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Education, Citizenship and Youth
Grade 12 Pre-Calculus Mathematics (40S) Outcomes by Unit
Unit A: Circular Functions
Unit B: Transformations
Unit C: Trigonometric Identities
Unit D: Exponents and Logarithms
Unit E: Permutations, Combinations, Binomial Theorem
Unit F: Conics
Unit G: Probability
Unit H: Geometric Sequences
Unit I: Statistics (Optional)
| Solve exponential, logarithmic, and trigonometric equations and identities |
| Represent and analyze trigonometric functions, using technology as appropriate |
| Distinguish between degree and radian measure, and solve problems, using both (A-1) |
| Describe the three primary trigonometric functions and their reciprocal functions as circular functions with reference to the unit circle and an angle in standard position (A-2) |
Determine the exact values of trigonometric ratios
for any multiples of 0° , 30° , 45°
, 60° , and 90° as well as 0,  ,
 ,  ,
and  (A-3) |
| Solve first and second degree trigonometric equations over specified domains (A-4) |
| Determine the general solutions to trigonometric equations where the domain is the set of real numbers (A-5) |
Draw (using technology), sketch, and analyze the
graphs of sine, cosine, and tangent functions and
their inverses for
|
| Perform, analyze, and create transformations of functions and relations that are described by equations or graphs |
Describe how various translations of functions affect
graphs and their related equations:
|
Describe how various stretches or compressions of
functions affect graphs and their related equations:
|
Describe how reflections of functions in both axes
and in the line 
affect graphs and their related equations:
|
Using the graph and/or the equation of  ,
describe and sketch  (B-4) |
Using the graph and/or the equation of  ,
describe and sketch  (B-5) |
| Describe and perform single transformations and combinations of transformations on functions and relations (B-6) |
| Model and solve problems using trigonometric functions (B-7) |
or
(B-1) 
(B-2) 
(B-3)
| Solve exponential, logarithmic, and trigonometric equations and identities |
| Analyze trigonometric identities graphically and verify them algebraically (C-1) |
| Use sum, difference, and double angle identities for sine, cosine, and tangent to verify and simplify trigonometric expressions (C-2) |
| Represent and analyze exponential and logarithmic functions, using technology as appropriate |
| Solve exponential, logarithmic, and trigonometric equations and identities |
| Graph and analyze exponential functions (D-1) |
| Solve exponential equations having bases that are powers of one another (D-2) |
| Define logarithm and change exponential statements to equivalent logarithmic statements and vice versa (D-3) |
| Graph and analyze logarithmic functions (D-4) |
| Simplify and expand logarithmic expressions using the laws of logarithms (D-5) |
| Solve and verify exponential and logarithmic equations (D-6) |
| Use the concept of base e in analyzing problems involving exponential and logarithmic functions (D-7) |
| Model, and apply exponential and logarithmic functions (D-8) |
| Solve problems based on the counting of sets, using techniques such as the fundamental counting principle, permutations, and combinationss |
| Use factorial notation and the fundamental counting principle for solving problems (E-1) |
| Determine the number of permutations of n different objects taken r at a time, and use this to solve problems (E-2) |
| Determine the number of combinations of n different objects taken r at a time, and use this to solve problems (E-3) |
Solve problems, using the binomial theorem for 
where N belongs to the set of natural numbers (E-4) |
| Classify conic sections, using their shapes and equations |
| Classify conic sections according to shape or according to a given equation in general or standard (completed square) form (vertical or horizontal axis of symmetry only) (F-1) |
| Convert a given equation of a conic section from general to standard form and vice versa (F-2) |
Sketch and analyze the graphs of conic sections for:
|
| Model the probability of a compound event, and solve problems based on the combining of simpler probabilities |
| Construct a sample space for two or three events (G-1) |
| Solve problems involving the probabilities of independent and dependent events (G-2) |
| Solve problems using the probabilities of mutually exclusive and complementary events (G-3) |
| Determine the conditional probability of two events (G-4) |
Solve probability problems involving
|
| Generate and analyze exponential patterns |
| Derive and apply expressions to represent general terms for geometric growth (H-1) |
| Solve problems involving finite geometric series (H-2) |
| Apply infinite geometric processes to solve problems (H-3) |
| Use normal and binomial probability distributions to solve problems involving uncertainty |
| Find the population standard deviation of a data set or probability distribution, using technology (I-1) |
| Use z-scores and z-score tables to solve problems (I-2) |
| Use the normal distribution and the normal approximation to the binomial distribution to solve problems involving confidence intervals for large samples (I-3) |
