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Mathematics

931 topics

Study of numbers, quantities, shapes, and pattern. All topics of the subject on YourAIZone. Open a topic to read the beginning of the lesson.

Grade 1 34 topics

  1. Properties of objects: color, shape, size, material
  2. Sorting and Comparing Objects by Attributes
  3. Understanding Spatial Positions
  4. Number Recognition 1-10
  5. The Number Zero (0)
  6. Comparing Numbers within 10
  7. Addition within 10
  8. Subtraction within 10
  9. Changing Order in Addition
  10. Connection between Addition and Subtraction
  11. Finding the Unknown in Addition and Subtraction
  12. Number Line and Comparing Numbers
  13. Counting to 20
  14. Number Recognition 11-20
  15. Place Value: Tens and Ones
  16. Comparing Numbers within 20
  17. Addition within 20 without place value transition
  18. Subtraction within 20 without place value transition
  19. Skip Counting by 2s, 5s, and 10s
  20. Addition within 20 with place value transition (bridging through ten)
  21. Subtraction within 20 with place value transition (bridging through ten)
  22. Point, Line, Line Segment, and Ray
  23. Basic 2D Shapes
  24. Basic 3D Shapes
  25. Centimeter
  26. Decimeter
  27. Measuring Broken Lines: Finding Total Length
  28. Kilogram
  29. Liter
  30. Measurement with Non-Standard Units
  31. Time Concepts: Hours and Half-Hours
  32. Introduction to Simple Patterns
  33. Introduction to Data Collection and Representation
  34. Counting to 100

Grade 2 53 topics

  1. Revision: Numbers 1-20
  2. Number Recognition to 100
  3. Even and Odd Numbers
  4. Adding two-digit numbers without place value transition
  5. Subtracting two-digit numbers without place value transition
  6. Adding two-digit numbers with place value transition
  7. Subtracting two-digit numbers with place value transition
  8. Mental math strategies (addition)
  9. Mental math strategies (subtraction)
  10. Number Sense and Mental Math Strategies
  11. Written Column Addition and Subtraction
  12. Commutative Property of Addition
  13. Associative Property of Addition
  14. Finding the Unknown Addend, Minuend, and Subtrahend
  15. Introduction to Multiplication as Repeated Addition
  16. Components of Multiplication
  17. Concept of Division, Components of the Operation
  18. Multiplication by 2. Division by 2
  19. Multiplication by 3. Division by 3
  20. Multiplication by 4. Division by 4
  21. Multiplication by 5. Division by 5
  22. Multiplication by 6. Division by 6
  23. Multiplication by 7. Division by 7
  24. Multiplication by 8. Division by 8
  25. Multiplication by 9. Division by 9
  26. Multiplication by 0 and by 1
  27. Division of Zero
  28. Multiplication and Division by 10
  29. Numerical Expressions Without Parentheses
  30. Numerical Expressions With Parentheses
  31. Order of Operations
  32. Comparing Numerical Expressions
  33. Simple Equations - Addition and Subtraction
  34. Simple Equations - Multiplication and Division
  35. Word Problems on Increasing and Decreasing by a Number
  36. Word Problems on Increasing and Decreasing by a Factor
  37. Point, Line, and Line Segment
  38. Broken Line (Polygonal Chain) and Its Length
  39. Angle and Types of Angles (Right, Acute, Obtuse)
  40. Triangle
  41. Quadrilateral and Polygon
  42. Rectangle and Properties of Its Sides
  43. Square
  44. Perimeter of a Polygon
  45. Units of Length: Millimeter, Centimeter, Decimeter, Meter
  46. Creating and Interpreting Picture Graphs
  47. Simple Events and Outcomes
  48. Bar Graphs and Simple Data Comparisons
  49. Symmetry and Congruence
  50. Introduction to Equal Sharing and Division Concepts
  51. Introduction to Fractions with Visual Models
  52. Introduction to Length Measurement with Rulers
  53. Introduction to Tally Marks and Frequency Tables

Grade 3 39 topics

  1. Understanding Three-Digit Numbers (0-1000)
  2. Addition within 1000: Mental and Written Methods
  3. Subtraction within 1000: Mental and Written Methods
  4. Introduction to Multiplication: Review and Foundations
  5. Introduction to Division
  6. Multiplication Table (Pythagorean Table): Multiplying and Dividing with 5, 6, 7, 8, and 9
  7. Multiplication Facts and Strategies
  8. Multiplying by 10: Patterns and Strategies
  9. Beyond-the-Table Multiplication and Division: Mental Computation within 100
  10. Multiplication of Three-Digit Numbers by One-Digit Numbers
  11. Commutative Property of Multiplication
  12. Associative Property of Multiplication
  13. Multiplying by 0 and 1
  14. Division of Multi-Digit Numbers by One-Digit Numbers
  15. Dividing a Sum by a Number
  16. Dividing by 10, 100, and Other Round Numbers
  17. Division with Remainder
  18. Division by Zero: Why It's Impossible
  19. Numerical Expressions: Order of Operations
  20. Simple Equations with All Four Operations: Finding the Unknown
  21. Circles and Circle Properties: Center, Radius, Diameter, and Construction with Compass
  22. Triangles: Types, Properties, and Perimeter
  23. Classification and Properties of 2D Shapes
  24. Perimeter of Polygons
  25. Lines, Angles, and Their Measurement
  26. Area: Understanding and Calculating Area of Rectangles and Squares
  27. Area of Irregular Shapes by Decomposition
  28. Length Measurement: Units, Relationships, and Conversions
  29. Mass Measurement: Grams, Kilograms, and Converting Between Units
  30. Time: Understanding and Measuring with Different Units
  31. Parts of a Whole: Understanding Halves, Quarters, and Thirds
  32. Number Patterns and Sequences
  33. Organizing and Classifying Data
  34. Collecting and Representing Data with Graphs
  35. Introduction to Pictographs and Scaled Bar Graphs
  36. Estimation and Rounding
  37. Introduction to Chance and Likelihood
  38. Simple Probability Experiments
  39. Introduction to Transformations and Slides

