x + y = A in pre-calc. Help me solve for x and y!
August 25, 2012 11:30 AM Subscribe
What do I need to know to be ready for pre-calculus?
I just found out that I am going into a pre-calc class next month and my math skills are not ready for it. Taking a lower level math class is really not an option at this point. I have taken algebra and statistics at the community college level but this was a few years ago so those skills are rusty. I have an intermediate algebra book that I have been working through but I get the feeling that a lot of what I am learning from the book may not actually be useful for the pre-calc class.
Are there any particular math skills that I should focus on while I get ready for the pre-calc class? Or would it just be best to study all of the algebra?
I am aware of the various websites that help teach math skills, but I find them to be a bit scattershot in that I cannot tell which skills build on previous skills and which ones would get me prepared for pre-calc.
I just found out that I am going into a pre-calc class next month and my math skills are not ready for it. Taking a lower level math class is really not an option at this point. I have taken algebra and statistics at the community college level but this was a few years ago so those skills are rusty. I have an intermediate algebra book that I have been working through but I get the feeling that a lot of what I am learning from the book may not actually be useful for the pre-calc class.
Are there any particular math skills that I should focus on while I get ready for the pre-calc class? Or would it just be best to study all of the algebra?
I am aware of the various websites that help teach math skills, but I find them to be a bit scattershot in that I cannot tell which skills build on previous skills and which ones would get me prepared for pre-calc.
Pre-calc is a bit of a weird class, and unlike, say, geometry, different states, school districts, and schools offer significantly different pre-calc course. So I have no idea which specifics you'll need. That said, being able to do trig and solve for x and graph functions (and understand the graphs of functions) will all come in handy.
Basically, pre-calc is a bit of a grab-bag course, and if you want specific recommendations, you'll need to be specific about what your pre-calc course covers.
posted by pmb at 11:47 AM on August 25, 2012 [1 favorite]
Basically, pre-calc is a bit of a grab-bag course, and if you want specific recommendations, you'll need to be specific about what your pre-calc course covers.
posted by pmb at 11:47 AM on August 25, 2012 [1 favorite]
These guys write a free pre-calc textbook with accompanying Youtube videos.
posted by XMLicious at 11:56 AM on August 25, 2012
posted by XMLicious at 11:56 AM on August 25, 2012
Response by poster: This is the specific data that I have on the class that is offered if it is helpful.
posted by sacrifix at 12:08 PM on August 25, 2012
posted by sacrifix at 12:08 PM on August 25, 2012
Best answer: I just taught pre-calc this summer. I found that the biggest problem students had was a lack of basic algebraic skills. Can you expand the following expression without freaking out?
(-1)(x3-2x+1)(x2-5) = ?
If not, you need to work on your algebra. Basic factoring is also very important, along with rules for exponents. For example:
xaxb=xa+b
(xa)b = xab
x-a = 1/xa
are all important identities. If you are comfortable with these things then you would have been at least in the middle of the pack in my class, which was at a very highly ranked public university.
posted by number9dream at 12:13 PM on August 25, 2012 [5 favorites]
(-1)(x3-2x+1)(x2-5) = ?
If not, you need to work on your algebra. Basic factoring is also very important, along with rules for exponents. For example:
xaxb=xa+b
(xa)b = xab
x-a = 1/xa
are all important identities. If you are comfortable with these things then you would have been at least in the middle of the pack in my class, which was at a very highly ranked public university.
posted by number9dream at 12:13 PM on August 25, 2012 [5 favorites]
Best answer: Ok, that content looks like being able to graphically interpret functions and doing simple derivatives.
Algebra is going to be the biggest skill. Factoring and expanding expressions, solving for a variable, and rearranging an equation into standard form (like y = mx + b or y = ax^2 + bx + c) are all necessary.
Second skill is being comfortable with the Cartesian plane. Plotting points, graphing functions (can you take y = 2x^2 - 3 and draw that function by finding points and connecting them appropriately?), that kind of thing. A lot of the interpretation of the graph will be covered in the course, but having a solid foundation in turning an equation into a graph will be helpful.
posted by philosophygeek at 12:26 PM on August 25, 2012
Algebra is going to be the biggest skill. Factoring and expanding expressions, solving for a variable, and rearranging an equation into standard form (like y = mx + b or y = ax^2 + bx + c) are all necessary.
