\( \newcommand{\abs}[1]{\left| \, {#1} \, \right| } \) \( \newcommand{\cm}{\mathrm{cm} } \) \( \newcommand{\sec}{ \, \mathrm{sec} \, } \) \( \newcommand{\vhat}[1]{\,\hat{#1}} \) \( \newcommand{\vhati}{\,\hat{i}} \) \( \newcommand{\vhatj}{\,\hat{j}} \) \( \newcommand{\vhatk}{\,\hat{k}} \) \( \newcommand{\vect}[1]{\boldsymbol{\vec{#1}}} \) \( \newcommand{\norm}[1]{\|{#1}\|} \) \( \newcommand{\arccot}{ \, \mathrm{arccot} \, } \) \( \newcommand{\arcsec}{ \, \mathrm{arcsec} \, } \) \( \newcommand{\arccsc}{ \, \mathrm{arccsc} \, } \) \( \newcommand{\sech}{ \, \mathrm{sech} \, } \) \( \newcommand{\csch}{ \, \mathrm{csch} \, } \) \( \newcommand{\arcsinh}{ \, \mathrm{arcsinh} \, } \) \( \newcommand{\arccosh}{ \, \mathrm{arccosh} \, } \) \( \newcommand{\arctanh}{ \, \mathrm{arctanh} \, } \) \( \newcommand{\arccoth}{ \, \mathrm{arccoth} \, } \) \( \newcommand{\arcsech}{ \, \mathrm{arcsech} \, } \) \( \newcommand{\arccsch}{ \, \mathrm{arccsch} \, } \)

17Calculus - Ideas For More Help With Your Classwork

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Calculus 1 Practice

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Practice Exams


Calculus Tools

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If you have found that you need more help than your class, instructor, this site and other sites can give you, we have some suggestions on how to get additional support and what to do for help, many of them free. College is not easy but it is possible to do well with the correct preparation and tools. These suggestions will help you after you have implemented all the study techniques listed on the study techniques page.

Support System

When you are having difficulty with math, science or engineering and you realize that you need help, having a support system strategy is important. There are two main sources for support systems, through your school or building your own.

Check Your School's Support System

Department Help Room - - Most schools have help rooms within each department, especially science, math and engineering departments. They are usually a drop-in type of help, so at least initially, your help may be hit and miss. Once you find someone that helps you, ask them when they are in the help room and plan your schedule to be there when they are there. These help rooms are usually free and staffed by grad students.
Tutoring Service - - This option is discussed below.

Build Your Own Support System

This is actually the better way to go, i.e. to build your own support system and not rely on your school to provide you with support.
Study Group - - Set up your own study group with other people that are in your class. See the study group page for details on how to do this effectively.
Instructor's Office Hours - - Some instructors are better at teaching one-on-one than in the classroom. Try to see the instructor during their office hours (if they seem open to it) and show up with specific questions and with a specific agenda. Don't just go in expecting them to teach you everything all over again.


In this section, we give you suggestions on how you can get the most out of your tutoring sessions and some suggestions on how to find tutors.

Tutoring Service Through Your School

This type of help usually costs something but not as much as you might expect. The tutors are usually students that have recently taken the course you are in and they do it very cheaply since they might get class credit for it. Usually you pay the school and then the school pays them. Check with the department to see if they know who to talk to. Again, this is hit and miss and they may assign someone to you that doesn't help you, so do not be afraid to ask for someone else.

Outside Tutoring

There are lots of tutoring services out there, some better than others. Again, remember that you are working with people and some of them are not going to help you, others will. So be flexible and try several before completely giving up.

