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The official Alberta Mathematics 30-1 curriculum
Alberta defines Mathematics 30-1 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 Alberta's official programs of studyRead it on the government site — alberta.ca ↗| Official strand | Outcomes | Where MapleMind teaches it |
|---|---|---|
| Relations and Functions | 14 | Relations and Functions |
| Trigonometry | 6 | Trigonometry |
| Permutations, Combinations and Binomial Theorem | 4 | Permutations, Combinations and Binomial Theorem |
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How MapleMind teaches Mathematics 30-1 — 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 1Relations and FunctionsOfficial strand · Relations and Functions
General outcome: develop algebraic and graphical reasoning through the study of relations. The algebra of functions (operations and composition), the full transformation toolkit (translations, stretches, reflections, inverses), logarithms and their laws, exponential and logarithmic functions and equations, and the graphs of polynomial, radical and rational functions.
Operations and Composition of Functions
- Operations on functions30-1.RF.1 — Combine two functions by sum, difference, product and quotient $(f\pm g)(x),\ (fg)(x),\ \left(\tfrac{f}{g}\right)(x)$, evaluating the result and determining the domain (excluding zeros of the divisor).
- Composition of functions30-1.RF.1 — Form compositions $(f\circ g)(x)=f(g(x))$ — evaluating the inner function first — determine the composite domain, and recognize that composition is generally not commutative.
Translations of Graphs
- Horizontal and vertical translations30-1.RF.2 — Analyze how $h$ and $k$ in $y - k = f(x - h)$ slide a graph horizontally and vertically, and write the transformed equation and mapping.
Stretches of Graphs
- Horizontal and vertical stretches30-1.RF.3 — Analyze how $a$ and $b$ in $y = af(bx)$ stretch or compress a graph vertically ($|a|$) and horizontally ($\tfrac{1}{|b|}$), and describe the effect on the equation.
Combining Transformations
- Combining translations and stretches30-1.RF.4 — Apply the full transformation $y = af\big(b(x - h)\big) + k$ in the correct order (stretches/reflections before translations) to sketch graphs and write equations.
Reflections of Graphs
- Reflections through the x- and y-axes30-1.RF.5 — Reflect graphs across the $x$-axis $\big(y = -f(x)\big)$ and the $y$-axis $\big(y = f(-x)\big)$ by negating the corresponding variable, and write the related equations.
- Reflection through the line y = x30-1.RF.5 — Reflect a graph across the line $y = x$ by SWAPPING coordinates $(x, y) \to (y, x)$, connect this to inverses, and write the related equation.
Inverses of Relations
- Inverses of relations30-1.RF.6 — Find the inverse of a relation by swapping $x$ and $y$, graph it as the reflection in $y = x$, and use the horizontal-line test to decide whether the inverse is a function (restricting the domain when needed).
Logarithms and Their Laws
- Understanding logarithms30-1.RF.7 — Interpret $\log_b x$ as the exponent that produces $x$ from base $b$: $\log_b x = y \iff b^y = x$. Convert between exponential and logarithmic form and evaluate simple logarithms.
- Product, quotient and power laws30-1.RF.8 — Apply the laws $\log_b(MN)=\log_b M+\log_b N$, $\log_b\!\left(\tfrac{M}{N}\right)=\log_b M-\log_b N$, and $\log_b(M^n)=n\log_b M$ to expand, condense and evaluate logarithmic expressions.
Exponential and Logarithmic Functions
- Graphing exponential functions30-1.RF.9 — Graph and analyze $y = b^x$ ($b>0,\ b\ne 1$): domain all reals, range $y > 0$, $y$-intercept $(0, 1)$, and the horizontal asymptote $y = 0$, distinguishing growth ($b>1$) from decay ($0<b<1$).
- Graphing logarithmic functions30-1.RF.9 — Graph and analyze $y = \log_b x$ as the inverse of $y = b^x$: domain $x > 0$, range all reals, $x$-intercept $(1, 0)$, vertical asymptote $x = 0$, and its reflection of the exponential in $y = x$.
- Solving exponential equations30-1.RF.10 — Solve exponential equations by matching bases (equate exponents) or, when bases will not match, by taking a logarithm of both sides and isolating the variable.
- Solving logarithmic equations30-1.RF.10 — Solve logarithmic equations by condensing to a single logarithm and rewriting in exponential form, then reject any solution that makes a logarithm argument zero or negative.
