Manitoba
Skills available for Manitoba grade 12 math curriculum
Objectives are in black and IXL math skills are in dark green. Hold your mouse over the name of a skill to view a sample question. Click on the name of a skill to practise that skill.
Show alignments for:
- WNCP Common Curriculum Frameworks: Foundations of Mathematics Grade 12 WNCP Common Curriculum Frameworks: Foundations of Mathematics Grade 12
- WNCP Common Curriculum Frameworks: Pre-Calculus Grade 12 WNCP Common Curriculum Frameworks: Pre-Calculus Grade 12
- WNCP Common Curriculum Frameworks: Apprenticeship and Workplace Mathematics Grade 12 WNCP Common Curriculum Frameworks: Apprenticeship and Workplace Mathematics Grade 12
Actions
T Trigonometry
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T.1 Develop trigonometric reasoning.
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T.1.1 Demonstrate an understanding of angles in standard position, expressed in degrees and radians.
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T.1.2 Develop and apply the equation of the unit circle.
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T.1.3 Solve problems, using the six trigonometric ratios for angles expressed in radians and degrees.
- Find trigonometric ratios using right triangles (12-N.5)
- Inverses of trigonometric functions (12-N.8)
- Trigonometric ratios: find a side length (12-N.10)
- Trigonometric ratios: find an angle measure (12-N.11)
- Solve a right triangle (12-N.12)
- Law of Sines (12-N.13)
- Law of Cosines (12-N.14)
- Solve a triangle (12-N.15)
- Area of a triangle: sine formula (12-N.16)
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T.1.4 Graph and analyze the trigonometric functions sine, cosine and tangent to solve problems.
- Find properties of sine functions (12-O.1)
- Write equations of sine functions from graphs (12-O.2)
- Write equations of sine functions using properties (12-O.3)
- Graph sine functions (12-O.4)
- Find properties of cosine functions (12-O.5)
- Write equations of cosine functions from graphs (12-O.6)
- Write equations of cosine functions using properties (12-O.7)
- Graph cosine functions (12-O.8)
- Graph sine and cosine functions (12-O.9)
- Symmetry and periodicity of trigonometric functions (12-P.2)
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T.1.5 Solve, algebraically and graphically, first and second degree trigonometric equations with the domain expressed in degrees and radians.
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T.1.6 Prove trigonometric identities, using:
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T.1.6.1 reciprocal identities
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T.1.6.2 quotient identities
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T.1.6.3 Pythagorean identities
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T.1.6.4 sum or difference identities (restricted to sine, cosine and tangent)
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T.1.6.5 double-angle identities (restricted to sine, cosine and tangent).
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R Relations and Functions
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R.1 Develop algebraic and graphical reasoning through the study of relations.
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R.1.1 Demonstrate an understanding of operations on, and compositions of, functions.
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R.1.2 Demonstrate an understanding of the effects of horizontal and vertical translations on the graphs of functions and their related equations.
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R.1.3 Demonstrate an understanding of the effects of horizontal and vertical stretches on the graphs of functions and their related equations.
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R.1.4 Apply translations and stretches to the graphs and equations of functions.
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R.1.5 Demonstrate an understanding of the effects of reflections on the graphs of functions and their related equations, including reflections through the:
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R.1.5.1 x-axis
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R.1.5.2 y-axis
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R.1.5.3 line y = x.
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R.1.6 Demonstrate an understanding of inverses of relations.
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R.1.7 Demonstrate an understanding of logarithms.
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R.1.8 Demonstrate an understanding of the product, quotient and power laws of logarithms.
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R.1.9 Graph and analyze exponential and logarithmic functions.
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R.1.10 Solve problems that involve exponential and logarithmic equations.
- Solve exponential equations by rewriting the base (12-G.4)
- Solve exponential equations using common logarithms (12-G.5)
- Solve logarithmic equations I (12-G.6)
- Solve logarithmic equations II (12-G.7)
- Exponential growth and decay: word problems (12-G.11)
- Compound interest: word problems (12-G.12)
- Continuously compounded interest: word problems (12-G.13)
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R.1.11 Demonstrate an understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree less than or equal to 5 with integral coefficients).
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R.1.12 Graph and analyze polynomial functions (limited to polynomial functions of degree less than or equal to 5).
- Characteristics of quadratic functions (12-C.1)
- Graph a quadratic function (12-C.3)
- Match quadratic functions and graphs (12-C.4)
- Write a polynomial from its roots (12-D.2)
- Find the roots of factored polynomials (12-D.3)
- Rational root theorem (12-D.4)
- Complex conjugate theorem (12-D.5)
- Conjugate root theorems (12-D.6)
- Match polynomials and graphs (12-D.9)
- Graph parabolas (12-Q.3)
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R.1.13 Graph and analyze radical functions (limited to functions involving one radical).
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R.1.14 Graph and analyze rational functions (limited to numerators and denominators that are monomials, binomials or trinomials).
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PCB Permutations, Combinations and Binomial Theorem
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PCB.1 Develop algebraic and numeric reasoning that involves combinatorics.
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PCB.1.1 Apply the fundamental counting principle to solve problems.
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PCB.1.2 Determine the number of permutations of n elements taken r at a time to solve problems.
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PCB.1.3 Determine the number of combinations of n different elements taken r at a time to solve problems.
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PCB.1.4 Expand powers of a binomial in a variety of ways, including using the binomial theorem (restricted to exponents that are natural numbers).
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