Can AP exams substitute a year of university?

  • #1
programmer123
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Hello. Well, it looks like I'm going to have to go back for another year of high school due to low marks. However, it is very boring and I regret not doing better because I know everything and far beyond all of the math, science, and english curricula. There were also some complications relating to my health that hindered my success.

So, I'm wondering if I can go to high school and also take AP exams in various subjects to earn my credits for the first year of university. So, I know there are at least 2 calculus AP exams, can I take those and substitute it for my first 2 calculus credits and then do the same for all of the other courses I would have taken in first year university? Then can I start in second year university when I get accepted there?

Are there other ways to earn university credits before graduating from high school? I am in Canada, if there is a difference, and will definitely be going to university in Canada (one day ...).

Thanks for reading and any input/information is appreciated.
 

Answers and Replies

  • #3
Vid
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See if you high school will let you schedule classes at a community college.
 
  • #4
programmer123
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Thank you undrcvrbro, I don't know how I ever missed that topic when scanning the first page. So I guess AP is not a proper substitute for university courses, but at least I could prepare myself on a higher level and just get the credits with AP.

@Vid, do community college courses count for credits in university? Do you know approximately how many university credits I could realistically get in one year via community college? They would probably cost too much, but it's worth looking into, thank you for the reply.
 
  • #5
Vid
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Usually the high school has to pay for the tuition since you need to take classes they can't offer you. At least that's how it seems to be in the US, not sure about Canada.

Look at the website for the community college. Most will have lists of university that accept transfer credit from there.
 
  • #6
programmer123
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Thanks, I'll look into it and ask my school.
 
  • #7
mathwonk
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what makes you think you know so much if you can't even get high grades in high school?
 
  • #8
programmer123
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I worded my post incorrectly, I don't know anything beyond high school. But I do know the high school curriculum fully, I had poor success due to poor attendance. I want to learn first year university with everyone else instead of being held back.

Sorry for the confusion, I didn't mean that I already know first year university.
 
  • #9
mathwonk
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the same question still applies. what makes you think you know even high school math if you can't convince your teachers?

\\the purpose of the question is to help you make an objective assessment of your future.
 
  • #10
Vanadium 50
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what makes you think you know so much if you can't even get high grades in high school?

That's a very good question.

The expressions, "I know the material but just can't get good grades", "I understand the material but just can't work the problems" and "But I understand everything when you say it" usually translate to "I don't really understand the material".
 
  • #11
programmer123
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I know what both of you mean, and you are right, but that is not my case. My problem is I was convincing them, I was getting pretty good marks. I just missed many weeks due to minor illness + procrastination and decided to leave the classes instead of returning to finish with mediocre results. It was an extremely poor choice (and I realize I should have gone to the doctor), but I can only try to make up for it.
 
  • #12
Tedjn
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Just to clarify, you don't need to take both AP calculus exams. The harder one (BC) will usually give you better options in terms of credit or placing out, etc. I haven't looked into the details, so I can't give you any specifics.
 
  • #13
programmer123
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Thank you for clarifying. I haven't investigated it yet so I didn't know that.
 
  • #14
viet_jon
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mathwonk is right...


regarding post #11

after all those weeks you missed + the procrascination, somehow you know what was taught in those weeks? I don't think you're being very realistic, and your marks is proof of this.

I think what your trying to say is that you are very capable of the material, it's just that you missed some lessons which is hindering your learning now.

I would: take the extra time and learn everything chronologically. School is a step by step program, which is very hard and sometimes frustrating, when you don't have pre-requisite skills to certain classes.
 
  • #15
mathwonk
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look at my thread who waNTS TO BE a mathematician?

and check out page 5 post 62? and try to read it. can you?
 
  • #16
viet_jon
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look at my thread who waNTS TO BE a mathematician?

and check out page 5 post 62? and try to read it. can you?


so you should know all that after first year right? not coming out of high school right?
 
