Do you need to take pre-calculus in order to take statistics?
No. There are virtually no pre-calculus concepts in an introductory statistics class and vice versa. Some introductory statistics courses may discuss cumulative distribution functions, but will likely not actually go into detail about integrating the density function, which is a concept in calculus.Later statistics courses will definitely implement calculus, however. For further reading, refer to How is calculus used in statistics, and how important is it for a career/theoretical statistician? For an applied statistician? For a practitioner of statistics?
Would taking an AP Calc AB class separately from school help me next year?
I think it would be largely beneficial to take the class at a local community college (that you're not planning on attending after high school) and either take the class for introduction purposes, or just to audit the course. Having at least some exposure before going into Calc is ideal and highly recommended.If you take the class in high school, and at the community college level, you will be more than prepared for university level calculus and even better prepared for your AP exams. If you take the class/audit it at the community college, just don't send over those transcripts if you don't do too well in their course. You only have to send prior college transcripts if you want those credits that you have previously taken.Good luck! Regardless of your precalc grades I would recommend taking AP calc, even if you plan to take the same calc in college. All teachers teach differently and extra exposure will never hurt.
Advice about Biomedical engineering?
No engineering job that requires a degree pays less than 50k on average to start, but they can pay less on the lower end. I answered your previous question about medicine versus engineering, so I will refer you to that for any answers to questions that you may have regarding engineering versus medicine. Biomedical engineering is a very very broad field -- essentially all forms of engineering come together with the goal of improving medical technology, everything from analog circuit design for better and cheaper amplifiers for EKG's and the like, to microfabrication principles for lab-on-a-chip concepts, to mechanical engineering to make better prosthetics, to chemical engineering to make better lab tests and better drugs, to computer engineering for constructing images from raw ultrasound, multidirectional x-ray or magnetic resonance data. There are a few different paths for biomedical engineering: Some colleges offer degrees in biomedical engineering as a major in and of itself, with core requirements being the essentials from all relevant fields and technical electives specializing in specific aspects of medical technology. Many do not, but instead offer degrees in electrical, computer, mechanical or chemical engineering with optional courses available in biomedical imaging (electrical/computer engineering), biomechanics (mechanical engineering) and pharmaceutical chemistry. Perhaps an interesting option for you would be the MD/Ph.D option, in which you go ahead and get a regular undergraduate degree in engineering, chemistry or biology. You start medical school and your first two years are regular medical school classes, but you take a 2 year break devoted to research and writing a dissertation, working out the theory and details of a new medical technology such as a new way to isolate proteins, a new way to use a laser to measure blood sugar levels without a needle, or a way to use microfabrication principles to make a nanosieve that can separate cholesterol molecules by size to get a much better view of LDLs vs HDLs. After finishing your research and dissertation, you spend another 2 years taking classes and you are done with medical school. If you wish to practice medicine, you still need to do a residency, but most MD/Ph.Ds end up staying in research.
Are calculus and trig closer to algebra or geometry?
Not really. In fact all those topics in math are there own thing. Like the other user mentioned. Geometry deals with shapes and figures of all kinds. That includes triangles. Trigonometry deals with the study of triangles. In fact trigonometry is a branch of geometry. Algebra deals with operations, procedures, equations, kn-owns, unknowns, etc.. . Calculus is the kind of math that deals with change, boundaries/limits, continuation, etc.. . In terms of math; it covers five concepts which are functions, limits, continuity, differentiation, and integration. Plus, in addition to all the other math that's been covered. (Including geometry, trigonometry, and so on.) Believe me I know what I'm talking about! I hope this clarifies things for you.
Is calculus without trig easy?
It is not difficult, however, if your algebra background is weak then it will be difficult. I would say that if your class grade in College Algebra is C+ or lower and/or your test average below 77 then you will have a tough time in Calculus. If your test average is above 83 in College Algebra, or you received at least a B {no minus} then you should be in great shape for non trig based Calculus. You are probably OK but it is hard to call for B- students. To one who says it is impossible to cover Calculus without trig, there are courses at many universities that have no trig based calculus. Usually, the Calculus offered for Business students covers no trig and the Calculus offered for liberal arts and social science students covers no trig, it simply teaches students who to evaluate derivatives and antiderivatives, and even gets into multivariable functions and partial derivatives. The course usually has lots of applications including economics. It is background for statistics too since knowledge of Calculus helps students understand continuous probability distributions in statistics. The Calculus and Analytic Geometry course sequence that students in math, the hard sciences and engineering take {the real calculus!!} requires a strong background in trigonometry. It's presentation of limits is also tougher, that sequence usually requires students to work with epsilon delta proofs of limits.
