Alberta · Grade 11
Mathematics 20-1
- MAT2791
Alberta’s Grade 11 math course, from Algebra and Number to Relations and Functions.
- Units
- 3
- Lessons
- 20
- Skills
- 43
- Provincial exam
- None
- Official curriculum
- Alberta Education
Unit by unit
Every skill in the course, numbered by unit.
Unit 1 · 13 skills
Algebra and Number
Absolute Value
Absolute value as distance
I can interpret absolute value as distance from zero.
Skill 1.1
Evaluating and ordering with absolute value
I can evaluate expressions with absolute value and use it to compare real numbers.
Skill 1.2
Operations on Radicals
Radicals with variable radicands
I can simplify radicals with variable radicands, stating restrictions.
Skill 1.3
Adding and subtracting radicals
I can add and subtract radicals by combining like radicals.
Skill 1.4
Multiplying, dividing and rationalizing
I can multiply and divide radical expressions and rationalize denominators.
Skill 1.5
Radical Equations
Solving radical equations
I can solve square-root equations and reject extraneous roots.
Skill 1.6
Problems with radical equations
I can model and solve real problems involving square-root relationships.
Skill 1.7
Rational Expressions
Non-permissible values
I can determine non-permissible values of rational expressions.
Skill 1.8
Simplifying rational expressions
I can simplify rational expressions by factoring, keeping restrictions.
Skill 1.9
Operations on Rational Expressions
Multiplying and dividing
I can multiply and divide rational expressions.
Skill 1.10
Adding and subtracting
I can add and subtract rational expressions with the lowest common denominator.
Skill 1.11
Rational Equations
Solving rational equations
I can solve rational equations, rejecting non-permissible candidates.
Skill 1.12
Problems with rational equations
I can model rate, work and mixture problems with rational equations.
Skill 1.13
The official wording · 13 outcomes
- 1.1
- Demonstrate an understanding of the absolute value of real numbers.
- 1.3
- Solve problems that involve operations on radicals and radical expressions with numerical and variable radicands.
- 1.6
- Solve problems that involve radical equations (limited to square roots).
- 1.8
- Determine equivalent forms of rational expressions (limited to numerators and denominators that are monomials, binomials or trinomials).
- 1.10
- Perform operations on rational expressions (limited to numerators and denominators that are monomials, binomials or trinomials).
- 1.12
- Solve problems that involve rational equations (limited to numerators and denominators that are monomials, binomials or trinomials).
Key ideas
|a| is the DISTANCE from a to zero — always non-negative: |7| = 7 and |−7| = 7.
Extract perfect squares from variables too: √(x³) = x√x — with the restriction x ≥ 0 so the root exists.
Isolate the radical FIRST, then square both sides, then solve what remains.
A rational expression is undefined wherever its DENOMINATOR equals zero — those are the non-permissible values (NPVs).
Factor EVERYTHING first, cancel common factors across numerators and denominators, then multiply what's left.
Watch out for
- Thinking |a| just 'removes the sign' symbol — then choking on |x| when x could be negative.
- Writing √(x²) = x without considering sign (it's |x| in general; with stated restrictions x ≥ 0 it's x).
- Squaring term by term instead of side by side ((a + b)² = a² + b²).
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 2 · 8 skills
Trigonometry
Angles in Standard Position
Standard position
I can sketch and identify angles in standard position from 0° to 360°.
Skill 2.1
Reference angles
I can find reference angles and relate angles that share one.
Skill 2.2
Trig Ratios from 0° to 360°
Ratios from a terminal-arm point
I can compute the three ratios from a point on the terminal arm.
Skill 2.3
Signs by quadrant
I can determine ratio signs by quadrant and exact values for special angles.
Skill 2.4
Finding angles from ratios
I can find all angles in 0°–360° with a given ratio value.
Skill 2.5
The Sine and Cosine Laws
The sine law
I can solve triangles with the sine law.
Skill 2.6
The cosine law
I can solve triangles with the cosine law.
Skill 2.7
The ambiguous case
I can analyze SSA data and find zero, one or two triangles.
Skill 2.8
The official wording · 8 outcomes
- 2.1
- Demonstrate an understanding of angles in standard position [0° to 360°].
- 2.3
- Solve problems, using the three primary trigonometric ratios for angles from 0° to 360° in standard position.
- 2.6
- Solve problems, using the cosine law and sine law, including the ambiguous case.
Key ideas
Standard position: vertex at the origin, initial arm along the positive x-axis, rotating COUNTER-clockwise.
For a point (x, y) on the terminal arm with r = √(x² + y²): sin θ = y/r, cos θ = x/r, tan θ = y/x.
a/sin A = b/sin B = c/sin C — each side over the sine of its OPPOSITE angle.
The terminal arm's quadrant classifies the angle: 0–90° QI, 90–180° QII, 180–270° QIII, 270–360° QIV.
r is always positive; x and y carry the quadrant's signs into the ratios.
Watch out for
- Rotating clockwise for positive angles.
- Making r negative in QIII (r is a distance — always positive).
- Pairing a side with a NON-opposite angle in the ratio.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 3 · 22 skills
Relations and Functions
Advanced Factoring
Trinomials and differences of squares
I can factor trinomials and differences of squares with rational coefficients.
Skill 3.1
Factoring in function form
I can factor function-form expressions by substitution.
Skill 3.2
Absolute Value Functions
Graphing y = |f(x)|
I can graph y = |f(x)| for linear and quadratic f.
Skill 3.3
Solving with absolute value graphs
I can solve absolute value equations graphically and by cases.
Skill 3.4
Quadratics in Vertex Form
Reading y = a(x − p)² + q
I can read all key characteristics from vertex form.
Skill 3.5
The roles of a, p and q
I can explain how a, p and q transform the base parabola and sketch efficiently.