  • #17
Larphraulen
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to the OP, i think i know pretty well what you may be going through. i had a very similar circumstance except instead of it taking place in high school, it took place during my 2nd semester of first year engineering. thus, i had to wait until the same time next year to repeat it. i really wanted to do the semester 4 months earlier because our co-op stream starts in first year but they wouldn't let me. so i was off-stream from my buddies. however, i don't regret it. didn't quite fix my habits fully but am a lot better now.

anyhow, i don't want to sound like a tape recorder or anything but take the advice/questions that mathwonk gave some serious thought (not that you haven't but continue to). it may suck but really try to fix the root of the problem. if you're smart and you know it then great you've got the confidence. however, if your work ethic and consistency isn't where you know it should be, then do what you need to do to fix it... even if that means doing a victory lap in high school.

the thing with high school is it's easy. however, the key to success is working hard. your knowledge of material may or may not transfer over to university courses. however, your experience being able to work hard despite being tempted otherwise because it seems easy, transfer over in any case... whether the material is hard or not!

btw, what schools/programs did you apply to?
 
  • #18
programmer123
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mathwonk, I read the first half of that pretty well but I couldn't finish it (I only had about 20 minutes). I think I would need to draw a diagram and break it down piece-by-piece. Is this bad, should I be able to read that easily if I know high school math?

@Larphraulen : Thank you, that was some great advice. I do know I have to fix my work ethic and commitment (and especially attendance). I guess repeating will teach me a lesson and allow me to fix bad habits. And I did not apply to any universities, there was no point.

@viet_jon:Thank you for the reply. I think I am going to go to the library and read all of the grade 12 math books, and see if there is anything I don't know in them. I think that is a fair way to assess if I know the high school curriculum or not.
 
  • #19
mathwonk
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my point that those notes are not easy for anyone coming out of high school, and yet they are my freshman honors course notes. so my advice is to someone bright coming out of high school, take such an honors course, do not skip to a non honors second year course.

one of the honors students in that class said it was the most challenging math class he had ever had in his life, and one of the most challenging in any field. now i cannot guarantee that every freshman honors instructor will give such a challenging course, so you have to check, but it is very common for freshmen to want to skip college courses and find out they will not do well if they do so.

the idea is to get good courses, courses designed for honors students, and that does not usually mean skipping from non honors calc 1 into non honors calc 2, it often means instead retaking calc 1 at an honors level.

but again, this is not true in every section, as some teachers have dumbed down their section even in honors, to below the level of incoming AP students.
 
  • #20
Vid
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but again, this is not true in every section, as some teachers have dumbed down their section even in honors, to below the level of incoming AP students.

I took "Honors" multivariate last semester. We still used Stewart, and it was actually less intense than a few of the regular sections. The only difference was the teacher proved as much as he could in class, but we still only had computational homework (it was online...) that I just pretty much refused to do as most of the problems were unnecessary exercises in tedium. I got A's on all the tests and the final, but ended up with a B after my online homework grade was averaged in. :/
 
  • #21
mathwonk
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vector calc test

heres a little non honors vector calc test.

2500 spring 2008 exam NAME.
I. A) True or false? and briefly why?
i) The path integral of any gradient field over any path is always zero.
ii) A vector field with curl equal to zero in any region is always a gradient field in that region.
iii) A vector field defined everywhere in three space, with divergence zero everywhere, has flux equal to zero through the boundary surface of any bounded region.
iv) The derivative of a function f in a given direction is obtained by dotting the gradient of f with the appropriate direction vector.

B) Give an explicit detailed computational answer:
i) If F = (M,N,P) is a vector field, then curl F = ?
ii) If F = (M,N,P) ) is a vector field, then div(F) = ?
iii) If f(x,y,z) is a smooth real valued function, then curl(grad(f)) = ?

