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Please see https://www.cemc.uwaterloo.ca/courseware/ for the most complete and current information about CEMC courseware.
Students will investigate the properties of polynomial, rational, exponential, logarithmic, trigonometric and radical functions and develop facility in applying these properties. This courseware is considered prerequisite learning for the Calculus and Vectors courseware.
Students will investigate the derivatives of polynomial, rational, exponential, logarithmic, and trigonometric functions, and apply these to the modelling of real-world relationships. Integral Calculus and its applications will be introduced. Students will solve problems involving vectors, lines and planes in three-space. This courseware is intended for students who have studied or are currently studying the Advanced Functions and Pre-Calculus courseware.
Exponential and sinusoidal functions. Properties, transformations, and applications.
Function notation. Domain and range. Transformations of functions. Inverses of functions. Inequalities, absolute values, and reciprocals.
Linear and non-linear relations. Solving linear equations and linear systems. Analytic geometry and statistics.
Pythagorean Theorem. Measurement of 2D figures and 3D solids. Optimization. Geometric relationships. Triangle trigonometry. Angles in standard position and trigonometric identities.
Exponent laws. Manipulating expressions including polynomials, radical, and rational expressions. Investigating prime factorization.
Graphs and tables. Standard, factored, and vertex forms. Algebra of quadratic relations. Quadratic equations. Intersections of lines and parabolas.
Arithmetic and geometric sequences. Financial applications including simple interest, compound interest, and annuities.
Students expand their knowledge of operations to include negative numbers and fractional quantities. Basic algebra is introduced with the addition of variables into topics including patterning, and proportional reasoning. Students make connections between geometry and algebra while studying properties of polygons, circles, and the Pythagorean theorem.
Students will develop their problem solving ability through the investigation of problem solving techniques and by working through the solutions to problems from a wide spectrum of mathematical topics.