Saskatchewan · Grade 11
Pre-Calculus 20
Saskatchewan’s Grade 11 math course, from Absolute Value and Radicals to Inequalities, Sequences, and Reciprocals.
- Units
- 5
- Lessons
- 11
- Skills
- 27
- Provincial exam
- None
- Official curriculum
- Saskatchewan Ministry of Education
Unit by unit
Every skill in the course, with its official code.
Unit 1 · 6 skills
Absolute Value and Radicals
Absolute Value
Absolute value of real numbers
I can determine the absolute value of a real number and simplify absolute-value expressions.
Official code: P20.1
Graphing y = |f(x)|
I can graph y = |f(x)| from y = f(x) and describe its features.
Official code: P20.1
Solving absolute value equations
I can solve an absolute value equation and check for extraneous solutions.
Official code: P20.1
Radicals
Mixed and entire radicals and simplifying
I can simplify radicals and convert between entire and mixed radicals, including variable radicands.
Official code: P20.2
Rationalizing denominators
I can rationalize a denominator using a matching radical or a conjugate.
Official code: P20.2
Radical equations and extraneous roots
I can solve a radical equation and reject extraneous roots.
Official code: P20.2
The official wording · 6 outcomes
- P20.1
- Demonstrate understanding of the absolute value of real numbers and equations and functions involving the absolute value of linear and quadratic functions.
- P20.1
- functions involving the absolute value of linear and quadratic functions.
- P20.1
- equations and functions involving the absolute value of linear and quadratic functions.
- P20.2
- Expand and demonstrate understanding of radicals with numerical and variable radicands including: • computations
- P20.2
- radicals with numerical and variable radicands including: • computations
- P20.2
- radicals with numerical and variable radicands including: • solving equations (limited to square roots and one or two radicals).
Key ideas
The absolute value |a| is the distance of a from 0, so it is never negative.
Factor out perfect squares (or perfect powers) to simplify a radical.
Absolute value fits into order of operations like grouping symbols.
A mixed radical like 3 root x can be written as an entire radical root(9x).
y = |f(x)| reflects the parts of the graph below the x-axis up above it.
Watch out for
- Thinking |a| just removes a negative sign in every context (|3 - 9| is 6, not evaluating inside wrong).
- Simplifying only the numerical part and leaving variable powers unsimplified.
- Treating absolute value as returning a negative for negative inputs.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 2 · 3 skills
Rational Expressions
Rational Expressions and Equations
Equivalent forms and simplifying
I can simplify a rational expression and state its non-permissible values.
Official code: P20.3
Operations on rational expressions
I can add, subtract, multiply, and divide rational expressions.
Official code: P20.3
Solving rational equations
I can solve a rational equation and reject solutions that are non-permissible.
Official code: P20.3
The official wording · 3 outcomes
- P20.3
- Expand and demonstrate understanding of rational expressions and equations (up to and including degree 2 numerators and denominators) including: • equivalent forms of expressions
- P20.3
- rational expressions and equations (up to and including degree 2 numerators and denominators) including: • operations on expressions
- P20.3
- rational expressions and equations (up to and including degree 2 numerators and denominators) including: • solving equations that can be simplified to linear or quadratic equations.
Key ideas
Factor numerator and denominator, then cancel common factors.
Non-permissible values (from the original denominator) must be stated even after simplifying.
Multiply by multiplying numerators and denominators; divide by multiplying by the reciprocal.
Add or subtract by finding a common denominator.
Multiply through by the common denominator to clear fractions.
Watch out for
- Cancelling terms that are not factors.
- Dropping non-permissible values after simplifying.
- Adding numerators and denominators separately.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 3 · 5 skills
Trigonometry
Trig Ratios and Reference Angles
Standard position and reference angles
I can sketch an angle in standard position and find its reference angle.
Official code: P20.4
Trig ratios from a point on the terminal arm
I can find sin, cos, and tan of an angle from a point on its terminal arm.
Official code: P20.4
Exact values for special angles
I can give the exact value of a trig ratio for a special angle without a calculator.
