What to know before taking Calc 1

[2slowtogofast]

what should one know before taking calc 1. i don't feel i was prepared enough going from high school math right to calc in college. to not be so general what in the past comes up most that you use a lot in calc.

 

[bel]

Know all your circular and hyperbolic functions well, and memorise your trigonometric identities.

 

[rocomath]

if u had asked this question at the beginning of the summer, i would have recommended you to buy this book that I'm currently using to review the concepts i should have mastered b4 taking Calculus

Calculus was hell for me bc i lacked foundation, post-Calculus and doing this review book ... Calculus would have been so much easier

 

[Winzer]

Well..I wouldn't say memorize but understand and know how to get trig identities and hyperbolic functions.
Master your algebraic manipulation skills. And when it comes time you learn calc, work and understand the proofs! And the most important, have fun.

 

[symbolipoint]

what should one know before taking calc 1. i don't feel i was prepared enough going from high school math right to calc in college. to not be so general what in the past comes up most that you use a lot in calc.

You should know Intermediate Algebra and Basic Trigonometry, including a few of the common identities. That should be the absolute minimum. The importance of hyperbolic functions in YOUR course may vary depending on the school you attend.

 

[2slowtogofast]

thank you everyone

 

[2slowtogofast]

Know all your circular and hyperbolic functions well, and memorise your trigonometric identities.

is this what you me by hyperbolic functions.
find the standard for of the hyperbolic equation given. center (5,-3) vertex (7,-3) and focus (9, -3)

 

[mathwonk]

basic algebra is the main obstacle for my students, and every other teacher I know says that too.

simple stuff like factoring a^3 - b^3, or dividing polynomials, or exponent rules.

some students cannot simplify (27)^1/3 without a calculator.

it helps to review also pythagoras, and similar triangles, and basic facts about equilateral triangles, and parallel lines.

the addition formulas for sin and cos are useful occasionally. and simple identities like cos^2 + sin^2 = 1.

equations for the straight line through two points.

and please remember that a^2 + b^2 does not equal (a+b)^2.

 

[symbolipoint]

basic algebra is the main obstacle for my students, and every other teacher I know says that too.

simple stuff like factoring a^3 - b^3, or dividing polynomials, or exponent rules.
some students cannot simplify (27)^1/3 without a calculator.
it helps to review also [some stuff clipped out] straight line through two points.
and please remember that a^2 + b^2 does not equal (a+b)^2.

Basic algebra was certainly not my trouble when I studied Calculus 1. A few of the new concepts of Calculus were my trouble, even to the extent of not fully understanding the meaning and use of "dx". Also the so-many varied theorems about differentiability and continuity I was not able to master. Things became clearer when I studied Calcululs 1 on my own, several months later. Although those particular troubles during the first time through, I "passed" successfully. (Grading curve was favorable because other students had some difficulty too).

 

[mathwonk]

basic algebra was not my problem either, but it is still the number one problem of most students.

 

[bel]

is this what you me by hyperbolic functions.
find the standard for of the hyperbolic equation given. center (5,-3) vertex (7,-3) and focus (9, -3)

Well, I actually meant identities like $$cosh^2(x)-sinh^2(x) \equiv 1$$ and things like that, but yes, being familar with conics would help you too.

 

[PowerIso]

Hmm, I suppose the key points to be familiar with are basic trig ideas and solid algebra skills. I don't suppose much else is needed and if something else is needed, you can pick it up on the fly.

 

[kocher]

Yes, definitely know as many trig identities as you can. Also know the unit circle. Half angle and double angle formulas

 

[rook_b]

Well, this is a somewhat embarrassing question, but how exactly does one factor a^3-b^3 or more generally a^n-b^n? I spent some time thinking about it once but it just isn't obvious to me.

 

[symbolipoint]

Well, this is a somewhat embarrassing question, but how exactly does one factor a^3-b^3 or more generally a^n-b^n? I spent some time thinking about it once but it just isn't obvious to me.

You are worrying too much. If n is even, this should be fairly easy to start; if n is odd, then try dividing by (a - b) and see what the quotient is. Can you factor this quotient by inspection and experience?

Alternatively, try performing some binomial multiplications and trinomial multiplications, and some binomial & trinomial multiplications. Simplify; and you should find some nice rules.

 

[Howers]

Learn sets and set notation. Sets are so important but misunderstood by so many first years. S = {p|q} means the set of all objects (elements) p with the property q. The property can be anything like, the elements have to be < 3 or have to be integers. Get into closed and open set notation too [). Understand logarithms, trig, and sigma notation, and limits. You won't need to worry about having derivatives down, as they will be reviewed extensively.

You can also get Stewart's Calculus and do the appendices, which can be done in about a week.

 

[leright]

Learn sets and set notation. Sets are so important but misunderstood by so many first years. S = {p|q} means the set of all objects (elements) p with the property q. The property can be anything like, the elements have to be < 3 or have to be integers. Get into closed and open set notation too [). Understand logarithms, trig, and sigma notation, and limits. You won't need to worry about having derivatives down, as they will be reviewed extensively.

