Saskatchewan · Grade 12
Pre-Calculus 30
Saskatchewan’s Grade 12 math course, from Trigonometry to Permutations, Combinations, and the Binomial Theorem.
- Units
- 3
- Lessons
- 13
- Skills
- 29
- Provincial exam
- None
- Official curriculum
- Saskatchewan Ministry of Education
Unit by unit
Every skill in the course, with its official code.
Unit 1 · 11 skills
Trigonometry
Angles in Standard Position
Standard position, degrees, and radians
I can sketch an angle in standard position and convert between degrees and radians.
Official code: PC30.1
Coterminal angles and arc length
I can find coterminal angles and use radians to find arc length.
Official code: PC30.1
The Unit Circle and Trigonometric Ratios
The unit circle and the six ratios
I can derive the unit circle and give the six trig ratios for any angle.
Official code: PC30.2
Exact values at special angles
I can find exact trig ratios for special angles without a calculator.
Official code: PC30.2
Solving problems with trigonometric ratios
I can find angles with a given ratio and solve trig problems.
Official code: PC30.2
Graphs of Trigonometric Functions
Graphing sine, cosine, and tangent
I can graph sin, cos, and tan and state their key characteristics.
Official code: PC30.3
Transforming trigonometric graphs
I can transform sine and cosine graphs and write their equations.
Official code: PC30.3
Trigonometric Equations
Solving trigonometric equations algebraically
I can solve a trig equation algebraically for exact solutions in a domain.
Official code: PC30.4
General solutions of trigonometric equations
I can write the general solution of a trig equation.
Official code: PC30.4
Trigonometric Identities
Reciprocal, quotient, and Pythagorean identities
I can prove an identity using reciprocal, quotient, and Pythagorean identities.
Official code: PC30.5
Sum, difference, and double-angle identities
I can use sum, difference, and double-angle identities to find exact values and prove identities.
Official code: PC30.5
The official wording · 11 outcomes
- PC30.1
- angles to angles in standard position, expressed in degrees and radians.
- PC30.1
- angles to angles in standard position, expressed in degrees and radians.
- PC30.2
- the unit circle and its relationship to the six trigonometric ratios for any angle in standard position.
- PC30.2
- the six trigonometric ratios for any angle in standard position.
- PC30.2
- the six trigonometric ratios for any angle in standard position.
- PC30.3
- the graphs of the primary trigonometric functions.
- PC30.3
- the graphs of the primary trigonometric functions.
- PC30.4
- first- and second-degree trigonometric equations.
- PC30.4
- first- and second-degree trigonometric equations.
- PC30.5
- trigonometric identities including: • reciprocal identities • quotient identities • Pythagorean identities
- PC30.5
- • sum or difference identities (restricted to sine, cosine, and tangent) • 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; positive angles rotate counterclockwise.
The unit circle x² + y² = 1 comes from the Pythagorean theorem / distance formula on a radius-1 circle.
y = sinx and y = cosx have amplitude 1, period 2π, range [−1, 1]; cos is sin shifted by π/2.
First-degree trig equations isolate the ratio, then use special angles and reference angles.
Reciprocal (cscx = 1/sinx), quotient (tanx = sinx/cosx), and Pythagorean (sin²x + cos²x = 1) identities are the toolkit.
Watch out for
- Treating a radian as a small fixed number instead of a ratio (arc/radius).
- Swapping sine and cosine (y vs x).
- Giving tangent an amplitude (it has none).
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 2 · 14 skills
Functions and Transformations
Operations and Compositions of Functions
Combining functions arithmetically
I can add, subtract, multiply, and divide functions and find the new domain.
Official code: PC30.6
Composing functions
I can compose functions, evaluate the result, and find its domain.
Official code: PC30.6
Transformations of Functions
Translations and stretches of functions
I can transform y = f(x) with translations and stretches and write its equation.
Official code: PC30.7
Reflections and Inverses
Reflecting functions
I can reflect a function through the x-axis, y-axis, or line y = x.
Official code: PC30.8
Inverse relations and functions
I can find an inverse and decide whether it is a function.
Official code: PC30.8
Logarithms
Logarithms and exponents
I can convert between logarithmic and exponential form and evaluate logarithms.
Official code: PC30.9
Laws of logarithms
I can derive and apply the product, quotient, and power laws of logarithms.
Official code: PC30.9
Solving exponential and logarithmic equations
I can solve exponential and logarithmic equations and reject extraneous solutions.
Official code: PC30.9
Graphing exponential and logarithmic functions
I can graph exponential and logarithmic functions and see they are inverses.
Official code: PC30.9
Polynomial Functions
Polynomial division and the factor theorem
I can divide polynomials and use the Remainder and Factor theorems.
Official code: PC30.10
Graphing polynomial functions
I can sketch a polynomial function from its zeros, degree, and leading coefficient.
Official code: PC30.10
Modelling and solving with polynomial functions
I can model a situation with a polynomial function and solve it from the graph.
Official code: PC30.10
Radical and Rational Functions
Radical functions
I can graph a radical function and read its domain, range, and roots.
Official code: PC30.11
Rational functions
I can sketch a rational function and locate its asymptotes and holes.
Official code: PC30.11
The official wording · 14 outcomes
- PC30.6
- operations on, and compositions of, functions.
- PC30.6
- operations on, and compositions of, functions.
