Mathematics develops thinking to analyze and organize; to find patterns and establish cause and effect relationships; to reason and draw conclusions; to think logically, strategically, and abstractly.
In this lesson, you will learn how to perform addition, subtraction, multiplication, and division with proper, improper, mixed, and decimal fractions, and solve related problems.
Learning to work with fractions next: In this lesson, you will learn how to work with decimals and also learn about periodical decimals.
In this lesson, you'll learn about exponents of numbers and their properties, including the rules of exponents and how to use them.
In this lesson, you will explore the concepts and differences between monomials and polynomials, expand brackets during addition and subtraction, multiply monomials by brackets, multiply brackets by brackets, factor expressions, and group terms effectively.
In this lesson, you will study the basic formulas of abbreviated multiplication and practice solving examples based exclusively on them.
In this lesson, you will focus on simplifying fractions with variables through multiplication and division, using factoring and cancellation techniques.
In this lesson, you will learn how to find a common denominator for algebraic fractions and simplify expressions effectively.
In this lesson, you will practice addition, subtraction, multiplication, and division of fractions and decimal fractions, including mixed operations.
In this lesson, you will solve medium and difficult level problems on adding, subtracting, multiplying, and dividing fractions.
In this lesson, you will learn how to divide polynomials, how to use the Bezos theorem, and how to use the synthetic division method to perform effective calculations.
In this lesson, you will study linear equations, quadratic equations, equations reducible to quadratic form, and apply Vieta's theorem to solve problems efficiently.
In this lesson, you will explore a range of equations reducible to quadratic form and practice solving them using the substitution method.
In this lesson, you will learn to solve power equations using Bézout’s method, including root guessing and dividing polynomials by a monomial in columns, as well as tackle equations of higher degrees.
In this lesson, you will learn how to solve irrational equations by raising both sides of the equation to a power, simplifying and solving for the variable.
In this lesson, you will learn how to solve irrational equations using substitution, simplifying the equation by replacing variables to make the equation solvable.
In this lesson, you will learn how to remove irrationality by rationalizing the denominator of fractions, making expressions easier to work with.
In this lesson, you will practice simplifying algebraic expressions through factoring, combining like terms, and using basic operations in easy to medium-level exercises.
In this lesson, you will tackle medium to hard problems involving the simplification of irrational algebraic expressions using advanced techniques.
In this lesson, you will learn methods to solve systems of equations involving one linear and one quadratic equation, using substitution and elimination techniques.
In this lesson, you will practice solving medium-level systems of equations, involving both linear and nonlinear relationships, using substitution and elimination methods.
In this lesson, you will explore advanced methods for solving complex systems of equations, focusing on the substitution technique to simplify and solve them effectively.
In this lesson, you will learn to solve basic inequalities and apply the interval method to find solution sets efficiently.
In this lesson, you will master the interval method for solving complex inequalities and learn to solve systems of inequalities with multiple variables.
In this lesson, you will learn techniques to solve equations involving absolute values, including splitting cases based on the definition of absolute value.
In this lesson, you will explore methods for solving inequalities involving absolute values, including case analysis and graphical interpretation.
In this lesson, you will practice solving irrational inequalities, using techniques like squaring and interval testing for easy to medium-level problems.
In this lesson, you will tackle medium to hard-level irrational inequalities, applying advanced techniques such as squaring and analyzing domains for accurate solutions.
In this lesson, you will learn Vieta’s theorem, its connection to the roots and coefficients of quadratic equations, and practice solving problems using this powerful tool.
In this lesson, you will explore the properties of arithmetic progressions, derive formulas for the 𝑛-th term and the sum of terms, and solve related problems.
In this lesson, you will study the properties of geometric progressions, learn how to find the 𝑛-th term and the sum of terms, and solve related problems.
In this lesson, you will explore infinite geometric progressions, learn the conditions for convergence, and calculate the sum of an infinite geometric series.
In this lesson, you will learn the fundamental concepts of functions, including their definition, notation, domain, and range, as well as how to graph basic functions.
In this lesson, you will learn how to plot graphs of various types of functions, including linear, quadratic, and exponential, as well as understand their key characteristics, such as intersection points, slopes, and asymptotes.
In this lesson, you will explore the key properties of linear equations, including slope, intercept, and their graphical representation, with examples to reinforce your understanding.
In this lesson, you will learn how to solve tasks involving parameters, including how to analyze and manipulate equations or systems of equations where one or more variables act as parameters.
In this lesson, you will practice solving word problems using linear equations and systems of linear equations, applying real-world scenarios to find solutions.
In this lesson, you will tackle word problems that involve quadratic equations and systems of equations, using appropriate methods to model and solve real-life situations.
In this lesson, you will solve word problems related to motion, including distance, speed, and time, using linear equations and systems to model and find solutions.
