# High School Math Tutoring

## Personalized Online Math Tutor for High School

## Algebra

#### 1. Expressions, Equations and Inequalities

- Construction, Interpretation, and Manipulation of Expressions
- Solutions of Equations and Inequalities

#### 2. Functions

- Definitions, Representations, and Attributes of Functions
- Operations and Transformations with Functions
- Models of Real-World Situations Using Families of Functions

#### 3. Families of Functions

- Lines and Linear Functions
- Exponential and Logarithmic Functions
- Quadratic Functions
- Power Functions
- Polynomial Functions
- Rational Functions
- Trigonometric Functions

#### Statistics

#### 1. Univariate Data

- Producing and Interpreting Plots
- Producing and Interpreting Plots
- Measures of Center and Variation
- The Normal Distribution

#### 2. Bivariate Data

- Scatter Plots and Correlation
- Pearson’s correlation coefficient
- Scatter Plots and Correlation
- Linear Regression
- Least squares regression line

#### 3. Sampling And Study Of B103 design

- Data Collection and Analysis
- Simple Random Sampling
- Stratified Random Sampling
- Cluster Sampling
- Surveys
- Completely Randomized and Randomized block designs

#### 4. Probability Models

- Law of Large Numbers
- Basic Probability Rules
- Law of Total Probability
- Bayes’ Theorem
- Random variable and Discrete Probability Distribution
- Effect of a linear transformation of a random variable on its mean and standard deviation.
- Binomial Distribution
- Geometric Distribution
- Hypergeometric Distribution
- Percentiles of normal distributions.
- Simulation
- Central Limit Theorem
- Confidence Intervals
- Control Limits

#### 5. Point And Interval Estimation

- Simulation of confidence interval
- t-distribution

#### 6. Significance Testing

- Testing of Hypothesis
- p-value
- Type I and Type II errors
- Chi-squared significance tests of homogeneity and independence
- Goodness-of-fit test

#### 7. Inference For Regression

- Statistical model for regression, including linearity, normality of errors, and constancy of error variance

#### Probability

#### 1. Probability Models and Probability Calculation

- Sample space
- Computing the Probability of mutually exclusive, independent, dependent, compound and complementary events
- Conditional Probability
- Venn diagrams
- Combinations and permutations
- Application of Probability concepts to practical situations

#### Geometry

#### 1. Figures And Their Properties

- Lines and Angles
- Euclidean and Coordinate Geometry

#### 2. Triangles

- Triangles and Their Properties
- Angles, side length, perimeter, and area of triangles.
- Quadratic Functions, Pythagorean Theorem and its applications
- Medians, altitudes and perpendicular bisectors, and the angle bisectors of a triangle.

#### 3. Quadrilaterals

- Quadrilaterals and Their Properties
- Proofs involving quadrilaterals
- Theorems about the interior and exterior angle sums of a quadrilateral.

#### 4. Polygons

- Other Polygons and Their Properties
- Perimeter and area of a regular n-gon, interior and exterior angles of a regular n-gon.

#### 5. Circles

- Circles and Their Properties
- Equation of a circle
- Conic Sections and Their Properties
- Identification and Graphs of parabolas, circles, ellipses, and hyperbolas

#### 6. Logical Reasoning

- Law of Syllogism

#### Geometry and Trigonometry

#### 1. Geometry and Trigonometry

- Relationships Between Area and Volume Formulas

#### 2. Relationships Between 2- Dimensional And 3-Dimensional Figures

- Identification and drawings

#### 3. Congruence and Similarity

- SSS, SAS, ASA and AAS conditions for congruency
- SSS, SAS and AAS conditions for similarity

#### 4. Transformations of figures in the plane

- Distance-preserving Transformations Isometries
- Shape-preserving Transformations: Dilations and Isometries

#### 5. Geometry and Spatial Sense Standard

- Visualization and Geometric Models
- Relate graphical and algebraic representations of lines, simple curves and conic sections.
- Recognize and compare specific shapes and properties in multiple geometries; e.g., plane, spherical and hyperbolic.

#### Trigonometry

#### 1. Trigonometric Ratios

- Sine, cosine, and tangent of angles
- Law of Sines and Cosines
- Values of Trigonometric Ratios for 0°, 30°, 45°, 60° angles

#### 2. Trigonometric Identities & Functions

- Graphs of transformations of the sine and cosine functions.
- Inverse Trigonometric Functions
- Basic Trigonometric Identities
- Solutions of trigonometric equations
- Radian and Degree Measures

#### Pre Calculus

#### 1. Functions

- Definition of a Function
- Algebraic Operations on Functions and apply Transformations.
- Composite Functions

#### 2. Exponential And Logarithmic Functions

- Relationship between exponential and logarithmic functions
- Graphs of logarithmic functions
- Solution of exponential and logarithmic functions
- Problems involving Exponential growth and decay

#### 3. Quadratic Functions

- Solution of quadratic equations by substitution
- Applications of quadratic functions

#### 4. Polynomial Functions

- Intervals and graphs of polynomial functions
- Solution of polynomial equations and inequalities of degree >=to three
- The Remainder Theorem
- Factor Theorem
- Fundamental Theorem of Algebra

#### 5. Rational Functions And Difference Quotients

- Solutions of equations and inequalities involving rational functions.
- Vertical and horizontal asymptotes

#### 6. Patterns, Functions and Algebra Standard

- Transcendental and Periodic Functions.

#### 7. Vectors , Matrices, System Of Equations.

- Operations on Vectors
- Operations on Matrices
- Inverse of a matrix
- Determinants
- Gaussian elimination
- Linear Programming

#### 8. Sequences, Series And Mathematical Induction.

- The sigma and factorial notation.
- Arithmetic sequences
- Geometric sequences
- Mathematical Induction
- Binomial Theorem
- Pascal’s Triangle

#### 9. Polar Coordinates, Parameterizations, And Conic Sections.

- Conversion between polar and rectangular coordinates.
- Graph of functions in polar coordinates.
- De Moivre’s Theorem
- Parametric and Rectangular forms of equations.
- Locus
- Graphs of parabolas, ellipses and hyperbolas

**Algebra**,

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**PreCalculus**,

**Calculus and Statistics**and for every other concept in math. Online

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