Page 49 - The Ontario Curriculum, Grades 11 and 12: Mathematics, 2007

2.5 solve problems involving the intersection of a linear function and a quadratic function graphically and algebraically (e.g., determine the time when two identical cylindrical water tanks contain equal volumes of water, if one tank is being filled at a constant rate and the other is being emptied through a hole in the bottom)
Sample problem: Determine, through investi- gation, the equations of the lines that have a slope of 2 and that intersect the quadratic function f(x) = x(6 – x) once; twice; never.
By the end of this course, students will:
3.1 simplify polynomial expressions by adding, subtracting, and multiplying
Sample problem: Write and simplify an expression for the volume of a cube with edge length 2x + 1.
3.2 verify, through investigation with and without technology, that √ab = √a x √b,
a ≥ 0, b ≥ 0, and use this relationship to simplify radicals (e.g., √24) and radical expressions obtained by adding, subtracting, and multiplying [e.g., (2 + √6)(3 – √12)]
3.3 simplify rational expressions by adding, subtracting, multiplying, and dividing, and state the restrictions on the variable values
Sample problem: Simplify
2x – 3 , and state the 4x2 + 6x 2x + 3
restrictions on the variable.
3.4 determine if two given algebraic expressions are equivalent (i.e., by simplifying; by substituting values)
Sample problem: Determine if the expressions 2x2 – 4x – 6 and 8x2 – 2x(4x – 1) – 6 are x+1
equivalent.
3. Determining Equivalent Algebraic Expressions*
*The knowledge and skills described in the expectations in this section are to be introduced as needed, and applied and consolidated, as appropriate, in solving problems throughout the course.
CHARACTERISTICS OF FUNCTIONS
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Functions
MCR3U