AlbertaGrade 12 Math Courses - Alberta Curriculum
Discover Alberta's Grade 12 Math curriculum, focusing on Mathematics 30-1. This courses offers advanced mathematical concepts, preparing students for post-secondary education in STEM fields.
Alberta Grade 12 Math Curriculum - Mathematics 30-1Help
LO_ID | Learning Outcome-Skills & Procedures | StudyPug Topic |
|---|---|---|
AB.SO.30-1.1 | Demonstrate an understanding of angles in standard position, expressed in degrees and radians: Sketch angles in standard position given measures in degrees or radians; Convert between degree and radian measures; Determine coterminal angles in degrees and radians; Relate radian measure to arc length on a circle |
AB.SO.30-1.2 | Develop and apply the equation of the unit circle: Derive the equation of the unit circle from the Pythagorean theorem; Describe trigonometric ratios using points on the unit circle; Generalize the equation of a circle with center (0,0) and radius r |
AB.SO.30-1.3 | Solve problems using the six trigonometric ratios for angles expressed in radians and degrees: Determine approximate and exact values of trigonometric ratios; Use technology to find trigonometric ratios for any angle; Determine angles given trigonometric ratios; Solve problems using trigonometric ratios |
AB.SO.30-1.4 | Graph and analyze the trigonometric functions sine, cosine and tangent to solve problems: Sketch and analyze graphs of sine, cosine, and tangent functions; Determine characteristics of trigonometric graphs (amplitude, period, phase shift, etc.); Apply transformations to trigonometric functions; Model situations using trigonometric functions |
AB.SO.30-1.5 | Solve, algebraically and graphically, first and second degree trigonometric equations with the domain expressed in degrees and radians: Verify solutions to trigonometric equations; Solve trigonometric equations algebraically and graphically; Determine general solutions of trigonometric equations; Relate solutions to zeros of trigonometric functions |
AB.SO.30-1.6 | Prove trigonometric identities, using various trigonometric identities: Verify trigonometric identities numerically and graphically; Prove trigonometric identities algebraically; Apply trigonometric identities to solve problems |
AB.SO.30-1.7 | Demonstrate an understanding of operations on, and compositions of, functions: Perform operations on functions (addition, subtraction, multiplication, division); Determine composite functions; Determine the domain and range of composite functions; Graph composite functions |
AB.SO.30-1.8 | Demonstrate an understanding of the effects of horizontal and vertical translations on the graphs of functions and their related equations: Analyze the effects of h and k in y-k = f(x-h); Sketch translated functions; Write equations of translated functions |
AB.SO.30-1.9 | Demonstrate an understanding of the effects of horizontal and vertical stretches on the graphs of functions and their related equations: Analyze the effects of a and b in y = af(bx); Sketch stretched functions; Write equations of stretched functions |
AB.SO.30-1.10 | Apply translations and stretches to the graphs and equations of functions: Sketch graphs of functions with multiple transformations; Write equations of functions with multiple transformations |
AB.SO.30-1.11 | Demonstrate an understanding of the effects of reflections on the graphs of functions and their related equations: Analyze reflections through x-axis, y-axis, and y=x; Sketch reflected functions; Write equations of reflected functions |
AB.SO.30-1.12 | Demonstrate an understanding of inverses of relations: Sketch inverse relations and functions; Determine if inverses are functions; Write equations of inverse functions; Determine restrictions for inverse functions |
AB.SO.30-1.13 | Demonstrate an understanding of logarithms: Convert between logarithmic and exponential forms; Evaluate logarithms without technology; Estimate values of logarithms |
AB.SO.30-1.14 | Demonstrate an understanding of the product, quotient and power laws of logarithms: Develop and apply laws of logarithms; Simplify logarithmic expressions; Solve logarithmic equations |
AB.SO.30-1.15 | Graph and analyze exponential and logarithmic functions: Sketch and analyze exponential and logarithmic functions; Apply transformations to exponential and logarithmic functions; Solve problems using exponential and logarithmic functions |
AB.SO.30-1.16 | Solve problems that involve exponential and logarithmic equations: Solve exponential equations; Solve logarithmic equations; Apply exponential and logarithmic equations to real-world problems |
AB.SO.30-1.17 | Demonstrate an understanding of factoring polynomials of degree greater than 2: Factor polynomials using long division and synthetic division; Apply the factor theorem; Relate factors to zeros of polynomial functions |
AB.SO.30-1.18 | Graph and analyze polynomial functions: Identify characteristics of polynomial functions from equations and graphs; Determine zeros and their multiplicities; Sketch polynomial functions |
AB.SO.30-1.19 | Graph and analyze radical functions: Sketch and analyze radical functions; Apply transformations to radical functions; Solve radical equations graphically |
AB.SO.30-1.20 | Graph and analyze rational functions: Determine characteristics of rational functions (asymptotes, holes, etc.); Sketch rational functions; Solve rational equations graphically |
AB.SO.30-1.21 | Apply the fundamental counting principle to solve problems: Use graphic organizers to count possibilities; Apply the fundamental counting principle to solve problems |
AB.SO.30-1.22 | Determine the number of permutations of n elements taken r at a time to solve problems: Calculate permutations; Solve problems involving permutations |
AB.SO.30-1.23 | Determine the number of combinations of n different elements taken r at a time to solve problems: Calculate combinations; Solve problems involving combinations |
AB.SO.30-1.24 | Expand powers of a binomial in a variety of ways, including using the binomial theorem: Expand binomials using various methods; Apply the binomial theorem; Use Pascal's triangle in binomial expansions |