# Honors Physics Math Review Key Math Skills Needed

• Slides: 31

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 • • 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 onehundreth 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__, __1000 m__ 1 m 1000 m 1 km

Conversions • Conversion Factors – How to read them • 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 meters.

Scientific Notation • General form: a x 10 n – 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 10 n – 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 • Write 0. 00012 in scientific notation • Write 149, 600, 000 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 10 n – 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 10 n – 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 – 8. 9 x 105 – 6 x 10 -1

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 • 1 x + 1 x = 2 x, 3 x + 4 x = 7 x • x(x) = x², 2 x(6 x) = 12 x², 2 x(3 x²) = 6 x³ – Example: 3 x + 14 – 5 x + x = 2 + 1 + 3(5) – 6 x 14 – x = 18 – 6 x

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 – 6 x 5 x = 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: 5 x = 4/5

Algebra • If the variable is in the denominator use cross multiplication • For example… 1. 2.

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) 2) 3) 4) 5) 6) 8) x + 10 = 7 6 x + 8 = -28 -6 + 7 x +3 x = -116 6(3 -x) = 48 – 3 x 2 x² = 50 9) 10) 7)

Two Equations, Two Unknowns • System of Equations: set of 2 or more equations that use the same variables. Ø 2 x – y = 7, 4 x + 3 y = 4 • Solve by substitution: 1. Solve for one of the variables. ü 2 x – y = 7 y = 2 x - 7

Two Equations, Two Unknowns 2. Substitute the expression for the variable that you solved step 1 for into the second equation. ü 4 x + 3 y = 4 4 x + 3(2 x – 7) = 4 x = 2. 5 3. Substitute the value of x into either equation. ü y = 2 x – 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 1. 2. 3. 4. -6 = 3 x – 6 y, 4 x = 4 + 5 y 2 m + 4 n = 10, 3 m + 5 n = 11 2 x – y = 12, (x+3)/4 + (y – 1)/3 = 1 y = x^2 + 3 x + 2, y = 2 x + 3