Factoring and Graphing Polynomials
- Factoring higher-degree polynomials30-1.RF.11 — Factor polynomials of degree $\le 5$ with integral coefficients using the integral zero theorem, the factor theorem and synthetic (or long) division to find factors from candidate roots.
- Graphing polynomial functions30-1.RF.12 — Graph polynomial functions of degree $\le 5$ using end behaviour (leading coefficient and degree), $x$-intercepts with their multiplicities (cross vs. touch), and the $y$-intercept.
Radical and Rational Functions
- Graphing radical functions30-1.RF.13 — Graph and analyze $y = a\sqrt{b(x - h)} + k$ from the base $y = \sqrt{x}$, stating the restricted domain (radicand $\ge 0$) and the resulting range.
- Graphing rational functions30-1.RF.14 — Graph and analyze rational functions such as $\dfrac{x^2 - 1}{x + 1}$, locating vertical asymptotes at non-permissible zeros, holes at common factors, and horizontal/oblique end behaviour.
The official wording — 14 outcomes in this unit
- 30-1.RF.1
Demonstrate an understanding of operations on, and compositions of, functions.
- 30-1.RF.2
Demonstrate an understanding of the effects of horizontal and vertical translations on the graphs of functions and their related equations.
- 30-1.RF.3
Demonstrate an understanding of the effects of horizontal and vertical stretches on the graphs of functions and their related equations.
- 30-1.RF.4
Apply translations and stretches to the graphs and equations of functions.
- 30-1.RF.5
Demonstrate an understanding of the effects of reflections on the graphs of functions and their related equations, including reflections through the: x -axis y -axis
- 30-1.RF.6
Demonstrate an understanding of inverses of relations.
- 30-1.RF.7
Demonstrate an understanding of logarithms.
- 30-1.RF.8
Demonstrate an understanding of the product, quotient and power laws of logarithms.
- 30-1.RF.9
Graph and analyze exponential and logarithmic functions.
- 30-1.RF.10
Solve problems that involve exponential and logarithmic equations.
- 30-1.RF.11
Demonstrate an understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients).
- 30-1.RF.12
Graph and analyze polynomial functions (limited to polynomial functions of degree ≤ 5 ).
- 30-1.RF.13
Graph and analyze radical functions (limited to functions involving one radical).
- 30-1.RF.14
Graph and analyze rational functions (limited to numerators and denominators that are monomials, binomials or trinomials).
Unit 2TrigonometryOfficial strand · Trigonometry
General outcome: develop trigonometric reasoning. Angles in standard position in degrees and radians, the unit circle, the six trigonometric ratios, the graphs of sine, cosine and tangent, solving trigonometric equations, and proving trigonometric identities.
Angles in Degrees and Radians
- Angles in standard position (degrees)30-1.T.1 — Sketch angles in standard position measured in degrees, identify the quadrant and reference angle, and find degree coterminal angles $\theta + 360^\circ n$.
- Radian measure and conversion30-1.T.1 — Understand radian measure via $180^\circ = \pi$ radians, convert between degrees and radians, find radian coterminal angles $\theta + 2\pi n$, and compute arc length $a = r\theta$.
The Unit Circle
- The equation of the unit circle30-1.T.2 — Develop and apply $x^2 + y^2 = 1$, using the terminal point $(\cos\theta,\ \sin\theta)$ on the unit circle to read exact coordinates for special angles.
The Six Trigonometric Ratios
- Primary ratios in radians and degrees30-1.T.3 — Evaluate and apply $\sin\theta,\ \cos\theta,\ \tan\theta$ for angles expressed in radians and degrees, including exact values for special angles read from the unit circle with the correct quadrant sign.
- Reciprocal ratios: cosecant, secant, cotangent30-1.T.3 — Evaluate and apply the reciprocal ratios $\csc\theta = \tfrac{1}{\sin\theta},\ \sec\theta = \tfrac{1}{\cos\theta},\ \cot\theta = \tfrac{1}{\tan\theta}$, matching each to its primary partner (the letters cross).
Graphing Trigonometric Functions
- Graphing sine and cosine30-1.T.4 — Graph and analyze $y = a\sin\big(b(x - c)\big) + d$ and the cosine analogue, reading amplitude $|a|$, period $\tfrac{2\pi}{|b|}$, phase shift $c$ and vertical displacement $d$ to solve problems.
- Graphing tangent30-1.T.4 — Graph and analyze the tangent function: period $\pi$, no amplitude, and vertical asymptotes where $\cos = 0$; apply transformations to locate its asymptotes and cycles.
