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What Math Skills are Necessary for Success in College Physics?

As a physics professor, I’ve discovered that there is one thing more than any other that prevents students from finding success in my algebra-based college physics course, proficiency in algebra. Students who start the course without sufficient mastery of algebra are like students starting a English literature course without being able to read English. If you are unsure of how prepared you are for college physics, take the short quiz below. If you have difficulty, you may want to think about taking a course in algebra to polish your skills before plunging into physics. Note that the problems below use symbols that will commonly be encountered in physics but you do not need to know what these symbols stand for to solve the problems.

1) Solve for v' in terms of ma, mb, va, and vb.
v' = v'a = v'b
mava + mavb = mav'a + mav'b

2) Solve for r in terms of G, m2, and v.
F = G(m1m2)/(r2)
F = m1v2/r

3) Sove for x in terms of x0, v0x, v0y, and ay (two solutions).
x = x0 + v0xt
0 = v0yt + (1/2)ayt2

4) Solve for t using the quadratic formula (two solutions).
y = -20
y0 = 10
v0y = 20
ay = -9.8
y = y0 + v0yt + (1/2)ayt2

The ability to use trigonometric functions and identities is also necessary for success in college physics. I review these skills as part of my course so mastery at the start of the semester is not required but a working knowledge of the trigonometry of right triangles is expected and advantageous.

5) Sove for μ in terms of θ.
ax = ay = 0
mg(sin(θ)) - FFR = max
FN - mg(cos(θ)) = may
FFR = μFN

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