Basic Math for Physics

1. AP Physics Rapid Learning Series - 02
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 1
Rapid Learning Center
Chemistry :: Biology :: Physics :: Math
Rapid Learning Center Presents …Rapid Learning Center Presents …
Teach Yourself
AP Physicsin 24 Hours
1/67 *AP is a registered trademark of the College Board, which does not endorse, nor is
affiliated in any way with the Rapid Learning courses.
Basic Math for as c at o
Physics
Physics Rapid Learning Series
Rapid Learning Center
www.RapidLearningCenter.com/
© Rapid Learning Inc. All rights reserved.
Wayne Huang, Ph.D.
Keith Duda, M.Ed.
Peddi Prasad, Ph.D.
Gary Zhou, Ph.D.
Michelle Wedemeyer, Ph.D.
Sarah Hedges, Ph.D.

2. AP Physics Rapid Learning Series - 02
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 2
Learning Objectives
„Using algebra to solve for a
ibl
By completing this tutorial, you will learn math
skills commonly used in physics:
variable
„Performing calculations
with significant figures
„Using scientific notation
„Performing calculations
with exponents & scientific
3/67
with exponents & scientific
notation
„Trigonometry
„Using the quadratic formula
„Calculator tips
Concept Map
experimental science
Physics is an
experimental science calculator tips
Follow
calculator tips
Requires
Previous content
New content
ExperimentationExperimentation
Conclusions
Results &
Conclusions
Data taken with
correct # of sig figs
Data taken with
correct # of sig figs
CalculationsCalculations
Follow rules
with sig figs
Follow rules
for calculations
with sig figs
Leads to
Often requires
During which
When doing,
Be sure to
May be written in
Depend on
4/67
Quadratic Quadratic
Formula
TrigonometryTrigonometryAlgebra
Rules for
exponents
Rules for
working with
exponents
Use scientific Use scientific
notation
Might use
When using, follow

3. AP Physics Rapid Learning Series - 02
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 3
Algebra
Algebra is often used when
sol ing ph sics problems
5/67
solving physics problems.
Algebra Rules
If a number is
being … to an
Then … that
number on both
Undo by doing the opposite to both sides:
Example
unknown
variable
sides
Added Subtract
Example
5 = x + 2
-2 -2
5-2 = x
6/67
Subtracted Add
3 = x – 6
+6 +6
3+6 = x

4. AP Physics Rapid Learning Series - 02
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 4
Algebra Rules-2
If a number is
being … to an
Then … that
number on both
Undo by doing the opposite to both sides:
Example
2 = 4x
4 4
2÷4 = x
unknown
variable
sides
Multiplied Divide
Example
7/67
Divided Multiply
2*6 = x*2
2
2*6 = x
Example: Velocity
Velocity problems require algebraic work:
displacement(d)
Velocity
time(t)
=
Example: Solve for distance
The unknown variable (d) is being divided by 25 s
time(t)
25s
d
m/s52 =
* 25 s
25 s *
8/67
The unknown variable (d) is being divided by 25 s.
Multiply both sides by 25 s
dm/s52*25s
=
d1300m=

5. AP Physics Rapid Learning Series - 02
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 5
Example: Force
Net force problems also require algebraic work:
frictionappliednetFFF +=
friction
F52N25N +=
Example:Solve for force of friction
The unknown variable (F
fi ti)isbeing
-52 N-52 N
9/67
The unknown variable (F
friction) is being
added to 52 N
Subtract 52 N from both sides
friction
F52N25N
=−
friction
F27N=−
Example: Gravitational Force
When solving for a variable on the bottom, you need to
move it to the top first:
Example:
Solve for d
( )
22118 g)(50kg)(50k
/kgNm1066N1017
−−
×=×
Move d to top
( )
2
d
/kgNm106.6N101.7 ×=×
( )
2
22118
d
g)(50kg)(50k
/kgNm106.6N101.7
−−
×=×d
2
*
* d
2
( )( ) g)(50kg)(50k/kgNm106.6N101.7d
221182 −−
×=×
Solve for d
10/67
( )( )
1.7x10
-8
N 1.7x10
-8
N
N)10(1.7
kg))(50kg)(50/kgNm10(6.6
d
8
2211
−
−
×
×
=
3.11md
=