Grade 4 48 topics

  1. Large Numbers: Place Value System from Ones to Billions
  2. Representing Multi-Digit Numbers as a Sum of Place Value Terms
  3. Comparing Multi-Digit Numbers: Strategies and Skills
  4. Multiplying and Dividing by 10, 100, 1000: Understanding Place Value Patterns
  5. Rules for Computing Mathematical Expressions
  6. Commutative and Associative Properties of Arithmetic Operations
  7. Addition and Subtraction of Multi-Digit Numbers
  8. Multiplication Facts and Properties
  9. Multiplication by Two-Digit and Three-Digit Numbers
  10. Division Facts and Strategies
  11. Dividing Large Numbers by Multi-Digit Divisors
  12. Divisibility Rules for 2, 5, and 10
  13. Finding Unknown Components in Multiplication and Division
  14. Understanding Parts and Wholes
  15. Fractions: Understanding Halves, Quarters, and Parts of a Whole
  16. Fractions: Numerator, Denominator, and Comparing Fractions
  17. Finding Part of a Whole and Whole by Its Part
  18. Line, Ray, Line Segment, and Angle
  19. Angles and Their Classification
  20. Classification of Polygons
  21. Introduction to Patterns and Relationships in Triangles
  22. Number Line (Coordinate Ray)
  23. Area of Rectangle and Square
  24. Units of Area Measurement
  25. Methods for Finding Area: Grid Method, Decomposition, and Practical Applications
  26. Perimeter and Area Relationships
  27. Tiling and Tessellations: Shapes That Cover the Plane
  28. Units of Length and Distance Measurement
  29. Units of Mass and Weight Measurement
  30. Units of Time Measurement
  31. Measurement with Standard Units
  32. Capacity and Volume: Measuring Liquids
  33. Multi-Step Word Problems Using All Four Operations
  34. Motion Problems: Speed, Time, and Distance
  35. Cost Problems: Price, Quantity, and Total Cost
  36. Work Problems: Productivity, Time, and Total Work
  37. Three-Dimensional Geometric Figures
  38. Faces of Three-Dimensional Figures: Finding Perimeter and Area
  39. Constructing Three-Dimensional Figures from Nets
  40. Projections of Objects onto a Plane
  41. Symmetry and Line of Symmetry
  42. Symmetry and Transformations
  43. Data Analysis and Line Plots
  44. Stem-and-Leaf Plots
  45. Patterns and Algebraic Thinking
  46. Number Patterns and Relationships
  47. Probability with Simple Events
  48. Probability Experiments with Spinners and Dice

Grade 5 57 topics

  1. Natural Number Sequence, The Number Zero
  2. Decimal System for Writing Natural Numbers
  3. Comparing Natural Numbers by Their Decimal Notation
  4. Addition. Laws of Addition
  5. Subtraction of Natural Numbers
  6. Multiplication. Laws of Multiplication
  7. Distributive Law of Multiplication
  8. Division of Natural Numbers
  9. Division with Remainder
  10. Problems Involving Parts (Ratio Problems)
  11. Line, Ray, and Line Segment
  12. Measuring Line Segments
  13. Metric Units of Length
  14. Natural Numbers on a Coordinate Ray (Number Line)
  15. Circle and Disk. Sphere and Ball
  16. Angles. Measuring Angles
  17. Triangles: Classification and Elements
  18. Quadrilaterals
  19. Area of a Rectangle. Units of Area
  20. Rectangular Parallelepiped (Cuboid)
  21. Volume of a Rectangular Parallelepiped. Units of Volume
  22. Divisibility Laws
  23. Divisibility Rules (Tests for Divisibility)
  24. Prime and Composite Numbers
  25. Divisors of Natural Numbers
  26. Greatest Common Divisor (GCD)
  27. Least Common Multiple (LCM)
  28. The Concept of a Fraction
  29. Equality of Fractions (Equivalent Fractions)
  30. Word Problems with Fractions
  31. Converting Fractions to a Common Denominator
  32. Comparing Fractions
  33. Addition of Fractions
  34. Subtraction of Fractions
  35. Multiplication of Fractions
  36. Division of Fractions
  37. Finding a Part of a Whole and Finding the Whole from its Part
  38. Joint Work Problems
  39. The Concept of a Mixed Number (Mixed Fraction)
  40. Addition of Mixed Numbers
  41. Subtraction of Mixed Numbers
  42. Multiplication of Mixed Numbers
  43. Division of Mixed Numbers
  44. Representing Fractions on a Coordinate Ray (Number Line)
  45. Concept of Equation with One Variable
  46. Probability with Fractions
  47. Complex River Motion Problems
  48. Numbers: Large numbers, Roman numerals, Rounding
  49. Coordinate Plane and Graphing Points
  50. Interpreting and Creating Line Graphs
  51. Introduction to Mean, Median, and Mode
  52. Sampling and Data Representation
  53. Box Plots and Quartiles
  54. Tree Diagrams for Probability
  55. Experimental Probability and Fair Games
  56. Introduction to Discrete Mathematics and Logic Puzzles
  57. Introduction to Coding and Algorithmic Thinking

