Manitoba · Grade 12
Pre-Calculus Mathematics, Grade 12 (40S)
Manitoba’s Grade 12 math course, from Trigonometry to Permutations, Combinations and Binomial Theorem.
- Units
- 3
- Lessons
- 11
- Skills
- 34
- Provincial exam
- 20% of the final mark
- Official curriculum
- Manitoba Education
Unit by unit
Every skill in the course, with its official code.
Unit 1 · 11 skills
Trigonometry
Angles in Standard Position
Sketching and converting angles
I can sketch angles in standard position and convert between degrees and radians.
Official code: 12P.T.1
Coterminal angles and arc length
I can find coterminal angles and use radian measure to find arc length.
Official code: 12P.T.1
The Unit Circle and Trigonometric Ratios
The equation of the unit circle
I can derive and apply the equation of the unit circle.
Official code: 12P.T.2
Exact trigonometric ratios
I can find exact trigonometric ratios for special angles.
Official code: 12P.T.3
Solving with trigonometric ratios
I can solve for angles and ratios using the six trigonometric ratios.
Official code: 12P.T.3
Trigonometric Functions and Graphs
Graphs of sine, cosine, and tangent
I can graph the basic sine, cosine, and tangent functions and read their characteristics.
Official code: 12P.T.4
Transforming trigonometric graphs
I can transform sine and cosine graphs and write their equations.
Official code: 12P.T.4
Solving trigonometric equations
I can solve trigonometric equations algebraically over a restricted domain.
Official code: 12P.T.5
General solutions and identities in equations
I can write the general solution of a trigonometric equation and use identities to solve.
Official code: 12P.T.5
Trigonometric Identities
Proving with reciprocal, quotient, and Pythagorean identities
I can prove trigonometric identities using the basic identity families.
Official code: 12P.T.6
Sum, difference, and double-angle identities
I can use sum, difference, and double-angle identities.
Official code: 12P.T.6
The official wording · 11 outcomes
- 12P.T.1
- Demonstrate an understanding of angles in standard position, expressed in degrees and radians.
- 12P.T.1
- Demonstrate an understanding of angles in standard position, expressed in degrees and radians.
- 12P.T.2
- Develop and apply the equation of the unit circle.
- 12P.T.3
- Solve problems, using the six trigonometric ratios for angles expressed in radians and degrees.
- 12P.T.3
- Solve problems, using the six trigonometric ratios for angles expressed in radians and degrees.
- 12P.T.4
- Graph and analyze the trigonometric functions sine, cosine, and tangent to solve problems.
- 12P.T.4
- Graph and analyze the trigonometric functions sine, cosine, and tangent to solve problems.
- 12P.T.5
- Solve, algebraically and graphically, first- and second-degree trigonometric equations with the domain expressed in degrees and radians.
- 12P.T.5
- Solve, algebraically and graphically, first- and second-degree trigonometric equations with the domain expressed in degrees and radians.
- 12P.T.6
- Prove trigonometric identities, using Q Q reciprocal identities Q Q quotient identities Q Q Pythagorean identities
- 12P.T.6
- Prove trigonometric identities, using Q Q sum or difference identities (restricted to sine, cosine, and tangent) Q Q double-angle identities (restricted to sine, cosine, and tangent)
Key ideas
An angle in standard position has its vertex at the origin and initial arm on the positive x-axis.
The unit circle x squared plus y squared equals 1 comes from the Pythagorean theorem.
Sine and cosine repeat every 2pi; tangent repeats every pi and has asymptotes.
An identity holds for every permissible value; an equation holds only for some.
180 degrees equals pi radians, so we convert by multiplying by pi/180 or 180/pi.
Watch out for
- Converting with the ratio inverted (using 180/pi when pi/180 is needed).
- Forgetting that the unit circle has radius 1.
- Giving the tangent function an amplitude (it has none).
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 2 · 18 skills
Relations and Functions
Operations and Compositions of Functions
Operations on functions
I can add, subtract, multiply, and divide functions and find the domain.
Official code: 12P.R.1
Compositions of functions
I can form and evaluate compositions of functions.
Official code: 12P.R.1
Transformations of Functions
Translations of graphs
I can translate a graph horizontally and vertically.
