Exam 1 Postmortem (What went wrong?) CSI MATH 111.122 YCP.

Exam 1 Postmortem

(What went wrong?)

CSI MATH 111.122 YCP

Definitions (continued)

A proposition makes a claim that may be either true or false.

A claim may be either

assertion

denial

A proposition must have the structure of a complete sentence

(i.e., questions are not propositions!)

Copyright © 2008 Pearson Education, Inc. Slide 1-12

1-A

If . . . Then Statements(Conditionals)


p q if p, then q

T T T T F F F T T F F T

Note: Conditional is true unless p is true and q is false.

1-B

Conditional Negation

Conditional

if p, then q

If you are sleeping, then you are breathing.

Conditional Negation

p and ~q

(why this is true will be shown later)

You are sleeping and you are not breathing.

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1-B

Units

The units of a quantity describe what is being measured or counted.


Read kilowatts hours as “kilowatt-hours.”

hyphenMultiplication

Read ft ft ft or ft3, as“cubic feet” or “feet cubed”

cube or cubicRaising to a third power

Read ft ft, or ft2, as“square feet” or “feet squared”

squareRaising to a second power

Read miles hours as “miles per hour”

perDivision

ExampleKey word or symbol

Operation

2-A

Using Units

Always keep units along with their quantities! Example

► 2500 watts x 3 hours = 7500 watt-hours► Not 2500 x 3 = 7500 watt-hours

Example► 1000 watt-hours = 1 kilowatt-hour► 500 watt-hours = 0.5 kilowatt-hour = 0.5 kw-hr

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1 watt x 1000 hours = 1 w x 1000 hr = 1000 w-hr

1000 watts x 1 hour = 1000 w x 1 hr = 1000 w-hr

REMEMBER: 1000 watts = 1 kilowatt, and

1000 w = 1 1 kw = 1 1 kw 1000 w

1 watt x 1000 hours = 1 w x 1000 hr = 1000 w-hr = 1 kw-hr

1000 watts x 1 hour = 1000 w x 1 hr = 1000 w-hr = 1 kw-hr

Examples

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Conversions

• Multiply, divide, or what?• Simplify by multiplying by 1 • Depends on what the problem is• The key to solving the problem is knowing

what units the solution should be• Example, if the answer should be

square yards (yd2), and your solution produces

yd4, then your solution is incorrectepw 9/25/06 8

Using Units

Know the units to expect Examples

The question asks for a cost in $

when using conversions, all units, except for dollars,

should cancel! The question asks for speed in km/hr

when using conversions, all units, except for km/hr,

should cancel!

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Conversion Format

ft

in. 12 or

foot 1

inches 12

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• There are 12 inches per 1 foot:

• Also, there is 1 foot per 12 inches:

Use whatever produces the desired units!

in. 12

ft or

inches 12

foot 1

Chain of Units Conversions

How many seconds are in one day?


2-A

24 hr 60 min 60 s

1 day 86,400 s1 day 1 hr 1 min

Cubic Units

How many cubic yards of soil are needed to fill a

planter that is 20 feet long by 3 feet wide by 4 feet tall?


The volume is 20 ft × 3 ft × 4 ft = 240 ft3

1 yd = 3 ft, so (1 yd)3 = (3 ft)3 = 27 ft3 or 1 yd3 = 1 27 ft3

2-A

U.S. Customary System


2-B

Knots and Nots

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A nautical mile is a unit of length on land, sea, and it the air. It corresponds approximately to one minute of latitude along any meridian (one minute of arc length on the Earth’s surface).

A knot is a measure of speed: 1 knot = 1 nautical mile hour

3.5 knots per hour = 3.5 nautical miles ÷ hour = 3.5 nautical miles hour hour2

Knots and Nots

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Which is faster, 1 mile per hour or 1 knot?

1 mile = 5280 feet hour hour

1 nautical mile = 6076.1 feet hour hour

Metric Conversions


2-B

Moving between metric units requires shifting the decimal placeone to the right when going to the next smaller unit and one to theleft when going to the next larger unit.

(Example: 5.23 cm = 52.3 mm)

Temperature Conversions

The conversions are given in both words and with formulas in which C, F, and K are Celsius, Fahrenheit, and Kelvin temperatures, respectively.


C = K 273.15Subtract 273.15Kelvin to Celsius

K = C + 273.15Add 273.15.Celsius to Kelvin

Subtract 32. Then divide by 1.8

Fahrenheit to Celsius

F = 1.8c + 32Multiply by 1.8. Then add 32.

Celsius to Fahrenheit

Conversion FormulaConversion in WordsTo Convert from

2-B

Units of Density and Concentration

Density describes compactness or crowding.

Material density – given in units of mass per unit volume; i.e., g/cm3

Population density – given by the number of people per unit area

Information density – how much information can be stored by digital media


2-B

Conversion Factors

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Every Conversion Factor can be Written Three Different Ways

1 in. = 2.54 cm

1 in. = 1

2.54 cm

2.54 cm = 1

1 in.

Convert Miles to Kilometers

• Given 1 in. = 2.54 cm• Calculate how many cm are in 1 foot• 1 ft = 12 in.• 1 ft = 12 in. x 2.54 cm = 30.48 cm

1 in.• 1 mile = 5280 ft x 30.48 cm = 160934.4 cm

ft

• 1 mile = 1.6093 km

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How Many Square Kilometers are in One Square Mile?

1 mi = 1.6093 km

(1 mi)2 = (1.6093 km)2

1 mi2 = 2.5898 km2

One square mile is 2.5898 square kilometers

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Exam 1 Postmortem (What went wrong?) CSI MATH 111.122 YCP.

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