Manitoba · Grade 11
Pre-Calculus Mathematics, Grade 11 (30S)
Manitoba’s Grade 11 math course, from Algebra and Number to Relations and Functions.
- Units
- 3
- Lessons
- 9
- Skills
- 32
- Provincial exam
- None
- Official curriculum
- Manitoba Education
Unit by unit
Every skill in the course, with its official code.
Unit 1 · 8 skills
Algebra and Number
Absolute Value and Radicals
Absolute value of real numbers
I can evaluate and order absolute values of real numbers.
Official code: 11P.A.1
Simplifying and operating on radicals
I can simplify radicals with variable radicands and add, subtract, and multiply them.
Official code: 11P.A.2
Rationalizing denominators
I can rationalize monomial and binomial denominators.
Official code: 11P.A.2
Radical equations
I can solve a radical equation and catch extraneous roots.
Official code: 11P.A.3
Rational Expressions and Equations
Equivalent rational expressions and non-permissible values
I can simplify a rational expression and state its non-permissible values.
Official code: 11P.A.4
Multiplying and dividing rational expressions
I can multiply and divide rational expressions in simplified form.
Official code: 11P.A.5
Adding and subtracting rational expressions
I can add and subtract rational expressions over a common denominator.
Official code: 11P.A.5
Rational equations
I can solve a rational equation and reject non-permissible roots.
Official code: 11P.A.6
The official wording · 8 outcomes
- 11P.A.1
- Demonstrate an understanding of the absolute value of real numbers.
- 11P.A.2
- Solve problems that involve operations on radicals and radical expressions with numerical and variable radicands.
- 11P.A.2
- Solve problems that involve operations on radicals and radical expressions with numerical and variable radicands.
- 11P.A.3
- Solve problems that involve radical equations (limited to square roots).
- 11P.A.4
- Determine equivalent forms of rational expressions (limited to numerators and denominators that are monomials, binomials, or trinomials).
- 11P.A.5
- Perform operations on rational expressions (limited to numerators and denominators that are monomials, binomials, or trinomials).
- 11P.A.5
- Perform operations on rational expressions (limited to numerators and denominators that are monomials, binomials, or trinomials).
- 11P.A.6
- Solve problems that involve rational equations (limited to numerators and denominators that are monomials, binomials, or trinomials).
Key ideas
The absolute value |a| is the distance of a from 0 on the number line.
A non-permissible value makes a denominator zero.
The distance between two numbers can be written as an absolute value.
Simplifying by a common factor keeps the same non-permissible values as the original.
A radical simplifies by extracting perfect-square factors, including variables: root of 12x cubed = 2x root of 3x.
Watch out for
- Thinking |a| just deletes the minus sign inside any expression before evaluating it.
- Cancelling terms instead of factors.
- Believing −|a| is always positive.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 2 · 5 skills
Trigonometry
Angles in Standard Position and Trig Ratios
Angles in standard position
I can sketch an angle in standard position and find its reference angle.
Official code: 11P.T.1
Trig ratios from a terminal-arm point
I can find trig ratios from a point on the terminal arm and predict their signs.
Official code: 11P.T.2
Exact values and solving trig equations
I can give exact trig values for special angles and solve basic trig equations.
Official code: 11P.T.2
The Sine and Cosine Laws
Deriving and applying the sine and cosine laws
I can justify and apply the sine and cosine laws to any triangle.
Official code: 11P.T.3
The ambiguous case
I can analyze the ambiguous case and find every valid triangle.
Official code: 11P.T.3
The official wording · 5 outcomes
- 11P.T.1
- Demonstrate an understanding of angles in standard position [0° to 360°].
- 11P.T.2
- Solve problems, using the three primary trigonometric ratios (sine, cosine, and tangent) for angles from 0° to 360° in standard position.
- 11P.T.2
- Solve problems, using the three primary trigonometric ratios (sine, cosine, and tangent) for angles from 0° to 360° in standard position.
- 11P.T.3
- Solve problems, using the cosine law and sine law, including the ambiguous case.