Grade 6 57 topics

  1. Decimal Fractions: Reading and Writing
  2. Comparing Decimal Fractions
  3. Addition of Positive Decimal Fractions
  4. Subtraction of Positive Decimal Fractions
  5. Moving the Decimal Point (Multiplying and Dividing by Powers of 10)
  6. Multiplication of Positive Decimal Fractions
  7. Division of Positive Decimal Fractions
  8. Rounding Decimal Fractions
  9. Converting Between Common Fractions and Decimals
  10. Error and Approximation
  11. Concept of Ratio
  12. Dividing in a Given Ratio
  13. Equivalent Ratios
  14. Concept of Proportion
  15. Fundamental Property of Proportion
  16. Direct Proportionality
  17. Inverse Proportionality
  18. Solving Problems Using Proportions
  19. Scale
  20. Concept of Percent
  21. Finding Percent of a Number
  22. Finding a Number from its Percent
  23. Expressing Ratio as Percent
  24. Percent Increase and Decrease
  25. Percent Word Problems
  26. Negative Integers
  27. Representing Integers on the Number Line
  28. Opposite Numbers
  29. Absolute Value (Modulus) of a Number
  30. Comparing Integers
  31. Addition of Integers
  32. Subtraction of Integers
  33. Multiplication of Integers
  34. Division of Integers
  35. Opening Brackets and Enclosing in Brackets
  36. Concept of Rational Number
  37. Comparing Rational Numbers
  38. Addition and Subtraction of Rational Numbers
  39. Multiplication and Division of Rational Numbers
  40. Algebraic Expressions
  41. Parts of an Algebraic Expression
  42. Evaluating Algebraic Expressions
  43. Addition and Subtraction of Algebraic Expressions
  44. Solving Linear Equations
  45. Solving Word Problems Using Equations
  46. The Coordinate Line
  47. Rectangular Coordinate System on a Plane
  48. Coordinates of a Point: Abscissa and Ordinate
  49. Plotting Points on the Coordinate Plane
  50. Rectangular Prism and Cube
  51. Prism and Pyramid
  52. Cylinder, Cone, Sphere and Ball
  53. Drawing 3D Shapes
  54. Nets of Polyhedra
  55. Concept of Volume. Units of Volume Measurement
  56. Volume of Rectangular Prism and Cube
  57. Introduction to Probability

Grade 7 86 topics

  1. Set. Element of a Set
  2. Subset
  3. Numerical Expressions
  4. Statistical Measures
  5. Expressions with Variables (Algebraic Expressions)
  6. Definition of Power with Natural Exponent
  7. Multiplication and Division of Powers
  8. Monomial. Multiplication of Monomials
  9. Raising a Monomial to a Power
  10. Identities
  11. Polynomial. Definition
  12. Standard Form of Polynomial
  13. Addition and Subtraction of Polynomials
  14. Multiplying a Monomial by a Polynomial
  15. Multiplying a Polynomial by a Polynomial
  16. Equation and Its Roots
  17. Linear Equation with One Variable
  18. Solving Word Problems Using Equations
  19. Factoring Out the Common Factor
  20. Factoring by Grouping
  21. Multiplying the Difference of Two Expressions by Their Sum
  22. Factoring the Difference of Squares
  23. Squaring a Sum and Difference
  24. Square of a Sum of Several Terms
  25. Cubing a Sum and Difference
  26. Factoring Sum and Difference of Cubes
  27. Factoring the Difference of n-th Powers
  28. Complex Numerical Expressions
  29. What is a Function
  30. Graph of a Function
  31. Direct Proportionality
  32. Linear Function and Its Graph
  33. Mutual Position of Graphs of Linear Functions
  34. Function y = x². Power Function with Even Exponent
  35. Function y = x³. Power Function with Odd Exponent
  36. Equations with Two Variables
  37. Solving Linear Equations with Two Variables in Integers
  38. System of Linear Equations. Graphical Solution
  39. Solving Systems of Linear Equations. Substitution Method
  40. Solving Systems of Linear Equations. Elimination Method (Addition Method)
  41. Piecewise-Defined Functions
  42. Angles. Degree Measure of an Angle
  43. Adjacent Angles and Vertical Angles
  44. Perpendicular Lines
  45. First Triangle Congruence Criterion (Side-Angle-Side)
  46. Perpendicular to a Line
  47. Medians, Angle Bisectors, and Altitudes of a Triangle
  48. Properties of Isosceles Triangle
  49. Second Triangle Congruence Criterion (Angle-Side-Angle)
  50. Third Triangle Congruence Criterion (Side-Side-Side)
  51. Circle - Basic Definitions
  52. Basic Geometric Constructions
  53. Definition of Parallel Lines
  54. Criteria for Parallel Lines
  55. Axiom of Parallel Lines
  56. Theorems about Angles Formed by Two Parallel Lines and a Transversal
  57. Angles with Correspondingly Parallel or Perpendicular Sides
  58. Theorem about the Sum of Angles in a Triangle
  59. Acute, Right, and Obtuse Triangles
  60. Theorem about Relationships between Sides and Angles of a Triangle
  61. Triangle Inequality Theorem
  62. Properties and Criteria of Right Triangles
  63. Congruence Criteria for Right Triangles
  64. Distance from a Point to a Line. Distance Between Parallel Lines
  65. Constructing a Triangle Given Three Elements
  66. Properties of the angle bisector
  67. Properties of the perpendicular bisector of a segment
  68. Properties of diameters and chords of a circle
  69. Relative positions of a circle and a line
  70. Tangent to a circle
  71. Inscribed and circumscribed circles of a triangle
  72. Figures symmetric with respect to a line
  73. Axial symmetry and its properties
  74. Introduction to Logic and Mathematical Reasoning
  75. Introduction to Tessellations
  76. Introduction to Angle Measurement and the Protractor
  77. Compound Probability and Sample Spaces
  78. Probability in Real-World Applications
  79. Probability Simulations and Technology
  80. Scale Drawings and Proportional Relationships
  81. Proportional Reasoning and Similar Figures
  82. Proportional Relationships in Graphs
  83. Statistical Investigations and Research Design
  84. Statistical Sampling Methods
  85. Statistical Displays and Interpretations
  86. Measures of Spread and Variability

