Class prep · TJ Intro to Calculus

Make sense of change,then justify each step.

An independent introduction to differential calculus, from limits and continuity through derivatives and their applications. Connect formulas, graphs and local behavior, then justify each conclusion. Every problem has a full worked solution. Built by Neil Kothari, a TJ alumnus.

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$395 covers the full school year. The first lesson is free.

Try one. This is a test-level question from the course.

Problem 1

Test level
Multiple choice
No calculator
4 pts

Which set is exactly described by $0<|x+2|<\tfrac12$ ?

original problems, each with a worked answer: 312; original problems, each with a worked answer
at test level or beyond: 216; at test level or beyond
short lessons, one for every topic: 24; short lessons, one for every topic
units, all open now: 4; units, all open now

Free lesson

Lesson 1.1: Local Function Behavior and Domains

Use exact domains and mathematical evidence to justify nearby function behavior.

Start with local function behavior and domains. Use formulas, tables and graphs to distinguish a function value from nearby behavior.

Problem 2

Core
True or false
No calculator
2 pts

Let $f(x)=2x-1$ for every real $x\ne3$ , and let $f(3)=8$ . Judge this claim: changing only $f(3)$ to $-4$ changes the value at $3$ but does not change any value at inputs satisfying $0<|x-3|<1$ . Explain using the stated formula.

Problem 3

Core
Multiple choice
No calculator
4 pts

Let $u(x)=1/(x+1)$ and $v(t)=\sqrt{t}$ . Both are real-valued on their natural domains. What is the domain of $v\circ u$ ?

Open the rest of this lesson, free

The full lesson and all 13 of its problems, with every worked answer.

How it works

Class prep that works alongside class

A complete introduction to differential calculus for students comfortable with algebra, functions and trigonometry. Work alongside your school course or study the material in sequence. Each lesson starts with a concrete example, develops the idea, and shows how to check your reasoning before you try the practice.

Original problems in several formats: true or false, multiple choice, multi-part and free response.
Each one is marked core, test level or beyond.
Read graphs, calculate limits and derivatives, and justify conclusions under explicit mathematical assumptions.
A worked answer for every problem, ending with the mistake that most often costs points.
Limits, continuity, derivatives and their applications, with original diagrams and careful worked reasoning.

What is inside

1Limits and Continuity6 lessons · 78 problems
2The Derivative as a Rate and Function6 lessons · 78 problems
3Rules of Differentiation6 lessons · 78 problems
4Applications and Mathematical Justification6 lessons · 78 problems

The front entrance of Thomas Jefferson High School for Science and Technology

Who built it

Neil Kothari

TJHSST alumnus · Co-founder, EduAvenues · 10+ years in TJ preparation

Neil is a TJ alumnus and has spent more than a decade working with TJ students and their families. He built this course so students can connect function behavior, limits, derivatives and mathematical reasoning. Every problem is written for the course and every answer is checked before it goes in.

Tuition

$395for the full school year

One tuition covers every unit of the course. All 4 units are open now. The Local Function Behavior and Domains lesson stays free for everyone.

All 4 units: 24 lessons and 312 original problems
A worked answer for every problem
Access through the end of the school year

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