How does US maths and physics courses compare with british A-level?

[finchie_88]

Just a matter of interest, but how do the US physics and mathematics courses for students before university (The final year before university) compare with the British A-level courses? what is the typical content of the US courses at this age? For example, what is included in "precalculus", and so on.

 

[0rthodontist]

Precalculus as I was taught it includes more on trigonometric functions, trigonometric identities, a little formal proof, some geometry, a little stuff about polynomials. It basically finished covering all math up to the SAT II Mathematics IIC test (see http://www.sparknotes.com/testprep/books/sat2/math2c/) , though there's no guarantee that a given student will learn all of it.

High school calculus as I learned it covered basic integration and differentiation in 1 variable, some techniques of integration, limits, some series and sequences, finding volumes of solids of revolution, and implicit differentiation/rates of change problems. It basically covered all math up to the AP Calculus AB or BC test (BC being the more advanced but some schools only teaching AB). See http://www.collegeboard.com/prod_downloads/ap/students/calculus/ap-cd-calc-0607.pdf

High school physics as I learned it was one year of non-calculus-based mechanics and wave motion.

 

[EbolaPox]

This is purely from my own experience in High School (I'm a 12th grade student currently) and that of people I've spoken to in other states and in different school systems.

Precalculus- At my school, this course is basically half a year of review over trignometry, functions, logarithms, exponential functions, basic algebra. In the halfway through the year, my teacher began teaching limits with epsilon-delta. The class spent a good time doing limits this way and studying limits in general. We moved on to Derivatives using the limit definition, proved many basic derivatives (e^x, sin(x), cos(x), etc.). The teacher proceded to teach derivatives, applications of derivatives, and anti-differentiation. We did no actual definite integration.

AP Calculus AB: This course is typically offered at my school. It covers a normal Calculus I course (I believe) starting with limits and continuity, continuing through with derivatives, applications of derivatives, integration, applications of integration (Volume via shell and cylinder methods.)

AP Calculus BC: This course covers a standard Calculus I and II course. It continues where AB Calculus left off and explores more applications of integration (Work, Arc Length, Surface Area), explores techniques of integration, does infinite series, power series, polar and parametric and basic vector derivatives and things of that sort.

Many High Schools in the US offer a system where a student can take classes at nearby universities. One of my friends opted to do this instead of taking large numbers of AP classes. He is currently in Multivariable Calculus and Differential Equations (I also go to DE, mostly for education but also because it is entertaining.)

Furthermore, some schools actually offer Linear Algebra, although I doubt it is on par with university level Linear Algebra.

I've spoken with many students from other states; they basically do the same AP Calculus work, but less proofs for basic derivatives and their precalculus lacked calculus. That's, from what I've seen, how the US does High School math.