Grade 8 96 topics

  1. Numerical Fractions and Fractions Containing Variables
  2. Properties of Fractions
  3. Addition and Subtraction of Fractions
  4. Representing a Fraction as a Sum of Fractions (Splitting Fractions)
  5. Multiplication of Fractions. Raising Fractions to a Power
  6. Division of Fractions (Algebraic)
  7. Transforming Rational Expressions
  8. Intersection, Union, and Difference of Sets
  9. One-to-One Correspondence
  10. Natural Numbers and Integers
  11. Properties of Divisibility
  12. Divisibility of Sums and Products
  13. Division with Remainder
  14. Modular Arithmetic
  15. Divisibility Rules
  16. Prime and Composite Numbers **
  17. Rational Numbers
  18. Real Numbers
  19. Number Intervals
  20. Grouped Data / Interval Data
  21. Absolute and Relative Error
  22. Arithmetic Square Root
  23. Evaluating and Estimating Square Roots
  24. The Function y = √x and Its Graph
  25. Square Root of a Product, Quotient, and Power
  26. Simplifying Expressions with Square Roots
  27. Simplifying Nested Radicals (Double Radicals)
  28. Definition of Quadratic Equations. Incomplete Quadratic Equations
  29. Formulas for the Roots of a Quadratic Equation
  30. Equations Reducible to Quadratic Equations
  31. Solving Word Problems Using Quadratic Equations
  32. Vieta's Theorem
  33. Symmetric Expressions in Terms of Roots
  34. Factoring Quadratic Trinomials
  35. Solving Rational Equations
  36. Solving Word Problems Using Equations
  37. Comparing Numbers
  38. Properties of Numerical Inequalities
  39. Estimating Values of Expressions
  40. Proving Inequalities
  41. Solving Inequalities in One Variable
  42. Solving Systems of Inequalities
  43. Unions of Inequalities (Disjunctions of Inequalities)
  44. Inequalities with Absolute Value
  45. Definition of Powers with Negative Exponents
  46. Properties of Powers with Integer Exponents
  47. Simplifying Expressions with Exponents
  48. Scientific Notation (Standard Form of a Number)
  49. Function, Domain, and Range
  50. Stretching and Compressing Graphs of Functions
  51. Translations of Function Graphs (Shifting Graphs)
  52. Functions y = 1/x and y = 1/x² and Their Graphs
  53. Inverse Proportion (Inverse Variation) and Its Graph
  54. Linear Fractional Function (Rational Function) and Its Graph
  55. Convex Polygon(8 grade)
  56. Quadrilateral(8 grade)
  57. Parallelogram(8 grade)
  58. Criteria for a Parallelogram(8 grade)
  59. Trapezoid(8 grade)
  60. Rectangle(8 grade)
  61. Rhombus and Square(8 grade)
  62. Central Symmetry(8 grade)
  63. Concept of the Area of a Polygon(8 grade)
  64. Area of a Square(8 grade)
  65. Area of a Rectangle(8 grade)
  66. Area of a Parallelogram
  67. Area of a Triangle
  68. Area of a Trapezoid
  69. The Pythagorean Theorem
  70. Converse of the Pythagorean Theorem
  71. Heron's Formula
  72. Proportional Segments
  73. Definition of Similar Triangles
  74. Ratio of Areas of Similar Triangles
  75. First Criterion for Similarity of Triangles (AA Similarity)
  76. Second Criterion for Similarity of Triangles (SAS Similarity)
  77. Third Criterion for Similarity of Triangles (SSS Similarity)
  78. Midsegment of a Triangle (Midline of a Triangle)
  79. Four Remarkable Points of a Triangle
  80. Proportional Segments in a Right Triangle
  81. Sine, Cosine, and Tangent of an Acute Angle in a Right Triangle
  82. Values of Sine, Cosine, and Tangent for Angles 30°, 45°, 60°
  83. Relative Positions of a Line and a Circle
  84. Relative Positions of Two Circles
  85. Common Tangents of Two Circles
  86. Degree Measure of a Circular Arc
  87. Inscribed Angle Theorem
  88. Angles Formed by Chords, Tangents, and Secants
  89. Inscribed Circle
  90. Circumscribed Circle
  91. Creating and Interpreting Infographics
  92. Measures of Variability
  93. Scatter Plots and Bivariate Data
  94. Transformational Geometry and Symmetry
  95. Probability Trees and Conditional Probability
  96. Introduction to Logic and Truth Tables

