Maximizing Studying Efficiency: Memorizing Formulas for Calculus Success

[JonDE]

I wasn't sure where to put this question, so if a Mod wants to move this to a place where it would fit better/get more responses I would appreciate it.

I'm about to finish pre-cal and take calculus during the fall. For my final we are allowed a half page of formulas. On it I have written down 29 categories of formulas with between 1-6 in each category. My question is, should I spend the summer memorizing each and every one of these formulas? Is it necessary or more of a waste of time? Are there some that are far more important that I should have memorized? etc...

 

[axmls]

Some formulas are so important that you need to memorize this. The good news is, for the most part, the ones that are that important are the ones that you use the most, and so by using them often, you'll end up memorizing them inadvertently anyway.

It just depends on the formula.

 

[berkeman]

I wasn't sure where to put this question, so if a Mod wants to move this to a place where it would fit better/get more responses I would appreciate it.

I'm about to finish pre-cal and take calculus during the fall. For my final we are allowed a half page of formulas. On it I have written down 29 categories of formulas with between 1-6 in each category. My question is, should I spend the summer memorizing each and every one of these formulas? Is it necessary or more of a waste of time? Are there some that are far more important that I should have memorized? etc...

Can you post a copy of your crib sheet? That would make it easier to give you suggestions on which ones (and which categories) you should consider memorizing.

 

[JonDE]

Can you post a copy of your crib sheet? That would make it easier to give you suggestions on which ones (and which categories) you should consider memorizing.

I'll just list the "cateogies" (you don't want to try and read my writing).
Sum and difference formulas for sin cos and tan.
Double angle formulas. sin2θ =..., half angle formulas, power reducing formulas.
Product to sum, and sum to product formulas. eg sinAsinB=...
Law of Sine and Cosines
Area of Oblique triangle A=1/2bcSinA etc..., heron's formula
Polar to rectangular, rectangular to polar, product and quotient of polar form, de moivres formula
Angle between vectors, finding magnitude, vectors in rectangular form
Finding foci of ellipse, hyperbolas, parabolas and lotus rectum
equations for finding nth term or sum of arithmetic and geometric sequences

 

[symbolipoint]

I'll just list the "cateogies" (you don't want to try and read my writing).
Sum and difference formulas for sin cos and tan.
Double angle formulas. sin2θ =..., half angle formulas, power reducing formulas.
Product to sum, and sum to product formulas. eg sinAsinB=...
Law of Sine and Cosines
Area of Oblique triangle A=1/2bcSinA etc..., heron's formula
Polar to rectangular, rectangular to polar, product and quotient of polar form, de moivres formula
Angle between vectors, finding magnitude, vectors in rectangular form
Finding foci of ellipse, hyperbolas, parabolas and lotus rectum
equations for finding nth term or sum of arithmetic and geometric sequences

You must be grateful to be allowed that list during your tests. You should not need to list Law of Sines or Law of Cosines; those should be well memorized.

"Lotus rectum"?

 

[micromass]

Sum and difference formulas for sin cos and tan.

I don't know this by heart, but I can derive them if I wanted to.

Double angle formulas. sin2θ =...,

I know this one by heart

half angle formulas, power reducing formulas.
Product to sum, and sum to product formulas. eg sinAsinB=...

Don't know these by heart, but I can find them.

Law of Sine and Cosines
Area of Oblique triangle A=1/2bcSinA etc...,

I know these.

heron's formula

Don't know this, but I can derive them.

Polar to rectangular, rectangular to polar, product and quotient of polar form, de moivres formula
Angle between vectors, finding magnitude, vectors in rectangular form

I know this one.

Finding foci of ellipse, hyperbolas, parabolas and lotus rectum

Don't know this one. Not sure if I would be able to derive it easily either.

equations for finding nth term or sum of arithmetic and geometric sequences

I know this by heart.

 

[Loststudent22]

I'll just list the "cateogies" (you don't want to try and read my writing).
Sum and difference formulas for sin cos and tan.
Double angle formulas. sin2θ =..., half angle formulas, power reducing formulas.
Product to sum, and sum to product formulas. eg sinAsinB=...
Law of Sine and Cosines
Area of Oblique triangle A=1/2bcSinA etc..., heron's formula
Polar to rectangular, rectangular to polar, product and quotient of polar form, de moivres formula
Angle between vectors, finding magnitude, vectors in rectangular form
Finding foci of ellipse, hyperbolas, parabolas and lotus rectum
equations for finding nth term or sum of arithmetic and geometric sequences

Power reducing formula isn't that a calculus one? I remember it being messy but it was the same as just integration by parts repeated.

The trig ones are important to know but you should be able to derive most of them. You will be reminded of them when you go over them for calculus and will know which are important as you do homework problems.

 

[JonDE]

You must be grateful to be allowed that list during your tests. You should not need to list Law of Sines or Law of Cosines; those should be well memorized.
"Lotus rectum"?

Thanks for your input, and while I am grateful that I am allowed these lists as is helps my grade, at the same time, I didn't want to be unprepared for calculus.
Also apparently that was supposed to be Latus rectum (which goes back to my previous post about my bad handwriting), anyways from what I remember its a line that is parallel to the directerix, that runs through the foci to the end points of the parabola. I believe the end points should also be an equal distance from the foci and from the directerix. When using the equation y²=4px the length should be equal to 4p.

I don't know this by heart, but I can derive them if I wanted to.
I know this one by heart
Don't know these by heart, but I can find them.
I know these.
Don't know this, but I can derive them.
I know this one.
Don't know this one. Not sure if I would be able to derive it easily either.
I know this by heart.

Thanks Micromass, this is pretty much exactly what I was looking for, I will make sure I know or be able to derive everything you have suggested before I take calculus.

Power reducing formula isn't that a calculus one? I remember it being messy but it was the same as just integration by parts repeated.

The trig ones are important to know but you should be able to derive most of them. You will be reminded of them when you go over them for calculus and will know which are important as you do homework problems.

Not sure if the power reducing formula is a calculus one or not as I have not taken it yet.

Anyways, thanks everyone for your input, it is greatly appreciated.

 

[clope023]

I wasn't sure where to put this question, so if a Mod wants to move this to a place where it would fit better/get more responses I would appreciate it.

I'm about to finish pre-cal and take calculus during the fall. For my final we are allowed a half page of formulas. On it I have written down 29 categories of formulas with between 1-6 in each category. My question is, should I spend the summer memorizing each and every one of these formulas? Is it necessary or more of a waste of time? Are there some that are far more important that I should have memorized? etc...

Best way that I've found to memorize formulas is learning how to derive them.

 

[JorisL]

Regarding multiples of angles in sine and cosine, I usually use the Euler identity.
It's a 30 second "derivation" which contains a lot of information.