Honors Physics Math Review

Key Math Skills Needed for Success! Conversions Know metric conversion factors Know how to properly convert from one unit to another Scientific Notation How to convert between scientific notation and standard notation Algebra Solve for x Geometry/Trig SOHCAHTOA

Conversions Metric Base units (100) Definition: Fundamental unit Mass: gram (g) Length: meter (m) Time: seconds (s) Temperature: kelvin (K) Amount of substance: mole (mol) Volume: Liter (L)

Conversions Prefixes Greater than base unit Less than base unit Deca- (101), Hecto- (102), Kilo- (103) Deca- = ten, Hecto- = hundred, Kilo- = thousand Abbreviations: Deca  da, Hecto  h, Kilo  k Example: 1 hectometer is the same as saying 100 meters or 102 meters Less than base unit Deci- (10-1), Centi- (10-2), Milli- (10-3) Deci- = 1/10, Centi- = 1/100, Milli- = 1/1000 Abbreviations: Deci  d, Centi  c, Milli  m Example: 1 centimeter is the same as saying one one-hundreth of a meter or 10-2 meters

Conversions Conversion factors All conversion factors must equal 1 Conversion factors take the form of a fraction Just as 5/5, 28/28, and 142/142 all equal 1, there are multiple ways of writing conversion factors that equal 1. Example: __100 cm__, __1 km__, __1000m__ 1 m 1000m 1 km

Conversions Conversion Factors How to read them 1 m Example: __1000 mm__, there are 1000 1 m millimeters in 1 meter. Ask yourself, “Does this make sense?” How to properly write them The smaller unit always gets the number greater than 1

Practice Write the conversion factors you would use to convert from… cm to m m to cm kg to g g to kg ms to s s to ms

Conversions How do I know which unit goes in the numerator and which unit goes in the denominator when making my conversion factor? The unit that you are converting FROM always goes in the denominator The unit you are converting TO always goes in the numerator

Practice Convert the following (make sure to properly write your conversion factor): 42 cg = ? g 6 m = ? km 132 ms = ? s 86 kg = ? g

Conversions What if I am not converting to my base unit? For example, 58 cm = ? km First convert your know quantity to your base unit 58 centimeters equals how many meters 58 cm = .58 m Second convert your base unit to your desired unit .58 meters equals how many kilometers .58 m = .00058 km

Practice 9 mm = ? cm 18 kg = ? dag 95 mg = ? kg 63 cg = ? hg 1,468 dm = ? km

Scientific Notation Scientific notation makes the expression of very large or very small numbers simpler. Makes it easier to keep track of significant figures. In Physics, you will deal with very large numbers such as the distance from the sun to the Earth which is 149,600,000,000 meters.

Scientific Notation General form: a x 10n a must be a number between 1 and 10 n must be an integer Example: These are NOT in scientific notation 34 x 105… Why? 4.8 x 100.5… Why?

Scientific Notation What’s the difference between a positive exponent and a negative exponent? Positive exponents tell you how many times to multiply by 10 Negative exponents tell you how many times to divide by 10

Scientific Notation Converting from standard form to scientific notation Remember… a x 10n Move the decimal point left or right until you wind up with a number between 1 and 10 The number you are left with is “a” The number of spaces the decimal point is moved is the exponent “n”

Scientific Notation Converting from standard notation to scientific notation…how do I know if my exponent is positive or negative? If the decimal is moved to the left, you will have a positive exponent In other words, “a” is less than the number you started with If the decimal is moved to the right, you will have a negative exponent In other words, “a” is greater than what you started with

Practice Write 3,040 in scientific notation The distance from Earth to the sun How many kilometers are in 1 meter? (write the answer in scientific notation) How many milligrams are in 1 kilogram? (write the answer in scientific notation)

Scientific Notation Converting from scientific notation to standard form Remember… a x 10n If “n” is positive, move the decimal point in “a” to the right In other words, if “n” is positive your answer will be greater than your original “a” If “n” is negative, move the decimal point in “a” to the left In other words, if “n” is negative your answer will be less than your original “a”

Scientific Notation How to enter a number in scientific notation into your calculator. Remember… a x 10n Enter “a” Press the “EE” button Enter “n” Do NOT press the multiplication button or enter the number 10 “EE” takes the place of this step

Practice Write the following in standard form 4.01 x 102 5.7 x 10-3

Algebra Solving for “x” Key things to remember What you do to the left side of the equation you MUST do to the right side of the equation. What you do to one term you must do to ALL terms on both sides of the equation Think back to… order of operations Please excuse my dear aunt sally Parentheses exponents multiply divide add subtract Left to right

Algebra Solving for “x” First combine all like terms abiding by order of operations Remember… variables do NOT mix with non-variables 1x + 1x = 2x, 3x + 4x = 7x x(x) = x², 2x(6x) = 12x², 2x(3x²) = 6x³ Example: 3x + 14 – 5x + x = 2 + 1 + 3(5) – 6x 14 – x = 18 – 6x

Algebra Solving for “x” Second, move all terms containing a variable to one side of the equation and all other terms to the other side. Remember… Opposite of addition is subtraction and vice versa Opposite of multiplication is division and vice versa Example: 14 – x = 18 – 6x 5x = 4

Algebra Solving for “x” Finally, make it so that the coefficient of “x” is 1 This means divide both sides by the coefficient of “x” If there are multiple terms on the opposite side, make sure to divide each term by the coefficient Example: 5x = 4 x = 4/5

Algebra If the variable is in the denominator use cross multiplication For example…

Algebra Solving for “x” If your “x” term is squared then make your last step to take the square root of both sides of the equation Remember… you can plug your answer back into the equation If the left side of the equation equals the right side then you solved for “x” correctly!

Practice 1) 8) 2) x + 10 = 7 6x + 8 = -28 -6 + 7x +3x = -116 9) 10)

Two Equations, Two Unknowns System of Equations: set of 2 or more equations that use the same variables. 2x – y = 7, 4x + 3y = 4 Solve by substitution: Solve for one of the variables. 2x – y = 7  y = 2x - 7

Two Equations, Two Unknowns Substitute the expression for the variable that you solved step 1 for into the second equation. 4x + 3y = 4  4x + 3(2x – 7) = 4  x = 2.5 Substitute the value of x into either equation. y = 2x – 7  y = 2(2.5) – 7  y = -2

Quadratic Equation When solving an equation in the form, ax^2 + bx + c = 0, you may need to use the quadratic formula if reverse FOIL does not work

Two Equations, Two Unknowns Examples -6 = 3x – 6y, 4x = 4 + 5y 2m + 4n = 10, 3m + 5 n = 11 2x – y = 12, (x+3)/4 + (y – 1)/3 = 1 y = x^2 + 3x + 2, y = 2x + 3