Grade 9 127 topics

  1. Increasing and Decreasing Functions
  2. Properties of Monotonic Functions
  3. Even and Odd Functions
  4. Properties of Even and Odd Functions
  5. Bounded and Unbounded Functions
  6. Functions y = ax², y = ax² + n, y = a(x − m)²
  7. Graph and Properties of Quadratic Functions
  8. Stretching and Compressing Graphs of Functions
  9. Graphs of Functions y = |f(x)| and y = f(|x|)
  10. Polynomial Equations and Their Roots
  11. Methods for Solving Polynomial Equations
  12. Vieta's Theorem for Higher-Degree Equations
  13. Solving Fractional-Rational Equations
  14. Solving Polynomial Inequalities
  15. Solving Fractional-Rational Inequalities
  16. Solving Equations with Absolute Value
  17. Solving Inequalities with Absolute Value
  18. Polynomial Equations with Parameters
  19. Fractional-Rational Equations with Parameters
  20. Equations in Two Variables and Their Graphs
  21. Systems of Equations in Two Variables
  22. Solving Systems by Substitution and Elimination (Addition Method)
  23. Linear Inequalities in Two Variables
  24. Inequalities in Two Variables of Higher Degree (Nonlinear Inequalities in Two Variables)
  25. Systems of Inequalities in Two Variables
  26. Inequalities in Two Variables with Absolute Value
  27. Numerical Sequences. Ways to Define Sequences
  28. Increasing and Decreasing Sequences
  29. Bounded and Unbounded Sequences
  30. Method of Mathematical Induction
  31. Arithmetic Progression. Formula for the n-th Term of an Arithmetic Progression
  32. Sum of the First n Terms of an Arithmetic Progression
  33. Geometric Progression. Formula for the n-th Term of a Geometric Progression
  34. Sum of the First n Terms of a Geometric Sequence
  35. Limit of a Sequence
  36. Sum of an Infinite Geometric Series
  37. Inverse of a Given Function
  38. Inverse of a Power Function with Natural Exponent
  39. Arithmetic Root of the n-th Degree
  40. Power with Rational Exponent
  41. Solving Irrational Equations
  42. Solving Irrational Inequalities
  43. Statements and Predicates. Quantifiers
  44. Operations on Statements and Predicates
  45. Conjunction, Disjunction, Implication
  46. Properties of Operations on Statements
  47. Permutations
  48. Arrangements
  49. Combinations
  50. Frequency and Probability
  51. Addition of Probabilities
  52. Multiplication of Probabilities
  53. Bernoulli Trials
  54. Numerical Characteristics of Probability Distributions
  55. Angle of Rotation
  56. Radian Measure of an Angle
  57. Definition of the Basic Trigonometric Functions
  58. Trigonometric Identities: Period, Symmetry and Sign
  59. Properties of Trigonometric Functions
  60. Graphs and Basic Properties of Sine and Cosine
  61. Graphs and Basic Properties of Tangent and Cotangent
  62. Reduction Formulas
  63. Relationships Between Trigonometric Functions of the Same Argument
  64. Transforming Trigonometric Expressions
  65. Sine, Cosine and Tangent of Sum and Difference of Angles
  66. Double Angle and Half Angle Formulas
  67. Sum and Difference Formulas for Trigonometric Functions
  68. Concept of a vector
  69. Equality of vectors
  70. Constructing a vector from a given point
  71. Sum of two vectors
  72. Laws of vector addition. Parallelogram rule
  73. Sum of several vectors
  74. Subtraction of vectors
  75. Multiplication of a vector by a scalar
  76. Applications of vectors in problem solving
  77. Decomposition of a Vector into Two Non-Collinear Vectors
  78. Coordinates of a Vector
  79. Relationship Between Vector Coordinates and the Coordinates of its Start and End Points
  80. Basic Problems in Coordinates
  81. Equation of a Line in a Plane
  82. Equation of a Circle
  83. Equation of a Straight Line
  84. Sine, Cosine, Tangent and Cotangent of an Angle
  85. The Fundamental Trigonometric Identity. Reduction Formulas
  86. Formulas for Computing Point Coordinates
  87. Slope of a Straight Line
  88. Triangle Area Theorem
  89. Law of Sines
  90. Law of Cosines
  91. Solving Triangles
  92. Angle Between Vectors
  93. Dot Product of Vectors
  94. Dot Product in Coordinates
  95. Properties of the Dot Product of Vectors
  96. Regular Polygon
  97. Circumscribed Circle of a Regular Polygon
  98. Inscribed Circle of a Regular Polygon
  99. Formulas for the Area of a Regular Polygon, Its Side and the Radius of the Inscribed Circle
  100. Construction of Regular Polygons
  101. Circumference of a Circle
  102. Area of a Circle
  103. Area of a Circular Sector
  104. Mapping of a Plane onto Itself
  105. The Concept of Plane Motion
  106. Parallel Translation
  107. Rotation
  108. The Concept of Symmetry of Figures
  109. Practical Applications of Symmetry
  110. Applying Motions to Problem Solving
  111. Introduction to Similar Figures
  112. Similar Polygons
  113. Theorems on Perimeters and Areas of Similar Polygons
  114. Homothety
  115. Properties of Homothety
  116. Similarity of Arbitrary Figures
  117. Applying Similarity to Solving Problems
  118. Introduction to Coordinate Geometry
  119. Similar Triangles and Proportional Reasoning
  120. Correlation and Regression Analysis
  121. Applications of Trigonometry in Real-World Contexts
  122. Function Notation and Transformations
  123. Scientific Notation and Significant Figures
  124. Introduction to Statistical Significance
  125. Introduction to Financial Literacy
  126. Introduction to Proofs and Mathematical Reasoning
  127. Introduction to Function Families and Their Characteristics