Official code: P20.4
The Sine and Cosine Laws
Sine and cosine laws
I can derive and apply the sine and cosine laws to solve non-right triangles.
Official code: P20.5
The ambiguous case
I can determine whether the ambiguous case yields zero, one, or two triangles.
Official code: P20.5
The official wording · 5 outcomes
- P20.4
- Expand and demonstrate understanding of the primary trigonometric ratios including the use of reference angles (0° ≤ θ ≤ 360°) and the determination of exact values for trigonometric ratios.
- P20.4
- primary trigonometric ratios including the use of reference angles (0° ≤ θ ≤ 360°)
- P20.4
- trigonometric ratios including the use of reference angles (0° ≤ θ ≤ 360°) and the determination of exact values for trigonometric ratios.
- P20.5
- Demonstrate understanding of the cosine law and sine law, including the ambiguous case.
- P20.5
- the cosine law and sine law, including the ambiguous case.
Key ideas
An angle in standard position has its vertex at the origin and initial arm on the positive x-axis.
Sine law: a/sin A = b/sin B = c/sin C.
The reference angle is the acute angle between the terminal arm and the x-axis.
Cosine law: c^2 = a^2 + b^2 - 2ab*cos C, derivable by dropping an altitude.
For P(x, y) with r = root(x^2 + y^2): sin = y/r, cos = x/r, tan = y/x.
Watch out for
- Measuring the reference angle to the y-axis instead of the x-axis.
- Choosing the sine law when three sides are known.
- Mislabelling the quadrant.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 4 · 7 skills
Quadratic Functions and Equations
Factoring Polynomial Expressions
Factoring advanced polynomial expressions
I can factor differences of squares and quadratic-in-form polynomial expressions.
Official code: P20.6
Quadratic Functions
Transformations and vertex form
I can graph y = a(x-p)^2 + q by applying transformations to y = x^2.
Official code: P20.7
Completing the square
I can complete the square to convert a quadratic to vertex form.
Official code: P20.7
Graphing and characteristics
I can determine all key characteristics of a quadratic function and sketch its graph.
Official code: P20.7
Quadratic Equations and Systems
Solving quadratic equations
I can solve a quadratic equation by more than one method.
Official code: P20.8
The discriminant
I can use the discriminant to determine the number of real roots of a quadratic.
Official code: P20.8
Linear-quadratic and quadratic-quadratic systems
I can solve a linear-quadratic or quadratic-quadratic system.
Official code: P20.8
The official wording · 7 outcomes
- P20.6
- Expand and demonstrate understanding of factoring polynomial expressions including those of the form:
- P20.7
- Demonstrate understanding of quadratic functions of the form y = ax² + bx + c and of their graphs, including: • vertex
- P20.7
- quadratic functions of the form y = ax² + bx + c and of their graphs, including: • axis of symmetry
- P20.7
- quadratic functions of the form y = ax² + bx + c and of their graphs, including: • vertex • domain and range • direction of opening • axis of symmetry • x- and y-intercepts.
- P20.8
- Demonstrate understanding of quadratic equations including the solution of: • single variable equations
- P20.8
- quadratic equations including the solution of: • single variable equations
- P20.8
- quadratic equations including the solution of: • systems of linear-quadratic and quadratic-quadratic equations in two variables.
Key ideas
Difference of squares: a^2x^2 - b^2y^2 = (ax - by)(ax + by).
In y = a(x-p)^2 + q: a stretches/reflects, p shifts horizontally, q shifts vertically.
Factoring, completing the square, and the quadratic formula all solve ax^2 + bx + c = 0.
Quadratic-in-form a(f(x))^2 - b(f(x)) + c factors like a quadratic in the argument f(x).
The vertex is (p, q) and the axis of symmetry is x = p.
Watch out for
- Trying to factor a sum of squares as a difference.
- Shifting the wrong direction for p (right for x - p).
