Skip to main content
Dr. Shreyank Educare
Curriculum-aligned learning support — not an official school, university, or ministry-approved course, and not a replacement for official credit.

Grade 11 · Mathematics · Core

Pre-Calculus 11

Real numbers, exponents, factoring, radicals, rational expressions, quadratics, trigonometry and financial literacy preparing for calculus.

Contents

readnot started

1

Rational Expressions

3 of 3 published

  1. 1.1
    Simplifying

    Reducing rational expressions.

    Published

  2. 1.2
    Operations

    Multiply, divide, add, subtract.

    Published

  3. 1.3
    Rational equations

    Solving equations.

    Published

2

Real Numbers & Exponents

0 of 2 published

  1. 2.1
    The real number system

    Classifying numbers as natural, whole, integer, rational or irrational.

    In preparation

  2. 2.2
    Powers with rational exponents

    Exponent laws with positive and negative rational exponents on numerical and variable bases.

    In review

3

Factoring

0 of 1 published

  1. 3.1
    Factoring composite expressions

    Extending trinomial factoring to a(f(x))^2 + b(f(x)) + c by substitution.

    In review

4

Quadratic Functions

3 of 3 published

  1. 4.1
    Vertex form

    Graphing parabolas.

    Published

  2. 4.2
    Factoring

    Solving by factoring.

    Published

  3. 4.3
    Quadratic formula

    The general solution.

    Published

5

Radicals

2 of 2 published

  1. 5.1
    Radical operations

    Simplifying radicals.

    Published

  2. 5.2
    Radical equations

    Solving with radicals.

    Published

6

Quadratic Equations & Inequalities

3 of 4 published

  1. 6.1
    The discriminant

    Nature of the roots.

    Published

  2. 6.2
    Completing the square

    Deriving the vertex.

    Published

  3. 6.3
    Inequalities

    Quadratic inequalities.

    Published

  4. 6.4
    Linear inequalities

    Solving single-variable linear inequalities with sign analysis and interval notation.

    In preparation

7

Trigonometry

3 of 4 published

  1. 7.1
    Angles & ratios

    Trig ratios in triangles.

    Published

  2. 7.2
    Sine law

    Solving oblique triangles.

    Published

  3. 7.3
    Cosine law

    Solving oblique triangles.

    Published

  4. 7.4
    Standard position and the unit circle

    Angles in standard position, reference and coterminal angles, special angles, the unit circle in degrees, and simple trigonometric equations.

    In review

8

Financial Literacy

0 of 1 published

  1. 8.1
    Compound interest, loans and leasing

    Compound interest, investments and loans with regular payments, and buy-versus-lease comparisons.

    In review

9

ExtensionExtension, not counted toward course totals

4 of 4 published

  1. 9.1
    Arithmetic sequences

    Common difference and nth term.

    Published

  2. 9.2
    Geometric sequences

    Common ratio and nth term.

    Published

  3. 9.3
    Series

    Summing sequences.

    Published

  4. 9.4
    Absolute value

    Definition and graphs.

    Published

What is Pre-Calculus 11 in British Columbia?

Short answer

Pre-Calculus 11 is the BC senior-math course that builds the algebra and function skills needed for calculus. It covers sequences and series, absolute value and radicals, rational expressions, quadratic functions and equations, and trigonometry. The emphasis is on manipulating expressions correctly and understanding how functions behave — the foundation Pre-Calculus 12 and Calculus 12 rely on.

Course overview

Pre-Calculus 11 shifts the focus from solving single equations to understanding whole families of functions. You extend arithmetic and geometric patterns into sequences and series, work fluently with radicals and rational expressions, and study quadratics from every angle — graph, factored form, and the quadratic formula. A first course in trigonometry connects angles to ratios and the unit circle.