6. AP Physics Rapid Learning Series - 02
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 6
Calculations &
Significant Figures
This section describes the role
11/67
of significant figures in calculations.
Calculations, Significant Figures Usage
Data is taken very carefully to the correct number of
significant figuressignificant figures.
12/67
When performing calculations, you cannot end up
with greater precision than what you actually
measured in the lab!

7. AP Physics Rapid Learning Series - 02
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 7
Always Round Last
Always complete all calculations first…
13/67
And then round as a final step.
Rounding: Adding & Subtracting
Adding & subtracting:
Perform the calculation1
Example:Perform the following operation:
10.027 g
15 g
3 decimal places
1 decimal place
Determine the least # of decimal placesin the problem
Round the answer to that many decimal places.
2
3
14/67
-1.5 g
8.527 g
1 decimal place
8.5 g
1
Least =1
2
3

8. AP Physics Rapid Learning Series - 02
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 8
Rounding: Multiplying & Dividing
Multiplying & Dividing:
Perform the calculation1
Example:Perform the following operation:
Determine the least # of significant figuresin the
problem
Round the answer to that many significant figures.
2
3
1
10.027 m
6 68467 m/s
5 sig figures
=
15/67
6.68 m/sLeast =3
2
3
1.50 s
6.68467 m/s
3 sig figures
=
Scientific Notation
Scientific notation is often used
th h t th t d f h i
16/67
throughout the study of physics.

9. AP Physics Rapid Learning Series - 02
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 9
Definition – Scientific Notation
Scientific Notation- A short-hand
method of writing very large or very
ll bsmall numbers.
Scientific Notation uses powers of
10.
17/67
Writing in Scientific Notation
Rules for writing scientific notation:
Decimal is moved to follow the 1
st
non-zero number
Number of times the decimal is moved = power of 10
1
2
Examples:Write in scientific notation:
1027500.456 g
1
Number of times the decimal is moved = power of 10
“Big” (>1) numbers Æpositive powers
“Small” (<1) numbers Ænegative powers
2
3
1 2 3 4 5 6
18/67
1.027500456 g
The decimal point was moved 6times 1.027500456
The original number was “big” so it will be a +6power
1.027500456 x 10
6
g
1
2
3
1 2 3 4 5 6

10. AP Physics Rapid Learning Series - 02
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 10
Writing in Scientific Notation 2
Rules for writing scientific notation:
Decimal is moved to follow the 1
st
non-zero number
Number of times the decimal is moved = power of 10
1
2
Examples:Write in scientific notation:
0.0007543 g
1
Number of times the decimal is moved = power of 10
“Big” (>1) numbers Æpositive powers
“Small” (<1) numbers Ænegative powers
2
3
1 2 3 4
19/67
7.543 g
The decimal point was moved 4times 0007.543
The original number was “small” so it will be a -4power
7.543 x 10
-4
g
1
2
3
1 2 3 4
Sig Figures & Scientific Notation
Scientific Notation can also be used to write a
specific number of significant figures.
Example:Your calculator gives you:10200 g
And you need to write the result with4 significant figures
10200 g 3 significant figures
10200. g 5 significant figures
43 21
20/67
1.020 X 10
4
g 4 significant figures!
Use scientific notation
43 21