- 11P.T.3
- Solve problems, using 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.
The sine law a/sin A = b/sin B follows from dropping an altitude in any triangle.
The reference angle is the acute angle between the terminal arm and the x-axis.
The cosine law c² = a² + b² − 2ab cos C generalizes the Pythagorean theorem.
For P(x, y) at distance r from the origin: sin θ = y/r, cos θ = x/r, tan θ = y/x.
Watch out for
- Measuring the reference angle from the y-axis.
- Using the sine law when only three sides are given.
- Placing the initial arm along the terminal position.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 3 · 19 skills
Relations and Functions
Advanced Factoring
Factoring trinomials and differences of squares
I can factor trinomials and differences of squares with rational coefficients.
Official code: 11P.R.1
Factoring quadratic patterns
I can factor expressions where a whole function takes the place of x.
Official code: 11P.R.1
Absolute Value Functions
Graphing absolute value functions
I can sketch y = |f(x)| and write it in piecewise notation.
Official code: 11P.R.2
Solving absolute value equations
I can solve absolute value equations and spot the impossible cases.
Official code: 11P.R.2
Quadratic Functions
Transformation effects in vertex form
I can explain what a, p, and q each do to the parabola y = x².
Official code: 11P.R.3
Sketching and analyzing from vertex form
I can sketch a vertex-form quadratic and state all its characteristics.
Official code: 11P.R.3
Completing the square
I can complete the square to convert a quadratic to vertex form.
Official code: 11P.R.4
Analyzing and modelling with general form
I can analyze a general-form quadratic and use one to model a situation.
Official code: 11P.R.4
Quadratic Equations, Systems, and Inequalities
Solving quadratics by factoring and completing the square
I can solve quadratic equations by square roots, factoring, and completing the square.
Official code: 11P.R.5
The quadratic formula and the discriminant
I can derive and apply the quadratic formula and read the discriminant.
Official code: 11P.R.5
Linear-quadratic and quadratic-quadratic systems graphically
I can solve a system involving a quadratic by graphing and interpret the intersections.
Official code: 11P.R.6
Solving quadratic systems algebraically
I can solve a system involving a quadratic by substitution and verify it.
Official code: 11P.R.6
Linear and quadratic inequalities in two variables
I can graph the solution region of a linear or quadratic inequality.
Official code: 11P.R.7
Quadratic inequalities in one variable
I can solve a quadratic inequality in one variable and interpret the interval.
Official code: 11P.R.8
Sequences, Series, and Reciprocal Functions
Arithmetic sequences
I can derive and use the general term of an arithmetic sequence.
Official code: 11P.R.9
Arithmetic series
I can derive and apply the sum formula for an arithmetic series.
Official code: 11P.R.9
Geometric sequences
I can derive and use the general term of a geometric sequence.
Official code: 11P.R.10
Geometric series and convergence
I can sum a geometric series and decide whether an infinite one converges.
Official code: 11P.R.10
Reciprocal functions
I can graph the reciprocal of a linear or quadratic function.
Official code: 11P.R.11
The official wording · 19 outcomes
- 11P.R.1
- Factor polynomial expressions of the form ax2 + bx + c, a ≠ 0 a2x2 – b2y2, a ≠ 0, b ≠ 0 where a, b, and c are rational numbers.
- 11P.R.1
- Factor polynomial expressions of the form a(f(x))2 + b(f(x)) + c, a ≠ 0 a2(f(x))2 – b2(g(y))2, a ≠ 0, b ≠ 0 where a, b, and c are rational numbers.
- 11P.R.2
- Graph and analyze absolute value functions (limited to linear and quadratic functions) to solve problems.
- 11P.R.2
- Graph and analyze absolute value functions (limited to linear and quadratic functions) to solve problems.
