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Pre-Calculus 11
Sequences, radicals, quadratics, rational expressions and trigonometry preparing for calculus.
6
units
18
lessons
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1Sequences & Series0/3 lessons · Current
2Absolute Value & Radicals0/3 lessons · Not started
3Rational Expressions0/3 lessons · Not started
4Quadratic Functions0/3 lessons · Not started
5Quadratic Equations & Inequalities0/3 lessons · Not started
6Trigonometry0/3 lessons · Not started
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
01 · Diagnose
Find the exact skill causing difficulty — not the chapter, the skill.
02 · Understand
Learn it through explanations, worked examples and visual reasoning.
03 · Practice
Work problems that adapt to how you are actually doing.
04 · Fix
A wrong answer becomes targeted remediation for the misconception behind it.
05 · Prove
Solve new, unseen problems independently before mastery is awarded.
Course curriculum
1Sequences & Series3 topics
- — Arithmetic sequences
- — Geometric sequences
- — Series
2Absolute Value & Radicals3 topics
- — Absolute value
- — Radical operations
- — Radical equations
3Rational Expressions3 topics
- — Simplifying
- — Operations
- — Rational equations
4Quadratic Functions3 topics
- — Vertex form
- — Factoring
- — Quadratic formula
5Quadratic Equations & Inequalities3 topics
- — The discriminant
- — Completing the square
- — Inequalities
6Trigonometry3 topics
- — Angles & ratios
- — Sine law
- — Cosine law
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. Factor: find two numbers that multiply to 6 and add to −5 → −2 and −3.
- 2. So x² − 5x + 6 = (x − 2)(x − 3) = 0.
- 3. Set each factor to zero: x = 2 or x = 3.
- 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?
- An introductory amount — right-triangle ratios and the unit circle. Pre-Calculus 12 goes much deeper into trigonometric functions, identities, and equations.
- 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
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.