MAT / SR / 01
Precalculus
Functions, logs and trigonometry from another angle.
Open the syllabusAlberta · Grade 12 · Mathematics 30-1
Mathematics 30-1 is the Grade 12 course Alberta designs for students heading to programs that need calculus, and it ends in a provincial diploma exam that counts for 30 per cent of the final mark. Most students who struggle with it are not weak at math: they lose marks on a short list of skills that Alberta’s own markers name every year. This page lays out the course from Alberta Education’s documents, then works through two of those skills step by step. We teach alongside your teen’s school course, and we do not grant provincial credits: that credit is the school’s to give.
Teaching live online since 2020 · 10,000+ students · Edmonton, Calgary and anywhere in Alberta
In short
Math 30-1 is Alberta’s Grade 12 math course for students bound for programs that require calculus: functions and their transformations, exponents and logarithms, polynomial, radical and rational functions, trigonometry, and permutations and combinations, finished by a diploma exam worth 30 per cent. Modern Age Coders tutors it live online through our Western Canada Grade 12 Math course, in a batch or one to one.
Learn it with a teacher
The first follows Alberta’s Grade 12 outcomes directly. The other two suit students who want a broader base or a head start on calculus.

MAT / 01
Grade 12. Paced to Math 30-1 and BC Pre-calculus 12, with written-response practice in the diploma style.
Open the syllabus →
MAT / 02
Grades 9 to 12. Rebuilds the algebra underneath 30-1 for students carrying gaps from earlier courses.
Open the syllabus →
MAT / 03
Grades 11 and 12. Limits and derivatives for students taking Math 31 or heading into first-year calculus.
Open the syllabus →Alberta’s own outcomes
Alberta Education describes the course this way in its 2026 to 2027 bulletin: Math 30-1 builds the “critical-thinking skills identified for entry into post-secondary programs that require the study of calculus”, and “algebraic, numerical, and graphical approaches are used to solve problems.” The program of studies groups the course under three general outcomes. The wording below is Alberta’s, as reprinted in its Assessment Standards and Exemplars document.
| Strand and general outcome | Specific outcomes, in Alberta’s words (shortened) | What that means at the desk (our reading) |
|---|---|---|
| Relations and Functions: “Develop algebraic and graphical reasoning through the study of relations.” | “operations on, and compositions of, functions”; translations, stretches and reflections “on the graphs of functions and their related equations”; “inverses of relations” | Reading a transformed equation like a set of instructions, mapping notation, finding an inverse and its restrictions |
| Relations and Functions, continued | “Demonstrate an understanding of logarithms.”; “the product, quotient, and power laws of logarithms”; “Graph and analyze exponential and logarithmic functions.”; “Solve problems that involve exponential and logarithmic equations.” | Switching between exponential and logarithmic form, combining log laws, solving equations with and without a common base |
| Relations and Functions, continued | “factoring polynomials of degree greater than 2”; “Graph and analyze polynomial functions”; “Graph and analyze radical functions”; “Graph and analyze rational functions” | Factor theorem and zeros with multiplicity, square-root graphs, asymptotes and holes |
| Trigonometry: “Develop trigonometric reasoning.” | “angles in standard position, expressed in degrees and radians”; “Develop and apply the equation of the unit circle.”; “the six trigonometric ratios”; graphs of sine, cosine and tangent | Radians as a ratio of arc to radius, exact values from the unit circle, amplitude, period and phase shift |
| Trigonometry, continued | “Solve, algebraically and graphically, first- and second-degree trigonometric equations”; “Prove trigonometric identities” using reciprocal, quotient, Pythagorean, sum or difference and double-angle identities | Solving with every solution in the domain, and writing a proof that works one side only |
| Permutations, Combinations, and Binomial Theorem: “Develop algebraic and numeric reasoning that involves combinatorics.” | “Apply the fundamental counting principle to solve problems.”; permutations “of n elements taken r at a time”; combinations “of n different elements taken r at a time”; “Expand powers of a binomial in a variety of ways, including using the binomial theorem” | Counting with cases and restrictions, telling order from no order, finding one term of an expansion without writing them all |
The general notes in the same document carry rules that cost marks when they are ignored. One is about order: “Stretches and reflections are performed prior to translations unless otherwise stated.” A student who translates first gets the right shape in the wrong place.
