AlbertaAB Grade 12 Mathematics 30-1 Curriculum
Video lessons and practice for every Mathematics 30-1 topic. Aligned to what Alberta Grade 12 schools teach, from trigonometry to the binomial theorem.
AB Grade 12 Mathematics 30-1 Curriculum | StudyPugHelp
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 |
Alberta Grade 12 Mathematics 30-1 Topics
Mathematics 30-1 is one of Alberta's most rigorous Grade 12 math courses, designed for students planning to pursue post-secondary programs in science, technology, engineering, or mathematics. The course is broad and covers five major strands: trigonometry, transformations and functions, exponential and logarithmic functions, polynomial and rational functions, and permutations and combinations.
Trigonometry in Math 30-1
Students begin by working with angles in standard position, converting between degrees and radians, and identifying coterminal angles. The unit circle is derived from the Pythagorean theorem and used to define trigonometric ratios. Students then move into graphing sine, cosine, and tangent functions, applying transformations such as amplitude changes, period shifts, and phase shifts. Solving trigonometric equations — both algebraically and graphically — and proving trigonometric identities round out this major section of the course.
Transformations and Functions
This strand covers how functions behave under translations, stretches, reflections, and combinations of these transformations. Students analyze the effects of parameters like a, b, h, and k on function graphs. Composite functions and inverse functions are introduced, with attention to domain and range restrictions. Understanding these concepts is essential for every other topic in Math 30-1.
Exponential and Logarithmic Functions
Students convert between logarithmic and exponential forms, evaluate logarithms without technology, and apply the laws of logarithms to simplify expressions and solve equations. Graphs of exponential and logarithmic functions are sketched and analyzed, including transformations. Real-world applications such as compound interest, population growth, and pH calculations are explored through exponential and logarithmic equations.
Polynomial and Rational Functions
Mathematics 30-1 revisits polynomial functions with a focus on factoring using long division, synthetic division, and the factor theorem. Students identify zeros, their multiplicities, and the end behaviour of polynomial graphs. Radical and rational functions are introduced, with students determining asymptotes, holes, and domain restrictions. Graphical methods are used to solve both radical and rational equations.
Permutations, Combinations, and the Binomial Theorem
The final strand introduces counting principles, including the fundamental counting principle, permutations, and combinations. Students use graphic organizers to organize possibilities and solve problems. The binomial theorem and Pascal's triangle are applied to expand binomial expressions efficiently.
- Angles in standard position and radian measure
- Unit circle and trigonometric ratios
- Graphing and transforming trigonometric functions
- Trigonometric equations and identities
- Function operations and composite functions
- Translations, stretches, and reflections of functions
- Inverse functions and their restrictions
- Logarithms and their laws
- Exponential and logarithmic functions and equations
- Polynomial functions, zeros, and multiplicities
- Radical and rational functions
- Permutations, combinations, and the binomial theorem
StudyPug covers every one of these topics with video lessons and practice problems aligned to the Alberta Mathematics 30-1 curriculum.