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

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(d) acceleration per unit time

(e) velocity multiplied by time

23. Any radioactive material has a speciﬁc period of time known as its

half-life, over which its radioactivity drops by 50%. Suppose the

half-life of element X is 100 years. Right now the radiation intensity

from a sample of element X is at a certain level. In 100 years, the

element X will be 50% as radioactive as it is right now. After another

100 years, the radioactivity of the element X will drop by another

50%. This process will repeat, century after century, eon after

eon. The radiation-intensity levels of any given sample of element

X, measured in constant ‘‘radiation units (RU)’’ at intervals of 100

years:

(a) increase without limit

(b) alternate between positive and negative

(d) add up to zero

(e) converge toward 1

24. Suppose you want to check the ﬂoor in a room to see if it is perfectly

horizontal. You know the ﬂoor is perfectly ﬂat throughout the room.

You have a carpenter’s level with which you can check to see if any

particular line along the ﬂoor is horizontal. What is the minimum

number of readings you must make with the level in order to know

whether or not the ﬂoor is perfectly horizontal?

(a) 1

(b) 2

(d) 4

(e) 5

25. Which of the following can be a unit of acceleration magnitude?

(a) Meters per second.

(b) Seconds per meter.

(d) Seconds per meter squared.

(e) Degrees per meter squared.

26. Imagine a room whose ﬂoor and ceiling are perfectly square, and

whose four walls are all perfect rectangles. Imagine one corner of

this room, where two walls intersect the ﬂoor. There are three line

segments that come together at this corner: the line segment where

Test: Part 4 391

the two walls intersect, the line segment where one wall intersects

the ﬂoor, and the line segment where the other wall intersects the

ﬂoor. At the corner where they all come together, these three line

segments are

(a) mutually parallel

(b) mutually perpendicular

(d) mutually equilateral

(e) none of the above

27. A ﬂat geometric plane in 3D space can be uniquely deﬁned by

(a) a point in the plane and a vector perpendicular to the plane

(b) three points that do not all lie on the same straight line

(d) two intersecting straight lines

(e) any of the above

28. Suppose you have a jar in which you keep change that accumulates

in the course of your shopping adventures. Every day, you put 76

cents into the jar. The amount of money in the jar increases day

by day, according to

(a) an arithmetic progression

(b) a geometric progression

(d) an exponential progression

(e) a convergent progression

29. Any radioactive material has a speciﬁc period of time known as its

half-life, over which its radioactivity drops by 50%. Suppose the half-

life of element Y is 80,000 years, someone has just handed you a sam-

ple of it, and the radiation level from it is 128 ‘‘radiation units (RU).’’

In 80,000 years, the sample will be half as radioactive as it is today.

After another 80,000 years, the radioactivity will go down by half,

again. This decay process will go on essentially forever. Suppose

the maximum safe level for human exposure to any radioactive sub-

stance is 16 RU. How long will it be before it’s no longer dangerous

to hang around the piece of element Y you’ve just been given?

(a) 240,000 years.

(b) 160,000 years.

(d) 40,000 years.

(e) 20,000 years.

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30. What would Fig. Test 4-3 most likely represent?

(a) The frequency setting of a hi-ﬁ stereo radio receiver.

(b) The direction in which a car or truck drives down a level street.

pointed.

(d) The compass bearing of a hiker in the wilderness.

(e) The acceleration of a speedboat on a lake.

31. In Fig. Test 4-3, what do 

, 

, and 

represent?

(a) Direction cosines.

(b) Direction angles.

(d) Elevation angles.

(e) Azimuth bearings.

32. In Fig. Test 4-3, what is represented by the lowercase, boldface letter a?

(a) A ray of light.

(b) An exponent.

(d) A scalar.

(e) A vector.

33. What is another thing that Fig. Test 4-3 might depict?

(a) The velocity at which a missile is ﬁred.

(b) Sunlight shining down on the surface of the earth.

Fig. Test 4-3. Illustration for Part Four Test Questions 30 through 34.

Test: Part 4 393

(d) The speed of the wind in a hurricane.

(e) The time and temperature in a certain place.

34. The diagram in Fig. Test 4-3 portrays?

(a) 1 spatial dimension.

(b) 2 spatial dimensions.

(d) 4 spatial dimensions.

(e) 5 spatial dimensions.

35. The human ear and brain perceive the loudness of a sound

(a) in proportion to the square of the sound power

(b) in proportion to the base-10 exponential of the sound power

(d) in proportion to the logarithm of the sound power

(e) in inverse proportion to the sound power

36. Suppose we are told the following sequence S is an arithmetic

sequence:

S ¼ 80ó 75ó xó yó zó 55ó 50

What is the diﬀerence between x and z?

(a) 5

(b) 10

(d) 20

(e) It cannot be determined without more information.

37. Suppose you are told that the intensity of some eﬀect Y varies

according to the 3/2 power of the strength of some other eﬀect X.

If the strength of eﬀect X doubles, by what factor does the intensity

of eﬀect Y increase?

(a) It does not change.

(b) It doubles.

(d) It increases by a factor of the square root of 8.

(e) More information is needed to answer this question.

38. Suppose you are building a coﬀee table. Your friend wants it to have

four legs attached to the table at the corners of a square. But you

want it to have only three legs, attached to the table at the vertices

of an equilateral triangle. You know that a three-legged table

PART 4 Math in Science

394

won’t wobble, even if the ﬂoor is irregular or if the legs don’t all turn

out to be exactly the same length. On what geometric principle is this

fact based?

(a) A vector normal to a ﬂat plane cannot lie in that plane.

(b) Two intersecting, straight lines uniquely deﬁne a ﬂat plane.

plane.

(d) Four points can lie in the same plane, but this is not always true.

