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Humber Polytechnic · CALC 1100

Humber Polytechnic CALC 1100 tutoring

Help with differential and integral calculus, functions and applications.

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Online 60 min: $55 CAD · PricingMidterm & final exam helpTry an optimization problem: build a boxFree study guide for CALC 1100
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Course overview

CALC 1100 covers differential and integral calculus, functions and their applications in Humber’s engineering degree pathways. The worked example below focuses on optimization: building a formula from the problem, finding the possible values of the variable, and checking which value gives the largest volume.

The topics here come from the 2025–26 course description. We have not confirmed their alignment with the 2026–27 outline. Your current outline, if you have it, helps us identify the topics you’re studying.

CALC 1100 topics to review

Limits and continuity; differentiationExtrema, asymptotes and curve sketchingOptimization and related ratesDefinite and indefinite integration, techniques and applications

Common difficulties

  • Optimizing before expressing the constraints
  • Reporting a stationary point without checking its role

Useful foundations to review

Review factoring, composite functions and geometric formulas. Translate every physical dimension into the same variable before differentiating an objective. Write the feasible interval beside the formula; algebraically valid critical points may describe impossible or collapsed objects.

Registration requirements

The guidance above is study preparation, not an eligibility decision. Confirm current prerequisites, restrictions and availability with Humber Polytechnic.

Check the official course catalogue

Optimize a folded box with a physical domain

Cut equal squares of side xx from the corners of a 12 cm square sheet, then fold up the sides. Ignoring material thickness, what cut maximizes the open box’s volume?

Show the reasoning

  1. Model the three dimensions

    The height is xx, and each base edge is 12−2x12-2x. Therefore V(x)=x(12−2x)2V(x)=x(12-2x)^2, with 0<x<60<x<6. The boundary values 0 and 6 produce zero-volume limiting shapes.

  2. Find feasible stationary points

    Differentiation gives V′(x)=144−96x+12x2=12(x−2)(x−6)V^{\prime}(x)=144-96x+12x^2=12(x-2)(x-6). Only x=2x=2 lies inside the feasible interval. The root 6 collapses the base.

  3. Justify and evaluate the maximum

    The derivative is positive on (0,2)(0,2) and negative on (2,6)(2,6), so the volume increases then decreases. A 2 cm cut gives base edges of 8 cm and maximum volume 2(8)2=128 cm32(8)^2=128\text{ cm}^3.

Try an independent variation

Start afresh with an 18 cm square sheet. Find the cut and maximum volume, including the feasible interval.

Check your reasoning

V=x(18−2x)2V=x(18-2x)^2, 0<x<90<x<9, and V′=12(x−3)(x−9)V^{\prime}=12(x-3)(x-9). The sign changes from positive to negative at x=3x=3, giving V=3(12)2=432 cm3V=3(12)^2=432\text{ cm}^3.

How tutoring can help

A tutor can help you start with the problem statement and build a diagram, a formula and its domain before differentiating. You can work through the constraints and a sign chart together to understand why a result is a maximum or minimum. Any work you’ve tried is useful, and you can also start from the beginning.

Exam preparation for CALC 1100

Mix limits, derivatives, related rates and integrals according to your assessment scope. For optimization, show the model, domain and maximum or minimum test. For integration, distinguish a family of antiderivatives from a definite value and verify by differentiation.

For optimization, try the box problem before looking at the answer. Record three decisions: how the dimensions determine the volume, which cuts describe a possible box and why the selected critical point gives the maximum. Then attempt the 18 cm variation with the solution closed. If you obtained a derivative but could not form the volume function, spend the next review on the model; if the function was correct but the maximum was not justified, review the sign change and domain. Your tutor can work on that specific step with you. Use these exercises if optimization is included in your current course or exam review.

Use your section’s outline to choose the chapters to review. We work through permitted practice and comparable problems, without completing graded assignments or exams on your behalf.

Independent practice

Free practice and study guides for CALC 1100

10 min

Derivative Rules: Choose the First Step

Choose the first derivative rule in three core questions, then explore an optional logarithmic-differentiation example and retry when both base and exponent vary.

35 min

How to Choose an Integration Method

Compare substitution, integration by parts, partial fractions and trigonometric substitution, with sign-aware radical choices, worked examples and progressive checks.

32 min

Implicit Differentiation and Related Rates

Connect changing quantities before differentiating. Three worked examples, two diagrams and four progressive questions explain implicit slopes, ladder motion and filling cones.

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CALC 1100 · official course reference