AN.1.3.3 Verify, by substitution, that the values determined in solving a radical equation algebraically are roots of the equation.
AN.1.3.4 Explain why some roots determined in solving a radical equation algebraically are extraneous.
AN.1.3.5 Solve problems by modelling a situation using a radical equation.
AN.1.4 Determine equivalent forms of rational expressions (limited to numerators and denominators that are monomials, binomials or trinomials).
AN.1.4.1 Compare the strategies for writing equivalent forms of rational expressions to the strategies for writing equivalent forms of rational numbers.
AN.1.4.2 Explain why a given value is non-permissible for a given rational expression.
AN.1.4.3 Determine the non-permissible values for a rational expression.
AN.1.4.4 Determine a rational expression that is equivalent to a given rational expression by multiplying the numerator and denominator by the same factor (limited to a monomial or a binomial), and state the non-permissible values of the equivalent rational expression.
T.1.1.6 Draw an angle in standard position given any point P (x,y) on the terminal arm of the angle.
T.1.1.7 Illustrate, using examples, that the points P(x,y), P(–x,y), P(–x,–y) and P(x,–y) are points on the terminal sides of angles in standard position that have the same reference angle.
T.1.2 Solve problems, using the three primary trigonometric ratios for angles from 0° to 360° in standard position.
T.1.2.1 Determine, using the Pythagorean theorem or the distance formula, the distance from the origin to a point P(x,y) on the terminal arm of an angle.
T.1.2.2 Determine the value of sin θ, cos θ or tan θ, given any point P(x,y) on the terminal arm of angle θ.
T.1.2.3 Determine, without the use of technology, the value of sin θ, cos θ or tan θ, given any point P(x,y) on the terminal arm of angle θ, where θ = 0&sup0;, 90&sup0;, 180&sup0;, 270&sup0; or 360&sup0;.
T.1.2.4 Determine the sign of a given trigonometric ratio for a given angle, without the use of technology, and explain.
T.1.2.5 Solve, for all values of θ, an equation of the form sin θ = a or cos θ = a, where –1 ≤ a ≤ 1, and an equation of the form tan θ = a, where a is a real number.
RF.1.4.6 Verify, with or without technology, that a quadratic function in the form y = ax² + bx + c represents the same function as a given quadratic function in the form y = a(x – p)² + q.
RF.1.4.7 Write a quadratic function that models a given situation, and explain any assumptions made.
RF.1.4.8 Solve a problem, with or without technology, by analyzing a quadratic function.
RF.1.5 Solve problems that involve quadratic equations.
RF.1.5.1 Explain, using examples, the relationship among the roots of a quadratic equation, the zeros of the corresponding quadratic function and the x-intercepts of the graph of the quadratic function.
RF.1.5.2 Derive the quadratic formula, using deductive reasoning.
RF.1.5.3 Solve a quadratic equation of the form ax² + bx + c = 0 by using strategies such as:
RF.1.5.4 Select a method for solving a quadratic equation, justify the choice, and verify the solution.
RF.1.5.5 Explain, using examples, how the discriminant may be used to determine whether a quadratic equation has two, one or no real roots; and relate the number of zeros to the graph of the corresponding quadratic function.
RF.1.11 Graph and analyze reciprocal functions (limited to the reciprocal of linear and quadratic functions).
RF.1.11.1 Compare the graph of y = 1/f(x) to the graph of y = f(x).
RF.1.11.2 Identify, given a function f(x), values of x for which y = 1/f(x) will have vertical asymptotes; and describe their relationship to the non-permissible values of the related rational expression.