All math rules. 8th, 9th, 10th, and 11th grade.
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