11. AP Physics Rapid Learning Series - 02
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 11
Reading Scientific Notation - 1
Rules for reading scientific notation:
Power of 10 = number of times to move the decimal
Piti Æ“Bi ” ( 1) b
1
Examples:Write out the following number
1
Positive powers Æ“Big” (>1) numbers
Negative powers Æ“Small” (<1) numbers
2
3.25 X 10
-6
g
00000
1 2 3 4 5 6
.
21/67
1
2
The decimal point will move 6times
The power is negative, so we’ll make the number
“small”—move the decimal forward (left)
0.00000325 g
12 3 4 5 6
Reading Scientific Notation - 2
Rules for reading scientific notation:
Power of 10 = number of times to move the decimal
Piti Æ“Bi ” ( 1) b
1
Examples:Write out the following number
1
Positive powers Æ“Big” (>1) numbers
Negative powers Æ“Small” (<1) powers
2
7.2004 X 10
3
mL
.
12 3
22/67
1
2
The decimal point will move 3times
The power is positive, so we’ll make the number
“big”—move the decimal point right (backwards)
7200.4 mL
12 3

12. AP Physics Rapid Learning Series - 02
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 12
Exponents
23/67
Exponent Use
Exponentsare used in unit
conversions and when using
scientific notation.
There are several
rules that govern
24/67
g
calculations with exponents.

13. AP Physics Rapid Learning Series - 02
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 13
Exponent Rule #1
“Rule of 1”
Abtth f1thiilb1
Example:
Any number to the power of 1 = the original number1
25
1
=25
25/67
Exponent Rule #2
“Rule of 0”
Abtth f012
Example:
Any number to the power of 0 = 12
16
0
=1
26/67

14. AP Physics Rapid Learning Series - 02
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 14
Exponent Rule #3
“Product rule”
Wh lti l i dd th t3
Example:
When multiplying, add the exponents.3
11
2
*11
4
=11
(2+4)
;
This rule does not apply when the bases
=11
(6)
27/67
;
pp y
are different!
Example:
11
2
*12
4
(11*12)
(2+4)=;
Exponent Rule #4
“Quotient rule”
Wh di idi bt t th t4
Example:
When dividing, subtract the exponents.4
=15
(8-3)
;
This rule does not apply when the bases
=15
(5)
15
8
15
3
28/67
;
pp y
are different!
Example:
15
8
12
3(
15
12)
(8-3)
=;

15. AP Physics Rapid Learning Series - 02
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 15
Exponent Rule #5
“Power rule”
When there is an exponent on an exponent multiply
5
Example:
When there is an exponent on an exponent, multiply
the two exponents together.
5
(8
2
)
3
=8
(2*3)
=8
(6)
29/67
(8)=8
()
=8
()
Exponent Rule #6
“Negative rule”
When a number with a negative exponent is placed on
6
Example:
When a number with a negative exponent is placed on
the opposite side of the fraction, the exponent is
made positive.
6
9
-2
=
1
9
2
30/67
9 =
9
2

16. AP Physics Rapid Learning Series - 02
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 16
Summary of Exponent Rules
Abtth f01
Any number to the power of 1 = the original number.
25
1
= 25
1
Exponent on an exponent: multiply the two exponents
5
Dividing: subtract the exponents. 3
2
÷3
8
= 3
-6
4
Multiplying: add the exponents. 3
2
*3
8
= 3
10
3
Any number to the power of 0 = 1 25
0
= 12
31/67
Negative exponent: place on the opposite side of the
fraction and the exponent is made positive
3
-2
= 1/3
2
6
together. (3
2
)
3
= 3
6
5
Calculations with Scientific Notation
There are several eeaeseea
similar rules when
working with
scientific notation
calculations.
Scientific
Notation
6.02x10
23
32/67

17. AP Physics Rapid Learning Series - 02
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 17
Sci. Notation Calculation Rule #1
Addition
Addthbdkth f101
Example:
Add the numbers and keep the same power of 101
6x10
4
+ 2x10
4
=(6+2)x10
4
;
This rule does not apply when the powers
=8x10
4
33/67
;
pp y p
of 10 are different!
Example:
6x10
3
+ 6x10
6
(6+6)x10
(3+6)=;
Sci. Notation Calculation Rule #2
Subtraction
Sbttthbdkth f102
Example:
Subtract the numbers and keep the same power of 102
3x10
2
- 1x10
2
=(3-1)x10
2
;
This rule does not apply when the powers
=2x10
2
34/67
;
pp y p
of 10 are different!
Example:
3x10
2
- 6x10
6
(3-6)x10
(2-6)=;

