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All math rules. 8th, 9th, 10th, and 11th grade.
Search for Math Rules
Mathematics for 8th grade
Square root
Real numbers
Rational numbers
Irrational numbers
Integers
Natural numbers
The function \(y=x^2 \) and Square root
Pythagorean Theorem
Quadratic equations
Solving quadratic equations
Quadratic formula
Viet's theorem
Quadrilaterals
The interior and exterior angles of a quadrilaterals
Parallelogram
Trapezium
The median line of a triangle
Rational expressions
Simplifying rational expressions
Addition, subtraction, multiplication, division, and exponentiation of rational expressions.
Function \(y= \frac{k}{x} \) and its graph
Area axioms of figures
Area of parallelogram
Area of triangle
Area of trapezium
Area of rhombus
Ratio, proportion, scale.
Proportional parts
Similar quadrilaterals, similar triangles.
Similarity signs of triangles
Similarity of right triangles
Area of similar figures
Inequalities
Properties of inequalities
Addition and multiplication of inequalities
Numerical intervals
Solving linear inequalities in one variable
Solving double inequalities
Simple inequalities with a variable inside the modulus sign. Absolute value inequalities.
Right triangle and trigonometric ratios
Trigonometric identities (1)
Coordinates of the midpoint of a piece
Equation of the straight line through two points
Transformation of figures, rotation.
Similarity transformation. Homothety.
Data collection and presentation
Measures of central tendency
Probability calculation
Independent and dependent events
Mathematics for 9th grade
The nth degree root
Rational exponents
Central angle. Arc of a circle.
Chord of a circle
Angle subtended inside a circle
Tangent of a Circle
Secant of a circle
Angle between the tangents and the secants
Quadratic function and its graph
y=|x| (modulus or absolute value) function and its graph
\(y=x^3 \) function (cubic function) and its graph
Formula for the distance between two points
Equation of a circle
Coordinates of points on the circle and trigonometric ratios
Sector and segment of the circle
Polynomial equation of degree (Higher-degree polynomial equations)
Rational equations
Absolute value equation
Irrational equations
Equations in two variables. System of equations.
System of equations in which one equation is first-degree and the other equation is second-degree
System of two second-degree equations in two variables
Polygons
Convex and concave polygons
The sum of the interior angles of a convex polygon
Inscribed and circumscribed polygon
Circles drawn inside and outside a triangle
Properties of a quadrilateral inscribed in and outside a circle
Circles inside and outside of a regular polygon
Area of a polygon. Area of the regular polygon
Quadratic inequalities
Solving rational inequalities by the interval method
Irrational inequalities
Vectors
The length of a vector (Magnitude)
The direction of a vector
Addition and Subtraction of Collinear Vectors
Methods of Addition and Subtraction of Non-Collinear Vectors
Adding Vectors Using Components
Scalar multiplication
Parallel transport
Transformation and congruent figures
Sequences
Arithmetic sequences
Geometric Sequences
Infinitely decreasing geometric sequence
Permutation
Combination
Mathematics for 10th grade
Domain and Range of a functions
Properties of functions
Classification of functions
\( y = x^n \) (power functions or monomials) functions
Operations on functions
Angle of rotation
Degree and Radian Measure
Trigonometric Functions and the Unit Circle
Trigonometric functions of any angle
Rotation formula
Trigonometric identities (2)
Simplifying trigonometric expressions
Law of Sines
Law of Cosines
Periodic functions. Periodicity of trigonometric functions.
Graphs of the functions sine y=sin(x) and cosine y=cos(x)
Transformations of sine and cosine functions
Graphs of the Tangent and Cotangent Functions
Inverse trigonometric functions
Polyhedron
Prisms
Surface area of the prism
The volume of a prism
Pyramid. Lateral surface area and total surface area of a pyramid.
Volume of a pyramid
Trigonometric equations
Trigonometric inequalities
Exponential functions
The graph of an exponential function
Value of e
Logarithm
Logarithmic function
Logarithmic scale
Exponential equations
Logarithmic equations
Exponential inequality
Logarithmic inequality
Complex numbers
Binomial theorem (expansion)
Bernoulli trials
Mathematics for 11th grade
Polynomials
Polynomial functions
Rational functions
Limit
One-Sided Limits
Limits Involving Infinity
Continuity
Limit of Trigonometric Functions
Limit of Exponential and Logarithmic Functions
Limit of a Sequence
Taylor and Maclaurin Series
Derivatives and Integrals
Curved Solids (area , volume)
Sphere (1)
Cone
Cylinder (1)
Derivative of a function
Integral
Volume formulas (Cube, Parallelepiped, Cylinder, Prism, Sphere )
Cube
Parallelepiped
Cylinder (2)
Prism
Sphere (2)
Russell's Paradox