Page 96 - The Ontario Curriculum, Grades 11 and 12: Mathematics, 2007

Grade 12, University Preparation
4. Solving Inequalities
By the end of this course, students will:
4.1 explain, for polynomial and simple rational functions, the difference between the solution to an equation in one variable and the solu- tion to an inequality in one variable, and demonstrate that given solutions satisfy an inequality (e.g., demonstrate numerically
and graphically that the solution to 1 <5 isx<–1orx>–4); x+1 5
4.2 determine solutions to polynomial inequali- ties in one variable [e.g., solve f(x) ≥ 0, where f(x) = x3 – x2 + 3x – 9] and to simple rational inequalities in one variable by graphing the corresponding functions, using graphing tech- nology, and identifying intervals for which x satisfies the inequalities
4.3 solve linear inequalities and factorable poly- nomial inequalities in one variable (e.g.,
x3 + x2 > 0) in a variety of ways (e.g., by deter- mining intervals using x-intercepts and evalu- ating the corresponding function for a single x-value within each interval; by factoring the polynomial and identifying the conditions for which the product satisfies the inequality), and represent the solutions on a number line or algebraically (e.g., for the inequality
x4 – 5x2+ 4 < 0, the solution represented algebraically is – 2 < x < –1 or 1 < x < 2)
THE ONTARIO CURRICULUM, GRADES 11 AND 12 | Mathematics
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