Second skill is being comfortable with the Cartesian plane. Plotting points, graphing functions (can you take y = 2x^2 - 3 and draw that function by finding points and connecting them appropriately?), that kind of thing. A lot of the interpretation of the graph will be covered in the course, but having a solid foundation in turning an equation into a graph will be helpful.
posted by philosophygeek at 12:26 PM on August 25, 2012
Best answer: Things you should brush up on:
- Order of operations
- Factoring quadratics and the quadratic equation
- Exponent rules
- Graphing simple first and second order equations
If you're ok with that stuff going in you should be fine.
posted by no regrets, coyote at 12:37 PM on August 25, 2012
- Order of operations
- Factoring quadratics and the quadratic equation
- Exponent rules
- Graphing simple first and second order equations
If you're ok with that stuff going in you should be fine.
posted by no regrets, coyote at 12:37 PM on August 25, 2012
Best answer: I agree with number9dream and philosophygeek. I taught pre-calc this summer and the previous two semesters at a flagship public university, and algebra skills were a very good predictor of overall success in the course.
Outside of basic algebraic errors, I think the most common pitfall I saw was incorrect identification of the goals of a problem. The first step to solving a problem is knowing what piece of information you are looking for; I have had a number of students who seemed to skip this step and just reach into a grab bag of techniques. This can lead to errors like trying to solve a cubic equation with the quadratic formula, or being unable to even begin a word problem because you can't label the quantity you want to find.
A final note: please try to minimize your dependence on your calculator/computer. I'm not sure my students ever believed me when I said this, but you are smarter than your calculator. If you reach for it at the beginning of every problem, you are letting the dumb machine do all the thinking.
posted by Aquinas at 12:52 PM on August 25, 2012 [1 favorite]
Outside of basic algebraic errors, I think the most common pitfall I saw was incorrect identification of the goals of a problem. The first step to solving a problem is knowing what piece of information you are looking for; I have had a number of students who seemed to skip this step and just reach into a grab bag of techniques. This can lead to errors like trying to solve a cubic equation with the quadratic formula, or being unable to even begin a word problem because you can't label the quantity you want to find.
A final note: please try to minimize your dependence on your calculator/computer. I'm not sure my students ever believed me when I said this, but you are smarter than your calculator. If you reach for it at the beginning of every problem, you are letting the dumb machine do all the thinking.
posted by Aquinas at 12:52 PM on August 25, 2012 [1 favorite]
This was years ago and in high school, but my pre-calc class also had a full unit (i.e. couple of months) of trig in addition to what's already been mentioned.
posted by smirkette at 2:19 PM on August 25, 2012
posted by smirkette at 2:19 PM on August 25, 2012
I highly recommend the book "Forgotten Algebra" by Barbara Lee Bleau (sorry for no link--I'm a dummy that way). Many years ago I worked through it and scored eligible to take first-year calculus on my school's math placement test. The book contains 31 short units. I was able to work through 1-2 units per day studying about 2 hours per night. Hope this helps!
posted by auntie maim at 2:59 PM on August 25, 2012
posted by auntie maim at 2:59 PM on August 25, 2012
I'm not sure about the boundaries between pre-calc and calc, but there was one thing that I learned late that would have helped tremendously in calculus & trig...Euler's formula:
e^(i * theta) = cos(theta) + i sin(theta)
and the derivative
d/dx e^ax = a e^ax
and
e^a * e^b = e^(a+b)
If you can remember (and use) those three things you can simply derive almost all of the trig identities as well as many of the integrals and derivatives of trig functions.
It's a mainstay of physics, but was left out of most of my early math education...
posted by NoDef at 6:33 PM on August 25, 2012
e^(i * theta) = cos(theta) + i sin(theta)
and the derivative
d/dx e^ax = a e^ax
and
e^a * e^b = e^(a+b)
If you can remember (and use) those three things you can simply derive almost all of the trig identities as well as many of the integrals and derivatives of trig functions.
