Courses

Alberta · Grade 12

Mathematics 30-2

  • MAT3792

Alberta’s Grade 12 math course, from Logical Reasoning to Mathematics Research Project.

Learn thisPractice exam
Units
4
Lessons
17
Skills
36
Provincial exam
30% of the final mark
Official curriculum
Alberta Education

Unit by unit

Every skill in the course, numbered by unit.

Unit 1 · 5 skills

Logical Reasoning

Puzzles, Games and Reasoning

Set Theory

The official wording · 5 outcomes
1.1
Analyze puzzles and games that involve numerical and logical reasoning, using problem-solving strategies.
1.3
Solve problems that involve the application of set theory.

Key ideas

  1. A strategy toolbox unlocks puzzles: guess-and-check, work backwards, look for a pattern, reason by cases, simplify to a smaller version.

  2. A set is a collection of distinct elements; the universal set UU holds everything under discussion, and the empty set ∅\varnothing holds nothing.

  3. Numerical and logical reasoning means justifying WHY a move or answer works — not just landing on it by luck.

  4. A Venn diagram places elements into overlapping regions so subsets, the complement A′A' and shared elements are visible at a glance.

  5. A winning strategy is a rule that guarantees a win no matter what the opponent does — it must cover EVERY opponent response.

Watch out for

  • Believing a single successful play proves a strategy always wins — one example is not a proof.
  • Confusing the empty set ∅\varnothing with the set {0}\{0\} or {∅}\{\varnothing\} (they are not empty).
  • Confusing 'I found an answer' with 'I can justify the answer' (guess-and-check still needs a reason).

Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit

Unit 2 · 12 skills

Probability

Odds and Probability

Mutually Exclusive and Non–Mutually Exclusive Events

The Probability of Two Events

The Fundamental Counting Principle

Permutations

Combinations

The official wording · 12 outcomes
2.1
Interpret and assess the validity of odds and probability statements.
2.3
Solve problems that involve the probability of mutually exclusive and non–mutually exclusive events.
2.5
Solve problems that involve the probability of two events.
2.7
Solve problems that involve the fundamental counting principle.
2.9
Solve problems that involve permutations.
2.11
Solve problems that involve combinations.

Key ideas

  1. Odds compare favourable to unfavourable (a:ba:b); probability compares favourable to TOTAL: P(A)=aa+bP(A) = \frac{a}{a+b}.

  2. Mutually exclusive events cannot happen together, so P(A∩B)=0P(A \cap B) = 0 and P(A∪B)=P(A)+P(B)P(A \cup B) = P(A) + P(B).

  3. Independent events don't affect each other, so P(A∩B)=P(A)×P(B)P(A \cap B) = P(A) \times P(B) — multiply for 'and'.

  4. If choices are made in sequence with mm ways then nn ways, there are m×nm \times n total ways — multiply the options at each stage.

  5. A permutation is an ORDERED arrangement: nPr=n!(n−r)!_nP_r = \frac{n!}{(n-r)!} counts the ways to arrange rr of nn distinct objects.

Watch out for

  • Treating odds of 3:23:2 as a probability of 32\frac{3}{2} (probabilities never exceed 1).
  • Confusing 'mutually exclusive' with 'independent' — exclusivity is about co-occurrence, independence is about influence.
  • Confusing independent with mutually exclusive — exclusive events multiply to 0, not to P(A)P(B)P(A)P(B).

Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit

Unit 3 · 16 skills

Relations and Functions

Rational Expressions

Operations on Rational Expressions

Rational Equations

Logarithms and the Laws of Logarithms

Exponential Equations

Modelling with Exponential and Logarithmic Functions

Modelling with Polynomial Functions

Modelling with Sinusoidal Functions

The official wording · 16 outcomes
3.1
Determine equivalent forms of rational expressions (limited to numerators and denominators that are monomials and binomials).
3.3
Perform operations on rational expressions (limited to numerators and denominators that are monomials and binomials).
3.5
Solve problems that involve rational equations (limited to numerators and denominators that are monomials and binomials).
3.7
Demonstrate an understanding of logarithms and the laws of logarithms.
3.9
Solve problems that involve exponential equations.
3.11
Represent data, using exponential and logarithmic functions, to solve problems.
3.13
Represent data, using polynomial functions (of degree ≤ 3), to solve problems.
3.15
Represent data, using sinusoidal functions, to solve problems.

