Review of Skills Covered in the Summer Assignment

Reporting Numerical Answers• Whenever reporting numbers, you MUST include• The appropriate number of sig figs (magnitude)• The direction (angle measurement, cardinal direction, linear

direction) if it’s a vector quantity• The units

• Sig Figs • Zeros to the left of the decimal and after a number are significant• Zeros to the right of a decimal that ALSO follow a number are

significant• Zeros in between numbers are significant• Zeros after a number that are NOT followed by a decimal are NOT

significant.• For numbers less than 1, zeros between the decimal and the first

digit are NOT significant

Sig Fig Examples• For the following numbers, report the correct number of sig

figs.

Keeping Sig Figs• When calculating, you must keep the appropriate sig figs! • Try to keep the numbers in your calculator as much as possible• Use the answer key

• Only round your answer to the appropriate number of sig figs at the end of the calculation.• When multiplying and dividing numbers, report your answer with

the same number of sig figs as the original number having the least number of sig figs

• When adding or subtracting, report your answer to the same decimal place as the original number having the least number of decimals.

Applying the Sig Fig Rules

Answer the following with the correct number of significant Figures• Adding/Subtracting:• 1) 9.748 - 9.67 = _______• 2) 22.9 + 61.678 = _______• 3) 4.285 + 1.8454 + 1.38 = _______• 4) 22.8392 + 7.971 + 45.83 = _______• 5) 7.5733 - 1.8 = _______

• Multiplying/Dividing:• 1) 68 x 8 x 20 = __________• 2) 6001 ÷ 79.8 = __________• 3) 0.0026 x 62 = __________• 4) 950 ÷ 9.73 = __________• 5) 8600 ÷ 7.970 = __________

Scientific Notation • Keeps things neat and concise. • NO extra numbers

• Example• Speed of light in a vacuum 300000000m/s

• Only one significant figure with many non-significant zeros becomes….

• 3x108 m/s

• Put answers into scientific notation as often as possible keeping the appropriate number of sig figs based on the given information.

Orders of Magnitude• Another way to keep numbers neat and concise • The exponent tells you how many zeros• Positive exponent means numbers greater than 1• Negative exponent means numbers less than 1

• You can replace the orders of magnitude with well know prefixes seen below

Reading the Table

1 kilometer = 1x103 meter

1 nanosecond = 1x10-9 seconds

Orders of Magnitude• A race is 5kilometers long• How many meters is that?• How many centimeters?• How many megameters?

• A flash of light lasts 0.00056 seconds• How many milliseconds is that?• How many microseconds?

• An object has a mass of 75kilograms• How many grams is that?

• A molecule is 1.5x10-10 m long• How many nanometers is it?• How many picometers is it?

Orders of Magnitude• A race is 5kilometers long• How many meters is that? 5000m• How many centimeters? 500,000cm• How many megameters? 0.005Mm

• A flash of light lasts 0.00056 seconds• How many milliseconds is that? 0.56ms• How many microseconds? 560μs

• An object has a mass of 75kilograms• How many grams is that? 75,000g

• A molecule is 1.5x10-10 m long• How many nanometers is it? 15nm• How many picometers is it? 0.015pm

Interpreting Graphs• Both axes stand for actual physical quantities (check their

units)• They y-intercept will give you the initial contitions.• The slope of the graph usually stands for a physical quantity

also• Divide the y-axis units by the x-axis units to determine what it is.

• The area between the graph and the x-axis also sometimes stands for a physical quantity.• Multiply the y-axis units by the x-axis units to determine what it is

• BEFORE ANSWERING ANY GRAPH QUESTIONS, YOU SHOULD ADDRESS THE FOUR POINTS ABOVE.

Analyzing Graphs• Assuming this is a graph of money in your bank account vs.

time, what can you tell me about your bank account?• Remember to address the 4 points above• talk segment by segment• Use descriptive words like constant, rate of change, increasing,

decreasing…

mon

ey

time

• Initial condition: at the start of time, there is no money in your bank account

• To A: the amount of money in your bank account increases at a constant rate.

• A to B: the amount of money in your bank account is still increasing, but the rate at which it is increasing is decreasing.

• At B: you stop earning money and start to lose it• B to C: you are losing money at an increasing rate, then reach

a point where you are neither losing or gaining money• Segment C: The amount of money in your bank account is

constant. You are not losing or gaining money.

mon

ey

time

• Segment D: You are again earning money at a constant rate that is the same as the rate to A

• At E: you instantaneously stop earning money and start to lose it at a constant bur faster rate as compared to how fast you were earning money

• At F: you have the same amount of money in your account that you did at C

• At G: you have no more money in your account at that instant• At H: you are still losing money at a constant rate and now

you are in debt. You have negative money in your bank account.

mon

ey

time

Translating one Graph to AnotherUsing your description of the flow of money just described, sketch a graph that depicts the rate at which your bank account is changing as a function of time.