It's a mainstay of physics, but was left out of most of my early math education...
posted by NoDef at 6:33 PM on August 25, 2012
Best answer: I would hope that a basic pre-calc course wouldn't require Euler's formula! Derivatives are a calculus thing, too, not pre-calc.
It might help to have a general sense of how all the different math classes fit together, in addition to the suggestions above. Pre-calculus is a course full of preliminary material that's supposed to help you understand calculus. Calculus is the study of the properties/behavior of functions. In calculus you mostly look at stuff like rate of change/slope of the graph of functions, area under the graph of a function, and new ways of defining functions (eg. sequences, and then series). In pre-calculus, you focus on more basic properties of functions, eg. stuff about their graphs (what they look like, domain and range, how small changes in the function end up changing the graph of the function), or algebraic properties.
There's a catalog of functions that you'll study:
1. Algebraic Functions -- functions formed by algebraic operations (addition, subtraction, multiplication, division)
* lines y = mx + b (slope-intercept form), y - (y_0) = m(x - x_0) (point-slope form)
* quadratic functions y = ax^2 + bx + c
* other polynomials (part of the progression from algebra to calculus is getting comfortable with more abstract notation and ways of thinking about math, eg. the "general" form of a polynomial, which could be of any degree, y = a_n x^n + a_{n-1} x^{n-1} + ... + a_1 x + a_0)
* rational functions p(x)/q(x), where p(x) and q(x) are both polynomials
2. Transcendental Functions
* exponentials, y = e^x, y = a^x
* logarithms, y = ln(x), y = log_a (x)
[3. Trigonometric Functions - in some pre-calc courses and definitely in calculus, but it doesn't look like your particular course deals with them]
So to study these functions, you need to be able to work with them. I second the recommendations that it's good to have strong arithmetic and algebra skills, including order of operations, factoring, working with algebraic expressions and variables and solving for x in basic linear or quadratic equations, as well as laws of exponents and logarithms. I'd also add working with fractions (adding and multiplying fractions, specifically).
Another important thing to keep in mind is that the algebra -> pre-calc -> calculus progression involves increasing levels of abstraction in the way you think about and work with the different mathematical objects and ideas. In algebra, rather than thinking of numbers as representing quantities, and fractions as, well, fractions of quantities, you think of numbers as being points on a number line, and negative numbers are introduced as giving direction away from zero, so that, eg., -4 and +4 are the same distance from zero (4), but in opposite directions on the number line. So that's still has this nice physical interpretation, but is a little bit more abstract. But then you introduce variables, and they're a bit more abstract too (though if you start with a word problem that is a real problem, not some pre-set-up problem like Dan Meyer rails against, then it makes a bit more sense why you might want to keep track of variables, because they help you keep things more organized when you're trying to think about and solve a more complicated problem). Pre-calc ads another level of abstraction: now instead of equations, you deal with functions. So functions are going to related to equations that you saw in algebra, but a little broader and more generalized. At each level, there will be stuff that seems familiar from the previous level, except you'll need to think about it slightly differently, in some slightly more abstract way. That's a good thing to be on the lookout for. So I guess I'd say that having the mindset of, "how is this a generalization or abstraction from what I've seen before, and why did people find it useful to make this generalization or abstraction?" is an important part of your preparation for pre-calc as well.
posted by sockpuppet13 at 9:06 PM on August 25, 2012 [1 favorite]
It might help to have a general sense of how all the different math classes fit together, in addition to the suggestions above. Pre-calculus is a course full of preliminary material that's supposed to help you understand calculus. Calculus is the study of the properties/behavior of functions. In calculus you mostly look at stuff like rate of change/slope of the graph of functions, area under the graph of a function, and new ways of defining functions (eg. sequences, and then series). In pre-calculus, you focus on more basic properties of functions, eg. stuff about their graphs (what they look like, domain and range, how small changes in the function end up changing the graph of the function), or algebraic properties.