Grade 10 45 topics

  1. Площадь поверхности и объем прямоугольного параллелепипеда, прямой призмы, пирамиды, цилиндра, конуса и шара
  2. Parallel lines in space
  3. Infinitely Decreasing Geometric Progression
  4. Power with Real Exponent
  5. Exponential Function, Its Properties and Graph
  6. Exponential Equations
  7. Exponential Inequalities
  8. Systems of Exponential Equations and Inequalities
  9. The Concept of Logarithm
  10. Properties of Logarithms
  11. Common and Natural Logarithms
  12. Logarithmic Function, Its Properties and Graph
  13. Logarithmic Equations
  14. Logarithmic Inequalities
  15. Angle Measure in Radians
  16. Rotation of a Point Around the Origin
  17. Signs of Sine, Cosine and Tangent
  18. Relationships Between Sine, Cosine and Tangent of the Same Angle
  19. Sine, Cosine and Tangent of Angles α and −α
  20. Sine, Cosine and Tangent of a Double Angle
  21. Sine, Cosine and Tangent of a Half Angle
  22. Sum and Difference of Sines. Sum and Difference of Cosines
  23. Equation cos x = a
  24. Equation sin x = a
  25. Equation tan x = a
  26. Solving Trigonometric Equations
  27. Examples of Solving Simple Trigonometric Inequalities
  28. Domain and Range of Trigonometric Functions
  29. Evenness, Oddness, Periodicity of Trigonometric Functions
  30. Properties of y = cos x and Its Graph
  31. Properties of y = sin x and Its Graph
  32. Properties of y = tan x and Its Graph
  33. Inverse Trigonometric Functions
  34. Introduction to 3D Vectors
  35. Quadratic Functions and Equations
  36. Geometric Transformations and Congruence
  37. Complex Numbers and Operations
  38. Conic Sections and Their Applications
  39. Matrices and Matrix Operations
  40. Unit Circle and Periodic Functions
  41. Data Analysis and Experimental Design
  42. Rational Functions and Asymptotes
  43. Introduction to Hypothesis Testing
  44. Introduction to Modular Arithmetic
  45. Introduction to Rates of Change and Derivatives

Grade 11 59 topics

  1. Increment of a Function
  2. Concept of the Derivative (definition via limit)
  3. Geometric Meaning of the Derivative
  4. Physical Meaning of the Derivative
  5. Continuity and the Derivative
  6. Rules of Differentiation (sum, difference, product, quotient)
  7. Derivative of a Power Function
  8. Derivatives of Elementary Functions
  9. Derivative of a Composite Function
  10. Derivatives of Trigonometric Functions
  11. Tangent Line to a Graph
  12. Increasing and Decreasing Functions
  13. Critical Points, Maxima and Minima
  14. Absolute Maximum and Minimum Values of a Function
  15. Sketching Graphs Using the Derivative
  16. Approximate Calculations
  17. The Derivative in Physics and Engineering
  18. Convexity of a Graph, Inflection Points
  19. Higher-Order Derivatives
  20. Taylor's Formula
  21. Concept of the Antiderivative
  22. Basic Property of the Antiderivative
  23. Rules for Finding Antiderivatives
  24. Antiderivatives of Elementary Functions
  25. Area of a Curvilinear Trapezoid
  26. The Definite Integral
  27. The Newton–Leibniz Formula
  28. Properties of the Definite Integral
  29. Approximate Calculation of a Definite Integral
  30. Calculating Areas Using Integrals
  31. Integration by Substitution
  32. Integration by Parts
  33. Introduction to Differential Equations
  34. Problems Leading to Differential Equations
  35. Introduction to Set Theory and Venn Diagrams
  36. The Multiplication Rule (Rule of Product)(in Combinatorics)
  37. Combinations with Repetition
  38. Inclusion-Exclusion Principle
  39. Binomial Theorem (Newton's Binomial)
  40. Combinations of Events. Complementary Event
  41. Classical Probability Model
  42. Experimental vs. Theoretical Probability
  43. Geometric Probability
  44. Conditional Probability
  45. Total Probability Formula
  46. Random Variables
  47. Binomial Probability and Distributions
  48. Probability Distributions and Expected Value
  49. Variance and Standard Deviation
  50. Normal Distribution and the Empirical Rule
  51. Basic Statistical Measures
  52. Probability Distributions and Statistical Inference
  53. Sampling Distributions and the Central Limit Theorem
  54. Hypothesis Testing — Basics
  55. Graphing Trigonometric Functions
  56. Introduction to Number Theory
  57. Introduction to Optimization Problems
  58. Introduction to Limits of Functions
  59. Parametric Functions and Their Applications

Grade 12 15 topics

  1. Limits and Continuity
  2. Integration and Applications
  3. Inferential Statistics and Hypothesis Testing
  4. Discrete Mathematics: Combinatorics and Counting Principles
  5. Differential Equations: Introduction and Applications
  6. Multivariable Calculus: Introduction to Partial Derivatives
  7. Linear Algebra: Eigenvalues and Eigenvectors
  8. Markov Chains and Stochastic Processes
  9. Sequences, Series, and Convergence Tests
  10. Confidence Intervals and Margin of Error
  11. Parametric Equations and Polar Coordinates
  12. Graph Theory: Fundamentals and Applications
  13. Taylor Series and Approximations
  14. Data Science: Exploratory Data Analysis and Visualization
  15. Introduction to Vector Calculus

