# Grade 12 Math Tutor

Twelfth 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 in 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^{®} exam 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 12 Math Sample Curriculum

#### Exponential and Logarithmic Functions

- Demonstrate an understanding of the relationship between exponential expressions and logarithmic expressions, evaluate logarithms, and apply the laws of logarithms to simplify numeric expressions
- Identify and describe some key features of the graphs of logarithmic functions, make connections among the numeric, graphical, and algebraic representations of logarithmic functions, and solve related problems graphically
- Solve exponential and simple logarithmic equations in one variable algebraically, including those in problems arising from real-world applications
- Solve problems involving exponential equations graphically, including problems arising from real-world applications

#### Trigonometric Functions

- Demonstrate an understanding of the meaning and application of radian measure
- Make connections between trigonometric ratios and the graphical and algebraic representations of the corresponding trigonometric functions and between trigonometric functions and their reciprocals, and use these connections to solve problems
- Solve problems involving trigonometric equations and prove trigonometric identities
- Determine the values of the trigonometric ratios for angles less than 360º, and solve problems using the primary trigonometric ratios, the sine law, and the cosine law
- Make connections between the numeric, graphical, and algebraic representations of sinusoidal functions
- Demonstrate an understanding that sinusoidal functions can be used to model some periodic phenomena, and solve related problems, including those arising from real-world applications.

#### Polynomial and Rational Functions

- Identify and describe some key features of polynomial functions, and make connections between the numeric, graphical, and algebraic representations of polynomial functions
- Identify and describe some key features of the graphs of rational functions, and represent rational functions graphically
- Solve problems involving polynomial and simple rational equations graphically and algebraically
- Demonstrate an understanding of solving polynomial and simple rational inequalities
- Recognize and evaluate polynomial functions, describe key features of their graphs, and solve problems using graphs of polynomial functions
- Solve polynomial equations by factoring, make connections between functions and formulas, and solve problems involving polynomial expressions arising from a variety of applications

#### Characteristics of Functions

- Demonstrate an understanding of average and instantaneous rate of change, and determine, numerically and graphically, and interpret the average rate of change of a function over a given interval and the instantaneous rate of change of a function at a given point
- Determine functions that result from the addition, subtraction, multiplication, and division of two functions and from the composition of two functions, describe some properties of the resulting functions, and solve related problems
- Compare the characteristics of functions, and solve problems by modelling and reasoning with functions, including problems with solutions that are not accessible by standard algebraic techniques

#### Calculus and Vectors: Rate of Change

- Demonstrate an understanding of rate of change by making connections between average rate of change over an interval and instantaneous rate of change at a point, using the slopes of secants and tangents and the concept of the limit
- Graph the derivatives of polynomial, sinusoidal, and exponential functions, and make connections between the numeric, graphical, and algebraic representations of a function and its derivative
- Verify graphically and algebraically the rules for determining derivatives; apply these rules to determine the derivatives of polynomial, sinusoidal, exponential, rational, and radical functions, and simple combinations of functions; and solve related problems

#### 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

#### Derivatives and their Applications

- Make connections, graphically and algebraically, between the key features of a function and its first and second derivatives, and use the connections in curve sketching
- Solve problems, including optimization problems, that require the use of the concepts and procedures associated with the derivative, including problems arising from real-world applications and involving the development of mathematical models

#### Geometry and Algebra of Vectors

- Demonstrate an understanding of vectors in two-space and three-space by representing them algebraically and geometrically and by recognizing their applications
- Perform operations on vectors in two-space and three-space, and use the properties of these operations to solve problems, including those arising from real-world applications
- Distinguish between the geometric representations of a single linear equation or a system of two linear equations in two-space and three-space, and determine different geometric configurations of lines and planes in three-space
- Represent lines and planes using scalar, vector, and parametric equations, and solve problems involving distances and intersections

#### Mathematics of Data Management: Counting and Probability

- Solve problems involving the probability of an event or a combination of events for discrete sample spaces
- Solve problems involving the application of permutations and combinations to determine the probability of an event

#### Probability Distributions

- Demonstrate an understanding of discrete probability distributions, represent them numerically, graphically, and algebraically, determine expected values, and solve related problems from a variety of applications
- Demonstrate an understanding of continuous probability distributions, make connections to discrete probability distributions, determine standard deviations, describe key features of the normal distribution, and solve related problems from a variety of applications

#### Organization of Data for Data Analysis

- Demonstrate an understanding of the role of data in statistical studies and the variability inherent in data, and distinguish different types of data
- Describe the characteristics of a good sample, some sampling techniques, and principles of primary data collection, and collect and organize data to solve a problem

#### Statistical Analysis

- Analyse, interpret, and draw conclusions from two-variable data using numerical, graphical, and algebraic summaries
- Demonstrate an understanding of the applications of data management used by the media and the advertising industry and in various occupations

#### Culminating Data Management Investigation

- Design and carry out a culminating investigation that requires the integration and application of the knowledge and skills related to the expectations of this course
- Communicate the findings of a culminating investigation and provide constructive critiques of the investigations of others

#### Applications of Geometry

- Represent vectors, add and subtract vectors, and solve problems using vector models, including those arising from real-world applications
- Solve problems involving two-dimensional shapes and three-dimensional figures and arising from real-world applications
- Determine circle properties and solve related problems, including those arising from real-world applications

#### Mathematical Models

- Evaluate powers with rational exponents, simplify algebraic expressions involving exponents, and solve problems involving exponential equations graphically and using common bases
- Describe trends based on the interpretation of graphs, compare graphs using initial conditions and rates of change, and solve problems by modelling relationships graphically and algebraically
- Make connections between formulas and linear, quadratic, and exponential relations, solve problems using formulas arising from real-world applications, and describe applications of mathematical modelling in various occupations

#### Personal Finance

- Demonstrate an understanding of annuities, including mortgages, and solve related problems using technology
- Gather, interpret, and compare information about owning or renting accommodation, and solve problems involving the associated costs
- Design, justify, and adjust budgets for individuals and families described in case studies, and describe applications of the mathematics of personal finance.

#### Data Management

- Collect, analyze, and summarize two-variable data using a variety of tools and strategies, and interpret and draw conclusions from the data
- Demonstrate an understanding of the applications of data management used by the media and the advertising industry and in various occupations

#### Reasoning with Data

- Collect, organize, represent, and make inferences from data using a variety of tools and strategies, and describe related applications
- Determine and represent probability, and identify and interpret its applications

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