Get help with Pre-Calculus Mathematics, Grade 11 (30S)
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The official Manitoba Pre-Calculus Mathematics, Grade 11 (30S) curriculum
Manitoba defines Pre-Calculus Mathematics, Grade 11 (30S) by strands and outcomes. MapleMind teaches the same curriculum reorganized for one-skill-at-a-time tutoring — the table shows exactly where every official strand lands, and the ministry's own wording is quoted under each unit below.
Official source Manitoba's official curriculumRead it on the government site — edu.gov.mb.ca ↗| Official strand | Outcomes | Where MapleMind teaches it |
|---|---|---|
| Strand A | 6 | Algebra and Number |
| Strand T | 3 | Trigonometry |
| Strand R | 11 | Relations and Functions |
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How MapleMind teaches Pre-Calculus Mathematics, Grade 11 (30S) — every unit, lesson, and skill
Every skill below runs as a short session: a plain-words lesson, a worked example, solving it together, then a five-question skill check that earns up to three stars. Guided Mode keeps it teaching instead of answer-handing — turning it off needs a parent's password.
Unit 1Algebra and NumberOfficial strand · Strand A
Absolute value of real numbers, radicals and radical equations, and rational expressions and equations with non-permissible values.
Absolute Value and Radicals
- Absolute value of real numbers11P.A.1 — Demonstrate an understanding of the absolute value of real numbers as distance from zero, evaluating absolute-value expressions and ordering them.
- Simplifying and operating on radicals11P.A.2 — Simplify radical expressions with numerical and variable radicands, convert between mixed and entire radicals, and perform operations on radical expressions.
- Rationalizing denominators11P.A.2 — Rationalize the denominator of a rational expression with monomial or binomial denominators, relating the binomial case to the difference of squares.
- Radical equations11P.A.3 — Solve problems that involve radical equations limited to square roots, determining restrictions, solving algebraically, and identifying extraneous roots.
Rational Expressions and Equations
- Equivalent rational expressions and non-permissible values11P.A.4 — Determine equivalent forms of rational expressions with monomial, binomial, or trinomial numerators and denominators, simplifying and stating non-permissible values.
- Multiplying and dividing rational expressions11P.A.5 — Determine, in simplified form, the product or quotient of rational expressions with monomial, binomial, or trinomial numerators and denominators, stating non-permissible values.
- Adding and subtracting rational expressions11P.A.5 — Determine, in simplified form, the sum or difference of rational expressions with like and unlike denominators, and simplify expressions involving two or more operations.
- Rational equations11P.A.6 — Solve problems that involve rational equations, determining non-permissible values, solving algebraically, and explaining why a value obtained may not be a solution.
The official wording — 6 outcomes in this unit
- 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.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.6
Solve problems that involve rational equations (limited to numerators and denominators that are monomials, binomials, or trinomials).
Unit 2TrigonometryOfficial strand · Strand T
Angles in standard position from 0 to 360 degrees, the primary trigonometric ratios beyond right triangles, and the sine and cosine laws with the ambiguous case.
Angles in Standard Position and Trig Ratios
- Angles in standard position11P.T.1 — Demonstrate an understanding of angles in standard position from 0 to 360 degrees, sketching angles, determining reference angles, and identifying quadrants.
- Trig ratios from a terminal-arm point11P.T.2 — Determine the value of sine, cosine, and tangent given any point on the terminal arm of an angle in standard position, using the distance from the origin, and determine the sign of a ratio by quadrant.
- Exact values and solving trig equations11P.T.2 — Determine the exact values of the trigonometric ratios for angles with reference angles of 30, 45, and 60 degrees and for quadrantal angles, and solve equations of the form sin θ = a, cos θ = a, or tan θ = a.
The Sine and Cosine Laws
- Deriving and applying the sine and cosine laws11P.T.3 — Solve problems using the cosine law and sine law, explaining the steps in a proof of each law and sketching diagrams for non-right triangles.
- The ambiguous case11P.T.3 — Describe and explain ambiguous-case problems that may have no solution, one solution, or two solutions, and solve for both triangles where two exist.
The official wording — 3 outcomes in this unit
- 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.3
Solve problems, using the cosine law and sine law, including the ambiguous case.
Unit 3Relations and FunctionsOfficial strand · Strand R
Advanced factoring, absolute value functions, quadratic functions and equations, systems and inequalities, arithmetic and geometric sequences and series, and reciprocal functions.
Advanced Factoring
- Factoring trinomials and differences of squares11P.R.1 — Factor polynomial expressions of the form ax² + bx + c and a²x² − b²y² where the coefficients are rational numbers, including common-factor identification.
- Factoring quadratic patterns11P.R.1 — Factor polynomial expressions with a quadratic pattern, including a(f(x))² + b(f(x)) + c and a²(f(x))² − b²(g(y))², by substituting for the inner expression.
Absolute Value Functions
- Graphing absolute value functions11P.R.2 — Graph and analyze absolute value functions of linear and quadratic functions, sketching y = |f(x)|, stating intercepts, domain and range, and generalizing piecewise notation.