- PC30.7
- transformations to include functions (given in equation or graph form) in general, including horizontal and vertical translations, and horizontal and vertical stretches.
- PC30.8
- reflections through the: • x-axis • y-axis • line y = x.
- PC30.8
- functions, relations, inverses and their related equations resulting from reflections through the: • x-axis • y-axis • line y = x.
- PC30.9
- logarithms including: • evaluating logarithms • relating logarithms to exponents
- PC30.9
- • deriving laws of logarithms
- PC30.9
- • solving equations
- PC30.9
- • graphing.
- PC30.10
- polynomials and polynomial functions of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients).
- PC30.10
- polynomials and polynomial functions of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients).
- PC30.10
- polynomials and polynomial functions of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients).
- PC30.11
- radical and rational functions with restrictions on the domain.
- PC30.11
- radical and rational functions with restrictions on the domain.
Key ideas
(f + g)(x) = f(x) + g(x), and similarly for −, ×, ÷ — combine the outputs at each x.
In y − k = af(b(x − h)): a is vertical stretch, b is horizontal stretch (by 1/b), h is horizontal shift, k is vertical shift.
y = −f(x) reflects through the x-axis; y = f(−x) reflects through the y-axis.
logb(x) = y means bʸ = x — a logarithm IS an exponent.
Long division and synthetic division divide a polynomial by (x − a); synthetic is a shortcut for that form.
Watch out for
- Forgetting to exclude domain values where a quotient's denominator is zero.
- Treating a horizontal stretch by factor b instead of 1/b.
- Confusing −f(x) (x-axis) with f(−x) (y-axis).
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 3 · 4 skills
Permutations, Combinations, and the Binomial Theorem
Permutations
The fundamental counting principle
I can use the fundamental counting principle to count arrangements.
Official code: PC30.12
The permutation formula
I can compute nPr and handle repeated elements.
Official code: PC30.12
Combinations and the Binomial Theorem
Combinations
I can compute nCr and tell combinations apart from permutations.
Official code: PC30.13
Pascal's triangle and the binomial theorem
I can expand (x + y)ⁿ with the binomial theorem and find a specific term.
Official code: PC30.13
The official wording · 4 outcomes
- PC30.12
- permutations, including the fundamental counting principle.
- PC30.12
- permutations, including the fundamental counting principle.
- PC30.13
- combinations of elements, including the application to the binomial theorem.
- PC30.13
- combinations of elements, including the application to the binomial theorem.
Key ideas
The fundamental counting principle multiplies the number of choices at each stage.
nCr = n! ÷ [r!(n − r)!] counts unordered selections; order does not matter.
We multiply, not add, because each choice at one stage pairs with every choice at the next.
nCr = nC(n−r) because choosing what to include is the same as choosing what to leave out.
Lists and tree diagrams organize the counting for small cases.
Watch out for
- Adding stage counts instead of multiplying.
- Using combinations when order matters.
- Miscounting when repetition is or isn't allowed.
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.
Which course?
Saskatchewan has 4 math courses for Grade 12. Here they are side by side.
- Calculus 303 units · 19 skillsNo provincial examWhat it coversFunctions and Limits · Differentiation · Integration
- Foundations of Mathematics 306 units · 23 skillsNo provincial examWhat it coversFinancial Mathematics · Logical Reasoning · Set Theory · Probability · Modelling Data with Functions · Research and Presentation Project
- Pre-Calculus 30This course3 units · 29 skillsNo provincial examWhat it coversTrigonometry · Functions and Transformations · Permutations, Combinations, and the Binomial Theorem
- Workplace and Apprenticeship Mathematics 303 units · 23 skillsNo provincial examWhat it coversReasoning and Measurement · Financial and Business Mathematics · Linear Relations and Statistics
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 Saskatchewan’s own curriculum for Pre-Calculus 30.
Textbooks
The textbooks Saskatchewan Ministry of Education lists for Pre-Calculus 30:
- McGraw-Hill Ryerson Pre-Calculus 12
From core resources, read October 27, 2026. curriculum.gov.sk.ca
Study it in MapleMind
MapleMind teaches Pre-Calculus 30 one skill at a time. Each skill gets a short lesson, practice as you go and a check worth up to three stars. It remembers where you stopped.
Course Companion
Your year in one workbook
A fun way to keep Pre-Calculus 30 organized, get to know your child better and see early when they need a hand. Fill it in on a screen, or print it.
- Pages
- 26
- Fillable fields
- 1,357
- Price
- $4.99
Questions about Pre-Calculus 30
What is Pre-Calculus 30?
Saskatchewan’s Grade 12 math course: 3 units and 29 skills, from Trigonometry to Permutations, Combinations, and the Binomial Theorem.
What units are in Pre-Calculus 30?
1. Trigonometry, 2. Functions and Transformations and 3. Permutations, Combinations, and the Binomial Theorem.
Is there a provincial exam for Pre-Calculus 30?
No. Saskatchewan gives no provincial exam for Pre-Calculus 30.
What textbook does Pre-Calculus 30 use?
The textbooks Saskatchewan Ministry of Education lists for Pre-Calculus 30: McGraw-Hill Ryerson Pre-Calculus 12.
Can MapleMind help with Pre-Calculus 30?
Yes. MapleMind teaches every skill of Pre-Calculus 30, 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 30
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