Another is about technology. For the transformation, inverse and logarithm outcomes, and for factoring polynomials, Alberta says that “students are expected to meet these outcomes without the use of technology”, even though they may use it to explore. In practice that means the graphing calculator can confirm an answer but cannot be the method.
Alberta lists seven mathematical processes that are meant to run through the whole course: Communication [C], Connections [CN], Mental Mathematics and Estimation [ME], Problem Solving [PS], Reasoning [R], Technology [T] and Visualization [V]. Every specific outcome is tagged with some of them.
Communication is the one families underestimate. The bulletin says students are expected to “communicate solutions clearly and effectively when solving both routine and non-routine problems.” On the diploma exam that is not a slogan: it is a quarter of the mark, the written-response part.
| Part of the blueprint | Alberta’s figure |
|---|---|
| Machine-scored questions | 32 questions, 75% of the exam |
| Written-response questions | 3 questions, 25% of the exam, equally weighted |
| Relations and Functions | 53% to 58% |
| Trigonometry | 27% to 33% |
| Permutations, Combinations, and Binomial Theorem | 14% to 18% |
| Cognitive level: conceptual, problem solving, procedural | 34%, 36% and 30% |
| Time | Designed for 3 hours; a further 3 hours allowed |
Sources: Mathematics 30-1 Assessment Standards and Exemplars (general notes and specific outcomes) and the Mathematics 30-1 Information Bulletin 2026-2027 (course objectives, processes, specifications), both read 22 October 2026. Alberta prints the course name with an en dash; we write Math 30-1. We have no connection with Alberta Education and Childcare.
Where marks go
Each year’s bulletin carries a commentary on how students did on past diploma exams. It is the most useful page a Math 30-1 student never reads. We use it as a teaching map: the left column is Alberta’s observation, the right is what we do about it in class.
| Alberta’s commentary says students... | How we teach it |
|---|---|
| have “difficulty using this notation to represent stretches” (mapping notation) | Every transformation is written as a mapping rule first, (x, y) to (new x, new y), before any graph is drawn |
| have “difficulty determining the number of invariant points associated with other transformations” | Students solve for the points a rule leaves unchanged instead of guessing from a sketch |
| have difficulty “combining multiple logarithm laws to simplify an expression into a single logarithm or to solve a logarithmic equation” | Laws are applied one per line, with the power law always first, and every solution checked in the original equation |
| have “difficulty determining the domain and range of a rational function that contains a point of discontinuity” | Factor first, cancel second, and record what the cancelled factor removed from the domain and the range: worked problem 1 below |
| have “difficulty solving equations when an identity substitution is required” | Students learn to spot a mixed equation, choose the identity that leaves one function, then factor: worked problem 2 below |
| struggle with identities “that involve conjugates, double angle identities, and the use of rational operations” | Proofs written in two columns, one side at a time, never moving terms across an equals sign |
| struggle with permutation problems with “three or more constraints or multiple cases” | Cases are listed in a table before any factorial is written, then added |
| have “difficulty determining specific terms in the expansion of a binomial with non-linear terms” | The general term is written out with its exponent as an expression in k, and k is solved for |
The written-response observations are blunter. Markers saw many students who do not grasp “the difference between simplifying or factoring an expression and solving an equation”, or “the difference between verifying and proving a trigonometric identity”. Those are not slips; they are misunderstandings of what the question asked.
Smaller habits cost marks too: students “forget to include the angle argument” (writing sin instead of sin x), drop brackets, and “write expressions in place of equations”. Alberta also warns that “Using abbreviations in written explanations is inappropriate and not acceptable.”