In this lesson, you will solve complex motion problems, including those involving objects moving towards each other, in pursuit, along a circular path, and calculating average speed.
In this lesson, you will solve word problems related to work, such as tasks completed by multiple workers at different rates, using equations and systems to find solutions.
In this lesson, you will learn the basics of percentages, including how to calculate percentage increases, decreases, and solve problems involving percentages in real-life scenarios.
In this lesson, you will solve mixture problems involving the combination of different substances, such as liquids or solids, using algebraic equations to find unknown quantities.
In this lesson, you will solve a variety of word problems related to age, money, and other real-life scenarios, applying algebraic techniques to find solutions.
This lesson covers the foundational principles of trigonometry, focusing on understanding trigonometric ratios and their use in solving problems involving right triangles.
This lesson covers the key trigonometric identities, such as the Pythagorean identities, reciprocal identities, and co-function identities, as well as reduction formulas for simplifying trigonometric expressions.
This lesson focuses on simplifying complex trigonometric expressions by applying basic trigonometric identities, such as Pythagorean, reciprocal, and quotient identities.
In this lesson, you will study the sum and difference formulas for trigonometric functions, including sine, cosine, and tangent, and practice solving problems using these formulas.
In this lesson, you will learn the double angle and half angle formulas for trigonometric functions, and practice applying them to simplify expressions and solve equations.
In this lesson, you will practice simplifying complex trigonometric expressions using fundamental identities, sum and difference formulas, and double and half-angle formulas.
In this lesson, you will practice solving level-two problems by applying trigonometric formulas and identities to simplify moderately complex expressions.
In this lesson, you will tackle level-three problems by applying advanced trigonometric formulas and identities to simplify complex expressions.
In this lesson, you will explore the properties, domains, and ranges of inverse trigonometric functions, and solve problems involving their applications in simplifying expressions and solving equations.
In this lesson, you will learn the foundational concepts of trigonometric equations, including their general forms and methods for finding solutions within given intervals.
In this lesson, you will learn how to solve trigonometric equations of intermediate complexity, including mixed types that combine various trigonometric functions. Techniques for simplifying, transforming, and applying identities will be covered to help solve these equations effectively.
In this lesson, you will practice solving trigonometric equations within specific intervals, applying appropriate techniques to find all possible solutions.
In this lesson, you will learn to solve trigonometric equations involving square roots and absolute values. Using algebraic methods and trigonometric identities, you'll simplify and solve these equations with ease.
In this lesson, you will learn how to solve systems of trigonometric equations, using substitution, elimination, and other methods to find solutions to multiple equations involving trigonometric functions.
In this lesson, you will learn how to solve trigonometric inequalities using the unit circle. You will explore how the unit circle assists in visualizing and simplifying the process of solving inequalities involving trigonometric functions.
In this lesson, you will learn how to solve trigonometric inequalities using graphical techniques and the interval method to find solution sets within specified ranges.
In this lesson, we will explore how to solve exponential equations by utilizing logarithms and the properties of exponents. You will gain a deeper understanding of the techniques for simplifying and solving these equations with precision and efficiency.
In this lesson, you will learn how to solve exponential inequalities, using logarithmic properties and other techniques to find solutions within given constraints.
In this lesson, you will explore the fundamentals of logarithms, including key formulas, properties, and basic arithmetic operations involving logarithmic expressions.
In this lesson, you will practice simplifying logarithmic expressions using logarithmic properties and rules, with step-by-step examples to reinforce understanding.
In this lesson, you will learn how to solve basic logarithmic equations by applying the properties of logarithms. You will practice using techniques such as converting between logarithmic and exponential forms to simplify and solve these equations.
In this lesson, you will learn to solve intermediate to advanced logarithmic equations, applying logarithmic properties and techniques for more complex expressions.
In this lesson, you will learn how to solve systems of logarithmic equations. You will explore methods for simplifying and solving multiple logarithmic equations simultaneously using properties of logarithms and algebraic techniques.
In this lesson, you will learn how to solve basic logarithmic inequalities, using substitution and logarithmic properties to find solution sets effectively.
In this lesson, you will learn how to solve logarithmic inequalities using the interval method, analyzing the solution sets and determining the valid intervals for the inequality.
In this lesson, you will explore how to solve logarithmic inequalities where the base is a variable, using logarithmic properties and techniques to find the solution sets.
In this lesson, you will dive into advanced logarithmic inequalities and learn the rationalization methodology for solving them. You will explore how to simplify complex logarithmic inequalities and use rationalization to find solutions effectively.
In this lesson, you will learn about complex numbers, their components (real and imaginary parts), operations (addition, subtraction, multiplication, and division), and how to represent them in the complex plane.
