Courses

Alberta · Grade 12

Mathematics 30-1

  • MAT3791

Alberta’s Grade 12 math course, from Relations and Functions to Permutations, Combinations and Binomial Theorem.

Learn thisPractice exam
Units
3
Lessons
18
Skills
35
Provincial exam
30% of the final mark
Official curriculum
Alberta Education

Unit by unit

Every skill in the course, numbered by unit.

Unit 1 · 18 skills

Relations and Functions

Operations and Composition of Functions

Translations of Graphs

Stretches of Graphs

Combining Transformations

  • Combining translations and stretches

    I can apply a full combination of stretches and translations in the correct order.

    1.5

    Learn itPractice testActivities

Reflections of Graphs

Inverses of Relations

Logarithms and Their Laws

Exponential and Logarithmic Functions

Factoring and Graphing Polynomials

Radical and Rational Functions

The official wording · 18 outcomes
1.1
Demonstrate an understanding of operations on, and compositions of, functions.
1.3
Demonstrate an understanding of the effects of horizontal and vertical translations on the graphs of functions and their related equations.
1.4
Demonstrate an understanding of the effects of horizontal and vertical stretches on the graphs of functions and their related equations.
1.5
Apply translations and stretches to the graphs and equations of functions.
1.6
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
1.8
Demonstrate an understanding of inverses of relations.
1.9
Demonstrate an understanding of logarithms.
1.10
Demonstrate an understanding of the product, quotient and power laws of logarithms.
1.11
Graph and analyze exponential and logarithmic functions.
1.13
Solve problems that involve exponential and logarithmic equations.
1.15
Demonstrate an understanding of factoring polynomials of degree greater than 2 (limited to polynomials of degree ≤ 5 with integral coefficients).
1.16
Graph and analyze polynomial functions (limited to polynomial functions of degree ≤ 5 ).
1.17
Graph and analyze radical functions (limited to functions involving one radical).
1.18
Graph and analyze rational functions (limited to numerators and denominators that are monomials, binomials or trinomials).

Key ideas

  1. Combine pointwise: (f+g)(x)(f+g)(x)=f(x)+g(x)=f(x)+g(x), (f−g)(x)(f-g)(x)=f(x)−g(x)=f(x)-g(x), (fg)(x)=f(x)g(x)(fg)(x)=f(x)g(x), (fg)(x)=f(x)g(x)\left(\tfrac{f}{g}\right)(x)=\tfrac{f(x)}{g(x)}.

  2. In y−k=f(x−h)y - k = f(x - h): kk shifts UP by kk (vertical), hh shifts RIGHT by hh (horizontal). The mapping is (x,y)→(x+h, y+k)(x,y)\to(x+h,\ y+k).

  3. In y=af(bx)y = af(bx): aa is a VERTICAL stretch by factor ∣a∣|a| (multiplies yy-values); bb is a HORIZONTAL stretch by factor 1∣b∣\tfrac{1}{|b|} (divides xx-values).

  4. For y=af(b(x−h))+ky = af\big(b(x-h)\big)+k, FACTOR out bb inside the bracket first so hh reads correctly, then apply stretches/reflections BEFORE translations.

  5. y=−f(x)y=-f(x) reflects across the xx-axis (negate the OUTPUT yy); y=f(−x)y=f(-x) reflects across the yy-axis (negate the INPUT xx).

Watch out for

  • Forgetting to exclude the zeros of the divisor in the quotient's domain.
  • Shifting f(x+3)f(x+3) to the RIGHT because the sign 'looks' positive (it goes LEFT).
  • Treating bb as the horizontal stretch factor directly instead of its reciprocal 1∣b∣\tfrac{1}{|b|}.

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

Unit 2 · 13 skills

Trigonometry

Angles in Degrees and Radians

The Unit Circle

The Six Trigonometric Ratios

  • Primary ratios in radians and degrees

    I can evaluate and apply the primary ratios sine, cosine and tangent in radians and degrees.

    2.4

    Learn itPractice testActivities

  • Reciprocal ratios: cosecant, secant, cotangent

    I can evaluate and apply the reciprocal ratios cosecant, secant and cotangent.

