Courses

British Columbia · Grade 11

Pre-calculus 11

  • PREC 11

British Columbia’s Grade 11 math course, from Real Numbers, Powers & Radicals to Financial Literacy: Compound Interest, Investments & Loans.

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Units
4
Lessons
7
Skills
19
Provincial exam
None
Official curriculum
BC Mathematics 11

Unit by unit

Every skill in the course, numbered by unit.

Unit 1 · 8 skills

Real Numbers, Powers & Radicals

The Real Number System & Rational Exponents

  • Classifying real numbers

    I can classify any real number as natural, whole, integer, rational, or irrational.

    1.1

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  • Powers with rational exponents

    I can evaluate and simplify powers with rational exponents, converting to and from radical form.

    1.2

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Radical Operations & Equations

  • Simplifying radicals and ordering irrationals

    I can convert between entire and mixed radicals and order irrational numbers.

    1.3

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  • Operations with radicals

    I can add, subtract, and multiply radical expressions and rationalize simple denominators.

    1.4

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  • Solving radical equations

    I can solve one-radical equations, state domain restrictions, and reject extraneous roots.

    1.5

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Factoring & Rational Expressions

  • Factoring: extended cases

    I can factor trinomials with any leading coefficient, differences of squares, and composite cases.

    1.6

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  • Simplifying rational expressions and non-permissible values

    I can operate on rational expressions and state their non-permissible values.

    1.7

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  • Solving rational equations

    I can solve rational equations and reject roots that collide with non-permissible values.

    1.8

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The official wording · 8 outcomes
1.1
real number system
1.2
powers with rational exponents
1.3
radical operations and equations
1.4
radical operations and equations
1.5
radical operations and equations
1.6
polynomial factoring
1.7
rational expressions and equations
1.8
rational expressions and equations

Key ideas

  1. The sets nest: natural ⊂ whole ⊂ integer ⊂ rational — and the irrationals sit beside the rationals, together filling the real line.

  2. Simplify by pulling out perfect-square factors: √50 = √(25·2) = 5√2.

  3. For ax² + bx + c: find two numbers multiplying to a·c and adding to b, then split the middle term and factor by grouping.

  4. Rational means expressible as a fraction of integers; decimals that terminate or repeat are rational.

  5. To compare mixed radicals, push the coefficient back inside: 3√5 = √45, so it beats √40.

Watch out for

  • Assuming every root is irrational — √25 = 5 is as rational as they come.
  • Pulling a factor out without rooting it: √50 = 5√2 because 25 leaves as 5, not as 25.
  • Declaring 4x² - 8x + 4 fully factored as (2x-2)(2x-2) — the GCF 4 should come out first: 4(x-1)².

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

Unit 2 · 6 skills

Quadratic Functions & Equations

Quadratic Functions: Graphs, Forms & Transformations

  • Characteristics of quadratic graphs

    I can identify the vertex, intercepts, axis of symmetry, domain, range, and extrema of a quadratic function.

    2.1

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  • Transformations of quadratic functions

    I can predict how a, p, and q in y = a(x-p)² + q transform the base parabola.

    2.2

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  • Solving quadratic equations

    I can solve quadratic equations by multiple methods and choose the efficient one.

    2.3

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  • Quadratic problems in context

    I can model situations with quadratic functions and answer max/min and zero questions in context.

    2.4

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Linear & Quadratic Inequalities

  • Solving inequalities with sign analysis

    I can solve linear and quadratic inequalities and identify where a function is positive, negative, or zero.

    2.5

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  • Interval notation and contextual restrictions

    I can write solutions in interval notation and read restrictions out of real contexts.

    2.6

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The official wording · 6 outcomes
2.1
quadratic functions and equations
2.2
quadratic functions and equations
2.3
quadratic functions and equations
2.4
quadratic functions and equations
2.5
linear and quadratic inequalities
2.6
linear and quadratic inequalities

Key ideas

  1. Vertex form y = a(x-p)² + q shows the vertex (p, q) directly; factored form shows the zeros; standard form shows the y-intercept c.

  2. Multiplying or dividing an inequality by a negative flips its direction — the one rule linear inequalities add.

  3. The axis of symmetry passes through the vertex — x = p — and mirrors every point.

  4. Quadratic inequalities: find the zeros, then test the sign of each interval between them — the parabola's sketch predicts the pattern.

  5. The sign of a decides opening and extremum: a > 0 opens up with a minimum; a < 0 opens down with a maximum. Range starts or ends at q.

Watch out for

  • Flipping the sign of p — in y = (x - 3)² the vertex sits at x = +3, not -3.
  • Solving x² > 9 as x > 3 only — the negative branch x < -3 is half the answer.
  • Giving a restricted domain for a quadratic — every parabola's domain is all real numbers; it's the RANGE that's clipped at the vertex.

