# MCT4C Mathematics For College Technology – Grade 12 (College)

PREREQUISITE: Functions and Applications, Grade 11, University/College Preparation, or Functions, Grade 11, University Preparation

AVAILABILITY: Full-time – All Campuses, Private – All campuses, Blyth Academy Online

THE ONTARIO CURRICULUMMathematics

## Course Overview

MCT4C online enables students to extend their knowledge of functions. Students will investigate and apply properties of polynomial, exponential, and trigonometric functions; continue to represent functions numerically, graphically, and algebraically; develop facility in simplifying expressions and solving equations; and solve problems that address applications of algebra, trigonometry, vectors, and geometry. Students will reason mathematically and communicate their thinking as they solve multi-step problems. MCT4C online prepares students for a variety of college technology programs.

### UNIT ONE Polynomials Functions - Factoring and Solving

Essential Question: What do effective problem solvers do when they get stuck?

In this unit, students will learn to factor polynomials no higher than degree 4 and solve polynomial equations using factoring or the quadratic formula. Students will also learn how to expand polynomials and collect like terms to put polynomials in their simplest form.

### UNIT TWO Polynomial Functions - Graphing Polynomials

Essential Question: How do the graphs of mathematical models and data help us better understand the world in which we live?

In this unit, students will learn how to substitute and evaluate polynomial functions and recognize linear and quadratic polynomials and state their domain and range, degree, leading coefficient and the end behaviour. Students will learn how to identify cubic and quartic functions by equations or graphs, state the maximum number of x-intercepts, the domain and range and the end behaviour. Students will draw graphs of polynomials using zeros and end behaviour as well as estimate the zeros from a graph and determine their exact value using technology. Students will also learn to determine the equation of a polynomial (up to degree 4) given the graph or the zeros and another point.

### UNIT THREE Polynomial Functions - Modelling with Polynomials

Essential Question: How do I know where to begin when solving a problem?

In this unit, students will solve problems related to real-world applications using polynomial functions and evaluate the reasonableness of the solution. Students will learn to read graphs and identify limitations on real-world applications using polynomial functions and solve for unknowns using formulas and rearrange formulas for specific values.

### UNIT FOUR Exponential Functions

Essential Question: How does the use of exponents simplify the writing of large numbers?

In this unit, students will evaluate powers and simplify algebraic expressions using laws of exponents and learn how to solve equations that involve exponents, both graphically and algebraically. Students will graph exponential equations with and without technology and use these graphs to estimate solutions to exponential equations. Students will also solve real-world applications that can be modelled by exponential equations and learn how to convert between exponential and logarithmic form and work with laws of logarithms to simplify expressions.

### UNIT FIVE Trigonometric Functions

Essential Question: How do people use trigonometry to find missing values?

In this unit, students will use the primary trig ratios (sine, cosine and tangent) along with Sine Law and Cosine Law to calculate the lengths of sides and the values of angles and apply this to real-world examples. Students will learn to determine exact values of sine, cosine and tangent of special angles and solve for the missing angles given a trigonometric ratio.

### UNIT SIX Graphing Trigonometric Functions

Essential Question: How do people use data to influence others?

In this unit, students will draw the graphs of the sine and cosine functions in degrees and draw the graphs using transformations. Students will learn to determine the amplitude, period, phase shift and vertical translation of a sinusoidal function and use it to write the equation using sine and cosine. Students will also learn to write the trigonometric equations to model real-world applications and use these equations to solve problems.

### UNIT SEVEN Geometry and Circle Geometry

Essential Question: What is the difference between a point, a line and a plane?

In this unit, students will perform conversions within the metric system, the imperial system and between the two. Students will solve problems involving perimeter, area, surface area and volume. Students will also learn to determine circle properties and solve related problems, including those arising from real-world applications.

### UNIT EIGHT Vectors

Essential Question: What is normal to a vector and how do I calculate it?

In this unit, students will learn how to distinguish between a vector and a scalar and be able to represent a vector in a variety of different ways. Students will learn how to resolve a vector into horizontal and vertical components, represent a vector as a directed line segment given horizontal and vertical components and determine the sum or difference of two vectors. Students will also calculate the sum or difference of two vectors and solve problems involving the addition and subtraction of vectors in problems arising from real-world applications.

Please consult our Frequently Asked Questions Page or the Exam section within your course for more details on final exams and the exam fee. More information can also be found in our Student Handbook.

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