In this lesson, you will learn the basics of matrices, including their definitions, types, and how to perform operations such as addition, subtraction, and multiplication.
In this lesson, you will explore the fundamentals of probability theory, including basic concepts such as events, outcomes, probability rules, and how to calculate the probability of simple events.
In this lesson, you will explore the fundamentals of combinatorics, focusing on permutations and combinations, learning how to calculate the number of ways to arrange or select items in various scenarios.
In this lesson, you will learn about permutations with repetitions and circular permutations, exploring how to calculate arrangements when items are repeated or arranged in a circle.
In this lesson, you will explore the fundamentals of statistics, including data analysis, probability, and the use of statistical tools to interpret and present information. You will learn how to work with various types of data and understand the importance of statistical methods in different fields.
In this lesson, you will learn the concept of derivatives, including how to calculate the derivative of a function using various rules such as the power rule, product rule, quotient rule, and chain rule.
In this lesson, you will learn how to apply derivatives in analyzing functions. You will explore how to use derivatives to find critical points, determine the behavior of functions, and analyze the concavity of graphs. This lesson focuses on how derivatives aid in understanding the properties and behaviors of functions.
In this lesson, you will learn how to use derivatives to sketch the graph of a function, analyzing critical points, inflection points, and the behavior of the function to create an accurate graph.
In this lesson, you will learn the geometrical interpretation of derivatives. The derivative represents the slope of the tangent line to a curve at any point, providing insight into the rate of change of a function.
In this lesson, you will explore the application of derivatives in physics, learn implicit differentiation, logarithmic differentiation, and how to find derivatives of parametric equations.
In this lesson, you will learn the fundamentals of limits, including how to evaluate limits of functions as they approach a specific point, and the basic properties of limits in calculus.
In this lesson, you will dive deeper into limits, exploring advanced techniques such as L’Hopital’s Rule, limits at infinity, and evaluating indeterminate forms, to better understand their application in calculus.
In this lesson, you will explore antiderivatives, which are the reverse process of differentiation. You will learn how to find the general solution of an antiderivative, understand the concept of constant of integration, and practice techniques such as substitution and recognizing common antiderivatives to solve problems.
In this lesson, you will learn how to solve integrals involving absolute values and calculate the area under the curve of a given function using definite integrals.
In this lesson, you will learn how to calculate integrals by putting expressions under the differential sign.
In this lesson, you will learn the technique of integration by parts, including the formula and step-by-step process for solving integrals of products of functions.
In this lesson, you will learn the substitution method for solving integrals. You will explore how to simplify complex integrals by substituting variables and using this technique to evaluate integrals more easily.
In this lesson, you will learn the method of undetermined coefficients for solving integrals, particularly focusing on finding specific solutions to integrals involving non-homogeneous functions.
In this lesson, you will dive into the fundamentals of integrals, covering both definite and indefinite types. You will also explore improper integrals, understand their unique properties, and learn how to evaluate them using practical examples.
In this lesson, you will learn how to represent points and equations using polar coordinates. We will cover the differences from Cartesian coordinates and key concepts with examples.
In this lesson, you will explore the practical applications of integration in geometry, physics, and economics. Learn how to solve real-world problems using integral techniques.
In this lesson, you will practice solving various integral problems using different techniques. Focus on applying methods like substitution, integration by parts, and partial fractions.
In this lesson, you will learn about numerical series and how to represent sums using sigma notation. We will cover common types of series and summation techniques.
In this lesson, you will learn the basics of integral equations and their classifications. We will also discuss methods for solving them with practical examples.
In this lesson, you will explore second-order curves such as ellipses, hyperbolas, and parabolas. Learn their standard equations and key properties.
In this lesson, you will explore the foundational concepts of geometry, including the properties of lines and segments, types of angles, and their relationships in geometric figures.
In this lesson, you will study the types of triangles, learn about their internal lines (height, median, bisector, and midline), understand the conditions for triangle existence, and calculate their perimeter.
In this lesson, you will explore the properties of right triangles, learn the rules governing them, and solve problems using the Pythagorean Theorem.
This lesson introduces the fundamental trigonometric ratios—sine, cosine, tangent, and cotangent—in the context of right triangles, along with their applications in solving problems.
In this lesson, you will learn the concept of mean proportionals and practice solving problems involving their application in geometric and algebraic contexts.
In this lesson, you will learn how to calculate the area of a right triangle using its base and height, and explore related problems for practice.
In this lesson, you will learn the Law of Cosines, its formula, and how to apply it to solve problems involving triangles, including finding unknown sides and angles.
In this lesson, you will explore the Law of Sines, its formula, and how to apply it to solve problems involving triangles, including finding unknown sides and angles in non-right triangles.
In this lesson, you will learn the unique properties of isosceles and equilateral triangles and practice solving problems involving their angles, sides, and symmetry.
