Grade 12 - Mathematics 30-1 (2008)

Trigonometry

Relations and Functions

Permutations, Combinations and Binomial Theorem

Develop trigonometric reasoning.

Demonstrate an understanding of angles in standard position, expressed in degrees and radians. 

Develop and apply the equation of the unit circle. 

Solve problems, using the six trigonometric ratios for angles expressed in radians and degrees. 

Graph and analyze the trigonometric functions sine, cosine and tangent to solve problems. 

Solve, algebraically and graphically, first and second degree trigonometric equations with the domain expressed in degrees and radians. 

Prove trigonometric identities, using: reciprocal identities, quotient identities, Pythagorean identities, sum or difference identities (restricted to sine, cosine and tangent), double-angle identities (restricted to sine, cosine and tangent)

Develop algebraic and graphical reasoning through the study of relations. 

Demonstrate an understanding of operations on, and compositions of, functions. 

Demonstrate an understanding of the effects of horizontal and vertical translations on the graphs of functions and their related equations. 

Demonstrate an understanding of the effects of horizontal and vertical stretches on the graphs of functions and their related equations. 

Apply translations and stretches to the graphs and equations of functions. 

Demonstrate an understanding of the effects of reflections on the graphs of functions and their related equations, including reflections through the: x-axis, y-axis, line y = x.

Demonstrate an understanding of inverses of relations. 

Demonstrate an understanding of logarithms. 

Demonstrate an understanding of the product, quotient and power laws of logarithms. 

Graph and analyze exponential and logarithmic functions. 

Solve problems that involve exponential and logarithmic equations. 

Demonstrate an understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree 5 with integral coefficients). 

Graph and analyze polynomial functions (limited to polynomial functions of degree ≤ 5 ). 

Graph and analyze radical functions (limited to functions involving one radical). 

Graph and analyze rational functions (limited to numerators and denominators that are monomials, binomials or trinomials). 

Develop algebraic and numeric reasoning that involves combinatorics. 

Apply the fundamental counting principle to solve problems. 

Determine the number of permutations of n elements taken r at a time to solve problems. 

Determine the number of combinations of n different elements taken r at a time to solve problems. 

Expand powers of a binomial in a variety of ways, including using the binomial theorem (restricted to exponents that are natural numbers).