High School Math Tutoring for Grades 8-12

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High School Math Concepts

Mathematics is a beautiful and useful language for understanding the basic concepts of education. Your math grades predict your lifetime earnings.

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

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