Is it a bad idea to take pre-calculus and AP statistics simultaneously?
I've heard so many things. Some say it's difficult to take AP stats without taking pre-cal first. Some say stats and pre-cal are completely different subjects so it does not really matter if you take one subject first, one later, or simultaneously. Some say you're doomed if you're taking two math classes at once. So, for those who have taken both subjects--what's your opinion? By the way, I'm taking a regular (college prep) pre-cal class.
What is the hardest concept covered in Geometry?
It gets far more abstract. You can do geometry on curved surfaces, more advanced geometry turns into multi-variable calculus just like the geometry you have learned already is closely related to algebra. Whether you find it harder or not depends on how much work you put into it. You found trig "easy", but you wouldn't have thought that 5 years ago. In 5 years time you might find advanced geometry equally "easy", particularly if you keep studying for your tests. There is no one hardest concept, and geometry is so closely related to so much else in mathematics that there are many very advanced concepts in different parts of geometry. Far more advanced than your examples. Most only understood by specialists. Geometry is a huge field. BTW, Einstein's theory of General Relativity is a geometric theory; this stuff matters.
What UC's can i get into if my gpa is 3.0 UC calulated? Can a high SAT score help me?
If you can get above 2000 on your SAT, you MIGHT have a shot at UC Irvine. This is only because they are noted for accepting people with lower GPAs but higher SAT scores; and vice versa. However, all those D's are really going to mess you up. It is very unlikely that you would get into UC Davis. UC Santa Barbara is a stretch too. I'm not 100% sure on this, but I'm PRETTY sure that D's aren't counted as credit for the A-G requirements. It is good that you have retaken your math classes that you received D's in, but it looks bad that you had to do that twice. Most UC Applicants actually have an average of 5 years of math on their application. (Algebra & Geometry taken in middle school count.) I would suggest taking some classes at a community college during your senior year, in MATH to make up for your lack of math achievement. I would highly suggest community college. I mean, it doesn't HURT to apply, and DEFINITELY highlight your depression when writing your essays, but make sure that you don't turn your essay into a pity party. You need to show how you overcame that depression. Colleges want students who will do well in their classes. College classes are difficult, especially at the UCs. If you are finding high school courses, this might be an indicator that you aren't quite ready for a UC, but don't worry! A community college will prepare you for this. I HIGHLY HIGHLY suggest that you apply to UC Merced and UC Riverside if you are really set on going to a UC. edit: ...and for the record, the essays DO COUNT...A LOT Ranked by importance Tier 1= GPA, SAT, difficulty of classes Tier 2= Essays, extracurriculars, awards Tier 3= Classes taken senior year, SAT2s, additional non a-g coursework The UCs can not base admissions on race since they are public institutions. You DON'T need a 4.6 to get into a UC. In fact, the UC GPA is capped at 4.4.
What math class should a high school freshman take?
Whatever challenges them.Most freshmen are taking Algebra I/Math 1. While I think this is a little underwhelming to be the majority’s math class, that is just me. If it challenges you, take it.Others test into Geometry/Math 2. The more advanced ones are in Algebra II/Math 3. Most of the ‘advanced math students’ will be found in Algebra II. These students will likely be in the same math classes with each other until their senior years. If you think you can take this challenge, do it.Still too easy?I’m taking AP Calculus AB. Three others in my grade are doing so as well.But how?Take classes over the summer.Over one summer, a friend and I took Algebra II and Trig over a summer. (Somehow, Jason managed to pass Trig with a B without knowing the unit circle. I don’t know how that happened.) Two other friends took two classes on separate summers. Same effect.You don’t have to take two summer classes if you’d like. But get yourself to a point where you’re challenging yourself.
Do you think majoring in economics and having a minor in mathematics are a good combination? I am currently a high school senior taking calculus BC and I feel like I am pretty good at math.
Yes, but I would consider doing the math major and econ minor. The body of theory in econ is likely to be shaken up over the next few decades. No one is going to be overturning Gauss's proofs. Also the research is increasingly employing methods that require us with economics backgrounds to learn more math. Do yourself a favor and get a strong foundation.Talk to some profs and see if you would be able to skip over the intro econ stuff. If you have the calculus background, you might benefit from skipping right over the intro and possibly intermediate theory. Find challenging and interesting courses. But don't assume you need the major without discussing it with some profs or academic advisors.