- 11P.R.3
- Analyze quadratic functions of the form y = a(x – p)2 + q and determine the vertex
- 11P.R.3
- Analyze quadratic functions of the form y = a(x – p)2 + q and determine the domain and range direction of opening axis of symmetry x- and y-intercepts
- 11P.R.4
- Analyze quadratic functions of the form y = ax2 + bx + c to identify characteristics of the corresponding graph, including vertex
- 11P.R.4
- Analyze quadratic functions of the form y = ax2 + bx + c to identify characteristics of the corresponding graph, including domain and range direction of opening axis of symmetry x- and y-intercepts
- 11P.R.5
- Solve problems that involve quadratic equations.
- 11P.R.5
- Solve problems that involve quadratic equations.
- 11P.R.6
- Solve, algebraically and graphically, problems that involve systems of linear-quadratic and quadratic-quadratic equations in two variables.
- 11P.R.6
- Solve, algebraically and graphically, problems that involve systems of linear-quadratic and quadratic-quadratic equations in two variables.
- 11P.R.7
- Solve problems that involve linear and quadratic inequalities in two variables.
- 11P.R.8
- Solve problems that involve quadratic inequalities in one variable.
- 11P.R.9
- Analyze arithmetic sequences and series to solve problems.
- 11P.R.9
- Analyze arithmetic sequences and series to solve problems.
- 11P.R.10
- Analyze geometric sequences and series to solve problems.
- 11P.R.10
- Analyze geometric sequences and series to solve problems.
- 11P.R.11
- Graph and analyze reciprocal functions (limited to the reciprocal of linear and quadratic functions).
Key ideas
A trinomial ax² + bx + c factors by decomposition of the middle term.
The graph of y = |f(x)| reflects every below-axis part of y = f(x) above the x-axis.
a stretches the parabola and flips it when negative; p shifts it horizontally; q shifts it vertically.
The roots of the equation are the zeros of the function and the x-intercepts of its graph.
An arithmetic sequence adds a common difference d each step: tn = t1 + (n − 1)d.
Watch out for
- Ignoring the leading coefficient when splitting the middle term.
- Reflecting the whole graph instead of only the negative parts.
- Shifting the wrong direction for (x − p) with positive p.
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?
Manitoba has 3 math courses for Grade 11. Here they are side by side.
- Applied Mathematics, Grade 11 (30S)6 units · 19 skillsNo provincial examWhat it coversMeasurement · Geometry · Logical Reasoning · Statistics · Relations and Functions · Mathematics Research Project
- Essential Mathematics, Grade 11 (30S)8 units · 25 skillsNo provincial examWhat it coversAnalysis of Games and Numbers · Interest and Credit · 3-D Geometry · Statistics · Managing Money · Relations and Patterns · Trigonometry · Design Modelling
- Pre-Calculus Mathematics, Grade 11 (30S)This course3 units · 32 skillsNo provincial examWhat it coversAlgebra and Number · Trigonometry · Relations and Functions
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 11 (30S).
Study it in MapleMind
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Course Companion
Your year in one workbook
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- Pages
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- Fillable fields
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Questions about Pre-Calculus Mathematics, Grade 11 (30S)
What is Pre-Calculus Mathematics, Grade 11 (30S)?
Manitoba’s Grade 11 math course: 3 units and 32 skills, from Algebra and Number to Relations and Functions.
What units are in Pre-Calculus Mathematics, Grade 11 (30S)?
1. Algebra and Number, 2. Trigonometry and 3. Relations and Functions.
Is there a provincial exam for Pre-Calculus Mathematics, Grade 11 (30S)?
No. Manitoba gives no provincial exam for Pre-Calculus Mathematics, Grade 11 (30S).
What comes after Pre-Calculus Mathematics, Grade 11 (30S)?
Applied Mathematics, Grade 12 (40S), Essential Mathematics, Grade 12 (40S), Pre-Calculus Mathematics, Grade 12 (40S) and Introduction to Calculus, Grade 12 (40S).
Can MapleMind help with Pre-Calculus Mathematics, Grade 11 (30S)?
Yes. MapleMind teaches every skill of Pre-Calculus Mathematics, Grade 11 (30S), 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 11 (30S)
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