How To Get The Most Out of Your Tutoring Sessions

Here are some tips on how to get your money's worth out of your tutoring sessions.
1. Arrive at your tutoring appointment early (at least 5 minutes) and have your materials laid out when your tutor arrives. This will maximise your productive time and you will not have to pay for time that you spend setting up. Do not be late since you will probably pay starting from when the tutor arrives.
2. Bring your textbook and all your homework and exams.
3. Come with specific questions about specific problems or things you do not understand.
4. Do not expect your tutor to teach the material to you. He/She is there to help straighten out your understanding of things you are missing or confused about. Before you meet, find the point where you started to begin getting confused and start there.
5. Keep in mind that you will find some tutoring sessions to be extremely helpful and others may be less helpful. Do not give up on your tutor if you are still progressing.
6. Do not waste time with a bad tutor or a tutor that teaches in a way that does not help you. Find another tutor, if you need to.
7. Do not wait too long to get a tutor, i.e. if you think a tutor will help you, get one early in the semester. It is possible to get too far into the semester and be so lost that you don't have time to get caught up. Try a session here and there to keep up on the material.
8. Do not be shy about paying your tutor. They are providing a service and it is right and proper to be paid for that service. They understand that and you should too.
Something To Watch For - - If you have a tutor and they seem to be helping you but you go into the exam and you fail, your tutor may not actually be helping you. Some tutors have a way of doing the work for you while making you think you are doing it. Watch carefully for this. They probably don't know they are doing it. If you are frustrated and stumbling but you are making progress and you know you are doing it on your own, then you are on the right track. The job of the tutor is to get you to a point where you are doing the problems on your own. If you rely too much on them, you will not do well in the class and on exams.

More Structured Online Courses

Here at 17calculus we do not yet have specific courses. However, if you are looking for more of a structured approach to learning, here are some suggestions.

You CAN Ace Calculus

Trig Formulas

The Unit Circle

The Unit Circle [wikipedia]

Basic Trig Identities

Set 1 - basic identities

\(\displaystyle{ \tan(t) = \frac{\sin(t)}{\cos(t)} }\)

\(\displaystyle{ \cot(t) = \frac{\cos(t)}{\sin(t)} }\)

\(\displaystyle{ \sec(t) = \frac{1}{\cos(t)} }\)

\(\displaystyle{ \csc(t) = \frac{1}{\sin(t)} }\)

Set 2 - squared identities

\( \sin^2t + \cos^2t = 1\)

\( 1 + \tan^2t = \sec^2t\)

\( 1 + \cot^2t = \csc^2t\)

Set 3 - double-angle formulas

\( \sin(2t) = 2\sin(t)\cos(t)\)

\(\displaystyle{ \cos(2t) = \cos^2(t) - \sin^2(t) }\)

Set 4 - half-angle formulas

\(\displaystyle{ \sin^2(t) = \frac{1-\cos(2t)}{2} }\)

\(\displaystyle{ \cos^2(t) = \frac{1+\cos(2t)}{2} }\)

Trig Derivatives

\(\displaystyle{ \frac{d[\sin(t)]}{dt} = \cos(t) }\)


\(\displaystyle{ \frac{d[\cos(t)]}{dt} = -\sin(t) }\)

\(\displaystyle{ \frac{d[\tan(t)]}{dt} = \sec^2(t) }\)


\(\displaystyle{ \frac{d[\cot(t)]}{dt} = -\csc^2(t) }\)

\(\displaystyle{ \frac{d[\sec(t)]}{dt} = \sec(t)\tan(t) }\)


\(\displaystyle{ \frac{d[\csc(t)]}{dt} = -\csc(t)\cot(t) }\)

Inverse Trig Derivatives

\(\displaystyle{ \frac{d[\arcsin(t)]}{dt} = \frac{1}{\sqrt{1-t^2}} }\)


\(\displaystyle{ \frac{d[\arccos(t)]}{dt} = -\frac{1}{\sqrt{1-t^2}} }\)

\(\displaystyle{ \frac{d[\arctan(t)]}{dt} = \frac{1}{1+t^2} }\)


\(\displaystyle{ \frac{d[\arccot(t)]}{dt} = -\frac{1}{1+t^2} }\)

\(\displaystyle{ \frac{d[\arcsec(t)]}{dt} = \frac{1}{\abs{t}\sqrt{t^2 -1}} }\)


\(\displaystyle{ \frac{d[\arccsc(t)]}{dt} = -\frac{1}{\abs{t}\sqrt{t^2 -1}} }\)

Trig Integrals

\(\int{\sin(x)~dx} = -\cos(x)+C\)


\(\int{\cos(x)~dx} = \sin(x)+C\)

\(\int{\tan(x)~dx} = -\ln\abs{\cos(x)}+C\)


\(\int{\cot(x)~dx} = \ln\abs{\sin(x)}+C\)

\(\int{\sec(x)~dx} = \) \( \ln\abs{\sec(x)+\tan(x)}+C\)


\(\int{\csc(x)~dx} = \) \( -\ln\abs{\csc(x)+\cot(x)}+C\)

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Topics Listed Alphabetically

Single Variable Calculus

Multi-Variable Calculus

Differential Equations





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