II. Vectors. Given the three points A = (-1,0,4), B = (2,2,6), C = (1,2,1), find:
i) the vectors v = B-A = ; w = C-A =
ii) (dot product) v.w = ; (cross product) v x w
iii) cosine of the angle A in triangle ABC.
iv) area of triangle ABC.
v) equation of plane containing A,B,C.
vi) parametric equation of line normal to that plane, and through point A.

III. Vector valued functions.
A. If r(t) = (cos(t), sin(t), 2 t^(3/2)),
i) find the velocity vector to the corresponding curve at t = π.
ii) find the equation of the tangent line to this curve at t = π.
iii) Find the arclength of the curve over the interval 0 ≤ t ≤ 9.

IV. Derivatives of functions of several variables
A) Let f(x,y,z) = xy + yz^2 + xz^3.
i) Find the gradient vector for this f.
ii) Find the derivative of this f in the direction of the vector u = (-2/3, -1/3, 2/3),
at the point p = (2,0,3).
iii) Find the equation of the tangent plane to the level surface {f = 3}, for this f, at the point p = (1,1,1).

B) Now let g(x,y) = x^3 – 3xy + y^3.
i) Find all “critical points” of g (i.e. points where grad(g) = (0,0)).
ii) Test those critical points and identify as local max, local min, or saddle point.

V. LaGrange multipliers:
Use LaGrange’s method to find the maximum and minimum values, of the function f = x+y restricted to the ellipse x^2 + 2y^2 = 6.



VI. Double integrals:
Compute the y coordinate of the centroid of the plane triangle bounded by the x and y axes and the line x+y = 1.

VII.Triple integrals: The (truncated) cone z^2 = x^2 + y^2, for 0 ≤ z ≤ 1, can also be described in cylindrical coordinates as the cone z = r, for 0 ≤ z ≤ 1.
i) Find the volume of the region inside this (flat topped) cone by triple integration in cylindrical coordinates.
ii) Find the z coordinate of the centroid of the same cone by triple integration in cylindrical coordinates.

VIII. The cone z^2 = x^2 + y^2, z ≥ 0, can be described in spherical coordinates as φ = π/4; and the sphere of radius ½ centered at (0,0,1/2) as ρ = cos(φ), 0 ≤ φ ≤ π/2. Find the volume of the “ice cream cone” lying above the cone and inside the sphere, by triple integration in spherical coordinates.

IX. Circulation and Green’s theorem: Let F = (M,N) where M = x - [y/(x^2+y^2)], and
N = y + [x/(x^2+y^2)].
i) Parametrize the unit circle C by polar coordinates (counter clockwise) and compute the path integral (circulation) of F around C.
ii) Compute ∂M/∂y.
iii) Compute ∂N/∂x.
iv) Are your results in i),ii),iii), consistent with (compatible with) Greens theorem? Explain.

X. Flux and Divergence: Let F = (z,y,x), and parametrize the unit sphere by x = sin(φ)cos(θ),
y = sin(φ)sin(θ), z = cos(φ).
i) Compute (∂x/∂φ, ∂y/∂φ, ∂z/∂φ).
ii) Compute (∂x/∂θ, ∂y/∂θ, ∂z/∂θ).
iii) Compute the cross product of the two vectors in i) and ii).
iv) Write down, but do not compute, the parametrized surface integral for the flux of F through the unit sphere, as a double integral in the variables (φ,θ).
v) Compute div(F), and use the divergence theorem to calculate the flux in iv) as a familiar volume integral.
 
  • #22
mathwonk
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how does my non honors multivariable test compare to your honors course vid? (I tried to make it easy. i.e. nothing on stokes theorem, lagrange multipliers only in the plane, no requirement to justify global nature of local extrema, i gave formulas for the figures in the multiple integrals, certainly no proofs...)
 
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  • #23
Vid
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If I remember correctly the questions on my final were harder than those on similar topics, but the main focus was on optimization, change of variables and change of order, chain rule, the fundamental theorem of line integrals, and Green's Theorem.