18. AP Physics Rapid Learning Series - 02
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 18
Sci. Notation Calculation Rule #3
Multiplication
M lti l th b d dd th f 103
Example:
Multiply the numbers and add the powers of 10.3
3x10
4
* 2x10
6
=(3*2)x10
(4+6)
=6x10
10
35/67
Sci. Notation Calculation Rule #4
Division
Di id th b d bt t th f 104
Example:
Divide the numbers and subtract the powers of 10.4
8x10
2
÷2x10
6
=(8 ÷2)x10
(2-6)
=4x10
-4
36/67

19. AP Physics Rapid Learning Series - 02
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 19
Sci. Notation Calculation Rule #5
Taking a scientific notation number to a power
T k th b t th d lti l th5
Example:
Take the number to the power and multiply the power
by the power of 10.
5
(3x10
2
)
3
=(3)
3
x10
(2*3)
=27x10
6
37/67
Sci. Notation Calculation Rule #6
Taking a root of a scientific notation number
T k th t f th b d di id th f6
Example:
Take the root of the number and divide the power of
10 by the root.
6
= =√3x10
2
√3x10
(2/2)
√3x10
(1)
38/67

20. AP Physics Rapid Learning Series - 02
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 20
Summary of Sci. Notation Rules
Subtraction:Subtract the numbers and keep the same2
Addition: Add the numbers and keep the same power of
10
2X10
3
+ 3X10
3
= 5X10
3
1
Division: Divide the numbers and subtract the powers of
10
2X10
4
/ 3X10
3
= 0.67X10
1
4
Multiplication: Multiply the numbers and add the powers
of 10
2X10
6
* 3X10
3
= 6X10
9
3
Subtraction: Subtract the numbers and keep the same
power of 10
2X10
3
-3X10
3
= -1X10
3
2
39/67
Roots: Take the root of the number and divide the power
of 10 by the root
√(3x10
2
)= √3 X 10
1
6
Powers: Take the number to the power and multiply the
power by the power of 10
(2X10
3
)
3
= 8X10
9
5
Geometry &
Trigonometry
Both aspects of math are
frequently used in physics
40/67
frequently used in physics.

21. AP Physics Rapid Learning Series - 02
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 21
Definition – Trigononmetric Functions
Trigonometric Functions– Functions
of an angle that give ratios of theof an angle that give ratios of the
sides of a triangle within that right
triangle.
41/67
Trigonometric Functions
The three common trig functions work with right
triangles.
it
Trig functions use one of the
hypotenuse
opposite
sinθ=
hypotenuse
adjacent
cosθ=
Trig functions use one of the
non-90°angles and discuss the
sides of the triangle as they
relate to that angle
t
e to θ
42/67
adjacent
opposite
tanθ=
Right angle
θ“Theta”—angle in
question
Opposi
t
Adjacent to θ

22. AP Physics Rapid Learning Series - 02
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 22
Remembering the Functions
Sin
Opposite
Make sure you
Hypotenuse
Cos
Adjacent
Hypotenuse
Make sure you
pronounce it with
a long “O” in
“SOH” so that
you don’t think
it’s an “A”!
43/67
Hypotenuse
Tan
Opposite
Adjacent
Example: Solve for the length of the hypotenuse
Trigonometry Example
25°
5.2 m
You know an angle and a length opposite the angle
and you want to know the hypotenuse. Opposite &
hypotenuse are used in “sin”
52
44/67
hypotenuse
5.2m
sin25=
D
Hypotenuse *
* Hypotenuse
sin 25°
sin 25°
D
sin25
5.2m
hypotenuse=
hypotenuse=12m

