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.
The first step toward learning math is to learn basic arithmetic operations: addition, subtraction, multiplication, and division. In this lesson you will also be introduced to the concept of fractions and learn basic operations with fractions.
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 will learn how to work with degrees and learn what negative and zero degrees are.
From numbers to letters: in this lesson you will be introduced to the concept of a single term and a polynomial and learn how to add and multiply them.
Some cases of multiplication of polynomials occur so often that you can write your own formulas for them. In this lesson, you will learn about the formulas for shortened. multiplication.
Algebraic fractions are fractions where polynomials can be in the numerator and denominator. In this lesson we will learn the basic rules of working with them.
We continue to study algebraic fractions and learn the important skill of finding their common denominators.
We practice working with algebraic fractions further with more complex examples.
In this lesson, we will study polynomial division, learn about Bézout's method and theorem for finding remainders when dividing, and also master Horner's scheme for simplifying polynomial calculations.
In this lesson, you will learn how to solve linear equations - equations where the unknown is present only in the first degree.
In this lesson, we will explore various types of equations that can be reduced to quadratic form. We will learn how to use the substitution method to solve complex equations by converting them into standard quadratic equations.
Biquadratic equations are equations of the fourth degree that can be easily reduced to square equations. Rational equations are equations involving algebraic fractions
In this lesson, we will explore irrational equations that can be solved using exponentiation. We will study methods for simplifying and solving these equations.
Irratsional tenglamalarni yechishda davom etamiz. Ushbu darsda siz oʻrin almashtirish usulidan foydalanishni va hatto cheksiz davom etuvchi ildizlar bilan tenglamalarni yechishni oʻrganasiz.
In math, you often have to get rid of the irrationality in the denominator, that is, the root in the denominator. In this lesson, you will learn how to do that, as well as how to solve examples with square roots.
In this lesson you will advance your skills in simplifying irrational algebraic expressions with a focus on intermediate to complex examples. Explore techniques for managing intricate radicals and enhancing problem-solving abilities.
Learn how to simplify irrational algebraic expressions using various methods, focusing on simple and intermediate problems.
You already know how to solve linear equations. The next step is systems of linear equations! This is when several equations must be done at the same time.
Explore intermediate-level systems of equations, focusing on solving and analyzing both linear and quadratic systems. Enhance your problem-solving skills with more complex examples and techniques.
Learn to solve complex systems of equations and apply substitution methods. Focus on advanced techniques for managing and simplifying intricate systems for effective problem-solving.
In this lesson, you will learn about inequalities and how to work with them.
What if inequalities get harder? In this lesson you will learn how to solve more complex inequalities using different methods.
In this lesson you will learn how to solve equations with modulus. And you can solve them using different methods!
In this lesson, we will study how to solve inequalities with modulus using different methods to simplify expressions.
In this lesson, we will study how to solve irrational inequalities of varying difficulty (Part-2).
In this lesson, we will study how to solve irrational inequalities of varying difficulty.
In this lesson, we will solve simple parameter-based problems and apply Vieta's Theorem to solve related tasks.
Arithmetic progression is a sequence in which each number is obtained from the previous one by adding a constant number to it.
A geometric progression is a sequence in which each number is obtained from the previous number by multiplying it by a constant number.
If a geometric sequence is decreasing, you can find its sum even if it has infinitely many numbers. In this lesson you will learn how to do this.
In this lesson, you will be introduced to one of the most important concepts in math, the function, and learn what they are.
In this lesson, we will learn how to draw graphs of various mathematical functions.
In this lesson, you will explore a linear function. Its graph is a straight line, so you will also explore the straight line.
In this lesson, we will solve parameter-based problems using graphs, ranging from intermediate to more advanced levels.
In this lesson, you will learn how to solve word problems by creating linear equations.
In this lesson, solutions to problems are demonstrated through the creation and solving of quadratic equations and systems of equations.
In this lesson you will learn how to solve text tasks on motion.
In this lesson you will learn how to solve text tasks on motion.
This lesson will help you to learn how to solve text tasks for work.
This lesson will be extremely useful to you because it is about percentages! You will learn what compound interest is and how to solve text tasks about percentages.
In this lesson, you will learn how to solve text tasks for mixtures.
In this lesson you will learn how to solve economic tasks. You will learn how to solve tasks related to deposits in a bank.
Trigonometry is the branch of mathematics that studies trigonometric functions and their applications in geometry. What is a trigonometric function? That's what you're going to learn in this lesson.
Trigonometry is the branch of mathematics that studies trigonometric functions and their applications in geometry. What is a trigonometric function? That's what you're going to learn in this lesson.
In this lesson, you will learn tasks to simplify trigonometric expressions.
In this lesson you will learn about addition formulas and how to calculate the sine of a sum or sum of sines, for example.
What are double angle formulas? You will answer this question in this lesson.
Repeat and solve trigonometric tasks.
Solve more difficult trigonometry tasks.
We continue solving tasks and learning how to work with trigonometric expressions.
In this lesson you will learn what inverse trigonometric functions are.
We continue working with inverse trigonometric functions.
Now it's time to learn how to solve trigonometric equations.