Key ideas

  1. Factor numerator and denominator completely (monomials and binomials here), then divide out common FACTORS to get an equivalent form.

  2. Multiply EVERY term by the LCD to clear denominators, then solve the resulting polynomial equation.

  3. log⁡bx=y\log_b x = y means exactly by=xb^y = x — a logarithm IS an exponent (the power the base is raised to).

  4. If both sides can be written with the SAME base, the exponents must be equal: bm=bn⇒m=nb^m = b^n \Rightarrow m = n.

  5. y=abxy = ab^x: aa is the initial value and bb is the growth (b>1b > 1) or decay (0<b<10 < b < 1) factor per unit.

Watch out for

  • Cancelling TERMS across addition (x+3x+5\frac{x + 3}{x + 5} 'reduced' to 35\frac{3}{5}) instead of factors.
  • Multiplying only some terms by the LCD.
  • Reading log⁡bx\log_b x as base times xx rather than 'the exponent on bb that gives xx'.

Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit

Unit 4 · 3 skills

Mathematics Research Project

Plan, Conduct and Present a Research Project

The official wording · 3 outcomes
4.1
Research and give a presentation on a current event or an area of interest that involves mathematics.

Key ideas

  1. Choose a current event or area of interest that genuinely INVOLVES mathematics, then frame a focused, answerable research question.

  2. Plan credible sources and a method BEFORE gathering — a narrow question beats a vague broad topic.

  3. Gather data and evidence, then apply appropriate mathematical tools (statistics, functions, probability) to analyze the topic.

  4. Cite sources honestly and distinguish reliable evidence from opinion or unsupported claims.

  5. Organize the presentation: question, what you found, the mathematics behind it, and a clear conclusion.

Watch out for

  • Picking a topic with no real mathematics in it (a report ABOUT math, not USING math).
  • Starting a question so broad it can't be answered in one project.
  • Presenting numbers without any actual mathematical analysis of them.

Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit

The exam

The mark you need

Your class mark counts for 70% of the final mark, the exam for 30%.

You need

59% on the exam

With 75% in class, your final mark lands between 52.5% (0 on the exam) and 82.5% (100% on it).

Which course?

Alberta has 4 math courses for Grade 12. Here they are side by side.

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 30-2.

Mathematics Grades 10–12 Program of Studies, 2008, Mathematics 30-2 / MAT3792Alberta Education · curriculum.learnalberta.ca · Read July 22, 2026

Strands

StrandOutcomesTaught in
Logical ReasoningOutcomes 2Taught in Unit 1
ProbabilityOutcomes 6Taught in Unit 2
Relations and FunctionsOutcomes 8Taught in Unit 3
Mathematics Research ProjectOutcomes 1Taught in Unit 4

Study it in MapleMind

MapleMind teaches Mathematics 30-2 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.

Mathematics 31 in the MapleMind app on a tablet: its units, Unit 1 open, and the skills done so far with their starsMathematics 31 in the MapleMind app on a phone: its units, Unit 1 open, and the skills done so far with their stars
Pictured: Mathematics 31, another Alberta course, partway through Unit 1.

Practise it

Course Companion

Your year in one workbook

A fun way to keep Mathematics 30-2 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
31
Fillable fields
1,517
Price
$4.99
See the Course Companion

Questions about Mathematics 30-2

What is Mathematics 30-2?

Alberta’s Grade 12 math course: 4 units and 36 skills, from Logical Reasoning to Mathematics Research Project.

What units are in Mathematics 30-2?

1. Logical Reasoning, 2. Probability, 3. Relations and Functions and 4. Mathematics Research Project.

Is there a provincial exam for Mathematics 30-2?

Yes. The Mathematics 30–2 Diploma Exam counts for 30% of the final mark. Next sitting: January 20, 2027.

Can MapleMind help with Mathematics 30-2?

Yes. MapleMind teaches every skill of Mathematics 30-2, 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.

Before this course

Get ready for Mathematics 30-2

Practise every skill of Mathematics 30-2 in MapleMind, free with daily limits.