- Solving absolute value equations11P.R.2 — Solve absolute value equations graphically and algebraically, verify the solutions, and explain why an equation with a negative right side has no solution.
Quadratic Functions
- Transformation effects in vertex form11P.R.3 — Analyze quadratic functions of the form y = a(x − p)² + q by comparing families of graphs to y = x² and generalizing rules for the effects of a, p, and q, including the vertex location.
- Sketching and analyzing from vertex form11P.R.3 — Sketch the graph of y = a(x − p)² + q using transformations, determine its domain and range, direction of opening, axis of symmetry, and intercepts, and write the function for a given graph.
- Completing the square11P.R.4 — Write a quadratic function given in the form y = ax² + bx + c in vertex form by completing the square, explaining the process and verifying the two forms represent the same function.
- Analyzing and modelling with general form11P.R.4 — Determine the characteristics of a quadratic function in the form y = ax² + bx + c, sketch its graph, and write a quadratic function that models a situation, explaining any assumptions.
Quadratic Equations, Systems, and Inequalities
- Solving quadratics by factoring and completing the square11P.R.5 — Solve quadratic equations by determining square roots, factoring, and completing the square, relating the roots to the zeros of the function and the x-intercepts of the graph.
- The quadratic formula and the discriminant11P.R.5 — Derive the quadratic formula using deductive reasoning, apply it to solve quadratic equations, and use the discriminant to determine whether an equation has two, one, or no real roots.
- Linear-quadratic and quadratic-quadratic systems graphically11P.R.6 — Model situations with systems of linear-quadratic or quadratic-quadratic equations and solve them graphically, explaining the meaning of the points of intersection and the possible solution counts.
- Solving quadratic systems algebraically11P.R.6 — Determine and verify the solution of a system of linear-quadratic or quadratic-quadratic equations algebraically, and explain why a system may have zero, one, two, or an infinite number of solutions.
- Linear and quadratic inequalities in two variables11P.R.7 — Solve problems that involve linear and quadratic inequalities in two variables, using test points to determine the solution region and choosing solid or broken boundaries.
- Quadratic inequalities in one variable11P.R.8 — Solve problems that involve quadratic inequalities in one variable using strategies such as case analysis, roots and test points, or sign analysis.
Sequences, Series, and Reciprocal Functions
- Arithmetic sequences11P.R.9 — Analyze arithmetic sequences, deriving a rule for the general term, relating arithmetic sequences to linear functions, and determining the first term, common difference, number of terms, or a specific term.
- Arithmetic series11P.R.9 — Analyze arithmetic series, deriving a rule for the sum of n terms and determining the first term, common difference, number of terms, or the sum in a problem.
- Geometric sequences11P.R.10 — Analyze geometric sequences, deriving a rule for the general term and determining the first term, common ratio, number of terms, or a specific term in a problem.
- Geometric series and convergence11P.R.10 — Analyze geometric series, deriving the sum of n terms, generalizing a rule for the sum of an infinite geometric series, and explaining why a series is convergent or divergent.
- Reciprocal functions11P.R.11 — Graph and analyze reciprocal functions of linear and quadratic functions, locating vertical asymptotes at the non-permissible values and comparing the reciprocal graph to the original.
The official wording — 11 outcomes in this unit
- 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.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.4
Analyze quadratic functions of the form y = ax2 + bx + c to identify characteristics of the corresponding graph, including vertex
- 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.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.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).
Printable workbook · A keepsake of the year
A Pre-Calculus Mathematics, Grade 11 (30S) workbook worth keeping
Built from the same official curriculum as this page. Before and after each skill above, your student colours in how sure they feel — so the two of you can see, on one page, what's clicking and what needs another look. It's a quiet way to follow how the year is really going.
By June it's full of their own handwriting: units worked through, confidence grown, a mid-year check-in, notes from parent-teacher night, and a certificate at the end. Less a worksheet, more a record of the year worth keeping on the shelf.
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Can MapleMind help me with Pre-Calculus Mathematics, Grade 11 (30S)?
Yes. MapleMind's AI tutor covers all 32 skills in Manitoba's Pre-Calculus Mathematics, Grade 11 (30S) — you pick the exact skill, and the tutor teaches it step by step: a short lesson, a worked example, solving together, then a skill check to show it stuck.
Is MapleMind aligned to Manitoba's official curriculum?
Yes. Every skill in this course maps to an official outcome code from Manitoba's Grade 11 Mathematics curriculum, and the ministry's own wording is quoted under each unit on this page — with the official government source linked so you can check it yourself.
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Yes — 14 languages, including French. Both the app and the tutor's explanations switch to the language you choose.
Where can I see the official Manitoba curriculum for Pre-Calculus Mathematics, Grade 11 (30S)?
The official source is linked on this page — Manitoba's official curriculum. The outline here follows it: every MapleMind skill carries its official outcome code, and the ministry's own wording is quoted under each unit.
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