I think we may had a question like state the divergence theorem, but we weren't tested on that or stokes theorem or surface integrals really. The one question on surface integrals was just a surface area of the form z = f(x,y).

I'm taking multivariable analysis in the fall which used Calculus on Manifolds last year so I'm hoping for good things from that class.
 
  • #24
mathwonk
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sounds like your guy did not cover the full syllabus.

heres my test 2 from 8 weeks ago.
Test2 Spring 2008 NAME:
Show all work for full credit.

I. True or False? (and give a brief reason if possible.)

i) If K is a circle lying in the interior of the domain of a C^1 function f, it is possible for gradf(p) to be tangent to K at every point p of K. ____________.
ii) A continuous function on a closed bounded region D in R^3 always has a global maximum on D. ______________.
iii) ) If the matrix of second partials of a C^2 function f has positive determinant at an interior point p of the domain, then p must be a local minimum of f._____________.
iv) If a C^1 function on an open region in R^3 has gradf(p) ≠ 0, then gradf(p) is perpendicular to the level surface of f passing through p._____________.
v) If a C^1 function f on a closed bounded region D in R^2, bounded by a smooth closed curve, has gradf(p) pointing outwards at all points p of the boundary curve, then f has at least one critical point interior to D.__________.

II. Let w = f(x,y,z) = 2y e^x –ln(z), and x = ln(1+t^2), y = arctan(t), z= e^t.

Compute: grad w =
Compute:
dx/dt =
dy/dt =
dz/dt =

Compute: dw/dt as a function of t,
and evaluate dw/dt, for t = 1:

III. i) Find a normal vector to the surface X^3 + 3X^2 Y^2 + Y^3 + 4XY –Z^2 = 0, at the point p = (1,1,3).
ii) ) Find a normal vector to the surface X^2 + Y^2 +Z^2 = 11, also at the point p = (1,1,3).
iii) Find a vector tangent to the intersection curve of those two surfaces at the point p. (It is unnecessary to find the intersection curve itself.)
iv) Find a parametric equation for the line tangent at p to that curve of intersection.

IV. Let f(x,y) = X^4 -8X^2 +3Y^2 -6Y.
i) Find gradf.
ii) Find all critical points of f.
iii) Compute the matrix of second partials of f.
iv) Apply the second derivative test to each critical point of f, and tell whether it reveals it to be a local min, local max, saddle point, or if the test fails.
v) Assuming f(x,y) is positive when either |x| ≥ 4 or |y| ≥ 4, explain why f has a global minimum at one of its critical points (but no global maximum. (Extra credit if you prove the assumption.)

V. Let f(x,y) = X^3 + Y^3 + 3X^2 – 3Y^2. Let D: {|x| ≤ 1, |y| ≤ 1}.
i) Find gradf.
ii) Find all critical points of f interior to D.
iii) Find all points on the boundary of D where grad f is perpendicular to the boundary.
iv) Evaluate f at all critical points, corners of the boundary, and points where gradf is perpendicular to the boundary.
v) Say why f has global max, and global min values on D, and find them.
 
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  • #25
mathwonk
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and here's test 3: spring 2008, test 3. NAME:
I. Let f be a smooth (C^1) function defined on (x,y,z) space R^3, and S a smooth closed bounded surface in R^3 (e.g. a sphere).
True or false? (and say briefly why)
a) The restriction of f to S has a global maximum and minimum.
b) At a local minimum p of the restriction of f to S, the gradient of f is perpendicular to (the tangent plane of) S.
c) The integral of f over the solid region bounded by S, defined as in the book only over rectangular subdivisions interior to S, is the same as that computed for the extension of f by zero to a larger block, and computed over all rectangular subdivisions of that block.

d) If B is the cylindrical region in R^3 defined by x^2 + y^2 ≤ 4, and 0 ≤ z ≤ 4, and A is the rectangular block defined by 0 ≤ r ≤ 2, 0 θ ≤ 2π, 0 ≤ z ≤ 4 in another copy of R^3 using coordinates (r,θ, z), then the integral ∫∫∫ f(x,y,z) dx dy dz taken over B, equals the
integral ∫∫∫ f(rcos(θ), rsin(θ), z) dr dθ dz taken over A.

e) If a C^2 function defined on all of R^2 has only one critical point p, and p is a local maximum for f, then p is also a global maximum for f on R^2.

