practice applying the techniques learned previously to tackle more complex inequalities and reinforce your understanding.
This module focuses on finding the coefficients of a third-degree polynomial given two roots and the y-intercept. You'll learn how to set up and solve polynomial equations effectively.
This module uses the sum of a geometric series to derive the formula for fixed mortgage payments. You'll learn how to apply geometric series concepts to real-world financial problems.