## Introduction

### Tutoring Program

High school math is the point where students will begin to truly understand the depth and breadth of the discipline of mathematics. The standard sequence for high school math is as follows:

Algebra 1

Algebra 2

Geometry

Pre-Calculus

Within these courses, there are certain standards of conceptual categories that must be met:

- Number and Quantity
- Algebra
- Functions
- Modeling
- Geometry
- Statistics and Probability

Our tutoring will not only prepare students to excel in these courses and topics, but they will also understand how to apply all previous years’ worth of knowledge in furthering their academic pursuits. Each of these topics has several important standards to be met, and these standards are the focal points of the instruction that students will receive:

###### Number and Quantity

- Extend properties of exponents to rational exponents, and use properties of both rational and irrational numbers
- Reason quantitatively and use units to solve problems
- Use complex numbers in equations, polynomial identities, and understand how to perform arithmetic operations with them
- Represent and model vector quantities, perform operations on vectors, and perform operations on matrices and use them in applications

###### Algebra

- Interpret the structure of expressions and write them in equivalent forms to solve problems (linear, quadratic, exponential, polynomial, and rational)
- Perform arithmetic operations on polynomials, understand the relationship between zeros and factors of polynomials, and use identities to solve problems
- Rewrite rational expressions and create equations that describe numbers or relationships
- Understand and explain solving equations as a process of reasoning
- Solve equations and inequalities in one variable as well as systems of equations, and represent equations and inequalities graphically

###### Functions

- Understand the concept of a function and use function notation
- Interpret functions that arise in applications in terms of the context and analyze functions using different representations
- Build a function that models a relationship between two quantities
- Construct and compare linear, quadratic, and exponential models and solve problems
- Interpret expressions for functions in terms of their context
- Extend the domain of trigonometric functions using the unit circle
- Model periodic behavior with trigonometric functions
- Prove and apply trigonometric identities

###### Modeling

- Understanding and choosing appropriate mathematics and statistics to analyze empirical situations
- Using mathematical and statistical methods to model quantities and their relationships in physical, economic, social, and other everyday situations

###### Geometry

- Experiment with transformations in the plane, understand congruence in terms of rigid motions, and make geometric constructions
- Prove geometric theorems and their converse
- Understand similarity and prove theorems involving similarity
- Define trigonometric ratios and solve problems involving right triangles and general triangles
- Understand and apply theorems about circles, and find arc lengths and areas of sectors of circles
- Translate between the geometric description and equation for a conic section
- Use coordinates to prove simple geometric theorems algebraically
- Explain volume formulas and use them to solve problems
- Visualize relationships between two and three dimensional objects

###### Statistics and Probability

- Summarize, represent, and interpret data on a single count or measurement variable, using calculators, spreadsheets, or other technology when appropriate
- Summarize, represent, and interpret data on two categorical and quantitative variables
- Understand and evaluate random processes underlying statistical experiments
- Make inferences and justify conclusions from sample surveys, experiments, and observational studies
- Understand independence and conditional probability and use them to interpret data
- Use probability rules to compute probabilities
- Calculate expected values and use them to solve problems, and use probability to evaluate outcomes of decisions

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