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← Calculus Honors

Calculus Honors Course Outline

Every unit and lesson in Calculus Honors: limits and continuity, differentiation, integration and their applications, including optimization, related rates, area and volume.

6 units33 lessons6 unit reviewsPrerequisite: PrecalculusHonors level

Try the student practice samples in the first expanded unit below. The detailed notes will be discussed during the course, with worked examples, guided practice, and time for questions. Enroll to work through the remaining lessons with your tutor.

Explore the study guide
1Unit 1: Precalculus ReviewA fast review of the function families calculus relies on.2 lessons + review
  • 1.1

    Functions, Graphs and Transformations

    Review function families, graphs and transformations.

    MCQ Sample
  • 1.2

    Exponential, Logarithmic and Trigonometric Review

    Review exponential, log and trig skills calculus uses.

    FRQ Sample
  • 1R

    Unit Review

    Mixed practice and a unit-test-style free-response set covering every lesson in Unit 1.

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2Unit 2: Limits and ContinuityLimits graphically, numerically and analytically; continuity and the IVT.5 lessons + review
  • 2.1

    Introduction to Limits

    Estimate limits with graphs and tables.

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  • 2.2

    Evaluating Limits Analytically

    Evaluate limits by substitution, factoring and conjugates.

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  • 2.3

    Continuity and One-Sided Limits

    Test continuity and find one-sided limits.

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  • 2.4

    Infinite Limits and Limits at Infinity

    Find vertical and horizontal asymptotes with limits.

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  • 2.5

    The Intermediate Value Theorem

    Use the IVT to prove a value exists.

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  • 2R

    Unit Review

    Mixed practice and a unit-test-style free-response set covering every lesson in Unit 2.

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3Unit 3: DifferentiationThe derivative from first principles through the chain rule, implicit differentiation and related rates.8 lessons + review
  • 3.1

    The Derivative and the Tangent Line

    Define the derivative as a limit and find tangent lines.

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  • 3.2

    Basic Rules and Rates of Change

    Use the power rule and interpret rates of change.

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  • 3.3

    Product and Quotient Rules

    Differentiate products and quotients.

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  • 3.4

    The Chain Rule

    Differentiate composite functions.

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  • 3.5

    Implicit Differentiation

    Find dy/dx for curves defined implicitly.

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  • 3.6

    Derivatives of Exponential, Logarithmic and Inverse Functions

    Differentiate e^x, ln x and inverse trig functions.

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  • 3.7

    Related Rates

    Relate changing quantities over time.

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  • 3.8

    Linear Approximation

    Approximate values with tangent lines.

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  • 3R

    Unit Review

    Mixed practice and a unit-test-style free-response set covering every lesson in Unit 3.

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4Unit 4: Applications of DifferentiationExtrema, the Mean Value Theorem, curve sketching, optimization and L'Hôpital's Rule.7 lessons + review
  • 4.1

    Extrema on an Interval

    Find absolute extrema with the Candidates Test.

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  • 4.2

    Rolle's Theorem and the Mean Value Theorem

    Apply Rolle's Theorem and the MVT.

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  • 4.3

    Increasing and Decreasing Functions

    Use the first derivative test.

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  • 4.4

    Concavity and the Second Derivative Test

    Find inflection points and use the second derivative.

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  • 4.5

    Curve Sketching

    Sketch graphs from f′ and f″.

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  • 4.6

    Optimization

    Maximize or minimize applied quantities.

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  • 4.7

    L'Hôpital's Rule

    Evaluate indeterminate limits.

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  • 4R

    Unit Review

    Mixed practice and a unit-test-style free-response set covering every lesson in Unit 4.

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5Unit 5: IntegrationAntiderivatives, Riemann sums, the definite integral, the Fundamental Theorem and substitution.6 lessons + review
  • 5.1

    Antiderivatives and Indefinite Integrals

    Find indefinite integrals and solve initial-value problems.

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  • 5.2

    Area and Riemann Sums

    Approximate area with left, right and midpoint sums.

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  • 5.3

    The Definite Integral

    Define definite integrals as limits of sums.

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  • 5.4

    The Fundamental Theorem of Calculus

    Evaluate integrals and use accumulation functions.

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  • 5.5

    Integration by Substitution

    Integrate by u-substitution.

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  • 5.6

    Numerical Integration

    Apply the trapezoidal rule and estimate error.

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  • 5R

    Unit Review

    Mixed practice and a unit-test-style free-response set covering every lesson in Unit 5.

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6Unit 6: Applications of IntegrationArea between curves, volumes of solids, average value, accumulation and motion.5 lessons + review
  • 6.1

    Area Between Curves

    Find area between two curves.

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  • 6.2

    Volume: Disk and Washer Methods

    Find volumes of revolution with disks and washers.

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  • 6.3

    Volume: Known Cross Sections

    Find volumes with square and semicircle cross sections.

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  • 6.4

    Average Value and Accumulation

    Find average value and net change.

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  • 6.5

    Motion Along a Line

    Analyze position, velocity, speed and distance.

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  • 6R

    Unit Review

    Mixed practice and a unit-test-style free-response set covering every lesson in Unit 6.

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Independently developed by Code Scholars Tutoring. Lesson order and pacing can be adapted to the student’s school syllabus.