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

Unit 3 · 3 skills

Trigonometry: Non-Right Triangles & Standard Position

The Sine & Cosine Laws

  • The sine law and the ambiguous case

    I can apply the sine law to solve triangles and handle the ambiguous (SSA) case.

    3.1

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  • The cosine law

    I can apply the cosine law to find sides and angles in SAS and SSS triangles.

    3.2

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  • Angles in standard position, special angles, and the unit circle

    I can find reference and coterminal angles, exact ratios of special angles, and solve simple trig equations from 0° to 360°.

    3.3

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The official wording · 3 outcomes
3.1
trigonometry: non-right triangles and angles in standard position
3.2
trigonometry: non-right triangles and angles in standard position
3.3
angles in standard position

Key ideas

  1. Sine law: a/sin A = b/sin B = c/sin C — usable whenever you have a matched angle-side pair plus one more piece.

  2. The ambiguous case is SSA: the given swing-side may fit two different triangles, one, or none.

  3. The second candidate angle is 180° minus the calculator's answer — test whether the triangle's angles still fit under 180°.

  4. Cosine law: c² = a² + b² - 2ab·cos C — the Pythagorean theorem with a correction term for the non-right angle.

  5. SAS (two sides and the angle between them) finds the third side; SSS rearranges to find any angle.

Watch out for

  • Accepting only the calculator's acute angle in SSA — the obtuse supplement may build a perfectly valid second triangle.
  • Using the sine law without any matched angle-side pair — with three sides or SAS, it has nothing to grip.
  • Using a side not opposite the chosen angle as c — the squared side alone on the left must face angle C.

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

Unit 4 · 2 skills

Financial Literacy: Compound Interest, Investments & Loans

Compound Interest, Investments & Loans

  • Compound interest

    I can calculate compound interest with A = P(1 + i)^n and explain why it outgrows simple interest.

    4.1

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  • Investments, loans, and buy-vs-lease

    I can reason about regular-payment investments and loans and compare options like buy versus lease.

    4.2

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The official wording · 2 outcomes
4.1
financial literacy: compound interest, investments, loans
4.2
financial literacy: compound interest, investments, loans

Key ideas

  1. A = P(1 + i)^n: i is the rate PER compounding period and n counts the periods — 6%/yr monthly for 3 years means i = 0.005, n = 36.

  2. Compound interest pays interest on interest — growth is exponential, and time is its most powerful ingredient.

  3. More frequent compounding at the same annual rate yields more: monthly beats annually, a little.

  4. Regular contributions stack compounding: each deposit grows for a different length of time — technology (finance apps, spreadsheets) sums the series.

  5. A loan runs compounding in reverse: interest accrues on the balance while payments chip it down; total paid = payment × count, and the excess over the principal is the cost of borrowing.

Watch out for

  • Using the annual rate with monthly periods — pairing i = 0.06 with n = 24 double-counts; the monthly i is 0.005.
  • Expecting compound and simple interest to match after year one — identical the first year, diverging every year after.
  • Comparing only monthly payments — the lower payment can cost more in total once the horizon and buyout are counted.

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

Which course?

British Columbia has 3 math courses for Grade 11. 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 British Columbia’s own curriculum for Pre-calculus 11.

Pre-calculusBC Mathematics 11 · curriculum.gov.bc.ca · Read August 8, 2026

Textbooks

In British Columbia, each school district chooses its own textbooks: the ministry no longer recommends them. The ministry’s page

Study it in MapleMind

MapleMind teaches Pre-calculus 11 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.

Chemistry 11 in the MapleMind app on a tablet: its units, Unit 1 open, and the skills done so far with their starsChemistry 11 in the MapleMind app on a phone: its units, Unit 1 open, and the skills done so far with their stars
Pictured: Chemistry 11, another British Columbia course, partway through Unit 1.

Practise it

Course Companion

Your year in one workbook

A fun way to keep Pre-calculus 11 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
28
Fillable fields
1,242
Price
$4.99
See the Course Companion

Questions about Pre-calculus 11

What is Pre-calculus 11?

British Columbia’s Grade 11 math course: 4 units and 19 skills, from Real Numbers, Powers & Radicals to Financial Literacy: Compound Interest, Investments & Loans.

What units are in Pre-calculus 11?

1. Real Numbers, Powers & Radicals, 2. Quadratic Functions & Equations, 3. Trigonometry: Non-Right Triangles & Standard Position and 4. Financial Literacy: Compound Interest, Investments & Loans.

Is there a provincial exam for Pre-calculus 11?

No. British Columbia gives no provincial exam for Pre-calculus 11.

What textbook does Pre-calculus 11 use?

Each school district in British Columbia chooses its own textbooks, so ask your teacher which one your class uses.

What comes after Pre-calculus 11?

Pre-calculus 12, Foundations of Mathematics 12 and Calculus 12.

Can MapleMind help with Pre-calculus 11?

Yes. MapleMind teaches every skill of Pre-calculus 11, 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

After this course

Get ready for Pre-calculus 11

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