The commentary is not all bad news. Alberta reports that students “continue to perform well” on coterminal angles, arc length and angles in standard position, that they can “solve exponential equations that can be simplified to a common base”, and that they relate the parameters of a sinusoidal equation to its graph.
That shapes how we spend time. A student already strong on sinusoidal graphs does not need another week of them; the hour goes to the identity substitution or the multi-case counting problem instead.
Source: the commentary pages of the Mathematics 30-1 Information Bulletin 2026-2027, read 22 October 2026. The table quotes Alberta’s observations; the teaching responses are ours.
Worked problems, ours
Both problems are our own, written for this page, and both sit on a line of Alberta’s commentary above. They are not Alberta Education questions. Each one is laid out as a full written response: every step shown, every restriction stated, every answer checked.
Problem 1: a rational function with a hole. For f(x) = (x2 − 4) / (x2 − x − 2), state the non-permissible values, the point of discontinuity, the asymptotes, and the domain and range.
Problem 2: an equation that needs an identity substitution. Solve 2cos2x − sin x − 1 = 0 algebraically for 0 ≤ x < 2π, giving exact values.
Alberta’s directing word algebraically means “Using mathematical procedures that involve variables or symbols to represent values”. A graphing calculator would find the three solutions of problem 2 in seconds, but a response that only reports them has not answered a question that says algebraically.
Writing one step per line also makes the response markable. Alberta scores each written-response part against a general scoring guide, and partial credit is available, so a student who sets up the substitution correctly and then slips still earns something.
In both, the trap is a restriction. In problem 1 it is a value the cancelled factor removed; in problem 2 it is the solutions hiding in a second quadrant. Neither is hard mathematics. Both are skipped by students in a hurry.
So our students finish every solution with the same question: what did I exclude, and did I find everything in the domain? It takes ten seconds and it is the habit we most want them to carry into the exam room.
Practice, ours
We wrote these ten for this page; none is an Alberta Education question and none comes from a released exam. They follow the course from functions to combinatorics. Work them without a calculator unless a question says otherwise, then check the answers in the next section.
Questions 2, 3, 4 and 7 come straight from the commentary’s list of weak spots, so a student who gets them right has fixed something markers see often. A question you cannot start is information, not failure: note it, and bring it to a class.
Answers, ours
Each answer was checked by substitution and in Python. The reasoning matters more than the number, because on the written-response part it is the reasoning that earns the marks.
A term plan, ours
Schools set their own unit order, so we start from the student’s course outline. When a family asks us for a default, this is the order we use and the reason for each step. It is our plan, not Alberta’s.
| Stage | Units | Finished when the student can |
|---|---|---|
| 1 | Transformations, inverses, function operations and composition | Write any transformation as a mapping rule and find invariant points by solving, not sketching |
| 2 | Exponential and logarithmic functions and equations | Combine three log laws in one line and reject an extraneous root with a reason |
| 3 | Polynomial, radical and rational functions | Find zeros with multiplicity, and the domain and range of a rational function with a hole |
| 4 | Angles, the unit circle, the six ratios and trigonometric graphs | Give exact values from memory and read amplitude, period and phase shift from an equation |
| 5 | Trigonometric equations and identities | Solve with an identity substitution, and prove an identity working one side |
| 6 | Permutations, combinations and the binomial theorem | Split a counting problem into cases and find one term of an expansion with a non-linear term |
| 7 | Mixed review and timed practice | Finish a full-length mixed set in three hours with the written responses fully laid out |
Relations and Functions is more than half of the exam blueprint, and its ideas return everywhere: a sinusoidal graph is a transformed sine function, and an exponential model is a function to be inverted. Students who master mapping notation early find the trigonometry unit shorter.
Logarithms come early for a different reason. They take repetition to become automatic, and a student who meets them in October has months of spaced practice before the exam. A student who meets them in May has days.
A class starts with five minutes of mixed retrieval from earlier units, then the current school topic taught from the student’s own homework, then one written response laid out in full. The student does the writing; the teacher asks questions.
