USA - High school Math Syllabus

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Algebra 1

1. Expressions, equations and functions
   • Expressions, variables and operations
   • Composing expressions
   • Composing equations and inequalities
   • Representing functions as rules and graphs
2. Exploring real numbers
   • Number system
   • Integers and real numbers
   • Properties of real numbers
3. Linear equations, functions, visualization
   • Basics of solving equations
   • Ratios and proportions
   • Slope of a line
   • Calculate the rate of change of a linear function
   • Similar figures
   • Graphs, coordinate plane, sole and intercept
4. Functions and real-world problems
   • Definition of functions
   • Input and output to a function
   • domain and range values 
   • Graphs
5. Solving Linear inequalities
   • Solving compound inequalities
   • Absolute value equations and inequalities
   • Linear inequalities in two variables
6. Systems of linear inequalities and equations
   • Systems of linear inequalities
   • Substitution and elimination methods
7. Exponents and exponential functions
   • interpret and write exponential functions in the form f(x) = abx
   • exponential functions with real world problem
   • exponential functions – growth and decay
8. Factoring and polynomials
   • Monomials and polynomials
   • Special products of polynomials
   • Factorization of polynomials
9. Quadratic equations
   • determine the domain and range of quadratic functions
   • graph quadratic functions on the coordinate plane
   • solve quadratic equations having real solutions by factoring, taking square roots
   • estimation and prediction using quadratic equations
10. Radical Expressions
    • Simplify radical expressions
    • Radical functions, graphs
    • Pythagorean theorem
    • Distance and mid-point formulas
11. Rational Expressions
    • Simplify rational expressions
    • Multiply rational expressions
    • Add, subtraction and division of polynomials
    • Solving rational expressions

Algebra 2

1. Equations and inequalities
   • Simplify expressions and equations
   • Absolute and Modulus values
   • Solving inequalities
2. Functions and linear equations
   • Solving linear equations, functions
   • Slope and intercept, graphs
   • Graph inequalities
3. Solving system of linear equations
   • Solving systems of equations in two variables
   • Solving systems of equations in three variables
4. Matrices
   • Introduction of Matrices
   • Operations with Matrices
   • Determinants
   • Using matrices when solving system of equations
5. Polynomials 
   • Simplify expressions
   • Factoring polynomials
   • Polynomials functions
   • Remainder and factor theorems
   • Roots and zeros 
6. Quadratic functions and inequalities
   • Solving quadratic equations
   • Roots and coefficients
   • Real world problems with Quadratic equations
7. Exponential and logarithmic functions
   • Exponential function
   • Logarithm functions and properties
8. Arithmetic sequences and series
   • Arithmetic sequences and series
   • Geometric sequences and series
   • Binomial theorem
9. Probability
   • Probabilities
   • Permutations and combinations
10. Trigonometry
    • Trigonometric functions
    • Lines and Angles
    • Circular functions
    • Inverse functions

Geometry

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Lines and Angles

1. Line
2. Line segment and Ray
3. Angle
4. Type of angles

Parallel Lines

1. Transversal
2. Parallel lines and relation between different angles formed by transversal and parallel lines

Triangles

1. Triangle
2. Basic properties of triangle
3. Angle sum property and different types of Triangles

Congruence of triangles

1. Congruency
2. SSS, SAS, ASA, AAS and RHS congruency of triangles

Concurrent lines in Triangles

1. Median-Centroid
2. Altitude-Orthocentre
3. Angular bisector-Incentre.

Polygons

1. Polygon
2. Different types of Polygons
3. Interior angle Sum
4. Exterior angle sum and No.Of diagonals.

Quadrilateral

1. Quadrilateral
2. Angle sum properties of Quadrilateral and basic properties of Quadrilateral.

Types of Quadrilateral

1. Quadrilateral
2. Trapezium
3. Parallelogram
4. Rectangle
5. Rhombus
6. Square and their properties.

Various theorems in Quadrilateral

1. Mid-Point theorem
2. Converse of Mid-Point theorem and Intercept theorem

Similar Triangles

1. Similarity
2. Properties of Similar Polygons
3. Basic Propertionality theorem and its Converse
4. Vertical Angle bisector theorem and its Converse

Criteria for Similarity of Triangles

1. SSS, SAS and AAA similarity

• Areas and Perimeters of Similar Triangles

1. The ratios of similar Triangles and Perimeters of Similar Triangles

• Right triangle and Pythagorean theorem

1. Pythagorean theorem and its Converse
2. Mean proportionality relations in Right triangle and conditions for verifying type of triangle

• Right triangle-Trigonometry

1. Different systems of measuring angles
2. Trigonometric ratios
3. T-ratios of (90 – x )

Circles

• Circle

1. Basic terms of Circle
2. Length of arc
3. area of a sector

• Circle theorems

1. Various theorems on Chord
2. Central angle theorem and its applications
3. Various theorems on Tangents

• Perimeter and Area

1. Perimeter and Area of various triangles, quadrilaterals and Circles

• Volume and Surface area

1. Volume and Surface area of Cuboid, cube, Cylinder, Cone and Sphere

PreCalculus

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Functions

• Functions and Relations
• Domain and Range
• Even and odd functions
• Transformation of functions
• Trigonometric equations 

Trigonometry

• Graphs of Sine and cosine
• Transformations of sine and cosine
• Inverse trigonometric functions
• Sinusoidal equations and models
• Angle addition
• Using trigonometric identities

Polynomials

• Addition and subtraction of polynomials 
• Division of polynomials
• Binomial theorem
• Graphs of polynomial functions  and solving equations
• Graphing rational functions and reciprocal functions

Exponential and Logarithms

• Applications of exponential functions
• Logarithms
• Solving exponential and logarithmic equations
• Graphing logarithmic functions

Conic sections

• Feature of a circle
• Equations of a circle
• Center, radii, focii of an ellipse
• Focus and directrix of a parabola
• Hyperbola

Vectors

• Introduction to vectors
• Operations with vectors
• Applications of vectors

Complex numbers

• Complex numbers and imaginary numbers
• The complex plane: Complex numbers
• Addition, Subtraction and Multiplication of complex numbers
• Distance and midpoint of complex numbers
• Complex conjugates and dividing complex numbers
• Identities with complex numbers
• Absolute value and angle of complex numbers
• Polar form of complex numbers, multiplication and division

Matrices

• Introduction
• Representing linear systems of equations with augmented matrices
• Matrix row operations
• Row-echelon form and Gaussian elimination
• Addition, Subtraction, Multiplication of Matrices
• Multiplying matrices by scalars
• Properties of matrix addition & scalar multiplication
• Properties of matrix multiplication
• Matrices as transformations
• The determinant of a 2×2 matrix
• Finding the inverse of a matrix using its determinant
• Solving equations with inverse matrices
• Model real-world situations with matrices

Note: Any other topic as per inputs by students provided during the course will be covered