SAT Reasoning Test Math section 69 topics

  1. Laws of exponents (SAT)
  2. Evaluating expressions with exponents (SAT)
  3. Simplifying square roots (SAT)
  4. Percent change (SAT)
  5. Simple Interest and Compound Interest (SAT)
  6. Percent Word Problems (SAT)
  7. Linear Growth and Decay (SAT)
  8. Exponential Growth and Decay (SAT)
  9. Proportion (SAT)
  10. Expressions - Combining Like Terms (SAT)
  11. Expressions - Expansion and Factoring (SAT)
  12. Expressions - Combining, Dividing, and Splitting Fractions (SAT)
  13. Equations I (SAT)
  14. Equations II (SAT)
  15. Systems of Equations - Substitution Method (SAT)
  16. Systems of Equations - Elimination Method (SAT)
  17. Systems of Equations - Systems with No Solutions (SAT)
  18. Systems of Equations - Infinite solutions (SAT)
  19. Systems of Equations - Word problems (SAT)
  20. Graphs of Systems of Equations (SAT)
  21. Inequalities (SAT)
  22. Motion Word Problems (SAT)
  23. Word Problems Leading to Linear Equations (SAT)
  24. Word Problems Involving Proportions (SAT)
  25. Word Problems - Writing Algebraic Expressions (SAT)
  26. Slope and Y-Intercept (SAT)
  27. Slope-Intercept Form of a Line's Equation (SAT)
  28. Point-Slope Form of a Line's Equation (SAT)
  29. Intersection of Two Lines (SAT)
  30. Parallel and Perpendicular Lines (SAT)
  31. Horizontal and Vertical Lines (SAT)
  32. Interpreting Linear Models (SAT)
  33. Function։ Introduction, Notation and Evaluation (SAT)
  34. Undefined Function (SAT)
  35. Finding the Solutions to a Function (SAT)
  36. Identifying Function Graphs (SAT)
  37. Tactics for Finding the Roots of Quadratic Equations (SAT)
  38. Completing the Square of Sum and Difference (SAT)
  39. Parabolla (SAT)
  40. Vertex Form of a Quadratic Function (SAT)
  41. The Discriminant (SAT)
  42. Quadratic Models (SAT)
  43. Absolute Value Equations and Inequalities (SAT)
  44. Exterior angle theorem (SAT)
  45. Parallel Lines and Angles (SAT)
  46. Polygon Angles and Properties (SAT)
  47. Isosceles and Equilateral Triangles (SAT)
  48. Right Triangles: Definition, Critera, Pythagorean Theorem and Special Triangles (SAT)
  49. Similar Triangles (SAT)
  50. Radians (SAT)
  51. Circles: Area and Circumference (SAT)
  52. Circles: Arc Length (SAT)
  53. Circles: Area of a Sector (SAT)
  54. Circles: Central and Inscribed Angles (SAT)
  55. Equations of a Circle (SAT)
  56. Trigonometric Ratios in Right Triangles: Sine, Cosine and Tangent (SAT)
  57. Trigonometric Identities (SAT)
  58. Evaluating Trigonometric Expressions (SAT)
  59. Reading Graphs and Charts (SAT)
  60. Probability (SAT)
  61. Statistical Measures: Mean, Median and Mode (SAT)
  62. Range and Standard Deviation (SAT)
  63. Histograms and Dot Plots (SAT)
  64. Word Problems Involving Averages (SAT)
  65. Statistical Sampling (SAT)
  66. Using and Interpreting the Line of Best Fit (SAT)
  67. Margin of Error (SAT)
  68. Confidence Intervals (SAT)
  69. Volume (SAT)

State Final Assessment Math (Grade 9) 25 topics

  1. Десятичные и обыкновенные дроби
 (Вычисление значение выражения) (ИГА 9)
  2. Избавление от иррациональности в знаменателе (ИГА 9)
  3. Разложение квадратного трехчлена на множители (ИГА 9)
  4. Четные и нечетные функций (ИГА 9)
  5. Область определения функции (ИГА 9)
  6. Арифметическая и геометрическая прогрессии (ИГА 9)
  7. Диаграммы и таблицы (ИГА 9)
  8. Степень с натуральным показателем (ИГА 9)
  9. Преобразования рациональных выражения (ИГА 9)
  10. Теорема Виета (ИГА 9)
  11. Система линейных уравнений с двумя переменными (ИГА 9)
  12. Текстовые задачи на прямую и обратную пропорциональность (ИГА 9)
  13. Неравенства второй степени с одной переменной – Поиск максимальных или минимальных решений (ИГА 9)
  14. Корень n-ой степени (ИГА 9)
  15. Взаимное расположение графиков линейных функций (ИГА 9)
  16. Частота и вероятность (ИГА 9)
  17. Свойства числовых неравенств (ИГА 9)
  18. Числовые последовательности (ИГА 9)
  19. Вычисление значений квадратичных и кубических функций (ИГА 9)
  20. Решение текстовых задач с помощью квадратных уравнений (ИГА 9)
  21. Решение текстовых задач с помощью дробно-рациональных уравнений (ИГА 9)
  22. Вычисление процента от значения выражения (ИГА 9)
  23. Задачи про движение (ИГА 9)
  24. Статистические характеристики (среднее арифметическое, мода, медиана, размах) (ИГА 9)
  25. Числовые выражения с дробями и степенями с целыми показателями (ИГА 9)

