Math for Physics Cheat sheet
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This document provides a summary of basic math concepts for physics including: 1) Algebraic operations for solving equations for variables such as adding, subtracting, multiplying, and dividing terms. 2) Procedures for calculations with significant figures when adding, subtracting, multiplying, and dividing quantities. 3) How to write numbers in scientific notation and perform calculations using scientific notation such as multiplication, division, powers, and roots.
Math for Physics Cheat sheet
- 1. RapidLearningCenter.com ©Rapid Learning Inc. All Rights Reserved AP Physics - Core Concept Cheat Sheet 02: Basic Math for Physics Algebra If a number is __to a variable Then to solve __ that number on both sides to solve for the variable Example Added Subtract 5 = x + 2 - 2 -2 5 - 2 = x Subtracted Add 3 = x – 6 + 6 +6 3 + 6 =x Multiplied Divide 2= 4x 4 4 2/4 = x Divided Multiply 2 · 6 = x · 2 2 2 · 6 = x Calculations with Significant Figures Adding & Subtracting: 1. Perform the calculation. 2. Determine which value in the problem has least decimal places. 3. Round answer to that number of decimal places. Example: 10.027 g → 3 decimal places - 1.5 g → 1 decimal place 8.527 g → 8.5 g (1 decimal place) Multiplying & Dividing: 1. Perform the calculation. 2. Determine which value in the problem has least sig fig 3. Round answer to that number of sig. figures. Example: 10.027 g → 5 sig figs 1.50 mL → 3 sig figs = 6.6847 g/mL → 6.68 g/mL (3 sig figs) Scientific Notation Scientific Notation—A short hand method of writing numbers using powers of 10. Writing scientific notation: 1. The decimal point is always moved to after the 1st non- zero number. 2. Count the number of times the decimal point is moved and use this as the power of 10. 3. “Big” numbers (>1) have positive exponents. “Small” numbers (<1) have negative exponents. Examples: 1027500.456 → 1.027500456 × 106 0.0007543 → 7.543 × 104 Reading scientific notation: 1. Power of 10 = number of times to move decimal point. 2. Positive powers = make the number “Big” (>1). Negative exponents = make the number “Small” (<1). Examples: 3.25 × 10-6 → 0.00000325 7.2004 × 104 → 7200.4 Math with Exponents Calculations with exponents: • Power of “1”: Anything to the power of “1” = itself. 251 = 25 • Power of “0”: Anything to the power of “0” = 1 250 = 1 • Multiplying (with the same base): Add the powers. 32 * 38 = 311 • Dividing (with the same base): Subtract the powers. 32 ÷ 38 = 3-6 • Power of a power: Multiply the powers. (32 )3 = 36 • Negative powers: Put the number on the opposite side of the fraction & the power becomes positive. 3-2 = 1/32 and 1/8-2 = 82 Calculations with scientific notation: • Adding (with same power of 10): Add numbers and keep power of 10. 2 × 103 + 3 × 103 = 5 × 103 • Subtracting (with same power of 10): Subtract numbers and keep power of 10. 3 × 103 – 1 × 103 = 2 × 103 • Multiplying: Multiply numbers & add powers of 10. 2 × 106 · 3 × 103 = 6 × 1018 • Dividing: Divide numbers & subtract powers of 10. 2 × 106 ÷ 3 × 103 = 0.67 × 103 • Taking it to a power: Take the number to the power and multiply the power of 10 by the power. (2 × 103 )3 = 8 × 109 • Roots: Take the number to the root and divide the power of 10 by the root. √(3 × 102 ) = √3 × 101 Trigonometric Functions Opposite sin θ = Hypotenuse -1 Opposite θ = sin Hypotenuse ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ Adjacent cos θ = Hypotenuse -1 Adjacent θ = cos Hypotenuse ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ Opposite tan θ = Adjacent -1 Opposite θ = tan Adjacent ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ To remember the functions use: SOHCAHTOA Quadratic Equation When ax2 + bx + c =0, 2 -b ± b - 4ac x = 2a Example: 1x2 + 5x - 8 = 0 Then: 2 -5 ± 5 - 4(1)(-8) x = 2(1) x = 6.27 and x = -1.27 Note: There are two solutions but they may not both make physical sense , for example time cannot be negative Calculator Survival • Always use the ÷ key to designate a number is on the bottom of an expression. • Always use the EE (or EXP) key to enter scientific notation. • Always use parenthesis around addition or subtraction when combining it with other operations • To make something negative (when taking the number to a power) keep the negative outside of the parenthesis. How to Use This Cheat Sheet: These are the keys related this topic. Try to read through it carefully twice then write it out on a blank sheet of paper. Review it again before the exams.