Every few weeks we set a short mixed set in the diploma style: machine-scored questions first, then one written response. Its mistakes go into a log the student keeps until exam week.
For the exam itself, Alberta’s schedule for 2026 to 2027 sets Mathematics 30-1 at 9 AM on Tuesday 3 November 2026, and on Wednesday 20 January, Thursday 8 April, Thursday 17 June and Thursday 5 August 2027. The exam earns a separate plan for its final weeks, built around the written-response rules, and we start that plan about eight weeks before the student’s sitting. Our comparison of Grade 12 math across Canada shows how Math 30-1 sits beside Pre-calculus 12 and MHF4U for families who move between provinces.
Calculator, Math 31 and the credit
Three questions families ask in the first class, answered from Alberta’s documents.
The bulletin says the Math 30-1 diploma exam “requires the use of an approved graphing calculator”, cleared and configured before and after the exam, with the approved list in Alberta’s 2026 to 2027 Calculator Information and Rules document. We teach on the model the student will write with.
Alberta’s Guide to Education, updated 4 September 2026, says “Mathematics 30-1 is a prerequisite or corequisite for Mathematics 31.” Its course chart shows Math 10C to 20-1 to 30-1 as the typical route, and notes that each math course is 5 credits.
The credit and the school-awarded 70 per cent come from the student’s own school, and the 30 per cent from Alberta’s diploma exam. Our classes run beside that school course, and we do not grant provincial credits.
Classes are live online, so a student in Edmonton, Calgary, Red Deer or a rural school division gets the same teacher and the same plan. What changes is only the clock.
Alberta keeps UTC-6 all year in the IANA time zone database (2026e), so there is no spring or autumn change to plan around. Our teachers work on India time, which is 11 hours 30 minutes ahead of Alberta throughout the year.
The most common start is the first month of the course, when the transformation unit is new and fixable. The second most common is about eight weeks before the diploma date, which still leaves room for the stage 7 review above.
Starting in the last fortnight is possible, but it changes what a teacher can do: by then the work is triage, choosing the two or three skills with the most marks attached and drilling them.
Sources: the Mathematics 30-1 Information Bulletin 2026-2027 (calculators); Alberta Education and Childcare, Guide to Education, transfer points and course sequences (version updated 4 September 2026); Diploma exams overview. All read 22 October 2026.
Where your teen is now
Our own stages, drawn from teaching Grade 12 students through pre-calculus courses like this one.
| Stage | How it shows up |
|---|---|
| 1. Answer-getter | Gets numbers on routine questions, often with the calculator doing the thinking, and loses written-response marks |
| 2. Step-writer | Shows each step, states restrictions, and can say why a root was rejected |
| 3. Connector | Sees a sinusoidal model or a log equation as a transformed function, and switches methods when one stalls |
| 4. Diploma-ready | Finishes a mixed timed set with every written response complete, labelled and checked |
Pick one solution from this week and have your teen talk you through it, restrictions included. Fluent talk there says more than a single test mark.
Stage 2 is where outside help pays off most. Writing every step feels slow, and a patient second teacher turns it into a habit before the exam makes it urgent.
When you check an answer, check the restriction too. It is the cheapest mark on the paper.
Keep a list of the directing words you meet in questions, with Alberta’s definition beside each. By May it will save you more time than any formula.
The catalogue
Every course runs live online with a regular teacher, in a batch or one to one.
MAT / SR / 01
Functions, logs and trigonometry from another angle.
Open the syllabusMAT / SR / 02
For students who enjoyed the counting unit.
Open the syllabusMAT / SR / 03
For students applying to US universities.
Open the syllabusMAT / CON / 01
Pascal to Euclid, for students who want harder problems.
Open the syllabusMAT / CON / 02
Proof and problem solving well past the course.
Open the syllabusMAT / CON / 03
Waterloo’s programming contest, step by step.
Open the syllabusMAT / NXT / 01
Graph a function, then make it move.
Open the syllabusMAT / NXT / 02
Exponential models fitted to real data.