(e) Four points can lie at the corners of a square, but this is not

always true.

39. Suppose your computer receives (unknown to you) an e-mail worm

that causes it to automatically send the same message to 100 other

computers. Ninety percent (90%) of the computers that receive this

e-mail block it out, but the other 10% get it and execute its nefarious

instructions. This process continues indeﬁnitely, with one iteration

taking place every minute. The number of these useless, unethical,

illegal e-mail messages clogging up the Internet increases, per unit

minute, according to

(a) an arithmetic progression

(b) a logarithmic progression

(d) a quadratic progression

(e) a cubic progression

40. Suppose you step on the ‘‘gas pedal’’ of a high-performance car while

you take a banked curve on a race track. The magnitude and direc-

tion of the acceleration of the car at a particular instant in time can

be fully deﬁned as

(a) a vector

(b) a logarithm

(d) a trigonometric function

(e) an exponent

Test: Part 4 395

Final Exam

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 75 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. Which of the following statements is false?

(a) A dependent variable can change in value, but its value is aﬀected

by at least one other factor.

(b) An independent variable can change in value, but its value is not

inﬂuenced by anything else in a given scenario.

(d) A mathematical relation is always a mathematical function.

(e) A function always has at least one dependent variable.

2. What is the product of 2/3 and 4/5?

(a) 6/15

(b) 8/15

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(d) 1

(e) 22/15

3. What is the equation shown by the straight line in Fig. Exam-1?

(a) 3x þ 2y ¼ 0

(b) 2x þ 3y ¼ 0

(d) 4x  6y ¼ 0

(e) 6x þ 3y ¼ 0

4. Consider the following equation:

ð y

 2y þ 1Þð y þ 4Þð y þ 5Þð y þ 6Þ¼0

How many real-number solutions are there to this equation?

(a) 1

(b) 2

(d) 4

(e) 5

5. It is known that 1 foot is equal to approximately 30.5 centimeters, and

that 1 inch is exactly 1/12 of a foot. Based on these facts, how many

centimeters are there in 1 inch?

(a) 0.305

(b) 0.393

(d) 3.28

(e) More information is needed to answer this question.

Fig. Exam-1. Illustration for Final Exam Question 3.

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6. Suppose you ﬂip an unbiased coin, and it comes up ‘‘heads’’ 4 times

in a row. If you ﬂip it a ﬁfth time, what is the probability that it will

come up ‘‘heads’’ again?

(a) 50%

(b) 25%

(d) 6.25%

(e) 3.125%

7. A nomograph

(a) consists of two graduated axes that intersect at a right angle

(b) consists of three graduated axes that intersect at right angles

(d) cannot be used to compare variables such as temperatures in

diﬀerent scales

(e) consists of points in a coordinate plane, connected by straight lines

8. If the rectangular-coordinate graph of an equation is a parabola

opening downward, the equation is

(a) linear

(b) circular

(d) cubic

(e) quartic

9. Dionysus is thinking of a real number. If he adds 7 to this number, he

gets the same result as if the number is doubled. What is the number?

(a) 7

(b) 2

(d) 2/7

(e) There is no such real number.

10. Imagine the set W of days in a week. Tuesday is

(a) a subset of W

(b) a proper subset of W

(d) a fraction of W

(e) a point of W

11. Which of the following (a), (b), (c), or (d) is not a real number?

(a) 4

1/2

(b) 4

1/3

1/4

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(d) 4

1/5

(e) All of the above are real numbers.

12. In probability, the set of all possible outcomes in the course of an

experiment is called

(a) the dependent variable

(b) the independent variable

(d) the population

(e) the event

13. Suppose your history teacher tells you that there is no good evidence

that the ancient Roman emperor Nero played a musical instrument

while the town burned. The teacher says, ‘‘It is nothing but a wild

tale. The probability is only 10% that Nero actually played a

musical instrument while Rome was on ﬁre.’’ This last statement is

an example of

(a) a sample space that is too small

(b) conﬂicting data

(d) mistaking a dependent variable for an independent variable

(e) mistaking a permutation for a combination

14. Imagine a quantity x. Suppose you add 7 to x, and get the same

result as if you subtract 5 from x. What is the real-number value

of x?

(a) 7

(b) 5

(d) 5/7

(e) The quantity x is not a real number.

15. Suppose two corporations want to advertise on a billboard. The

billboard has a trapezoidal shape, as shown in Fig. Exam-2. The

corporations decide that the most equitable way to divide up

the space is to divide it horizontally across the middle, so the top por-

tion (light shading) and bottom portion (dark shading) are of equal

height. The dimensions are as shown. Assume they are exact to the

nearest millimeter. How long is the central, horizontal line that

divides the light and dark shaded regions?

(a) More information is necessary to answer this.

(b) 11.750 meters.

Final Exam 399

(d) 12.000 meters.

(e) 12.250 meters.

16. In the situation shown by Fig. Exam-2, the area of the top portion

(light shading) of the billboard represents

(a) 28.57% of the total billboard area

(b) 33.33% of the total billboard area

(d) 45.83% of the total billboard area

(e) less than half of the total billboard area, but more information is

necessary to calculate the exact percentage

17. Suppose you have a standard 52-card deck. The deck is complete,

and there is exactly one of each card (4 suits with 13 cards in each

suit, and no jokers). You draw a card from this deck, then put the

card back, shuﬄe the deck several times, and then draw another

card. What is the probability that you’ll get the same card twice?

(a) 1/140,608

(b) 1/2704

(d) 1/13

(e) 1/4

18. What is the value of 3 þ 5  1

5

 7?

(a) The expression is ambiguous without parentheses telling us in

what order we should perform the operations.

(b) 56

(d) 3

(e) 1

Fig. Exam-2. Illustration for Final Exam Questions 15 and 16.

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