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  1. ← All courses

MathematicsGrade 12

Precalculus

Strengthen your foundation. Make your thinking visible.

3 open units / , 17 topics to explore

Current material: Units 1, 2, 3. Units 4, 5, 6, 7, 8, 9, 10 are optional future study · Subject to change.

Course detailsYour guide to studying

Precalculus
2026 to 2027 · Mr. Khan

  1. Learn it

    Choose a unit below. Open a lesson for notes, pictures and examples.

  2. Practice it

    Try the activities, then revisit an idea whenever you need it.

  3. Homework

    Homework lives inside its lesson. Follow the turn-in steps your teacher gives you.

LessonsPracticeKey wordsCalculator
Find a lesson

Current units

  1. Unit 1: Essential Review
    1. Find a starting point
    2. Evaluate and compare expressions
    3. Read powers and multiply expressions
    4. Solve equations and describe intervals
    5. Essential algebra review
  2. Unit 2: Functions
    1. Read and use function notation
    2. Combine functions in the right order
    3. Keep inputs and outputs allowed
    4. Describe change and graph behavior
    5. Reverse a function safely
    6. Use symmetry to compare inputs
    7. Functions review
  3. Unit 3: Linear Functions
    1. Build a model with constant change
    2. Write and compare line equations
    3. Reverse a linear model
    4. Build and read piecewise rules
    5. Linear functions review
Optional future study · Subject to change

Unassigned previews outside the current course sequence.

  1. Unit 4: Exponential Functions · Optional future study · Subject to change
    1. Simplify with exponent laws
    2. Interpret rational exponents over the reals
    3. Build repeated-factor models
    4. Solve equations with a common base
    5. Read exponential graphs and their limits
    6. Exponentials review
  2. Unit 5: Quadratics · Optional future study · Subject to change
    1. Factoring patterns
    2. Factoring trinomials
    3. Completing the square
    4. Quadratic models
    5. Linear quadratic systems
    6. Quadratics review
  3. Unit 6: Transformations · Optional future study · Subject to change
    1. Shifts and reflections
    2. Stretches and compressions
    3. Move and reshape a function
    4. Transformations review
  4. Unit 7: Polynomials · Optional future study · Subject to change
    1. Polynomial structure
    2. Polynomial behavior
    3. Polynomial graphs
    4. Polynomials review
  5. Unit 8: Rational Functions · Optional future study · Subject to change
    1. Simplify rational functions safely
    2. Divide polynomials and check remainders
    3. Combine rational expressions
    4. Solve rational equations and check candidates
    5. Rational expressions and equations review
  6. Unit 9: Trigonometry · Optional future study · Subject to change
    1. Right-triangle models
    2. Radians and circular arcs
    3. The unit circle
    4. Trigonometric identities
    5. Linear trigonometric equations
    6. Trigonometry review
  7. Unit 10: Trigonometric Graphs · Optional future study · Subject to change
    1. Sine and cosine models
    2. Period, frequency, and phase
    3. Build a sine or cosine model
    4. Sine and cosine graphs review

Precalculus · Grade 12

Start here

Find a starting point

Unit 1: Essential Review

Start review

Classwork handouts

Find the paper you used in class. Open a digital copy, practice its questions, or try something new.

  • Unit 2 · Functions

    Domain and range

    9-page class handout. Online practice covers 60 prompts: 29 answer checks and 31 worked examples to compare with your own work. Four unclear graphs remain PDF-only.

    Open PDF ↗: Domain and range (opens in a new tab)Download PDF: Domain and range

    Optional practice · No points or turn-in

    Practice this handout →: Domain and rangeExtra practice: new questions for Domain and range

    Extra practice uses new questions on the same ideas.

  • Unit 2 · Functions

    Average rate of change

    2-page class handout, printed pages 31 and 32. Practice the same 12 numbered questions online, with checks for all 16 answer parts.

    Open PDF ↗: Average rate of change (opens in a new tab)Download PDF: Average rate of change

    Optional practice · No points or turn-in

    Practice this handout →: Average rate of changeExtra practice: new questions for Average rate of change

    Extra practice uses new questions on the same ideas.

If a PDF does not open, ask your teacher for the class copy.

Your course journey

  1. 01Unit 1, Essential Review,You are here0 of 5 finished
  2. 02Unit 2, Functions,Open0 of 7 finishedBuilds on Unit 1.
  3. 03Unit 3, Linear Functions,Open0 of 5 finishedBuilds on Unit 2.
Optional future study · Subject to change

These units are outside the current course sequence. Explore them if you like. Their lessons and homework previews are unassigned and may change.

  1. 04Unit 4, Exponential Functions,Subject to change
  2. 05Unit 5, Quadratics,Subject to change
  3. 06Unit 6, Transformations,Subject to change
  4. 07Unit 7, Polynomials,Subject to change
  5. 08Unit 8, Rational Functions,Subject to change
  6. 09Unit 9, Trigonometry,Subject to change
  7. 10Unit 10, Trigonometric Graphs,Subject to change

Practice tools

Quick practice from the current units.

  • Night BeforeCheck what you know. Brush up on the big ideas.
  • 10FQuick 10Try up to 10 quick cards and true or false questions.
  • ?Missed CardsGive your Still learning cards another go.
  • Key wordsFind meanings, lessons and connected ideas.

Practice, not a grade

What could I practise next?

Suggestions use your best whole-test results in this browser, lowest fraction first. Best results can be old: they do not show your latest attempt or prove that you know a topic.

Results from a different question count are left out. A test without a result is not a wrong answer.

Start with a lesson or self-test. Whole-test results can give you a place to revisit later.

Try a self-test: Find a starting pointRead the lesson first

Practise your Still learning cards