Algebra 120 topics

  1. Statements, logical operations
  2. Numerical Sets (ℕ, ℤ, ℚ, ℝ)
  3. Numerical Sets (ℕ, ℤ, ℚ, ℝ) (new)
  4. Powers and Roots
  5. Logarithms
  6. Linear equations and inequalities
  7. Quadratic Equations
  8. Systems of equations
  9. Inequalities with modulus
  10. Polynomials and their roots
  11. Exponential Equations and Inequalities
  12. Logarithmic Equations and Inequalities
  13. Arithmetic Progression (Arithmetic Sequence)
  14. Geometric Progression (Geometric Sequence)
  15. Function, Domain and Range
  16. Inverse Function
  17. Composite Functions (Function Composition)
  18. Even and Odd Functions
  19. Monotonicity and Extrema (Algebraic Approach)
  20. Sum Rule and Product Rule
  21. Permutations
  22. Arrangements (Permutations of n Objects Taken k at a Time)
  23. Combinations (unordered selections of k objects from n distinct objects without repetition)
  24. Binomial Theorem
  25. Degrees and Radians Conversion
  26. The Unit Circle
  27. Basic Trigonometric Functions
  28. The Pythagorean Identity
  29. Angle Addition and Subtraction Formulas
  30. Double-Angle and Half-Angle Formulas
  31. Sum-to-Product and Product-to-Sum Formulas
  32. Inverse Trigonometric Functions
  33. Trigonometric Equations
  34. Trigonometric Inequalities
  35. Limits of Sequences: Formal Definition
  36. Limit of a Function at a Point
  37. The First Remarkable Limit (limit of sin x / x)
  38. The Second Remarkable Limit (the number e)
  39. Continuity of a Function
  40. The Derivative: Limit Definition
  41. The Table of Derivatives
  42. Differentiation Rules
  43. The Chain Rule
  44. Derivative of an Inverse Function
  45. Analyzing Functions with Derivatives: Monotonicity and Extrema
  46. The Second Derivative and Convexity
  47. L'Hôpital's Rule
  48. The Antiderivative
  49. Indefinite Integrals and Basic Integration Techniques
  50. Integration by Parts, Including Repeated Application
  51. Integration of Rational Functions
  52. Trigonometric Substitutions and Trigonometric Integrals
  53. Definite Integrals: Riemann Sums to Newton–Leibniz
  54. Improper Integrals
  55. Geometric Applications of the Definite Integral
  56. Vectors in 2D and 3D
  57. The Dot Product (Scalar Product)
  58. The Cross Product (Vector Product)
  59. Matrices: Definition and Types
  60. Matrix Operations: Addition and Scalar Multiplication
  61. Matrix Multiplication
  62. The Determinant
  63. The Inverse Matrix
  64. Systems of Linear Equations in Matrix Form
  65. Linear Dependence and Independence
  66. Basis and Dimension
  67. Eigenvalues and Eigenvectors
  68. Diagonalization of Matrices
  69. Orthogonalization and the Gram–Schmidt Process
  70. Orthogonal and Unitary Matrices
  71. Quadratic Forms
  72. Singular Value Decomposition (SVD)
  73. Complex Numbers: Algebraic Form
  74. Operations with Complex Numbers
  75. The Complex Plane (Argand Diagram)
  76. Euler's Formula
  77. Roots of Complex Numbers
  78. Foundations of Probability: Events and Equally Likely Outcomes
  79. Independence of Events
  80. Conditional Probability and the Chain Rule
  81. Bayes' Theorem
  82. Repeated Independent Trials: The Bernoulli Scheme
  83. Numerical Series and Convergence Tests
  84. Absolute and Conditional Convergence
  85. Power Series and the Radius of Convergence
  86. Taylor and Maclaurin Expansions of Elementary Functions
  87. Functions of Several Variables: Basic Concepts
  88. Limits of Functions of Several Variables
  89. Partial Derivatives: Definition and Computation
  90. The Total Differential and Differentiability
  91. Directional Derivatives
  92. The Gradient
  93. Higher-Order Partial Derivatives
  94. The Jacobian Matrix and Determinant
  95. The Hessian and Classification of Critical Points
  96. Constrained Extrema and Lagrange Multipliers
  97. The Double Integral: Definition and Properties
  98. Double Integrals over General Regions
  99. Change of Variables in Double Integrals
  100. The Triple Integral
  101. Line Integrals of the First Kind (with respect to Arc Length)
  102. Line Integrals of the Second Kind (Work Integrals)
  103. Green's Theorem
  104. Surface Integrals
  105. Divergence of a Vector Field
  106. Curl of a Vector Field
  107. Stokes' Theorem and the Divergence Theorem (Gauss–Ostrogradsky)
  108. Conservative and Solenoidal Vector Fields
  109. Ordinary Differential Equations: Classification and the Initial Value Problem
  110. Separable First-Order Equations
  111. Linear First-Order Equations: Variation of the Constant
  112. The Bernoulli Equation
  113. Second-Order Linear Homogeneous Equations with Constant Coefficients
  114. Second-Order Linear Non-Homogeneous Equations
  115. Systems of First-Order Linear ODEs
  116. The Laplace Transform
  117. Fourier Series
  118. The Fourier Transform
  119. How RSA Works
  120. Vector calculation

Basic physics 1 topic

  1. Double slit experiment

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