23. AP Physics Rapid Learning Series - 02
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 23
Solving for an Angle
If you know the two sides of the triangle, use the “arc”
trig function to solve for the angle
The “arc” is symbolized with
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
−
hypotenuse
opposite
sinθ
1
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
−
hypotenuse
adjacent
cosθ
1
y
“-1” exponent and is found as
a “2
nd
” function on your
calculator
t
e to θ
45/67
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
−
adjacent
opposite
tanθ
1
Right angle θ
“Theta θ” - angle in question
Opposi
t
Adjacent to θ
Example:Solve for the unknown angle
Trigonometry Example - Solving for Angle
?
You know the sides opposite and adjacent to an
unknown angle. “tan
-1
” can be used
3.7 m
7.5 m
46/67
3.7m
7.5m
tanθ
1−
=
D
63.7θ=

24. AP Physics Rapid Learning Series - 02
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 24
Definition - Vector
Vectors– Quantities with a magnitude
and a direction.
Trigonometry is used when
calculating with vectors
47/67
calculating with vectors..
Quadratic
Equation
The next topic will be the
dti ti
48/67
quadratic equation.

25. AP Physics Rapid Learning Series - 02
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 25
Definition – Quadratic Formula
Quadratic Formula– n. formula used
to find “x” in an equation that
contains “x” and “x
2
” .
4acbb
x
2
−±− =
49/67
2a
0cbxaxwhere
2
=++
Example
When working velocity problems, you may end up
with equations that contain an “x” and an “x
2
Example:Solve for x (“x” represents “time”)
2a
4acbb
x
2
−±−
=
085x1x
2
=−+
1*2
8)*1*(455
x
2
−−±−
=
From above: a = 1, b = 5, c = -8
50/67
12
2
575
x
±−
=
Using the + give x = 1.27
Using the – gives x = -6.27
A negative answer isn’t possible for time

26. AP Physics Rapid Learning Series - 02
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 26
Graphing
Graphing is commonly used in
51/67
physics.
Graphing and Slopes
Graphing is used extensively in physics to
visualize and analyze data. Slopes can give
meaningful information.
Y-axis
Position
Velocity
X-axis
Time
Time
Slope
Velocity
Acceleration
52/67
In Calculus, these are called derivatives…Velocity is the
derivative of position.

27. AP Physics Rapid Learning Series - 02
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 27
Finding Average Slopes
Use the final and initial conditions to find the average
slope.
80
0
10
20
30
40
50
60
70
53/67
0
0246810
Initial conditions: x = 0 and y = 3
Final conditions: x = 8 and y = 67 12
12xx
yy
slope
−−
= 8
08
367
slope =
−
−
=
Average slope = 8
Finding Instantaneous Slopes
Use tangents to find the slope at an instant on a curve
Find slope at x = 5
10
20
30
40
50
60
70
80
54/67
0
10
0246810
Initial conditions: x = 5 and y = 28
Final conditions: x = 7.7 and y = 53 12
12xx
yy
slope
−−
= 9.3
57.7
2853
slope =
−
−
=
Instantaneous slope at x = 5 is 9.3

28. AP Physics Rapid Learning Series - 02
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 28
35
Graphing Direct Relationships
Many relationships in physics are direct
0
5
10
15
20
25
30
024681012
Position
Slope is a
straight line
55/67
Time
Equation of line is in format: y = mx + b
where: m = slope
b = y-intercept
Graphing Quadratic Relationships
Some relationships in physics are quadratic
80
0
10
20
30
40
50
60
70
56/67
0
0246810
Equation of line is in format: y = kx
2
+ b
where: k = a constant
b = y-intercept

29. AP Physics Rapid Learning Series - 02
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 29
Graphing Inverse Relationships
Some relationships in physics are inverse
29
3
2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
57/67
0123 45678
Equation of line is in format: y = k (1/x)
where: k = a constant
Calculator Survival
Finally, we will discuss important
if i ll
58/67
tips for using your calculator
correctly.