Let's practice solving trigonometric equations next.
In this lesson, you will learn more difficult trigonometric tasks.
In this lesson you will learn how to solve trigonometric equations with modulus and with roots.
This lesson is about systems of trigonometric equations.
Now we will talk about trigonometric inequalities!
In this lesson you will learn how to apply the interval method to solve trigonometric inequalities.
In this lesson you will learn how to solve exponential equations, where the degree base is real numbers, and in the exponent there lies the unknown. You will see how to solve equations, not only analytically, but also graphically.
This lesson is designed for those who are already fluent (on the "You") with exponential equations. We will learn how to solve exponential inequalities: what to do if the exponential function decreases, and if it increases, how does the sign of the inequality change? You will learn the answer to all these and other questions concerning exponential inequalities through this lesson.
In this lesson, you will learn the concept of logarithm and logarithmic function.
In this lesson you will learn how to work with logarithmic expressions and simplify them.
Now it's time to learn how to solve logarithmic equations.
Continue solving equations with logarithms.
In this lesson you will learn how to solve systems of logarithmic equations.
Now it's time to learn how to solve logarithmic inequalities.
In this lesson you will learn how to apply the interval method to solve logarithmic inequalities.
In this lesson you will learn logarithmic inequalities where both the base and argument of the logarithm are functions of some sort.
In this lesson you will find more complicated logarithmic inequalities.
The square of a number can be negative! But the number is now a complex number. And what it is, you will learn in this lesson.
In this lesson you will learn about what a matrix is. Unlike numbers, matrices cannot be swapped when multiplied.
Probability theory is a branch of mathematics that studies random events and random variables. In this lesson, you will learn how to find the probabilities of different events.
We continue solving probability tasks.
Combinatorics is a branch of mathematics devoted to solving tasks related to the selection and arrangement of elements.
We continue solving combinatorial tasks.
Mathematical Statistics - a branch of mathematics that studies the description and analysis of data from observations and experiments. In this lesson, you will learn about the basics of mathematical statistics.
What is the derivative of a function? In this lesson, you will learn about this important concept.
The derivative is a powerful tool for investigating functions. Learn how to do it in this lesson.
In this lesson, you will learn how to sketch graphs of functions using the derivative.
The derivative also has a geometric meaning. This lesson will tell you more about it.
In this lesson, you will learn about the mechanical meaning of the derivative and how the derivative helps in physics.
In this lesson, you will learn about the concept of limits and learn how to find them.
We continue talking about limits. Learn about what " wonderful limits" are in this lesson.
In this lesson, you will learn about what a first integral, indefinite integral, and definite integral are.
In this lesson, you will learn how to calculate integrals with modulus.
In this lesson, you will learn how to calculate integrals by putting expressions under the differential sign.
In this lesson, you will learn an important method of integration - integration by parts.
In this lesson, you will learn how substitution of variables can help you calculate an integral.
In this lesson, you will learn how to calculate the integral of a fractional rational function using the method of indefinite quotients.
In this lesson, you will learn about the concept of the improper integral.
In this lesson, you will learn what polar coordinates are.
This lesson explains how the integral helps you calculate the length of a curve, the area of a curvilinear trapezoid, and the volume of bodies of rotation.
How do you find the area of a figure obtained by intersecting different graphs of functions? You will learn about it in this lesson.
In this lesson you will learn how to find the sums of some interesting sequences
In this lesson you will solve many tasks and learn how to find the maximum and minimum values of a function.
We continue solving tasks: you will learn many tasks on limits of sequences.
Solving more difficult tasks on integrals.
In this lesson you will continue to solve different tasks on calculating integrals.
In this lesson you will find tasks on integrals from rational expressions.
This lesson is dedicated to solving different tasks on integrals.
In this lesson, you will explore one of the fundamental mathematical inequalities — Cauchy’s inequality. You will learn its statement, proofs, and key applications, including problems involving maxima and minima. This inequality serves as the basis for many mathematical methods and theorems.
This lesson covers the equations of ellipses, hyperbolas, and parabolas. You will study their graphs, properties, and concepts like directrices, foci, and eccentricity. These curves play a significant role in analytic geometry and other branches of mathematics.
This lesson introduces the basics of set theory, one of the core areas of mathematics. You will learn about sets, subsets, basic operations on sets (union, intersection, difference), and their properties. Cartesian products and set cardinality will also be discussed.
This lesson focuses on the basics of analytic geometry, where geometric figures and their properties are studied using algebraic methods. You will learn to write equations for lines, circles, parabolas, ellipses, and hyperbolas, and analyze their properties.
In this lesson, you will delve into the fundamentals of differential equations — mathematical expressions that relate a function to its derivatives. You will learn to solve basic equations and understand their applications in problems describing physical, biological, and economic processes.
Integral equations are equations that involve an unknown function under an integral sign. They are widely used in modeling physical phenomena such as heat transfer, wave processes, and mechanics. You will explore the main types of integral equations, methods for solving them, and their connection to differential equations.
The study of geometry begins with angles and segments. In this lesson you will learn what they are and what angles are formed when parallel lines intersect a secant line.