Official code: 12P.R.2
Compressions and stretches
I can stretch and compress a graph horizontally and vertically.
Official code: 12P.R.3
Combining transformations
I can apply several transformations to a graph at once.
Official code: 12P.R.4
Reflections of graphs
I can reflect a graph through the axes and the line y = x.
Official code: 12P.R.5
Inverses of relations
I can find the inverse of a relation and decide whether it is a function.
Official code: 12P.R.6
Logarithms
Understanding logarithms
I can convert between logarithmic and exponential form and evaluate a logarithm.
Official code: 12P.R.7
Laws of logarithms
I can use the product, quotient, and power laws of logarithms.
Official code: 12P.R.8
Exponential and Logarithmic Functions
Graphing exponential functions
I can graph and analyze an exponential function.
Official code: 12P.R.9
Graphing logarithmic functions
I can graph and analyze a logarithmic function.
Official code: 12P.R.9
Solving exponential and logarithmic equations
I can solve exponential and logarithmic equations.
Official code: 12P.R.10
Applications of exponential and logarithmic equations
I can solve real problems using exponential and logarithmic equations.
Official code: 12P.R.10
Polynomial, Radical, and Rational Functions
Long and synthetic division of polynomials
I can divide a polynomial by a binomial using long or synthetic division.
Official code: 12P.R.11
The remainder and factor theorems
I can use the remainder and factor theorems to factor a polynomial.
Official code: 12P.R.11
Graphing polynomial functions
I can graph a polynomial function and relate its zeros to its graph.
Official code: 12P.R.12
Radical functions
I can graph a radical function and state its domain and range.
Official code: 12P.R.13
Rational functions
I can graph a rational function and identify its asymptotes and holes.
Official code: 12P.R.14
The official wording · 18 outcomes
- 12P.R.1
- Demonstrate an understanding of operations on, and compositions of, functions.
- 12P.R.1
- Demonstrate an understanding of operations on, and compositions of, functions.
- 12P.R.2
- Demonstrate an understanding of the effects of horizontal and vertical translations on the graphs of functions and their related equations.
- 12P.R.3
- Demonstrate an understanding of the effects of horizontal and vertical compressions and stretches on the graphs of functions and their related equations.
- 12P.R.4
- Apply translations, compressions, and stretches to the graphs and equations of functions.
- 12P.R.5
- Demonstrate an understanding of the effects of reflections on the graphs of functions and their related equations, including reflections through the Q Q x-axis Q Q y-axis Q Q line y = x
- 12P.R.6
- Demonstrate an understanding of inverses of relations.
- 12P.R.7
- Demonstrate an understanding of logarithms.
- 12P.R.8
- Demonstrate an understanding of the product, quotient, and power laws of logarithms.
- 12P.R.9
- Graph and analyze exponential and logarithmic functions.
- 12P.R.9
- Graph and analyze exponential and logarithmic functions.
- 12P.R.10
- Solve problems that involve exponential and logarithmic equations.
- 12P.R.10
- Solve problems that involve exponential and logarithmic equations.
- 12P.R.11
- Demonstrate an understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients).
- 12P.R.11
- Demonstrate an understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients).
- 12P.R.12
- Graph and analyze polynomial functions (limited to polynomial functions of degree ≤ 5).
- 12P.R.13
- Graph and analyze radical functions (limited to functions involving one radical).
- 12P.R.14
- Graph and analyze rational functions (limited to numerators and denominators that are monomials, binomials, or trinomials).
Key ideas
Functions combine value by value: (f + g)(x) = f(x) + g(x).
y - k = f(x) shifts the graph up by k; y = f(x - h) shifts it right by h.
log base b of x equals y means b to the power y equals x.
An exponential function y = a to the x has a horizontal asymptote at y = 0.
Synthetic division is a shortcut for dividing by x - a.
Watch out for
- Combining functions without restricting the domain.
- Shifting y = f(x - h) left instead of right.
- Confusing the base and the argument of a logarithm.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 3 · 5 skills
Permutations, Combinations and Binomial Theorem
Counting and Arrangements
The fundamental counting principle
I can count outcomes using the fundamental counting principle.