Open the syllabusMAT / NXT / 03
Where logs and functions turn up next.
Open the syllabusHow classes run
Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays.
Weekdays
After school on Alberta time, fixed once you pick a batch.
Weekends
Weekend mornings suit many Grade 12 timetables in Alberta.
1-on-1
Booked around unit tests and the diploma date.
The same person from the first unit to the exam.
Your teen’s unit order, not ours.
Laid out in full, every class.
Used to check, never to replace a step.
Kept by the student, read before exams.
A batch of fifteen to twenty, or one student.
Student work
Projects by students who use functions and data in their own code, from graphs to simulations. More on the student labs page.

AI and ML
An AI nutrition coach that reads what you eat and works you toward a target.

AI and ML
A chatbot that answers mathematics and programming questions, built and deployed by a student.

AI and ML
An assistant that helps a young person recognise unsafe situations online.

Web app
A weather forecasting site with live conditions for any location.
Fees
The first class is free. From then on it is a monthly fee for eight live classes a month, shown below in your own currency; there is no term contract, and you can cancel before any new month begins.
Free first class
Free
no card required
Group batch
$100 USD
a month, eight live classes
One to one
$150 USD
a month, eight live classes
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Questions from Alberta families
Mathematics 30-1 is the Grade 12 Alberta math course for students heading to post-secondary programs that require calculus. Its three strands are Relations and Functions, Trigonometry, and Permutations, Combinations and Binomial Theorem, and it ends with a provincial diploma exam.
No. We teach alongside your teen's Math 30-1 class and do not grant provincial credits. The credit and the school-awarded mark come from their own school, and the diploma exam portion is set and marked by Alberta Education and Childcare.
Alberta says the weighting of diploma exams returned to 30 percent on 1 September 2023: 70 percent of the final mark comes from course work and 30 percent from the diploma exam.
For 2026 to 2027 the bulletin lists 32 machine-scored questions worth 75 percent and 3 written-response questions worth 25 percent. Relations and Functions carries 53 to 58 percent, Trigonometry 27 to 33 percent, and the counting strand 14 to 18 percent.
Alberta schedules it at 9 AM on Tuesday 3 November 2026, Wednesday 20 January 2027, Thursday 8 April 2027, Thursday 17 June 2027 and Thursday 5 August 2027. Schools register first-time students.
Alberta's own commentary points to logarithm equations that combine several laws, rational functions with a hole, trigonometric equations that need an identity substitution, identity proofs, and counting problems with several cases. Those are the units we spend most time on.
Yes, an approved graphing calculator is required on the diploma exam, cleared and configured before and after. But Alberta expects several outcomes, including transformations and logarithm laws, to be met without technology, so steps still have to be shown.
Alberta's Guide to Education shows Math 10C, then Math 20-1, then Math 30-1 as the typical route, and says Math 30-1 is a prerequisite or corequisite for Mathematics 31.
Yes, live online for students anywhere in Alberta, including Edmonton and Calgary. Alberta is on UTC-6 all year, so class times stay the same through the school year.
Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays. Class times are set in Alberta time.
Nothing for the first class. Families who continue pay one monthly fee covering eight live classes, with no term contract. The current batch and one-to-one figures appear in the Fees part of this page.
Elsewhere on this site
Pages that pair well with Math 30-1.
All of our pages for Canadian families.
Coding and math for Alberta learners of every age.
Math 30-1 beside Pre-calculus 12 and MHF4U.
Math help from Grade 1 to Grade 12.
Functions and trigonometry in more depth.
For Math 31 and first-year calculus.
The ratios underneath the unit circle.
Waterloo’s contest for senior students.
What happens in a live class, minute by minute.
Start here
Send us the unit your teen is on, the date of the next test and whether they are writing the diploma in November, January, April, June or August. The first class starts from their own work.
Want to look first? How we teach describes a class in detail, and the Western Canada Grade 12 Math syllabus lists the plan week by week.
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