Exam 1 Review - Math 1030 008
DON’T FORGET TO MEMORIZE THE FOLLOWING!!
Unit conversions
1 in = 2.54 cm
1 ft = 0.3048 m
1 mi = 1.6093 km
1 lb = 0.4536 kg
1 L = 61.03 in3
Metric Prefixes
kilo (k) 103
hecto (h) 102
deca (da) 101
base (meter, liter, gram, etc) 100
deci (d) 10−1
centi (c) 10−2
milli (m) 10−3
Miscellaneous
Absolute change = new value − reference value
change
Relative change = absolute
reference value
Absolute difference = compared value − ref. value
difference
Relative difference = absolute
reference value
Absolute error = measured error − true value
error
Relative error = absolute
true value
KEY IDEAS AND SKILLS
1. Set relationships
• subsets
• disjoint sets
• overlapping sets
2. Four categorical propositions
• All S are P
• No S are P
• Some S are P
• Some S are not P
3. Uses of Venn diagrams
• illustrating set relationships
• organizing information
4. Evaluating arguments
• inductive arguments in terms of strength
• deductive arguments in terms of validity and soundness
• Venn diagram tests of validity
5. Identify: units with key words per, square, or cube or with hyphens.
6. Write: conversion factors in three equivalent forms.
7. Work: with units to check answers and help solve problems.
8. Understand and convert basic USCS and metric units.
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9. Know metric prefixes.
10. Know temperature units and convert between ◦ F, ◦ C, and Kelvin.
11. Understand energy units and power units.
• Energy is what makes matter move or heat up.
• Power is the rate at which energy is used.
12. Apply the concept of density to materials and population.
13. Know formulas for absolute and relative change and difference.
14. Understand the of versus more than rule.
15. Understand percentage points versus %.
16. Solve percentage problems.
17. Identify common abuses of percentages.
18. Write and interpret numbers in scientific notation.
19. Put numbers in perspective through
• comparisons
• scaling
20. Know formulas for Absolute and Relative error.
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1. Write the following sets in set notation.
(a) The set of whole numbers between 10 and 50, not including 10 and 50.
(b) The set of integers less than −5.
2. Draw a Venn diagram for each problem representing each of the following scenarios.
(a) In a group of 60 politicians,
20 are Republican and male.
10 are Democrat and female.
5 are Democrat and male.
How many are Republican and female?
(b) In a group of 100 students,
9 have a bicycle, but not a scooter or a car.
11 have a scooter, but not a bicycle or a car.
17 have a car, but not a bicycle or a scooter.
12 have a bicycle and car, but not a scooter.
23 have a bicycle and scooter, but not a car.
5 have a scooter and car, but not a car.
10 have a bicycle, a scooter and a car.
How many students don’t have any of the three vehicles? How many students have a bicycle and
a scooter?
3. Evaluate the strength of the following inductive arguement.
Premise:
Sparrows are birds and they fly.
Premise:
Eagles are birds and they fly.
Premise:
Hawks are birds and they fly.
Premise:
Larks are birds and they fly.
Conclusion: All birds fly.
4. Determine if the following deductive arguement is sound and/or valid.
Premise:
All students who study do well in school.
Premise:
Erica does well in school.
Conclusion: Erica studies.
5. Mr. Turtle runs at a speed of 1 mm per second. What is Mr. Turtle’s speed in miles per hour?
6. A rectangle has sides of 10 cm and 17 cm. What is the area of the rectangle in inches?
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7. Perform the following temperature conversions.
(a) 76◦ F to C and K.
(b) 35◦ C to F and K.
(c) 300 K to C and F.
8. You are on vacation in Japan. You see a camera that you want to buy priced at 250, 000 yen.
You have 120 British pounds. Do you have enough to buy this camera assuming that there is a
place near by that can convert British pounds to Japanese yen?
9. You are taking a trip and you must drive 300 miles. You drive a car that gets 19 miles per
gallon and has 15 gallons of gas in it. Will you need to stop during your trip to get gas?
10. You drive a Ford Taurus that has a value of $15, 000. Over a 5 year period, it depreciates to
a value of $12, 000. Find the absolute and relative change in the value of your car over the 5 year
period.
11. In a recent year, the United States made $12.1 billion in international arms sales and Russia
made $5.8 billion in arm sales. Find the absolute and relative difference between the US and
Russian international arms sales.
12. At a local convience store, you buy a bag of Doritos for $0.99 and a Full Throttle energy drink
for $1.99. If there is 6% sales tax, how much will you spend at the convenience store?
13. Recently, you’ve been slacking off at work. Your boss threatens to reduce your salary by 10% if
you don’t start working seriously. You continued to slack off and your boss reduced your salary by
10% so that you’re now making $27, 820 annually. How much did you make annually before your
pay cut?
14. Convert the following numbers to scientific notation.
(a) 5,230,000
(b) 0.0000000124
(c) 1350
15. Convert the following numbers written in scientific notation to standard form.
(a) 4.806 × 107
(b) 1.2 × 10−4
(c) 2.529 × 10−9
16. You have a map where 1 cm = 10 km. What is the scale ratio?
17. The planet Jupiter has a diameter of 143, 000 km and an average distance to the sun of 778.3
million km. Using a scale ratio of 1 to 10 billion, calculate the scaled size and distance from the
sun for Jupiter.
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