You can also get Stewart's Calculus and do the appendices, which can be done in about a week.

I don't recall using set theory much in calculus.

 

[2slowtogofast]

You can also get Stewart's Calculus and do the appendices, which can be done in about a week.

Thats actully the book I am working out of. I have another question. I go to school to day for my first day an apparently i need another course befor i take calc. but i was told the course i took in High School was good enough. My prof gave me the option of what i want to do. Heres the description of the course i already took.

A study of trigonometry and analytic geometry. Topics included will be fundamental trigonometry, graphs of trigonometric functions, trigonometric identities and equations, inverse trigonometric functions, oblique triangles, complex numbers, analytic geometry, systems of quadratic equations, and inequalities

heres what they say i should have taken

Sets and real numbers, functions, theory of polynomials, transcendental functions, sequences and series, 2-and 3-dimensional coordinate systems, vectors and matrices, Binomial Theorem, mathematical induction.

So stay in calc or take this course above. the book for the course i should have taken only differs from my book in the course i already took by 2 chapters. so what do you think??

 

[symbolipoint]

Thats actully the book I am working out of. I have another question. I go to school to day for my first day an apparently i need another course befor i take calc. but i was told the course i took in High School was good enough. My prof gave me the option of what i want to do. Heres the description of the course i already took.

A study of trigonometry and analytic geometry. Topics included will be fundamental trigonometry, graphs of trigonometric functions, trigonometric identities and equations, inverse trigonometric functions, oblique triangles, complex numbers, analytic geometry, systems of quadratic equations, and inequalities

heres what they say i should have taken

Sets and real numbers, functions, theory of polynomials, transcendental functions, sequences and series, 2-and 3-dimensional coordinate systems, vectors and matrices, Binomial Theorem, mathematical induction.

So stay in calc or take this course above. the book for the course i should have taken only differs from my book in the course i already took by 2 chapters. so what do you think??

So you are saying that the course you need first is "PreCalculus", or Elementary Functions, before you take Calculus 1. That seems reasonable. DO IT! You will help to ensure a strong review of Trigonometry and you will extend some of your Algebra knowledge and skills. You will be less likely of being weak in Algebra. The course might also at least introduce you to the "Limit" idea, and well as review sequences and series in more detail than what you found in "Intermediate Algebra".

If you have the time during this first semester, you could restudy a few earlier sections from your Stewart Calculus book, just to maintain some of the earlier concepts, so you will simply be stronger when you officially study Calculus 1 (next semester).

 

[Link-]

You should know a lot of algebra. Look for a Pre-calculus book, they would explain you almost everything you need for calculus.

 

[Howers]

Thats actully the book I am working out of. I have another question. I go to school to day for my first day an apparently i need another course befor i take calc. but i was told the course i took in High School was good enough. My prof gave me the option of what i want to do. Heres the description of the course i already took.

A study of trigonometry and analytic geometry. Topics included will be fundamental trigonometry, graphs of trigonometric functions, trigonometric identities and equations, inverse trigonometric functions, oblique triangles, complex numbers, analytic geometry, systems of quadratic equations, and inequalities

heres what they say i should have taken

Sets and real numbers, functions, theory of polynomials, transcendental functions, sequences and series, 2-and 3-dimensional coordinate systems, vectors and matrices, Binomial Theorem, mathematical induction.

So stay in calc or take this course above. the book for the course i should have taken only differs from my book in the course i already took by 2 chapters. so what do you think??

If your pre-calc is as weak as you say, I would recommend you take precalc before you do calc. That stuff mentioned in your "other course" is really easy stuff, and if you'r using the appendix from Stewart you already covered atleast half of it.

However, if you have some working knowledge of math there is no reason you can't do both simultaenously.

These requirements seem pretty basic, and most of them come up in the second semester of first year calc anyway.

Sets and real numbers - you'll find this in stewarts appendix. Very basic set stuff I mentioned before, and real numbers are just any kind of number that is no imaginary (to put in bluntly).

functions - any kind of equation that has only 1 y for every x, or in other words it passes the vertical line test.

theory of polynomials - I am guessing this is just how to solve equations and factor

transcendental functions - trig (which u did) and log functions

sequences and series - sigma notation which you may not have, however this comes up in second semester

2-and 3-dimensional coordinate systems - basically graphs in 2-d and 3-d

vectors and matrices, Binomial Theorem, mathematical induction - you don't really need this for first year calc, and whatever little appears will be in second semester


If my over simplied definitions sound familiar, you can take calc simultanously with this prealgebra course. If not however, you'd need atleast a working knowledge to work through.

By the soudns of things, you already did trig and inequalities, and I'd say you're at a good level for calc. You have all the prereqs.

 

[Howers]

I don't recall using set theory much in calculus.

This is very basic set theory I'm talking about. I'm sure it came up when you were doing monotonic and concavity intervals. Intervals are sets.