    2.5

    Learn itPractice testActivities

Graphing Trigonometric Functions

Solving Trigonometric Equations

Proving Trigonometric Identities

The official wording · 13 outcomes
2.1
Demonstrate an understanding of angles in standard position, expressed in degrees
2.2
understanding of angles in standard position, expressed in degrees and radians
2.3
Develop and apply the equation of the unit circle.
2.4
Solve problems, using the six trigonometric ratios for angles expressed in radians and degrees.
2.6
Graph and analyze the trigonometric functions sine, cosine and tangent to solve problems.
2.8
Solve, algebraically and graphically, first and second degree trigonometric equations with the domain expressed in degrees and radians.
2.10
Prove trigonometric identities, using: reciprocal identities quotient identities
2.11
Prove trigonometric identities, using: Pythagorean identities
2.12
Prove trigonometric identities, using: sum or difference identities (restricted to sine, cosine and tangent)
2.13
Prove trigonometric identities, using: double-angle identities (restricted to sine, cosine and tangent)

Key ideas

  1. Standard position: vertex at the origin, initial arm on the positive xx-axis, rotating counter-clockwise for positive angles.

  2. The unit circle has equation x2+y2=1x^2+y^2=1; the terminal point of angle θ\theta is (cos⁡θ, sin⁡θ)(\cos\theta,\ \sin\theta), so cos⁡2θ+sin⁡2θ=1\cos^2\theta+\sin^2\theta=1.

  3. For angles in radians or degrees, evaluate sin⁡θ,cos⁡θ,tan⁡θ\sin\theta,\cos\theta,\tan\theta from the unit circle or reference triangle.

  4. For y=asin⁡(b(x−c))+dy=a\sin\big(b(x-c)\big)+d (and cosine): amplitude =∣a∣=|a|, period =2π∣b∣=\tfrac{2\pi}{|b|}, phase shift =c=c, and midline y=dy=d.

  5. Isolate the trig ratio, find the reference angle from its magnitude, then use the SIGN to place every solution in the domain.

Watch out for

  • Rotating clockwise for a positive angle.
  • Swapping the coordinates — using (sin⁡θ,cos⁡θ)(\sin\theta,\cos\theta) instead of (cos⁡θ,sin⁡θ)(\cos\theta,\sin\theta).
  • Giving a positive value in a quadrant where the ratio is negative.

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

Unit 3 · 4 skills

Permutations, Combinations and Binomial Theorem

Counting Principle and Permutations

Combinations and the Binomial Theorem

The official wording · 4 outcomes
3.1
Apply the fundamental counting principle to solve problems.
3.2
Determine the number of permutations of n elements taken r at a time to solve problems.
3.3
Determine the number of combinations of n different elements taken r at a time to solve problems.
3.4
Expand powers of a binomial in a variety of ways, including using the binomial theorem (restricted to exponents that are natural numbers).

Key ideas

  1. If a task has independent stages with mm, then nn, … choices, the total is the PRODUCT m×n×⋯m\times n\times\cdots.

  2. When ORDER does NOT matter, nCr_nC_r=(nr)=\dbinom{n}{r}=n!r! (n−r)!=\dfrac{n!}{r!\,(n-r)!} — it's nPr_nP_r divided by r!r! (removing the orderings).

  3. Handle restrictions first (fixed positions, no-repeats) then multiply the remaining choices.

  4. Decide by asking 'does rearranging give a new outcome?': committees, hands of cards, and subsets are combinations.

  5. When ORDER matters, nPr=n!(n−r)!_nP_r=\dfrac{n!}{(n-r)!} counts arrangements of rr from nn distinct elements.

Watch out for

  • ADDING the choices at each stage instead of multiplying.
  • Using nPr_nP_r (order) for a selection problem where order is irrelevant — overcounting by r!r!.
  • Ignoring a no-repeat restriction and reusing an element that's already placed.

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 30-1.

Mathematics Grades 10–12 Program of Studies, 2008, Mathematics 30-1 / MAT3791Alberta Education · curriculum.learnalberta.ca · Read July 22, 2026

Strands

StrandOutcomesTaught in
Relations and FunctionsOutcomes 14Taught in Unit 1
TrigonometryOutcomes 6Taught in Unit 2
Permutations, Combinations and Binomial TheoremOutcomes 4Taught in Unit 3

Study it in MapleMind

MapleMind teaches Mathematics 30-1 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 30-1 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
29
Fillable fields
1,457
Price
$4.99
See the Course Companion

Questions about Mathematics 30-1

What is Mathematics 30-1?

Alberta’s Grade 12 math course: 3 units and 35 skills, from Relations and Functions to Permutations, Combinations and Binomial Theorem.

What units are in Mathematics 30-1?

1. Relations and Functions, 2. Trigonometry and 3. Permutations, Combinations and Binomial Theorem.

Is there a provincial exam for Mathematics 30-1?

Yes. The Mathematics 30–1 Diploma Exam counts for 30% of the final mark. Next sitting: January 20, 2027.

Can MapleMind help with Mathematics 30-1?

Yes. MapleMind teaches every skill of Mathematics 30-1, 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 30-1

Practise every skill of Mathematics 30-1 in MapleMind, free with daily limits.