Gibilisco S. Everyday Math Demystified: A Self-Teaching Guide

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1000 to obtain 25 m/s as the posted speed limit. Finally, convert meters

to feet. Multiply 25 by 3.281 to get 82.025. This must be rounded oﬀ to

82 ft/sec because the posted speed limit is expressed to only two signiﬁcant

ﬁgures.

Quiz

Refer to the text in this chapter if necessary. A good score is eight correct.

Answers are in the back of the book.

1. Which of the following terms commonly represents more than one

measurable quantity or phenomenon?

(a) meter

(b) pound

(d) degree

2. The mole is a unit that expresses the

(a) number of electrons in an ampere

(b) number of particles in a sample

(d) time required for an electron to orbit an atomic nucleus

3. The nomograph of Fig. 4-8 can be used to convert:

(a) feet to meters

(b) inches to centimeters

(d) grams to pounds

4. A joule is the equivalent of a

(a) foot-pound

(b) meter per second

(d) watt-second

Fig. 4-8. Illustration for Quiz Question 3.

CHAPTER 4 How Things Are Measured 91

5. An example of a dimensionless unit is

(a) the kilogram

(b) the meter

(d) none of the above

6. Force is equivalent to

(a) mass multiplied by distance

(b) mass multiplied by time

(d) mass multiplied by speed

7. Two islands are 1345 nautical miles apart. How many kilometers is

this?

(a) 2492

(b) 2164

(d) It is impossible to say without more information.

8. The number of kilograms an object has can be converted to pounds

only if you also know the

(a) temperature of the object

(b) size of the object

(d) number of moles of atoms in the object

9. The pound is a unit of

(a) mass

(b) distance

(d) none of the above

10. The SI system is an expanded form of the

(a) English system

(b) metric system

(d) American system

PART 1 Expressing Quantities

Test: Part 1

Do not refer to the text when taking this test. You may draw diagrams or use

a calculator if necessary. A good score is at least 30 correct. Answers are in

the back of the book. It’s best to have a friend check your score the ﬁrst time,

so you won’t memorize the answers if you want to take the test again.

1. The binary number 10010 is equivalent to the decimal number

(a) 8

(b) 12

(d) 18

(e) 34

2. In the graph of Fig. Test 1-1, how many orders of magnitude are

shown on the horizontal axis?

(a) 1

(b) 2

(d) 100

(e) Inﬁnitely many.

3. In Fig. Test 1-1, why does the graph of y ¼ x look like a curve, not a

straight line?

(a) Because one scale is linear (graduated evenly) and the other is not.

(b) Because neither scale is linear.

(d) Because y is not a function of x in this example.

(e) Because the two scales encompass the same range of values.

4. Suppose you graph the barometric pressure at 30-minute intervals

during the passage of a hurricane, with time on the horizontal scale

and pressure (in millibars) on the vertical scale. After you have plotted

the points, you connect them with a curve that represents your ‘‘best

educated guess’’ as to the moment-to-moment pressure. In this graph,

the pressure is

(a) the independent variable

(b) the dependent variable

(d) a relation

(e) a coeﬃcient

5. In the graph described in the previous question, suppose you connect

the points with straight lines to get an approximate graph of the

barometric pressure plotted with respect to time. This lets you infer

the pressure at any given point in time according to

(a) extrapolation

(b) inversion

Fig. Test 1-1. Illustration for Part One Test Questions 2 and 3.

PART 1 Expressing Quantities

(d) exponentiation

(e) curve ﬁtting

6. In the graph described in Question 4, suppose you connect the points

with a ‘‘best educated guess’’ curve in an attempt to create a precise,

moment-to-moment graph of the barometric pressure plotted with

respect to time. This lets you infer the pressure at any given point in

time according to

(a) extrapolation

(b) inversion

(d) exponentiation

(e) curve ﬁtting

7. Consider a number that is equal to 5.00  2

. In power-of-10

notation, rounded to three signiﬁcant ﬁgures, this is

(a) 5.24  10

(b) 2.00  10

(d) 1.00  10

(e) impossible to determine without more information

8. Fig. Test 1-2 shows the speed of an accelerating car (in meters per

second) as a function of time (in seconds). The fact that the graph

is a straight line indicates that the rate of acceleration (expressed

in meters per second per second, or m/s

) is constant. What is this

constant acceleration?

(a) 1 m/s

(b) 2 m/s

(d) 20 m/s

(e) It cannot be determined without more information.

9. In the scenario shown by Fig. Test 1-2, suppose a mass of one kilogram

(1 kg) is substituted for the car. According to the laws of physics, con-

stant acceleration of an object having constant mass is produced by a

constant force or thrust. Force is expressed in units of kilogram-meters

per second per second (kg  m/s

), also known as newtons (N), as you

learned in Chapter 4. What force, in newtons, is necessary to cause a

1-kg mass to accelerate at the rate shown by the graph?

(a) 1 N

(b) 2 N

Test: Part 1 95

(d) 20 N

(e) It cannot be determined without more information.