There's a catalog of functions that you'll study:
1. Algebraic Functions -- functions formed by algebraic operations (addition, subtraction, multiplication, division)
* lines y = mx + b (slope-intercept form), y - (y_0) = m(x - x_0) (point-slope form)
* quadratic functions y = ax^2 + bx + c
* other polynomials (part of the progression from algebra to calculus is getting comfortable with more abstract notation and ways of thinking about math, eg. the "general" form of a polynomial, which could be of any degree, y = a_n x^n + a_{n-1} x^{n-1} + ... + a_1 x + a_0)
* rational functions p(x)/q(x), where p(x) and q(x) are both polynomials
2. Transcendental Functions
* exponentials, y = e^x, y = a^x
* logarithms, y = ln(x), y = log_a (x)
[3. Trigonometric Functions - in some pre-calc courses and definitely in calculus, but it doesn't look like your particular course deals with them]
So to study these functions, you need to be able to work with them. I second the recommendations that it's good to have strong arithmetic and algebra skills, including order of operations, factoring, working with algebraic expressions and variables and solving for x in basic linear or quadratic equations, as well as laws of exponents and logarithms. I'd also add working with fractions (adding and multiplying fractions, specifically).
Another important thing to keep in mind is that the algebra -> pre-calc -> calculus progression involves increasing levels of abstraction in the way you think about and work with the different mathematical objects and ideas. In algebra, rather than thinking of numbers as representing quantities, and fractions as, well, fractions of quantities, you think of numbers as being points on a number line, and negative numbers are introduced as giving direction away from zero, so that, eg., -4 and +4 are the same distance from zero (4), but in opposite directions on the number line. So that's still has this nice physical interpretation, but is a little bit more abstract. But then you introduce variables, and they're a bit more abstract too (though if you start with a word problem that is a real problem, not some pre-set-up problem like Dan Meyer rails against, then it makes a bit more sense why you might want to keep track of variables, because they help you keep things more organized when you're trying to think about and solve a more complicated problem). Pre-calc ads another level of abstraction: now instead of equations, you deal with functions. So functions are going to related to equations that you saw in algebra, but a little broader and more generalized. At each level, there will be stuff that seems familiar from the previous level, except you'll need to think about it slightly differently, in some slightly more abstract way. That's a good thing to be on the lookout for. So I guess I'd say that having the mindset of, "how is this a generalization or abstraction from what I've seen before, and why did people find it useful to make this generalization or abstraction?" is an important part of your preparation for pre-calc as well.
posted by sockpuppet13 at 9:06 PM on August 25, 2012 [1 favorite]
I notice the course lists "Satisfactory score on the mathematics placement test MATH 105 or 108". Might be worth looking for textbooks from 105 or 108. Or see if you can track down an old copy of the "mathematics placement test", or of tests used in 105 or 108, with answer keys, take them and grade them yourself, and use them to decide where your weaknesses might be.
Also try setting up a meeting with the instructor, either now or on the first day of class, and again whenever you find the class assumes you already know something that you don't. In the worst case: the early you speak up, the easier it will be to transfer to a different class if you find out you're not ready. In the more likely case: you'll be missing some minor pieces and the instructor should be able to point you to resources that can help you fill them in.
Also, http://www.foothill.edu/tutor/index.php might help?
Everywhere's different, but my experience is that often office hours and tutoring centers are zoos the week before exams and relatively empty otherwise, so it pays to take advantage of them early.
posted by bfields at 11:43 AM on August 26, 2012
Also try setting up a meeting with the instructor, either now or on the first day of class, and again whenever you find the class assumes you already know something that you don't. In the worst case: the early you speak up, the easier it will be to transfer to a different class if you find out you're not ready. In the more likely case: you'll be missing some minor pieces and the instructor should be able to point you to resources that can help you fill them in.
Also, http://www.foothill.edu/tutor/index.php might help?
Everywhere's different, but my experience is that often office hours and tutoring centers are zoos the week before exams and relatively empty otherwise, so it pays to take advantage of them early.
posted by bfields at 11:43 AM on August 26, 2012
Response by poster: Wow even as a long(?) time member I am very impressed by the quality of these answers! Thank you all for your guidance, it has been very helpful.
posted by sacrifix at 12:00 PM on August 26, 2012
posted by sacrifix at 12:00 PM on August 26, 2012
This thread is closed to new comments.
posted by xyzzy at 11:44 AM on August 25, 2012 [1 favorite]