Rate

of c

hang

e of

the

mon

ey

time

Translating one Graph to AnotherAddress the four points to make sure this graph makes sense

time

Rate

of c

hang

e of

the

mon

ey

Fraction Math 101• When adding and subtracting• Turn mixed numbers into improper fractions• Find a common denominator• Add/subtract• Reduce

• When multiplying• Turn mixed numbers into improper fractions• Multiply all numerators• Multiply all denominators• Reduce

• When dividing• Turn mixed numbers into improper fractions• Keep the first, change to multiplying, reciprocate the second fraction• Follow multiplying rules

1925

6556

71722

161932

1516

18

16

1914

212

12

Other Math Skills• Algebra• Solving for x• Quadratic equation• System of equations

• Trig• Sohcahtoa• Pythagorean theorem

• Graphs• Calculating slope

• Geometry• Area of…

• Circle• Triangle• rectangle

Algebra• Solve for the indicated variable either numerically or

symbolically

Solve A = bh for b

Solve P = 2l + 2w for w

Solve Q = for d

Solve V = for t

Algebra• Solve for the indicated variable either numerically or

symbolically

Solve A = bh for b b=

Solve P = 2l + 2w for w w=

Solve Q = for d d=2Q-C

Solve V = for t t=

X=-2

X=-2

X=-2

Using the quadratic formulaSolve for x

Using a system of equations• Solve for x and y

Using a system of equations• Solve for x and y

X=1y= 1/6

X=17/9y= -89/18

X=-3y= 2

X=1y= 3/2

Multiplying / Dividing with Exponents• Square roots• Other exponents• Multiplying different exponents with the same base

• Add the exponents• Dividing different exponents with the same base

• Subtract the exponents• Raising an exponent to a different power

• Multiply the two exponents • Different bases

• Try to change the base by changing the exponents• 82 x 23 = (4 x 2)2 x 23 = (22 x 2)2 x 23 = (23)2 x 23 = 26 x 23 = 29

Answer is under here

Definition of a Scalar• A quantity that has an magnitude (size or amount) and NO

direction

• Just memorize• Time• Mass• Temperature• Distance• Speed• Work and Energy• Charge

Definition of a Vector• A quantity that has an magnitude (size or amount) and

direction (north, south, east, west OR up, down, left, right OR an angle)

• MADFIVE• Momentum• Acceleration• Displacement• Force• Impulse• Velocity• Electric Field Strength

Vector Components

Original given magnitude = A

Reference lineθ

Original given direction (North of East)

Horizontal or x – component of vector AAx = A cos θ

Vertical ory – component of vector AAy = A sin θ

Vector Addition• Any vectors pointing in the EXACT same direction: add the

magnitudes• Any vectors pointing in the EXACT opposite direction: subtract

the magnitudes• 2 vectors Pointing at EXACT right angles to each other: use the

Pythagorean theorem to find the magnitude, use trig to find the direction

• 2 vectors pointing in any other directions• Break the angled vector into its components• Then follow the rules above

Same Direction

7m

• Put them head to tail• Draw resultant• Add magnitudes

3m

resultant

Magnitude: 7m+3m=10m Direction: to the right

Opposite Direction

7m

• Put them head to tail• Draw resultant• Subtract magnitudes

12m

resultant

Magnitude: 7m-12m= -5m = 5m Direction: to the left (the negative sign means ‘to the left’)

Right Angles

7m

• Put them head to tail• Draw resultant• Use Pythagorean Theorem to find the magnitude• Use trig to find the direction (angle)

3m

resultant

Magnitude: 7.6mDirection: 23o south of east

θ

Other Angles

7m

• Put them head to tail• Break angled vector into its components• Draw resultant• Add/subtract all x-components• Add/subtract all y-components• Use Pythagorean Theorem to find the magnitude of the resultant• Use trig to find the direction (angle) of the resultant

resultant

Magnitude: 11.3mDirection: 17o north of east

θAx = A cos θ = 5m cos 40O

= 3.8M

Ay = A sin θ = 5m sin 40o

= 3.2m

40o

5m

7m+3.8m = 10.8m

3.2m

Translating Wave function Equations

𝑦 (𝑡 )=𝐴 sin (𝜔𝑡 )

The y-value at the time t given

The amplitude of the wave (it is constant)

Omega is the angular frequency of the wave. It can tell you about the period of the wave.MUST BE IN RADIANS!!!!

𝑇=2𝜋𝜔

Period of a wave

f

Frequency of a wave

Interpret this function

• The amplitude of wave is…• 5m

• Which means the maximum y-value is +5 and minimum y-value is -5

• ω is 2 which means…• The period of the wave is π• The frequency of the wave is 1/ π

• Period and frequency are always inverses of each other

𝑦 (𝑡 )=5sin (2 𝑡 )