30. AP Physics Rapid Learning Series - 02
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 30
Calculator Survival
Many times a student has a problem set up
correctly, but makes a mistake entering it into the
calculator.
59/67
The following slides will show how to avoid
common calculator mistakes.
Calculator Tip #1
Dividing by more than one number
L)atm)(2.5(1.25
K)L)(273atm)(1.0(1.00
T
2
=Example:
Common mistake:
;
Typing in * tells the calculator that the number
following it is on top of the expression.
1.00 * 1.0 * 273 ÷1.25 * 2.5Entering in:
60/67
Correct method:
1.00 * 1.0 * 273 ÷1.25 ÷2.5Entering in:
Always use ÷to designate a number on the
bottom.

31. AP Physics Rapid Learning Series - 02
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 31
Calculator Tip #2
Using scientific notation
2
3
10*9.8
10*1.5
D=
Example:
Common mistake:
1.5 * 10 ^ 3 ÷9.8 * 10 ^ 2Entering in:
;
Typing in * tells the calculator that the number
following it is on top of the expression.
61/67
Correct method:
1.5 EE 3÷9.8 EE 2Entering in:
Always use EE (or EXP) key to enter in
scientific notation.
Calculator Tip #3
Adding/subtracting & multiplying/dividing together
100*
1.37
1.371.25
error%
−
=
Example:
Common mistake:
1.25 - 1.37 ÷1.37 * 100Entering in:
Always use parenthesis around addition
;
Addition and subtraction must happen
first…before multiplication and division.
62/67
Correct method:
(1.25 - 1.37)÷1.37 * 100Entering in:
Always use parenthesis around addition
and subtraction when combining with other
operations.

32. AP Physics Rapid Learning Series - 02
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 32
Calculator Tip #4
Using powers with negative numbers
2
10−Example:
Common mistake:
(-10)
2Entering in:
To make something negative keep the
;
Anything inside the parenthesis will be
squared as well.
63/67
Correct method:
-(10
2
)Entering in:
To make something negative, keep the
negative sign out of the exponent operation.
Or-10
2
Summary of Calculator Tips
S i tifi t ti Al EE ( EXP) k t t
Dividing by more than one number: Always use ÷to
designate a number on the bottom
1
Powers & negative numbers:To make something
Combining operations: Always use parenthesis around
addition and subtraction when combining with other
operations
3
Scientific notation: Always use EE (or EXP) key to enter
in scientific notation
2
64/67
Powers & negative numbers: To make something
negative, keep the negative sign out of the exponent
operation
4

33. AP Physics Rapid Learning Series - 02
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 33
Trigonometric
functions are
Trigonometric
functions are
Algebra is
often used to
solve for
Algebra is
often used to
solve for
After working
hard on a
problem, avoid
After working
hard on a
problem, avoid
Learning Summary
used in
physics.
used in
physics.
solve for
variables in
physics.
solve for
variables in
physics.
common
calculator
mistakes!
common
calculator
mistakes!
Results ofResults of
65/67
Follow rules for
working with
exponents &
scientific notation.
Follow rules for
working with
exponents &
scientific notation.
Results of
calculations must
be reported with
the correct # of sig
figures.
Results of
calculations must
be reported with
the correct # of sig
figures.
Congratulations
You have successfully completed
the core tutorial
Basic Math for Physics
Rapid Learning CenterRapid Learning Center

34. AP Physics Rapid Learning Series - 02
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 34
Rapid Learning Center
Wh t’ N t
Chemistry :: Biology :: Physics :: Math
What’s Next …
Step 1: Concepts – Core Tutorial (Just Completed)
ÆStep 2: Practice – Interactive Problem Drill
Step 3: Recap – Super Review Cheat Sheet
67/67
Go for it!
http://www.RapidLearningCenter.com