Skill 3.6
Quadratics in Standard Form
Analyzing y = ax² + bx + c
I can analyze a quadratic in standard form.
Skill 3.7
Completing the square
I can convert standard form to vertex form by completing the square.
Skill 3.8
Quadratic Equations
Roots by factoring and graphing
I can solve quadratic equations by factoring and connect roots to the graph.
Skill 3.9
The quadratic formula and the discriminant
I can solve with the quadratic formula and interpret the discriminant.
Skill 3.10
Linear–Quadratic and Quadratic–Quadratic Systems
Solving systems graphically
I can solve linear–quadratic and quadratic–quadratic systems graphically.
Skill 3.11
Solving systems algebraically
I can solve these systems by substitution and interpret the resulting equation.
Skill 3.12
Inequalities in Two Variables
Linear inequalities
I can graph linear inequalities in two variables.
Skill 3.13
Quadratic inequalities
I can graph quadratic inequalities in two variables.
Skill 3.14
Quadratic Inequalities in One Variable
Solving with the graph
I can solve quadratic inequalities by reading the parabola.
Skill 3.15
Solving with roots and sign analysis
I can solve quadratic inequalities algebraically with roots and interval testing.
Skill 3.16
Arithmetic Sequences and Series
Arithmetic sequences
I can analyze arithmetic sequences with the general term.
Skill 3.17
Arithmetic series
I can compute arithmetic series sums.
Skill 3.18
Geometric Sequences and Series
Geometric sequences
I can analyze geometric sequences with the general term.
Skill 3.19
Geometric series
I can compute geometric series sums.
Skill 3.20
Reciprocal Functions
Reciprocals of linear functions
I can graph reciprocals of linear functions.
Skill 3.21
Reciprocals of quadratic functions
I can graph reciprocals of quadratic functions with zero, one or two asymptotes.
Skill 3.22
The official wording · 22 outcomes
- 3.1
- Factor polynomial expressions of the form ax² + bx + c (a ≠ 0), a²x² − b²y² (a ≠ 0, b ≠ 0), a(f(x))² + b(f(x)) + c (a ≠ 0), and a²(f(x))² − b²(g(y))² (a ≠ 0, b ≠ 0), where a, b and c are rational numbers.
- 3.3
- Graph and analyze absolute value functions (limited to linear and quadratic functions) to solve problems.
- 3.5
- Analyze quadratic functions of the form y = a(x − p)² + q and determine the: vertex; domain and range; direction of opening; axis of symmetry; x- and y-intercepts.
- 3.7
- Analyze quadratic functions of the form y = ax² + bx + c to identify characteristics of the corresponding graph, including: vertex; domain and range; direction of opening; axis of symmetry; x- and y-intercepts; and to solve problems.
- 3.9
- Solve problems that involve quadratic equations.
- 3.11
- Solve, algebraically and graphically, problems that involve systems of linear-quadratic and quadratic-quadratic equations in two variables.
- 3.13
- Solve problems that involve linear and quadratic inequalities in two variables.
- 3.15
- Solve problems that involve quadratic inequalities in one variable.
- 3.17
- Analyze arithmetic sequences and series to solve problems.
- 3.19
- Analyze geometric sequences and series to solve problems.
- 3.21
- Graph and analyze reciprocal functions (limited to the reciprocal of linear and quadratic functions).
Key ideas
The 10C patterns extend to rational coefficients: ax² + bx + c by decomposition, a²x² − b²y² as (ax − by)(ax + by).
Graph f first; keep everything on or above the x-axis; REFLECT the below-axis parts up. Corners form at the x-intercepts of f.
Vertex (p, q) — beware the sign: y = a(x − 3)² + 1 has p = 3, and (x + 2) means p = −2. Axis of symmetry x = p.
The axis of symmetry is x = −b/(2a); substitute it back for the vertex's y. c is the y-intercept, and a still controls opening and width.
Set the equation to zero, factor, apply the zero-product property: each factor gives a root.
Watch out for
- Decomposing with a pair that multiplies to c instead of a×c.
- Reflecting the WHOLE graph up (only below-axis parts flip).
- Reading (x + 3) as p = +3.
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?
Alberta has 3 math courses for Grade 11. Here they are side by side.
- Mathematics 20-1This courseMAT27913 units · 43 skillsNo provincial examWhat it coversAlgebra and Number · Trigonometry · Relations and Functions
- Mathematics 20-2MAT27926 units · 27 skillsNo provincial examWhat it coversMeasurement · Geometry · Number and Logic · Statistics · Relations and Functions · Mathematics Research Project
- Mathematics 20-3MAT27935 units · 40 skillsNo provincial examWhat it coversMeasurement · Geometry · Number · Algebra · 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 Alberta’s own curriculum for Mathematics 20-1.
Study it in MapleMind
MapleMind teaches Mathematics 20-1 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 Mathematics 20-1 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
- 30
- Fillable fields
- 1,581
- Price
- $4.99
Questions about Mathematics 20-1
What is Mathematics 20-1?
Alberta’s Grade 11 math course: 3 units and 43 skills, from Algebra and Number to Relations and Functions.
What units are in Mathematics 20-1?
1. Algebra and Number, 2. Trigonometry and 3. Relations and Functions.
Is there a provincial exam for Mathematics 20-1?
No. Alberta gives no provincial exam for Mathematics 20-1.
What comes after Mathematics 20-1?
Mathematics 30-1, Mathematics 30-2, Mathematics 31 and Mathematics 30-3.
Can MapleMind help with Mathematics 20-1?
Yes. MapleMind teaches every skill of Mathematics 20-1, 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 Mathematics 20-1
Practise every skill of Mathematics 20-1 in MapleMind, free with daily limits.