II. We wish to maximize the volume of an open topped rectangular box of area A = 12 square units, and edges of length x,y,z. Do this as follows:
Write a formula for the volume function V(x,y,z),

and a formula for the area function A(x,y,z) [be careful!].

Compute the gradients of both functions.

Explain why at a critical point for the restriction of V to A = 12, we may assume that
(∂A/∂x)/(∂V/∂x) = (∂A/∂y)/(∂V/∂y) = (∂A/∂z)/(∂V/∂z).

Using that fact, find the unique critical point for the restriction of V to A = 12, and the value of V at that point.

Extra credit:
It can be shown that outside the cube where 0 ≤ x, y, z ≤ 100, we have V(x,y,z) < 2. Why does this imply your critical value above is a global maximum for V on the set A=12?

III. Set up and compute an integral for the volume of the region in R^3, lying in the half space y ≥ 0, above the (x,y) plane, below the plane z = y, and inside the cylinder
x^2 + y^2 = 1.

IV. Compute the integral of the function f(x,y,z) = x^2 + y^2, over the part of the unit ball {x^2 + y^2 + z^2 ≤ 1} which lies in the first octant in R^3.
 
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  • #26
mathwonk
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actually i think your instructor made a smart choice to emphasize the most important topics (chain rule, fubini, green) and apparently test them a little more deeply, rather than trying to cram in everything in the subject. i made the decision to try to actually cover all the material on our rather ambitious syllabus, although i did not write the syllabus, and would not have made it so large myself.

there are many different styles of teaching, some people throw everything at you but without proofs or deep coverage, others cover a few topics carefully, believing in the value of understanding. I tend to agree with the latter school of thought, as if you understand something well, you can generalize it more widely yourself.

still there are times when i have been hampered by lack of familiarity with material that was omitted from my education.
 
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  • #28
Vid
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Though to be fair, it was an honors class for all honors students not for math majors. The majority of the class was either engineering or chemistry majors.
 
  • #29
mathwonk
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well those look pretty good. but they are just computational, no theory at all, and in an honors class.

no testing of understanding of theorems or subtleties. i seem to have covered considerably more theory in a non honors class, but that is the way my molecules are wired.

i believe routine computational skills, although basic, are not worth much in a era of computers. to be smarter than a 10 dollar calculator, and hence to earn a living nowadays, you need to understand the ideas behind the material.
 
  • #30
mathwonk
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e.g. in test 2, of your class, problem 2 asks you to find the min of a function that is not guaranteed to have a min. i.e. the domain is not closed and bounded but is an entire infinite plane.

your instructor ignores this and merely finds the critical points. the books also tend to ignore this point, that on needs to actually guarantee that a critical point is an extremum.

compare my test 3, problem 2, or test 2 problem 5, where this point is explicitly addressed.
 
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  • #31
tycon69
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Is it out of the question to go to summer school? Alot of my advanced peers are failing AP english and are going to summer school to make that up. One guy who is an extremely good athlete is going to summer school for 5/7 classes, but its probably just because they need him for the football team.
 
  • #32
programmer123
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I see, good point mathwonk, I guess it is better to not skip courses. Also, your mathematician thread is really good. I'll definitely remember it for future reference.

@tycon69: Well, summer school is an option for only 1-2 courses here in Canada, and even then it is penalized on your transcript similar to or worse than a repeated course as far as I know.

Thank you everyone for the good responses!
 

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