In this lesson you will become familiar with what types of triangles there are, learn about its properties and basic elements.
What is an equilateral triangle? What is the Pythagorean theorem? This is all you will learn in this lesson!
In this lesson you will learn about the basic trigonometric functions found in geometry.
What is a projection? This lesson is all about right-angled triangles!
In this lesson you will learn how to find the areas of triangles, solve tasks on medians.
The cosine theorem helps you solve tasks to find the sides of a triangle. This lesson is about how to do that.
In this lesson, you will learn about the sine theorem and how to apply it.
An isosceles triangle is a triangle with two equal sides. This lesson is all about them!
The median is the segment that connects the vertex of a triangle and the midpoint of the opposite side. In this lesson you will learn how to find its length and solve the tasks.
What is a bisection and what are its properties? Find out in this lesson!
We will study basic and average tasks for calculating the area of an arbitrary triangle.
In this lesson, you will learn a lot of tasks about triangles!
Learn about inscribed circles in triangles and the exercises associated with them.
In this lesson we will analyze the problems and properties of the described circles around the triangles.
In this lesson we will learn to work with equality and similarity of triangles through different problems and examples.
From triangles to quadrilaterals. This lesson is all about quadrilaterals!
In this lesson, you will find tasks about squares and rectangles.
A rhombus is a parallelogram with all sides equal. Learn about its properties in this lesson!
In this lesson you will learn more about parallelograms and solve tasks on them.
A trapezoid is a quadrilateral in which two sides are parallel and the other two sides are not. In this lesson you will learn about the properties of a trapezoid.
In this lesson, you will learn about circles circumscribed about quadrilaterals, as well as circles inscribed in them.
This lesson is about trapezoid and circle. You will learn tasks on the inscribed and circumscribed trapezoid.
This topic covers the basic concepts and properties associated with circles, circles, arcs, sectors, segments, and central and inscribed angles. This topic explores concepts such as radius, diameter, center of a circle, arc length, sector area, and the different types of angles formed around circles. Problems on this topic may include finding the length of an arc, the area of a segment, calculating central and inscribed angles, and applying this knowledge to solve geometric problems.
This topic studies the properties of tangents, secants and chords of circles, as well as their relationships. Problems include finding line lengths, angles, and other parameters, as well as proving geometric statements related to these elements.
Stereometry is the study of three-dimensional shapes and their properties. Includes basic rules for volumes, areas, and edge lengths. The three perpendicular theorem states that in a right triangle, the perpendiculars from the vertex of the right angle to the sides are equal. Problems on this topic often involve calculating the volumes and areas of three-dimensional figures.
The topic includes the study of oblique and perpendicular lines in space, as well as the projections of points and figures on a plane. Problems on this topic may include finding angles between oblique and perpendicular lines, determining the coordinates of points after their projections onto a plane, and calculating distances and angles between the projections of various objects.
A prism and a parallelepiped are geometric figures consisting of rectangular faces. A prism has two parallel bases and side faces, which are rectangles or parallelograms. A parallelepiped is a prism in which all the side faces are rectangular and parallel in pairs.
A pyramid is a geometric body that has one flat base and triangular or polygonal side faces that converge at the apex.
Bodies of rotation are bodies that are formed as a result of the rotation of a flat figure around an axis. A cone is a body in which one of the flat surfaces (base) is connected to the top. A cylinder is a body in which two parallel planes (bases) are connected by a curved surface. A ball is a body all points of which are equidistant from the center.
A truncated pyramid is a pyramid in which the upper part (apex) is removed parallel to the base. A truncated cone is a cone whose top has been removed parallel to the base.
A sphere inscribed in a prism touches all its faces, while a sphere circumscribed around a prism touches all its vertices.
A ball inscribed in a pyramid touches all its side faces, while a ball inscribed around a pyramid touches all its vertices.
A section in stereometry is an image obtained when a three-dimensional figure intersects a plane.
These topics in geometry describe how to measure the distance from a point to a line or plane in space, and how to find the angle between two lines passing through that point.
This topic in geometry examines the angle between a line and a plane in three-dimensional space.
This topic in geometry studies the angle between two planes in three-dimensional space.
When we talk about the distance between lines in space, we are looking for the length of the shortest segment that connects these two lines. This distance is determined by a perpendicular drawn from one straight line to another. If the lines are parallel, then the distance between them is equal to the distance between the parallel planes on which they lie. If the lines intersect, then the distance is zero, since they lie on the same plane and have a common point.
The use of derivatives in geometry makes it possible to solve problems of searching for extrema, tangents and normals to curves, as well as to study changes in the characteristics of geometric objects.
Vectors in geometry are used to describe direction, force, and movement in space. Vector problems can include operations of addition, subtraction, multiplication by a number, as well as finding the modulus, scalar and vector products.
In geometry, vectors are directional line segments that are used to describe force, direction, and movement in space. Vector problems include operations of addition, subtraction, multiplication by a number, as well as finding the modulus, scalar and vector products.
The coordinate method in stereometry allows you to solve geometric problems using algebraic methods. It is based on the representation of points and shapes in space using coordinates and allows you to solve problems related to the position, distances and angles between objects.