Solving Trigonometric Equations
- First-degree trigonometric equations30-1.T.5 — Solve first-degree trigonometric equations algebraically and graphically over a domain in degrees or radians, using reference angles and quadrant signs to give ALL solutions (and the general solution $\theta + 2\pi n$).
- Second-degree trigonometric equations30-1.T.5 — Solve second-degree trigonometric equations by factoring like quadratics (e.g. $2\sin^2\theta - \sin\theta - 1 = 0$) or applying an identity first, then solving each factor over the stated domain.
Proving Trigonometric Identities
- Reciprocal and quotient identities30-1.T.6 — Prove identities using the reciprocal identities and the quotient identities $\tan\theta = \tfrac{\sin\theta}{\cos\theta},\ \cot\theta = \tfrac{\cos\theta}{\sin\theta}$, transforming one side by rewriting every ratio in sines and cosines.
- Pythagorean identities30-1.T.6 — Prove identities using the Pythagorean identities $\sin^2\theta + \cos^2\theta = 1$ (and its $\tan/\sec$ and $\cot/\csc$ forms), substituting to simplify or replace $1 - \cos^2\theta$ etc.
- Sum and difference identities30-1.T.6 — Prove identities and evaluate exact values using the sum and difference identities for sine, cosine and tangent (e.g. $\cos(A - B) = \cos A\cos B + \sin A\sin B$).
- Double-angle identities30-1.T.6 — Prove identities and simplify using the double-angle identities for sine, cosine and tangent (e.g. $\sin 2\theta = 2\sin\theta\cos\theta$; the three forms of $\cos 2\theta$).
The official wording — 6 outcomes in this unit
- 30-1.T.1
Demonstrate an understanding of angles in standard position, expressed in degrees
- 30-1.T.2
Develop and apply the equation of the unit circle.
- 30-1.T.3
Solve problems, using the six trigonometric ratios for angles expressed in radians and degrees.
- 30-1.T.4
Graph and analyze the trigonometric functions sine, cosine and tangent to solve problems.
- 30-1.T.5
Solve, algebraically and graphically, first and second degree trigonometric equations with the domain expressed in degrees and radians.
- 30-1.T.6
Prove trigonometric identities, using: reciprocal identities quotient identities
Unit 3Permutations, Combinations and Binomial TheoremOfficial strand · Permutations, Combinations and Binomial Theorem
General outcome: develop algebraic and numeric reasoning that involves combinatorics. The fundamental counting principle, permutations of n objects taken r at a time, combinations, and expanding a binomial power with the binomial theorem.
Counting Principle and Permutations
- The fundamental counting principle30-1.PCB.1 — Apply the fundamental counting principle — multiply the number of choices at each independent stage — to count arrangements and outcomes, handling restrictions.
- Permutations of n taken r at a time30-1.PCB.2 — Count ordered arrangements with $_nP_r = \dfrac{n!}{(n - r)!}$, including permutations with repeated (identical) elements, where order matters.
Combinations and the Binomial Theorem
- Combinations of n taken r at a time30-1.PCB.3 — Count unordered selections with $_nC_r = \dbinom{n}{r} = \dfrac{n!}{r!\,(n - r)!}$, where order does NOT matter, and distinguish selection problems from arrangement problems.
- Expanding with the binomial theorem30-1.PCB.4 — Expand $(a + b)^n$ using the binomial theorem $\displaystyle\sum_{k=0}^{n}\binom{n}{k}a^{n-k}b^{k}$ and Pascal’s triangle, and find a specific term without expanding fully.
The official wording — 4 outcomes in this unit
- 30-1.PCB.1
Apply the fundamental counting principle to solve problems.
- 30-1.PCB.2
Determine the number of permutations of n elements taken r at a time to solve problems.
- 30-1.PCB.3
Determine the number of combinations of n different elements taken r at a time to solve problems.
- 30-1.PCB.4
Expand powers of a binomial in a variety of ways, including using the binomial theorem (restricted to exponents that are natural numbers).
Printable workbook · A keepsake of the year
A Mathematics 30-1 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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Common questions
Can MapleMind help me with Mathematics 30-1?
Yes. MapleMind's AI tutor covers all 35 skills in Alberta's Mathematics 30-1 — 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 Alberta's official curriculum?
Yes. Every skill in this course maps to an official outcome code from Alberta's Grade 12 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 Alberta curriculum for Mathematics 30-1?
The official source is linked on this page — Alberta's official programs of study. 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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