This document is a concise but comprehensive guide to the facts and formulas typically used in the material covered by the SAT Subject physics test. The test is designed to determine how well you have mastered the physics concepts taught in a typical one-year college-prep high school course. This guide is mainly intended as a reference, as opposed to a full tutorial (which would probably be book-length), and so the explanatory material is pretty brief. You can use the guide as a simple formula reference, or as a quick review of the material that you’ve already studied elsewhere. Either way, good luck on your Subject Test!
Although this guide is for the SAT Subject test in Physics, you’ll need to know quite a bit of math. If you’re thinking that you’ll just use your calculator to do the math, don’t forget that calculators are not allowed on the SAT Subject Physics test. Here is a summary of the really important math facts and formulas. Exponents xa · xb = xa+b (xa )b = xa·b x =1 Scientiﬁc Notation Scientiﬁc notation is a short-hand form to write numbers which would have a lot of zeros when written as decimals. For example, instead of writing 1230000, you can just write 1.23 × 1000000, or 1.23 × 106 . The familiar powers of ten include: 10−3 = 0.001, 10−2 = 0.01, 10−1 = 0.1, 100 = 1, 101 = 10, 102 = 100, 103 = 1000. To go from scientiﬁc notation to a plain decimal number, move the decimal to the right or left according to the sign of the exponent, putting a zero down when you have no other digits there. For example, for 3.7 × 1012 , move the decimal right 12 places and add 11 zeros. Move the decimal to the left for a negative exponent.
11 zeros 0
xa /xb = xa−b (xy)a = xa · y a √ √ √ xy = x · y
1/xb = x−b (−1)n = +1, −1, if n is even; if n is odd.
37 00000000000 . = 3.7 × 1012
. 0000000000 23 = 2.3 × 10−11
To go from a plain decimal number to scientiﬁc notation, just move the decimal to the right or left (counting how many places you move) until there is only one digit to the left of the decimal point, then add “ ×10n ” where n is the number of places you moved the decimal point (positive if you went left and negative if you went right). www.erikthered.com/tutor pg. 1
SAT Subject Physics Facts & Formulas
Basic Metric Preﬁxes Common powers of ten (both positive and negative) have names that come before the metric unit of measurement, i.e., they are preﬁxes. The most typically used ones are given below. Preﬁx Symbol Power of Ten Common Example nano micro milli centi kilo mega Basic Trigonometry e us en ot
n µ m c k M
10−9 10−6 10−3 10−2 103 106
nanometer microsecond milligram centimeter kilogram megawatt
θ a adjacent
In the ﬁrst triangle above, a2 + b2 = c2 (pythagorean theorem)
Referring to the second triangle, there are three important functions which are deﬁned for angles in a right triangle: sin θ = opposite hypotenuse cos θ = adjacent hypotenuse tan θ = opposite adjacent
(the last line above shows a mnemonic to remember these functions: “SOH-CAH-TOA”) An important relationship to remember which works for any angle θ is: sin2 θ + cos2 θ = 1. Vectors Many important quantities in physics are represented by vectors, which specify both a number (the length of the vector) along with a direction (where the vector points). In contrast, scalars are simple numbers without a direction. www.erikthered.com/tutor pg. 2
SAT Subject Physics Facts & Formulas
For example, velocity is a vector (represented by a boldface v) and is given by a number (say, 50 m/sec) along with a direction (say, 30◦ north of east). Mass (m) is just a number (say, 80 kg), for which a direction doesn’t make any sense, so it is a scalar. We can deﬁne components of a vector as the projection (or “shadow”) of the vector on the x and y axes, as in the ﬁgure below. y vy θ vx x v
Using basic trigonometry,