10. In a graph intended to show the correlation between two variables,

the total absence of any correlation is indicated by points that

(a) all lie near a horizontal line

(b) all lie near a vertical line

(d) all lie tightly clustered near the center of the graph

(e) are arranged in some manner other than the four described above

11. How does a numeral diﬀer from a number?

(a) A number represents a diagram, but a numeral represents a set.

(b) A numeral is a symbol that represents a number.

(d) Numerals are letters of the alphabet, but numbers are symbols

such as the plus sign, the minus sign, and the forward slash.

(e) There is no diﬀerence.

12. What is the value of 3  5  6/3 þ 10?

(a) 6

(b) 9/10

(d) 3

(e) It is undeﬁned, because it is ambiguous as written.

13. In a vertical bar graph, function values are portrayed as

(a) the heights of bars having equal width

Fig. Test 1-2. Illustration for Part One Test Questions 8 and 9.

PART 1 Expressing Quantities

(b) the widths of bars having equal height

(d) points connected by a curve

(e) points plotted all by themselves, not connected by anything

14. The milligram is a unit of

(a) temperature

(b) electrical quantity

(d) frequency

(e) mass

15. The mole is an example of a

(a) linear unit

(b) nonlinear unit

(d) dimensionless unit

(e) temporal unit

16. The sum of two integers

(a) is always an integer

(b) is always a positive integer

(d) is never zero

(e) is always a dependent variable

17. A radian is equivalent to approximately

(a) 57.3 meters of displacement

(b) 57.3 degrees of angular measure

(d) 57.3 degrees Fahrenheit

(e) 57.3 degrees Celsius

18. In order to get the Fahrenheit (8F) temperature when the Kelvin

temperature (8K) is known, this formula is commonly used:



F ¼ 1:800 



K  459:67

Suppose we are told that the temperature outdoors is 300 8K. What is

the temperature in 8F to the maximum justiﬁable number of signiﬁ-

cant ﬁgures?

(a) 80.3 8F

(b) 80.33 8F

Test: Part 1 97

(d) 287.4 8F

(e) None of the above.

19. If the independent and dependent variables of a function are

reversed, the result

(a) is always a function

(b) is sometimes a function

(d) is not deﬁned

(e) has negative correlation

20. Suppose there are two quantities, and one of them is exactly 0.001

the size of the other. These quantities diﬀer by

(a) 0.001 orders of magnitude

(b) 1 order of magnitude

(d) 10 orders of magnitude

(e) 1000 orders of magnitude

21. In the octal system, the number 67 is followed by the number

(a) 68

(b) 69

(d) 77

(e) 100

22. The numbers 6.78870000  10

6

and 6.7887  10

6

diﬀer in the

sense that

(a) the ﬁrst is expressed with a greater degree of accuracy than the

second

(b) the ﬁrst is four orders of magnitude larger than the second

(d) the ﬁrst is rounded, but the second is truncated

(e) the ﬁrst is the reciprocal of the second

23. Every rational number is

(a) a natural number

(b) an integer

(d) positive

(e) nonzero

24. Consider that a meter (m) is equivalent to 39.37 inches (in), a foot (ft)

is equivalent to 12.000 in, and a statute mile (mi) is equivalent

PART 1 Expressing Quantities

to 5280 ft. Based on this information, how many feet are there in a

kilometer?

(a) 3281 ft

(b) 1609 ft

(d) 1.732  10

(e) More information is needed to calculate this.

25. Based on the information given in the previous question, how many

millimeters (mm) are there in a statute mile?

(a) 6.336  10

(b) 1.341  10

(d) 6.336  10

(e) More information is needed to calculate this.

26. In the hexadecimal system, the number 11 is followed by the number

(a) 12

(b) A

(d) 1A

(e) 1B

27. How many radians are there in a degree Kelvin?

(a) Approximately 57.3, the same number of degrees as there are in a

radian.

(b) Approximately 273.15, the diﬀerence between 8K and 8C.

(d) It depends on the radius of the circle under consideration.

(e) This question is meaningless because the units are incompatible.

28. Suppose a and b are rational numbers, both larger than 1 but less

than 10, and both expressed in decimal form to the same number

of signiﬁcant ﬁgures. Suppose m and n are integers. What is the

product of a  10

and b  10

(a) There is no way to express this in the general case.

(b) (a þ b)  10

(d) ab  (10m)

(e) ab  10

(m þ n)

29. The steradian is a unit of

(a) solid angular measure

Test: Part 1 99

(b) temperature

(d) frequency

(e) electrical current

30. In Fig. Test 1-3, the gray shaded area represents

(a) the set A  B

(b) the set A \ B

(d) the set A  B

(e) the set A

31. In Fig. Test 1-3, which of the points P, Q,orR lies within the set

A \ B?

(a) Point P only.

(b) Point Q only.

(d) Points Q and R.

(e) None of the points.

32. In Fig. Test 1-4, the point shown represents

(a) a natural number

(b) an integer

(d) an irrational number

(e) none of the above

33. A one-dimensional graph, consisting of two scales lined directly up

against each other, is called a

(a) linear comparison

(b) bar graph

(d) nomograph

(e) functional graph

Fig. Test 1-3. Illustration for Part One Test Questions 30 and 31.

PART 1 Expressing Quantities

100