In this lesson, you will explore the concept of a triangle’s medians, their properties, and how to solve problems involving medians in various types of triangles.
In this lesson, you will learn about the properties of a triangle’s bisectors, their significance, and practice solving problems involving bisectors in different types of triangles.
In this lesson, you will work through simple to medium-level problems on calculating the area of a triangle, applying different methods such as basic area formulas and more complex techniques like Heron's formula.
In this lesson, you will tackle medium to hard-level problems involving the calculation of a triangle’s area, using advanced methods such as Heron’s formula, trigonometric approaches, and special properties of triangles.
In this lesson, you will learn about the incircle of a triangle, its properties, and how to solve problems related to the incenter, radius, and area involving the incircle.
In this lesson, you will explore the concept of an excircle of a triangle, its properties, and practice solving problems related to the excenter, radius, and area involving the excircle.
In this lesson, you will explore the concepts of congruence and similarity of triangles, their properties, and practice solving problems related to these topics.
In this lesson, you will learn the fundamental concepts and rules of quadrilaterals, explore their various types, and solve problems to deepen your understanding of their properties.
In this lesson, you will study the properties of rectangles and squares, learn their formulas for perimeter and area, and practice solving related problems.
In this lesson, you will explore the properties of a rhombus, including its diagonals, angles, and formulas for perimeter and area, and practice solving related problems.
In this lesson, you will study the properties of parallelograms, including their sides, angles, and diagonals, and practice solving problems involving perimeter, area, and other key characteristics.
In this lesson, you will learn about the properties of trapeziums, including their bases, heights, and midlines, and practice solving problems involving their perimeter, area, and other related concepts.
In this lesson, you will explore the properties of circumscribed and inscribed circles in quadrilaterals, with a focus on cyclic quadrilaterals, and practice solving related geometric problems.
This lesson covers the conditions for a circle to be circumscribed around a trapezoid, its properties, and solving problems involving such trapezoids.
In this lesson, you will explore the key properties of circles, including circumferences, arcs, sectors, and segments, as well as central and inscribed angles, and solve problems involving these concepts.
This lesson covers the properties of tangents, secants, and chords in circles, explores the relative positions of two circles, and provides practice through problem-solving.
In this lesson, you will learn the foundational rules of stereometry, explore the Theorem of Three Perpendiculars, and solve problems applying these concepts to three-dimensional geometric figures.
In this lesson, you will study the properties of oblique and perpendicular lines, learn about projections onto a plane, and solve related geometric problems involving these concepts.
In this lesson, you will learn about the properties of prisms and parallelepipeds, including their volume, surface area, and other key features, and solve problems involving these 3D geometric shapes.
In this lesson, you will explore the properties of pyramids, including their volume, surface area, and other key characteristics, and solve problems related to pyramids in 3D geometry.
In this lesson, you will study the properties of cones, cylinders, and spheres, including their volume and surface area formulas, and solve problems involving these 3D geometric shapes.
In this lesson, you will explore the geometric properties of truncated pyramids and truncated cones, learn their volume and surface area formulas, and practice solving related problems.
This lesson focuses on the conditions and properties of spheres inscribed in and circumscribed around prisms. You will also solve problems involving these geometric relationships.
In this lesson, you will explore the properties and conditions of spheres inscribed in and circumscribed around pyramids and solve problems related to these geometric configurations.
In this lesson, you will learn how to construct sections of three-dimensional geometric figures and practice solving problems related to these sections, enhancing your spatial reasoning skills.
This lesson covers the methods for finding the distance between two points in space, the distance from a point to a plane, and the angle between lines in space. You will also solve related problems to deepen your understanding of these concepts.
In this lesson, you will explore the method for determining the angle between a line and a plane in space, and practice solving problems to apply this concept in various geometric contexts.
This lesson focuses on understanding how to calculate the angle between two planes in space. You will explore key concepts and solve problems to apply this knowledge in stereometry.
In this lesson, you will learn how to calculate the distance between skew lines in space, explore the geometric principles behind this concept, and solve related problems to deepen your understanding.
This lesson covers the application of derivatives in geometry, including how they are used to find slopes, tangents, normals, and other key geometric properties. You will practice solving problems related to these concepts.
In this lesson, you will explore the concept of vectors, their properties, and operations such as addition, subtraction, and scalar multiplication. You will also practice solving problems related to vectors in both two and three dimensions.
This lesson focuses on using the coordinate method to solve stereometry problems. You will learn how to apply coordinates in three-dimensional space to find distances, angles, and other geometric properties of 3D figures.
In this lesson, you will explore the fundamentals of analytic geometry in three-dimensional space. Topics include equations of planes, lines, and other geometric elements in space, with problem-solving exercises to apply these concepts.
