A calculus workbook · by Ryan Ross

The Language
of Calculus™

Functions, algebra, and trigonometry, practiced until you can do them without thinking. That is most of the work in any calculus problem, and it is where most points are lost.

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39lessons
185pages
3checkpoints
$5one-time

The secret nobody tells you

You will not fail
calculus on the calculus.

Every calculus professor knows a secret they rarely say out loud: students do not fail calculus on the calculus. They fail on rusty algebra and half-remembered trig.

In a typical problem, about 90% of the work is algebra and only one step is the genuinely new idea. Miss the algebra and you lose the mark on a line that has nothing to do with calculus.

How it works

Master the fundamentals, and all that is left is the calculus.

01

See the picture

Every topic opens with an intuition: a graph, a shape, an analogy.

02

Drill the problems

You cannot learn this by watching. Every lesson ends in problems you solve yourself.

03

Check your answers

Every answer leads with the result, then explains it. Study only what you missed.

Inside the book

Every lesson, listed.

DifficultyUsefulness
Start here
Day 1The Day-1 benchmarkthe diagnostic you rematch at the end
The Algebra Toolkit
TK1Factoring Iun-multiplying★★★★★★★★★★
TK2Factoring IIthe ugly exponents★★★★★★★★★★
TK3Exponent & radical rulesone idea wearing costumes★★★★★★★★★★
TK4Factoring by groupingthe four-term move★★★★★★★★★★
TK5Negative & fractional exponentsthe kind calculus hands you★★★★★★★★★★
TK6Simplifying to final formcancel factors, never terms★★★★★★★★★★
TK7The factoring gauntletknowing which tool the problem wants★★★★★★★★★★
TK8Rewriting into power formthe reverse move, for the power rule★★★★★★★★★★
TK9Complex fractionsthe calculus cases★★★★★★★★★★
Functions
FN1What a function really isand how to read one off a graph★★★★★★★★★★
FN2Transformations & piecewisemoving graphs and stitching them★★★★★★★★★★
FN3Domainwhere functions break★★★★★★★★★★
FN4Sign-charts & end behaviorthe complete sketch★★★★★★★★★★
FN5Composition & inversesnesting functions and undoing them★★★★★★★★★★
FN6Exponentials & logarithmssolving for the exponent★★★★★★★★★★
The Parent-Function Library
PF1Lines, parabolas & cubicsthe polynomial parents★★★★★★★★★★
PF2Square root & cube rootwhere the domain breaks★★★★★★★★★★
PF3The absolute-value functionthe V, and nailing its range★★★★★★★★★★
PF4Rational functionsholes, walls, and the horizon★★★★★★★★★★
PF5Exponentials & logsmirror images across y = x★★★★★★★★★★
PF6Sine and cosinethe two waves, rebuilt from key points★★★★★★★★★★
PF7Tangent & the reciprocalswhere the asymptotes come from★★★★★★★★★★
CP1Checkpoint 1functions and foundations, mixed and unlabeled
Reading the form
RF1Parameters from a graphwhich number is the amplitude★★★★★★★★★★
RF2Matching a requested formwhen the shape is dictated★★★★★★★★★★
Trigonometry
TR1The unit circlea verification pass on what you already own★★★★★★★★★★
TR2Trig equationsthe quadratic in a costume★★★★★★★★★★
TR3The six functionsall of them from one rotating point★★★★★★★★★★
TR4Core identitiesone master equation and its children★★★★★★★★★★
TR5Inverse trigand two quick loose ends★★★★★★★★★★
CP2Checkpoint 2the whole trig pillar, no labels
Vectors, polar and complex
VP1Vectorsarrows you can add★★★★★★★★★★
VP2Polar coordinateslength and angle, not legs★★★★★★★★★★
VP3Complex numbersand why they are vectors★★★★★★★★★★
VP4Matriceswhat they do to a vector★★★★★★★★★★
Algebra in Action
AA1Rational expressionsthe algebra calculus runs on★★★★★★★★★★
AA2Solving & rationalizingclosing the toolkit★★★★★★★★★★
CP3Checkpoint 3algebra fluency, where marks get lost
The readiness final
FINALReadiness Finalthe whole course, and the benchmark rematch
The calculus doorway
CX1What a limit really isthe name for a move you already own★★★★★★★★★★
CX2Continuitywhen a graph has no surprises★★★★★★★★★★
CX3The derivativethe thing you were already computing★★★★★★★★★★

Real pages

This is what you get.

Four pages, exactly as they print: the picture, the explanation, the ruled space you work in, and the answers. Click any one to read it full size.

A page showing three parent function graphs
See the picture
A page explaining the factoring moves
Read the explanation
A page of problems with ruled space to work in
Work the problems
An answers page, result first
Check the answers

Get it

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Free

The preview

  • Five full lessons, start to finish
  • The diagnostic, factoring, functions, waves, your first limit
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The complete workbook

  • All 39 lessons · 185 pages
  • Three checkpoints and a readiness final
  • Yours to keep. Print it or fill it on a tablet
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Questions

Before you buy.

I have already started Calculus I. Is it too late?

No. The algebra does not stop mattering after week one, it is what every homework set leans on. Work the Toolkit lessons alongside your course and use the checkpoints to find what is actually costing you marks.

Do I have to print it?

No. Every problem has ruled space so it works on paper, and the whole thing is built to be filled in on a tablet. Answers are repeated at the end of each lesson, so nothing depends on tapping anything.

How is this different from Khan Academy?

Khan is a library. This is a sequence. Thirty-three lessons in a deliberate order, each ending in problems you work yourself, with a diagnostic at the start and the same problems again at the end so you can measure the gap. Several lessons point you at Khan for extra volume once you understand the idea.

What exactly do I get?

One PDF. 185 pages, 39 lessons, three mixed checkpoints and a readiness final. One payment, yours to keep, no subscription and no account to make.

How is this different from a math textbook?

A textbook is written to cover a subject. This is written to get you through one course. It is 185 pages instead of 900, the lessons come in a fixed order rather than as a reference you dip into, and there is a diagnostic at the start and a finish line at the end so you can see the distance you moved. Nothing is in here because a syllabus demanded it. Every page earned its place by being something that actually costs people marks.

What if it does not help me?

Full refund within 14 days, no questions asked. Email ryanross949@gmail.com and I will sort it out.

About

Who wrote this.

I am a college student majoring in computer engineering. I built this workbook for myself after finding out where Calculus I actually goes wrong. It is not the calculus. It is the algebra and trigonometry underneath it. I designed the sequence, wrote the diagnostic, solved every problem myself, and rewrote the lessons that did not work. I am not a professor, and that is the point. I sat exactly where you are, and this is the preparation I wish someone had handed me.