  # USA CURRICULUM

1. Linear Equations

• 1.1 Solving Simple and two variable Equations

• 1.2 Solving Absolute Value Equations

• 1.3 Rewriting Equations and Formulas

2. Linear Inequalities

• 2.1 Writing and Graphing Inequalities

• 2.2 Solving Inequalities Using Addition and Subtraction

• 2.3 Solving Inequalities Using Multiplication and division

• 2.4 Solving Multi-Step Inequalities

• 2.5 Solving Absolute value Compound Inequalities

3. Graphing Linear Functions

• 3.1 Functions – Relations – Domain – Ranges

• 3.2 Linear Functions

• 3.3 Graphing Linear Equations in Standard Form

• 3.4 Graphing Linear Equations in Slope-Intercept Form

• 3.5 Transformations of Graphs of Linear Functions

• 3.6 Graphing Absolute Value Functions

4.Writing Linear Functions

• 4.1 Writing Equations in Slope-Intercept Form

• 4.2 Writing Equations in Point-Slope Form

• 4.3 Writing Equations of Parallel and Perpendicular Lines

• 4.4 Scatter Plots and Lines of Fit

• 4.5 Analyzing Lines of Fit

• 4.6 Arithmetic Sequences

• 4.7 Piece-wise Functions

5. Solving Systems of Linear Equations

• 5.1 Solving Systems of Linear Equations by Graphing

• 5.2 Solving Systems of Linear Equations by Substitution

• 5.3 Solving Systems of Linear Equations by Elimination

• 5.4 Solving Special Systems of Linear Equations

• 5.5 Solving Equations by Graphing

• 5.6 Graphing Linear Inequalities in Two Variables

• 5.7 Systems of Linear Inequalities

6. Exponential functions and sequences

• 6.1 Properties of Exponents

• 6.2 Radicals and Rational Exponents

• 6.3 Exponential Functions

• 6.4 Exponential Growth and Decay

• 6.5 Solving Exponential Equations

• 6.6 Geometric Sequences

• 6.7 Recursively Defined Sequences

7. Polynomial equations and factoring

• 7.1 Adding and Subtracting Polynomials

• 7.2 Multiplying Polynomials

• 7.3 Special Products of Polynomials

• 7.4 Solving Polynomial Equations in Factored Form

• 7.5 Factoring of Polynomials

• 8.1 Graphing f (x) = ax2

• 8.2Graphingf(x)=ax2+c

• 8.3Graphingf(x)=ax2+bx+c

• 8.4Graphingf(x)=a(x−h)2+k

• 8.5 Using Intercept Form

• 8.6 Comparing Linear, Exponential,and Quadratic Functions

• 9.2 Solving Quadratic Equations by Graphing

• 9.3 Solving Quadratic Equations Using Square Roots

• 9.4 Solving Quadratic Equations by Completing the Square

• 9.6 Solving Nonlinear systems of equations

• 10.1 Graphing Square Root Functions

• 10.2 Graphing Cube Root Functions

• 10.4 Inverse of a Function

11. Data Analysis and displays

• 11.1 Measures of Center and Variation

• 11.2 Box-and-Whisker Plots

• 11.3 Shapes of Distributions

• 11.4 Two-Way Tables

• 11.5 Choosing a Data Display

• Equations and inequalities ( 5 hours)
• Simplify expressions and equations
• Absolute and Modulus values
• Solving inequalities
• Linear relations and functions ( 6 hours)
• Solving linear equations, functions
• Slope and intercept, graphs
• Graph inequalities
• Solving system of linear equations ( 5 hours )
• Solving systems of equations in two variables
• Solving systems of equations in three variables
• Rational functions and relations (6 hours)
• Multiplying,dividing, adding, subtracting rational expressions
• Graphing rational functions
•  Solving rational equations and inequalities
• Matrices ( 5 hours)
• Introduction of Matrices
• Operations with Matrices
• Determinants
• Using matrices when solving system of equations
• Polynomials ( 6 hours)
• Simplify expressions
• Factoring polynomials
• Polynomials functions
• Remainder and factor theorems
• Roots and zeros
• Quadratic functions and inequalities ( 6 hours)
• Roots and coefficients
• Real world problems with Quadratic equations
• Exponential and logarithmic functions( 6 hours)
• Exponential function
• Logarithm functions and properties
• Logarithmic functions(5 hours)
• Arithmetic sequences and series ( 7 hours)
• Arithmetic sequences and series
• Geometric sequences and series
• Binomial theorem
• Probability and Statistics ( 9 hours)
• Statistical analysis
• Probabilities
• Permutations and combinations
• Probability and distributions
• Normal distribution, Binomial distribution
• Trigonometry ( 10 hours)
• Trigonometric functions
• Lines and Angles
• Circular functions
• Inverse functions
Trigonometric graphs

Basics Of Geometry

Points, lines, and planes
Measuring and constructing segments

Using midpoint and distance formulas

Perimeter and area in the coordinate plane

Measuring and constructing angles

Describing pairs of angles

Reasoning and Proofs

Conditional statements

Inductive and deductive reasoning

Postulates and diagrams

Algebraic Reasoning

Proving statements about segments and angles

Parallel and Perpendicular Lines

Pairs of lines and angles

Parallel lines and transversals

Proofs with parallel lines

Proofs with perpendicular lines

Equations of parallel and perpendicular lines

Transformations

Translations
Reflections
Rotations
Congruence and transformations Dilations

Similarity and Transformations

Congruent Triangles

Angles of triangles

Congruent polygons

Proving triangle congruence by SAS

Equilateral and isosceles triangles

Proving triangle congruence by SSS

Proving triangle congruence by ASA and AAS

Using congruent triangles

Coordinate proofs

Relationships within Triangles

Perpendicular and angle bisectors
Bisectors of Triangles
Medians and altitudes of triangles
The triangle midsegment theorem
Indirect proof and inequalities in one triangle

Inequalities in two triangles

Polygons and Its angles

Parallelogram

Rectangle

Rhombus

Square

Trapezoid and Kite

Similarity of Triangles

Similarity and SSS Similarity of Triangles
SAS, AAA or AA Similarity
Perimeters and Area ratios of Similar triangles
Medians, Altitudes and Angle bisectors ratios of Similar triangles Proportionality Theorem

Angle bisector theorem

Right Angle and Trigonometry

The pythagorean theorem Special right triangles Similar right triangles
The tangent ratio

The sine and cosine ratio

Solving right triangles

Law of sines and law of cosines

Circles

Lines and Segments that intersect Circles Finding arc measures
Using Chords
Inscribed angles and Polygons

Angle relationships in Circles

Segment relationships in Circles

Circles in the Coordinate plane

Circumference, Area and Volume

Circumference and arc length Areas of circles and sectors Areas of polygons
3D figures

Volumes of prisms and Cylinders

Volumes of pyramids

Surface ares and volumes of cones

Surface ares and volumes of spheres

Probability

Sample spaces and probability
Independent and dependent events
Two way tables and probability
probability of disjoint and overlapping events Permutations and combinations
Binomial distributions

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

Using trigonometric identities

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

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

Course Structure-
Number of Sessions/week – 02
Each lesson will be of One hour
Monthly Test- 01
Homework will be assigned after every class
For further quarries or Crash Courses kindly try to contact – +919830399679

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