- Sign errors in the quadratic formula.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 5 · 6 skills
Inequalities, Sequences, and Reciprocals
Inequalities
Two-variable inequalities
I can graph the solution region of a two-variable inequality.
Official code: P20.9
One-variable quadratic inequalities
I can solve a one-variable quadratic inequality and express the solution set.
Official code: P20.9
Sequences and Series
Arithmetic sequences and series
I can find a term and a sum of an arithmetic sequence or series.
Official code: P20.10
Geometric sequences and series
I can find a term and a finite sum of a geometric sequence.
Official code: P20.10
Infinite geometric series
I can find the sum of an infinite geometric series when it converges.
Official code: P20.10
Reciprocal Functions
Graphing reciprocal functions
I can graph a reciprocal function and identify its asymptotes.
Official code: P20.11
The official wording · 6 outcomes
- P20.9
- Expand and demonstrate understanding of inequalities including: • two-variable linear and quadratic inequalities.
- P20.9
- inequalities including: • one-variable quadratic inequalities
- P20.10
- Demonstrate understanding of arithmetic and geometric (finite and infinite) sequences and series.
- P20.10
- arithmetic and geometric (finite and infinite) sequences and series.
- P20.10
- geometric (finite and infinite) sequences and series.
- P20.11
- Demonstrate understanding of reciprocal functions of: • linear functions • quadratic functions.
Key ideas
Graph the boundary (solid for <= or >=, broken for < or >) then shade using a test point.
Arithmetic sequence: t_n = t_1 + (n - 1)d, where d is the common difference.
The reciprocal function y = 1/f(x) has a vertical asymptote where f(x) = 0.
A quadratic boundary is a parabola; the region is inside or outside it.
Arithmetic series sum: S_n = n/2 (t_1 + t_n).
Watch out for
- Using a solid boundary for a strict inequality.
- Using n instead of (n - 1) in the term formula.
- Placing the asymptote where f is large instead of where f is zero.
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 3 math courses for Grade 11. Here they are side by side.
- Foundations of Mathematics 204 units · 19 skillsNo provincial examWhat it coversReasoning and Proof · Proportional Reasoning and Geometry · Statistics · Inequalities and Quadratic Modelling
- Pre-Calculus 20This course5 units · 27 skillsNo provincial examWhat it coversAbsolute Value and Radicals · Rational Expressions · Trigonometry · Quadratic Functions and Equations · Inequalities, Sequences, and Reciprocals
- Workplace and Apprenticeship Mathematics 203 units · 20 skillsNo provincial examWhat it coversMeasurement and Geometry · Personal Finance · Slope, Scale, and Data
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 20.
Textbooks
The textbooks Saskatchewan Ministry of Education lists for Pre-Calculus 20:
- McGraw-Hill Ryerson Pre-Calculus 11
From core resources, read October 27, 2026. curriculum.gov.sk.ca
Study it in MapleMind
MapleMind teaches Pre-Calculus 20 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 20 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
- 32
- Fillable fields
- 1,417
- Price
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Questions about Pre-Calculus 20
What is Pre-Calculus 20?
Saskatchewan’s Grade 11 math course: 5 units and 27 skills, from Absolute Value and Radicals to Inequalities, Sequences, and Reciprocals.
What units are in Pre-Calculus 20?
1. Absolute Value and Radicals, 2. Rational Expressions, 3. Trigonometry, 4. Quadratic Functions and Equations and 5. Inequalities, Sequences, and Reciprocals.
Is there a provincial exam for Pre-Calculus 20?
No. Saskatchewan gives no provincial exam for Pre-Calculus 20.
What textbook does Pre-Calculus 20 use?
The textbooks Saskatchewan Ministry of Education lists for Pre-Calculus 20: McGraw-Hill Ryerson Pre-Calculus 11.
What comes after Pre-Calculus 20?
Foundations of Mathematics 30, Pre-Calculus 30, Workplace and Apprenticeship Mathematics 30 and Calculus 30.
Can MapleMind help with Pre-Calculus 20?
Yes. MapleMind teaches every skill of Pre-Calculus 20, 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.
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