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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.
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 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.
Analyse, interpret, and draw conclusions from one-variable data using numerical and graphical summaries;
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.
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.
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.
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.
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.
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.
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.
Reading and Literature Studies