Specific Expectations

MCR3U.3.1 Manipulating Polynomials, Rational Expressions, and Exponential Expressions

By the end of this course, students will:

• MCR3U.3.1.a solve first-degree inequalities and represent the solutions on number lines;
• MCR3U.3.1.b add, subtract, and multiply polynomials;
• MCR3U.3.1.c determine the maximum or minimum value of a quadratic function whose equation is given in the form y = ax² + bx + c, using the algebraic method of completing the square;
• MCR3U.3.1.d identify the structure of the complex number system and express complex numbers in the form a + bi, where i² = –1 (e.g., 4i, 3 – 2i);
• MCR3U.3.1.e determine the real or complex roots of quadratic equations, using an appropriate method (e.g., factoring, the quadratic formula, completing the square), and relate the roots to the x-intercepts of the graph of the corresponding function;
• MCR3U.3.1.f add, subtract,multiply, and divide complex numbers in rectangular form;
• MCR3U.3.1.g add, subtract,multiply, and divide rational expressions, and state the restrictions on the variable values;
• MCR3U.3.1.h simplify and evaluate expressions containing integer and rational exponents, using the laws of exponents;
• MCR3U.3.1.i solve exponential equations (e.g., 4x = 8x + 3, 22x – 2x = 12).

MCR3U.3.2 Understanding Inverses and Transformations and Using Function Notation

By the end of this course, students will:

• MCR3U.3.2.a define the term function;
• MCR3U.3.2.b demonstrate facility in the use of function notation for substituting into and evaluating functions;
• MCR3U.3.2.c determine, through investigation, the properties of the functions defined by f (x) = √x [e.g., domain, range, relationship to f (x) = x²] and f (x) = [e.g., domain, range, relationship to f (x) = x.];
• MCR3U.3.2.d explain the relationship between a function and its inverse (i.e., symmetry of their graphs in the line y = x; the interchange of x and y in the equation of the function; the interchanges of the domain and range), using examples drawn from linear and quadratic functions, and from the functions f (x) = √x and f (x) = ;
• MCR3U.3.2.e represent inverse functions, using function notation, where appropriate;
• MCR3U.3.2.f represent transformations (e.g., translations, reflections, stretches) of the functions defined by f(x) = x, f(x) = x², f(x) = √x, f(x) = sin x, and f(x) = cos x, using function notation;
• MCR3U.3.2.g describe, by interpreting function notation, the relationship between the graph of a function and its image under one or more transformations;1 1x
• MCR3U.3.2.h state the domain and range of transformations of the functions defined by f(x) = x, f(x) = x2, f(x) = √x, f(x) = sin x, and f(x) = cos x.

MCR3U.3.3 Communicating Mathematical Reasoning

By the end of this course, students will:

• MCR3U.3.3.a explain mathematical processes, methods of solution, and concepts clearly to others;
• MCR3U.3.3.b present problems and their solutions to a group, and answer questions about the problems and the solutions;
• MCR3U.3.3.c communicate solutions to problems and to findings of investigations clearly and concisely, orally and in writing, using an effective integration of essay and mathematical forms;
• MCR3U.3.3.d demonstrate the correct use of mathematical language, symbols, visuals (e.g., diagrams, graphs), and conventions;
• MCR3U.3.3.e use graphing technology effectively (e.g., use appropriate menus and algorithms; set the graph window to display the appropriate section of a curve).