# 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
• 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
• 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
• 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

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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.

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

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