For Calculus I · University, first year
Calculus I practice questions and exam prep
Differential calculus as first-year university courses teach it: limits and continuity, the derivative and its rules, related rates and linear approximation, the Mean Value Theorem and L'Hôpital's rule, curve sketching, optimization, Newton's method and Taylor polynomials, and an introduction to integration. Short lessons, then practice until it sticks.
- Made for first-year Calculus I
- Worked solution for every question
- Free during the launch promotion
Unlimited
practice questions
239
lesson cards
13
units
81
skills
Popular Calculus I practice topics
- Limit laws and algebraic techniques
- The chain rule
- Implicit differentiation
- Related rates
- L'Hôpital's rule
- Applied optimization
- Taylor polynomials
What's covered
Every Calculus I unit, topic by topic
Your course skips a topic? Take it out of your practice, or add it back any time.
1Functions review
4 lessons- Functions, domains and graphs3 skills · 5 lesson cards
- Composition and inverses2 skills · 5 lesson cards
- Exponentials and logarithms2 skills · 5 lesson cards
- Trigonometric and inverse trigonometric functions2 skills · 5 lesson cards
2Limits
5 lessons- What a limit is2 skills · 4 lesson cards
- Limit laws and algebraic techniques4 skills · 5 lesson cards
- Trigonometric limits and the squeeze theorem2 skills · 5 lesson cards
- Limits involving infinity2 skills · 5 lesson cards
- The precise definition of a limit1 skills · 3 lesson cards
3Continuity
4 lessons- Continuity at a point1 skills · 5 lesson cards
- Types of discontinuity1 skills · 4 lesson cards
- Making a function continuous1 skills · 5 lesson cards
- The Intermediate Value Theorem1 skills · 5 lesson cards
4The derivative
5 lessons- Rates of change1 skills · 5 lesson cards
- The derivative from the definition1 skills · 5 lesson cards
- Tangent and normal lines1 skills · 5 lesson cards
- The derivative as a function1 skills · 5 lesson cards
- Differentiability1 skills · 5 lesson cards
5Differentiation rules
5 lessons- The power and sum rules1 skills · 4 lesson cards
- The product and quotient rules2 skills · 5 lesson cards
- Exponential and trigonometric derivatives2 skills · 5 lesson cards
- The chain rule2 skills · 5 lesson cards
- Higher derivatives1 skills · 4 lesson cards
6More differentiation
4 lessons- Implicit differentiation2 skills · 5 lesson cards
- Derivatives of inverse functions2 skills · 5 lesson cards
- Logarithms and logarithmic differentiation2 skills · 4 lesson cards
- Hyperbolic functions1 skills · 4 lesson cards
7Rates and approximation
3 lessons- Related rates3 skills · 5 lesson cards
- Linear approximation and differentials2 skills · 5 lesson cards
- Exponential growth and decay1 skills · 4 lesson cards
8The Mean Value Theorem and L'Hôpital's rule
3 lessons- The Mean Value Theorem1 skills · 5 lesson cards
- L'Hôpital's rule2 skills · 5 lesson cards
- Other indeterminate forms2 skills · 5 lesson cards
9Curve sketching
3 lessons- What the first derivative tells you3 skills · 5 lesson cards
- What the second derivative tells you2 skills · 5 lesson cards
- Asymptotes and full sketches2 skills · 5 lesson cards
10Optimization
4 lessons- Absolute extrema1 skills · 4 lesson cards
- Applied optimization1 skills · 5 lesson cards
- Distance and time1 skills · 4 lesson cards
- Optimization in economics1 skills · 4 lesson cards
11Newton's method and Taylor polynomials
3 lessons- Newton's method1 skills · 5 lesson cards
- Taylor polynomials1 skills · 5 lesson cards
- The error of a Taylor polynomial1 skills · 4 lesson cards
12Antiderivatives and differential equations
4 lessons- Antiderivatives1 skills · 5 lesson cards
- Initial value problems and motion2 skills · 5 lesson cards
- Separable differential equations1 skills · 4 lesson cards
- Slope fields and Euler's method2 skills · 4 lesson cards
13Introduction to integration
4 lessons- Sigma notation and Riemann sums2 skills · 5 lesson cards
- The definite integral1 skills · 5 lesson cards
- The Fundamental Theorem of Calculus2 skills · 5 lesson cards
- Substitution1 skills · 4 lesson cards
How you'll practice
Tools built for calculus
Exact answers, graphs and worked solutions — the kinds of thinking unit tests and finals reward.
Practice by topic
Read a short lesson, then practice with typed math answers, a hint ladder and a worked solution after every question.
Graph questions
Drag points onto a parabola, shade where an inequality holds, mark intercepts and asymptotes — marked on the spot.
Progress tracking
Mastery by skill and unit, weak spots and recommended Daily practice, so you know what's actually solid.
My mistakes
Go over what you missed and try fresh questions on the same idea.
Unit tests and mock exams
Timed unit tests, a mock midterm and a mock final in the familiar format, with a breakdown by unit and skill.
Find the mistake
0 worked solutions with one planted error: find the line that goes wrong and see why.
Free for every Learn4Less account during our launch promotion. See pricing
Fits your term
How it follows Calculus I
- 01
Week by week
Read the lesson, then practice topic by topic. Mark the units your course has covered and Daily practice stays on them.
- 02
Before a midterm
Take a timed unit test or the mock midterm, marked with full worked solutions and a breakdown by skill.
- 03
Final exam
A mock final across every unit in your course, plus Rescue for your weakest topic and your mistakes to retry.
Questions
Calculus I FAQ
Do I need a new account?+
No. Sign in with your Learn4Less account — the same one you use on learn4less.ca.
Does it follow my course?+
It follows the most common first-year syllabus, unit by unit. Take out any unit, topic or skill your course doesn't cover, and add back anything it does.
How is my typed answer marked?+
Instantly, by a math engine that accepts every equivalent form, so you can write an answer the way you would on paper. A worked solution follows every question.
Start your Calculus I practice today
Pick a topic and answer your first question in under five minutes.
Start freeL4L Math is an independent study tool by Learn4Less Tutoring Services Ltd..