Official code: 12P.P.1
Permutations
I can count arrangements using permutations.
Official code: 12P.P.2
Combinations
I can count selections using combinations.
Official code: 12P.P.3
The Binomial Theorem
Pascal's triangle and binomial patterns
I can use Pascal's triangle to find binomial coefficients.
Official code: 12P.P.4
Expanding with the binomial theorem
I can expand a binomial power and find a specific term.
Official code: 12P.P.4
The official wording · 5 outcomes
- 12P.P.1
- Apply the fundamental counting principle to solve problems.
- 12P.P.2
- Determine the number of permutations of n elements taken r at a time to solve problems.
- 12P.P.3
- Determine the number of combinations of n different elements taken r at a time to solve problems.
- 12P.P.4
- Expand powers of a binomial in a variety of ways, including using the binomial theorem (restricted to exponents that are natural numbers).
- 12P.P.4
- Expand powers of a binomial in a variety of ways, including using the binomial theorem (restricted to exponents that are natural numbers).
Key ideas
When choices are made in sequence, the counts multiply.
Each row of Pascal's triangle gives the coefficients of a binomial expansion.
A tree diagram lays out every combination of choices.
Each entry is the sum of the two entries above it, and equals a combination.
A permutation is an arrangement where order matters.
Watch out for
- Adding the number of choices instead of multiplying.
- Getting the coefficients out of order.
- Missing a stage of choices.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Plan the term
Pick your term and the days you study. Each unit gets its share of the weeks and comes back a week later for a review. The last two weeks go over the whole course.
The mark you need
Your class mark counts for 80% of the final mark, the exam for 20%.
You need
50% on the exam
With 75% in class, your final mark lands between 60% (0 on the exam) and 80% (100% on it).
Which course?
Manitoba has 4 math courses for Grade 12. Here they are side by side.
- Applied Mathematics, Grade 12 (40S)6 units · 27 skillsGrade 12 Applied Mathematics Achievement TestWhat it coversFinancial Mathematics · Logical Reasoning · Probability · Relations and Functions · Mathematics Research Project · Design and Measurement
- Essential Mathematics, Grade 12 (40S)9 units · 24 skillsGrade 12 Essential Mathematics Achievement TestWhat it coversAnalysis of Games and Numbers · Vehicle Finance · Statistics · Precision Measurement · Career Life · Home Finance · Geometry and Trigonometry · Business Finance · Probability
- Introduction to Calculus, Grade 12 (40S)45S4 units · 19 skillsNo provincial examWhat it coversLimits · Derivatives · Applications of Derivatives · Integration (Integrals)
- Pre-Calculus Mathematics, Grade 12 (40S)This course3 units · 34 skillsGrade 12 Pre-Calculus Mathematics Achievement TestWhat it coversTrigonometry · Relations and Functions · Permutations, Combinations and Binomial Theorem
What a university, college or program asks for is theirs to say: check its admission page, and your school’s course guide.
The official curriculum
This page follows Manitoba’s own curriculum for Pre-Calculus Mathematics, Grade 12 (40S).
Study it in MapleMind
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Course Companion
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Questions about Pre-Calculus Mathematics, Grade 12 (40S)
What is Pre-Calculus Mathematics, Grade 12 (40S)?
Manitoba’s Grade 12 math course: 3 units and 34 skills, from Trigonometry to Permutations, Combinations and Binomial Theorem.
What units are in Pre-Calculus Mathematics, Grade 12 (40S)?
1. Trigonometry, 2. Relations and Functions and 3. Permutations, Combinations and Binomial Theorem.
Is there a provincial exam for Pre-Calculus Mathematics, Grade 12 (40S)?
Yes. The Grade 12 Pre-Calculus Mathematics Achievement Test counts for 20% of the final mark. Next sitting: January 28, 2027.
Can MapleMind help with Pre-Calculus Mathematics, Grade 12 (40S)?
Yes. MapleMind teaches every skill of Pre-Calculus Mathematics, Grade 12 (40S), step by step, with practice and checks, and its tutor answers questions about any of them. It’s free with daily limits, on iPhone, Android and the web.
Get ready for Pre-Calculus Mathematics, Grade 12 (40S)
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