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Math for Physics Cheat sheet

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Timothy Welsh

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San Joaquin County Office of Education

May. 14, 2014

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5,457 views

Math for Physics Cheat sheet

May. 14, 2014

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0 likes

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5,457 views

Timothy Welsh

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San Joaquin County Office of Education

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Education

Math for Physics Cheat sheet

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Math for Physics Cheat sheet

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: 1×2 + 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.