# Grade 11 Math Tutor

Eleventh grade math is a crucial year for students who intend applying for college or furthering their studies. A good math grade really improves your chances of getting into the best schools. If your student is struggling with this advanced math, then consider in-home tutoring now, rather than leaving it just before the SAT or ACT crunch.

Our one-on-one tutors work with the local curriculum. In the eleventh grade, students must master not only important mathematical concepts, but also the following academic skills:

- Problem solving.
- Reasoning skills to make mathematical conjectures, assess conjectures, and justify conclusions, and plan and construct organized mathematical arguments.
- Reflecting and monitoring their thinking to help clarify their understanding as they complete an investigation or solve a problem.
- Selecting tools and computational strategies to investigate mathematical ideas and to solve problems.
- Connecting: make connections among mathematical concepts and procedures, and relate mathematical ideas to situations or phenomena drawn from other contexts.
- Representing: create a variety of representations of mathematical ideas, connect and compare them, and select and apply the appropriate representations to solve problems.
- Communicate mathematical thinking orally, visually, and in writing, using mathematical vocabulary and a variety of appropriate representations, and observing mathematical conventions.

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### Grade 11 Math Sample Curriculum

#### Characteristics of Functions

- Demonstrate an understanding of functions, their representations, and their inverses, and make connections between the algebraic and graphical representations of functions using transformations
- Determine the zeros and the maximum or minimum of a quadratic function, and solve problems involving quadratic functions, including problems arising from real-world applications;
- Demonstrate an understanding of equivalence as it relates to simplifying polynomial, radical, and rational expressions

#### Exponential Functions

- Evaluate powers with rational exponents, simplify expressions containing exponents, and describe properties of exponential functions represented in a variety of ways
- Identify and represent exponential functions, and solve problems involving exponential functions, including problems arising from real-world applications
- Simplify and evaluate numerical expressions involving exponents, and make connections between the numeric, graphical, and algebraic representations of exponential functions
- Demonstrate an understanding of compound interest and annuities, and solve related problems

#### Discrete Functions

- Demonstrate an understanding of recursive sequences, represent recursive sequences in a variety of ways, and make connections to Pascal’s triangle
- Demonstrate an understanding of the relationships involved in arithmetic and geometric sequences and series, and solve related problems
- Make connections between sequences, series, and financial applications, and solve problems involving compound interest and ordinary annuities

#### Trigonometric Functions

- Determine the values of the trigonometric ratios for angles less than 360º; prove simple trigonometric identities; and solve problems using the primary trigonometric ratios, the sine law, and the cosine law
- Demonstrate an understanding of periodic relationships and sinusoidal functions, and make connections between the numeric, graphical, and algebraic representations of sinusoidal functions
- Identify and represent sinusoidal functions, and solve problems involving sinusoidal functions, including problems arising from real-world applications

#### Quadratic Functions

- Expand and simplify quadratic expressions, solve quadratic equations, and relate the roots of a quadratic equation to the corresponding graph
- Demonstrate an understanding of functions, and make connections between the numeric, graphical, and algebraic representations of quadratic functions
- Solve problems involving quadratic functions, including problems arising from real-world applications

#### Mathematical Models

- Make connections between the numeric, graphical, and algebraic representations of quadratic relations, and use the connections to solve problems
- Demonstrate an understanding of exponents, and make connections between the numeric, graphical, and algebraic representations of exponential relations
- Describe and represent exponential relations, and solve problems involving exponential relations arising from real-world applications

#### Personal Finance

- Compare simple and compound interest, relate compound interest to exponential growth, and solve problems involving compound interest
- Compare services available from financial institutions, and solve problems involving the cost of making purchases on credit
- Interpret information about owning and operating a vehicle, and solve problems involving the associated costs

#### Data Management

- Solve problems involving one-variable data by collecting, organizing, analysing, and evaluating data
- Determine and represent probability, and identify and interpret its applications.

#### Earning and Purchasing

- Interpret information about different types of remuneration, and solve problems and make decisions involving different remuneration methods
- Demonstrate an understanding of payroll deductions and their impact on purchasing power
- Demonstrate an understanding of the factors and methods involved in making and justifying informed purchasing decisions

#### Saving, Investing and Borrowing

- Describe and compare services available from financial institutions
- Demonstrate an understanding of simple and compound interest, and solve problems involving related applications
- Interpret information about different ways of borrowing and their associated costs, and make and justify informed borrowing decisions

#### Transportation and Travel

- Interpret information about owning and operating a vehicle, and solve problems involving the associated costs
- Plan and justify a route for a trip by automobile, and solve problems involving the associated costs
- Interpret information about different modes of transportation, and solve related problems