W/L Ch 12 Applied Math Review Quiz

Question 1

Simplify 5x^4 * x.

a. 6x^4
b. 5x^5
c. 5x^3
d. Already simplified

Answer 1

b. 5x^5

x is essentially x^1; therefore the exponent for x is 1 + 4 = 5.

Question 2

Simplify (a^2)^5.

a. a^10
b. a^7
c. a^32
d. a^25

Answer 2

a. a^10

The exponents 2 and 5 are multiplied, resulting in an exponent of 10.

Question 3

Simplify 5(3b)^2.

a. 15b^2
b. 5(9b^2)
c. 45b^2
d. Already simplified

Answer 3

c. 45b^2

Both 3 and b are squared, resulting in 9b^2. Then 5 and 9 are multiplied to result in 45b^2.

Question 4

Solve for x in the equation 4x – 4 = 12.

a. 6
b. ±6
c. 4
d. ±4

Answer 4

c. 4

4x – 4 = 12
+4 = +4

4x = 16
x = 4

Question 5

Solve for x in the equation x^2 – 1 = 0.

a. 0
b. 1
c. –1
d. ±1

Answer 5

d. ±1

Both sides add 1, resulting in x^2 = 1. Then both sides are square rooted to leave x = ±1.

Question 6

Solve for x in the equation 4(x + 6) = 6x – 16.

a. 1.6
b. 3.2
c. 4
d. 12

Answer 6

c. 4

Question 7

Solve for x in the equation x^8/x^6 = 100.

a. –10
b. ±10
c. 10
d. 1

Answer 7

c. 10

The exponent 8 is subtracted from the exponent 6, resulting in x^2 = 100. The square root of both sides is taken, leaving x = 10.

Question 8

Find the log of log453.

a. 2.656
b. 6.116
c. –19.08
d. 8.752

Answer 8

a. 2.656

log453
or
raise 10^ by answers to see which one gives you 453 in this case

The logarithm of a number to a given base is the power or exponent to which the base must be raised in order to produce the number.

Question 9

Express log10 100 = 2 in exponential notation.

a. 1.0 x 10^2
b. 10^2 = 100
c. 2^10 = 100
d. 10 = v100

Answer 9

b. 10^2 = 100
In mathematical notation, the logarithm is written logb(N) = x, where b is the base, N is the desired product, and x is the power. In exponential notation, this is written bx = N.

Question 10

Express log2 16 = 4 in exponential notation.

a. 4 = v16
b. 4^2 = 16
c. 1.6 = 10^2
d. 2^4 = 16

Answer 10

d. 2^4 = 16

Question 11

Convert 8.25 R into the SI unit of exposure.

a. 3.20 x 10^3 C/kg
b. 3.20 x 10^4 C/kg
c. 2.13 x 10^–3 C/kg
d. 2.13 x 10^–4 C/kg

Answer 11

c. 2.13 x 10^–3 C/kg

The roentgen (R) is the unit of radiation exposure that represents a measure of the amount of ionization created by radiation in the air. A derived unit for exposure is the coulomb/kilogram (C/kg). Thus, the relationship between these two quantities is 1 roentgen = 2.58 x 10^–4 C/kg.

?

Question 12

Convert 2 Gy into rad.

a. 2 rad
b. 20 rad
c. 200 rad
d. 2000 rad

Answer 12

c. 200 rad

A rad is equal to 0.01 gray or, restated, 100 rads equals 1 gray (Gy). Therefore, 1 rad equals 1 centigray (cGy).

Question 13

Which of the following is an example of a random error?

a. Inaccuracies in the laser positioning system
b. Patient movement
c. Human error
d. Difference in cushioning capacity of couch materials between simulator and treatment table

Answer 13

b. Patient movement

An uncontrolled rapid change in temperature or barometric pressure, accidental movement of a patient during setup, and electronic noise are all examples of random errors.

Question 14

Express 10^3 in scientific notation.

a. 10^3
b. 1 x 10^3
c. 1000
d. log 1000 = 3

Answer 14

b. 1 x 10^3

Numbers written in scientific notation are written in the following form: n.nnn x 10^p, where n.nnn indicates the first four numerical values of the specified number. The power to which the base of 10 is raised (p) depends on the size of the specified number.

Question 15

Express 8.333 in scientific notation.

a. 8.333 x 10^–1
b. 8.333 x 10^1
c. 8.333 x 10^0
d. Cannot be written in scientific notation

Answer 15

c. 8.333 x 10^0

Question 16

Which of the following is not a fundamental SI unit?

a. Time
b. Distance
c. Weight
d. Electrical current

Answer 16

c. Weight

The metric system is based on fundamental units of time, distance, mass, and electrical current.

Question 17

Transposition of numbers in a patient’s chart is an example of which type of error?

a. Systematic
b. Random
c. Blunder
d. None of the above

Answer 17

c. Blunder

Question 18

How many significant figures are there in 0.0068?

a. Two
b. Three
c. Four
d. Five

Answer 18

a. Two

Question 19

How many significant figures are there in 6,800?

a. Two
b. Three
c. Four
d. Unable to determine

Answer 19

d. Unable to determine

When a number ends in zeroes that are not to the right of a decimal point, the zeroes are not necessarily significant: 190 miles may have two or three significant figures, 5,040 cGy may have three or four significant figures.

Question 20

The relationship between distance and radiation dose follows which of the following?

a. Direct proportionality
b. Indirect proportionality
c. Inverse proportionality
d. Linear interpolation

Answer 20

c. Inverse proportionality

Question 21

Which of the following numeric expressions is written in scientific notation?

a. 8.333 x 10^4
b. 83.33 x 10^3
c. 833.3 x 10^2
d. 8333 x 10^1

Answer 21

a. 8.333 x 10^4

Question 22

Which of the following numeric expressions is written in scientific notation?

a. 1222 x 10^1
b. 122.2 x 10^2
c. 12.22 x 10^3
d. 1.222 x 10^4

Answer 22

d. 1.222 x 106^4