What you will learn

  • Analyse arithmetic and geometric sequences and series
  • Simplify radicals, absolute-value expressions, and rational expressions
  • Graph and interpret quadratic functions in different forms
  • Solve quadratic equations and inequalities by factoring, completing the square, and the quadratic formula
  • Apply right-triangle and unit-circle trigonometry

Who this course is for

  • • BC students taking Pre-Calculus 11 who plan to continue to Pre-Calculus 12 or Calculus 12
  • • Students who want stronger algebra fluency before calculus
  • • Anyone who struggles with quadratics, rational expressions, or trigonometry and wants targeted practice

Commonly difficult topics

  • • Quadratics — moving fluently between standard, factored, and vertex form
  • • Rational expressions — finding restrictions and simplifying without losing solutions
  • • Radicals — keeping track of extraneous roots when squaring
  • • Trigonometry — connecting the unit circle to angle measures and ratios

How Dr. Shreyank Educare teaches this course

  1. 01 · Diagnose

    Find the exact skill causing difficulty — not the chapter, the skill.

  2. 02 · Understand

    Learn it through explanations, worked examples and visual reasoning.

  3. 03 · Practice

    Work problems that adapt to how you are actually doing.

  4. 04 · Fix

    A wrong answer becomes targeted remediation for the misconception behind it.

  5. 05 · Prove

    Solve new, unseen problems independently before mastery is awarded.

Course curriculum

1Rational Expressions3 topics
  • — Simplifying
  • — Operations
  • — Rational equations
2Real Numbers & Exponents2 topics
  • — The real number system
  • — Powers with rational exponents
3Factoring1 topics
  • — Factoring composite expressions
4Quadratic Functions3 topics
  • — Vertex form
  • — Factoring
  • — Quadratic formula
5Radicals2 topics
  • — Radical operations
  • — Radical equations
6Quadratic Equations & Inequalities4 topics
  • — The discriminant
  • — Completing the square
  • — Inequalities
  • — Linear inequalities
7Trigonometry4 topics
  • — Angles & ratios
  • — Sine law
  • — Cosine law
  • — Standard position and the unit circle
8Financial Literacy1 topics
  • — Compound interest, loans and leasing
9Extension4 topics
  • — Arithmetic sequences
  • — Geometric sequences
  • — Series
  • — Absolute value

A sample learning experience

Solve x² − 5x + 6 = 0 by factoring, and state what the solutions mean on the graph of y = x² − 5x + 6.

  1. 1. Factor: find two numbers that multiply to 6 and add to −5 → −2 and −3.
  2. 2. So x² − 5x + 6 = (x − 2)(x − 3) = 0.
  3. 3. Set each factor to zero: x = 2 or x = 3.
  4. 4. These are the x-intercepts of the parabola — the points where the graph crosses the x-axis.

Frequently asked questions

Is Pre-Calculus 11 hard?
It is more abstract than earlier math because you work with whole families of functions, not just single answers. Quadratics and rational expressions are the usual sticking points; focused practice on those specific skills makes the course much more manageable.
Do I need Pre-Calculus 11 for Pre-Calculus 12?
Yes. Pre-Calculus 12 assumes fluency with quadratics, radicals, rational expressions, and basic trigonometry — all core Pre-Calculus 11 topics.
What is the difference between Pre-Calculus 11 and Foundations of Math?
Pre-Calculus 11 is the algebra-heavy pathway designed to lead into calculus. Foundations of Mathematics focuses on applied and consumer math and is not intended as calculus preparation.
How much trigonometry is in Pre-Calculus 11?
It covers right-triangle ratios, then extends to oblique triangles with the sine law and cosine law, including the ambiguous case. It also covers angles in standard position, reference and coterminal angles, the special 30-60-90 and 45-45-90 angles, the unit circle in degrees, and solving simple trigonometric equations. Pre-Calculus 12 goes further, with trigonometric functions, identities, and equations across a full range of contexts.
What is the best way to study Pre-Calculus 11?
Identify the exact step you get stuck on — factoring, restrictions, or a trig ratio — and drill that step rather than re-reading whole chapters. Short, targeted practice beats passive review.

Related courses

Pre-Calculus 12 →Calculus 12 →

Explore all Mathematics courses →

Curriculum & sources

Content source: original lessons, worked examples and diagrams created for Dr. Shreyank Educare.

Curriculum alignment: Grade 11 Mathematics (BC curriculum).

Curriculum-aligned learning support — not an official school, ministry, or College Board course, and not a replacement for official credit.

Last updated . Authored and maintained in-house by the Dr. Shreyank Educare teaching team — see our editorial standards, methodology and source policy.