1. Honors Physics
Math Review

2. 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

3. 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)

4. 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

5. 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 m km

6. 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

7. 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

8. 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

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

10. 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 = km

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

12. 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.

13. 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?

14. 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

15. 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”

16. 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

17. 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)

18. 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”

19. 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

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

21. 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

22. 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 = (5) – 6x
14 – x = 18 – 6x

23. 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

24. 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

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

26. 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!

27. Practice 1) 8) 2) x + 10 = 7 6x + 8 = -28 -6 + 7x +3x = -1169)
10)

28. 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

29. 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

30. 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

31. 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