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Master Calculus

Watch calculus videos, practice with step-by-step solutions

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Derivatives were killing me until StudyPug. The video breakdowns made chain rule finally click. Went from C to A- in 6 weeks.

Alex Kim

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Why Calculus Students Choose StudyPug

The complete learning system to master Calculus

Search with Photo

Search with Photo

Upload Calculus problems—AI searches and finds the right lesson teaching the concept

Expert Video Teaching

Expert Video Teaching

Certified teachers break down limits, derivatives, and integrals step-by-step

Unlimited Practice

Unlimited Practice

5,000+ teacher-created practice questions prepare you for Calculus exams

How Illinois Students Use StudyPug

1

Select Grade Level
Select Grade Level

Choose your Illinois grade (K-12) and current math topics.

2

Get Unstuck
Get Unstuck

Upload homework problems or browse curriculum-aligned lessons.

3

Practice & Master
Practice & Master

Work through similar problems until concepts stick.

4

See Results
See Results

Track progress and watch grades improve week by week.

Calculus Help: Master Concepts Fast | IllinoisHelp

Print

ID

Standard

StudyPug Topic

Concept of Limits

Understand limits graphically and numerically; evaluate basic limits using substitution

Continuity

Determine continuity at a point and identify types of discontinuities

Limits at Infinity

Find limits at infinity and describe end behavior of functions

Derivative Concept

Understand derivative as rate of change and slope of tangent line

Derivative Rules

Find derivatives using power rule; product rule; quotient rule; and chain rule

Derivatives of Special Functions

Find derivatives of trigonometric; exponential; and logarithmic functions

Implicit Differentiation

Find derivatives of implicitly defined functions

Tangent Lines

Find equations of tangent lines and use for linear approximation

Critical Points and Extrema

Find critical points; local maxima and minima; and solve optimization problems

Curve Analysis

Analyze increasing/decreasing behavior and concavity; sketch curves using derivatives

Related Rates

Solve related rates problems in real-world contexts

Motion and Rates

Apply derivatives to velocity; acceleration; and other rate problems

Antiderivatives

Find antiderivatives of basic functions and use initial conditions

Riemann Sums

Approximate definite integrals using left; right; and midpoint Riemann sums

Fundamental Theorem of Calculus

Use FTC to evaluate definite integrals and find antiderivatives

Basic Integration Techniques

Use substitution method to evaluate integrals

Area Under Curves

Find area under curves and between curves using definite integrals

Average Value

Calculate average value of functions over intervals using integrals
Complete Illinois Calculus Coverage

Calculus Lessons

33

Video Explanations

252

Practice Problems

444

Illinois Standards

100% Aligned

Why Illinois Calculus Students Love StudyPug

SAT Math Preparation

SAT Math Preparation

Practice with real SAT-style calculus questions—be ready for test day

Certified Teachers

Certified Teachers

Learn from expert Illinois teachers who know exactly what you need for Calculus

Learn Anywhere

Learn Anywhere

Desktop, tablet, or phone—your Calculus lessons sync across all devices

Success Stories

Integration by parts was impossible until StudyPug's videos. The examples made it so clear. Aced my final with a 92%.

Jordan Lee

Used StudyPug all semester for limits and derivatives. The practice problems matched our tests perfectly. Went from failing to B+.

Taylor Martinez

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Frequently Asked Questions

Everything you need to know about mastering Calculus with StudyPug

What does Calculus coverage include?

Complete Calculus curriculum with video lessons on limits, derivatives, integrals, practice problems, step-by-step solutions, and progress tracking for every topic.

How does the AI photo search work?

Take a photo of any Calculus problem, and our AI finds the exact lesson teaching that concept. It's like having a personal tutor who knows exactly what you need.

Are the teachers certified Illinois educators?

Yes! Our teachers are certified Illinois educators who understand state curriculum and create lessons specifically for Calculus standards taught in Illinois schools.

Can I use StudyPug on my phone or tablet?

Absolutely! StudyPug works on desktop, tablet, and mobile. Your progress syncs automatically so you can learn Calculus anywhere, anytime.

How will StudyPug help me prepare for the SAT?

We include SAT-style practice questions covering Calculus concepts and teach the exact problem-solving strategies you need. Students report significantly improved test scores and confidence.

Practice Smart, See Real Progress

Unlimited Targeted Practice
Unlimited Targeted Practice

10,000+ questions adjust to your exact skill level. Never run out of problems that challenge you.

Visual Progress Tracking
Visual Progress Tracking

See mastery percentage for every topic. Parents get weekly progress emails automatically.

Achievement System
Achievement System

Earn badges for consistency and improvement. Build learning streaks that motivate daily practice

Detailed Analytics
Detailed Analytics

Time spent, problems solved, concepts mastered. Identify exactly where more practice is needed.

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