# Air Force 4R031 Diagnostic Imaging ASVAB Study Guide

 Branch Air Force MOS 4R031 Title Diagnostic Imaging Description Operates equipment to produce diagnostic images and assists radiologist or physician with special procedures. Prepares equipment and patients for diagnostic studies and therapeutic procedures. Performs technical and administrative radiology activities. Ensures health protective measures such as universal precautions and radiation protection measures are established and employed. Assists the radiation oncologist. Manages diagnostic imaging functions and activities.Experience operating x-ray equipment, and producing and processing radiographs.experience managing radiologic, nuclear medicine, ultrasound, or MRI functions and activities.Operates fixed and portable radiographic equipment to produce routine diagnostic medical images. Computes techniques and adjusts control panel settings such as kilovoltage, milliamperage, exposure time, and focal spot size. Positions patient to image desired anatomic structures. Selects image recording media, adjusts table or cassette holder, aligns x-ray tube for correct distance and angle, and restricts radiation beam for maximum patient protection. Exposes and processes images. Uses specialized equipment to perform nuclear medicine, mammography, ultrasound, computerized tomography, and magnetic resonance imaging. Selects imaging protocols and required accessories, and makes adjustments based on the specific examination requirements. Records and processes the image. Manipulates the recorded image using computer applications. Assists physicians with fluoroscopic, interventional, and special examinations. Instructs patients preparing for procedures. Prepares and assists with contrast media administration. Maintains emergency response cart. Assists physician in treating reactions to contrast material. Prepares sterile supplies and equipment. Operates accessory equipment such as automatic pressure injectors, serial film changers and digital imagers, stereotactic biopsy devices, and vital signs monitoring equipment. Performs image subtraction and manipulation techniques. Assists radiation oncologist in radiation treatment of disease. Operates treatment simulator. Constructs custom blocks and compensating filters. Uses electromagnetic and radioactive-source radiations in treating disease. Prepares and positions patients and equipment for, and delivers therapeutic and palliative radiation treatments. Sets and verifies dosage settings on equipment. Monitors patients during treatment activities. Documents patient treatment record. Performs and supervises general diagnostic imaging activities. Mixes film processing solutions, loads and unloads film holders, and reproduces images. Cleans and inspects equipment and performs preventive maintenance. Receives patients, schedules appointments, prepares and processes examination requests and related records, and files images and reports. Enters and maintains data in radiology information systems. Assists with phase II didactic and performance training, evaluation and counseling of students, and maintenance of student academic records. Participates in formal research projects. Establishes and maintains standards, guidelines, and practices. Composes protocols. Prepares routine positioning guides and technique charts. Reviews images to ensure quality standards are met. Performs equipment quality control checks such as processor sensitometry, film-screen contact tests, collimation and light field alignment tests, and safelight fog tests. Monitors personnel to ensure protective procedures such as those in the As Low As Reasonably Achievable (ALARA) radiation safety, hazardous material communications, and Air Force occupational safety and health programs are followed. Performs tests on radiation protection equipment. Assesses staff competence, and monitors appropriateness of care and completeness of examination requests. Subtests Arithmetic Reasoning, Paragraph Comprehension, Word Knowledge

# Arithmetic Reasoning

• 13 Questions
• 54 Problems
• 36 Flash Cards

### Fundamentals

##### Number Properties
###### Integers

An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.

###### Rational Numbers

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form $${a \over b}$$ where a is the numerator and b is the denominator. An improper fraction ($${5 \over 3}$$) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number ($$1 {2 \over 3}$$) which has a whole number part and a fractional part.

###### Absolute Value

The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: $$\left|-5\right| = 5$$. In the case of a variable absolute value ($$\left|a\right| = 5$$) the value of a can be either positive or negative (a = -5 or a = 5).

###### Factors & Multiples

A factor is a positive integer that divides evenly into a given number. The factors of 8 are 1, 2, 4, and 8. A multiple is a number that is the product of that number and an integer. The multiples of 8 are 0, 8, 16, 24, ...

###### Greatest Common Factor

The greatest common factor (GCF) is the greatest factor that divides two integers.

###### Least Common Multiple

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.

###### Prime Number

A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.

##### Operations on Fractions
###### Simplifying Fractions

Fractions are generally presented with the numerator and denominator as small as is possible meaning there is no number, except one, that can be divided evenly into both the numerator and the denominator. To reduce a fraction to lowest terms, divide the numerator and denominator by their greatest common factor (GCF).

###### Adding & Subtracting Fractions

Fractions must share a common denominator in order to be added or subtracted. The common denominator is the least common multiple of all the denominators.

###### Multiplying & Dividing Fractions

To multiply fractions, multiply the numerators together and then multiply the denominators together. To divide fractions, invert the second fraction (get the reciprocal) and multiply it by the first.

##### Operations on Exponents
###### Defining Exponents

An exponent (cbe) consists of coefficient (c) and a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b1 = b) and a base with an exponent of 0 equals 1 ( (b0 = 1).

###### Adding & Subtracting Exponents

To add or subtract terms with exponents, both the base and the exponent must be the same. If the base and the exponent are the same, add or subtract the coefficients and retain the base and exponent. For example, 3x2 + 2x2 = 5x2 and 3x2 - 2x2 = x2 but x2 + x4 and x4 - x2 cannot be combined.

###### Multiplying & Dividing Exponents

To multiply terms with the same base, multiply the coefficients and add the exponents. To divide terms with the same base, divide the coefficients and subtract the exponents. For example, 3x2 x 2x2 = 6x4 and $${8x^5 \over 4x^2}$$ = 2x(5-2) = 2x3.

###### Exponent to a Power

To raise a term with an exponent to another exponent, retain the base and multiply the exponents: (x2)3 = x(2x3) = x6

###### Negative Exponent

A negative exponent indicates the number of times that the base is divided by itself. To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal: $$b^{-e} = { 1 \over b^e }$$. For example, $$3^{-2} = {1 \over 3^2} = {1 \over 9}$$

##### Operations on Radicals
###### Defining Radicals

Radicals (or roots) are the opposite operation of applying exponents. With exponents, you're multiplying a base by itself some number of times while with roots you're dividing the base by itself some number of times. A radical term looks like $$\sqrt[d]{r}$$ and consists of a radicand (r) and a degree (d). The degree is the number of times the radicand is divided by itself. If no degree is specified, the degree defaults to 2 (a square root).

###### Simplifying Radicals

The radicand of a simplified radical has no perfect square factors. A perfect square is the product of a number multiplied by itself (squared). To simplify a radical, factor out the perfect squares by recognizing that $$\sqrt{a^2} = a$$. For example, $$\sqrt{64} = \sqrt{16 \times 4} = \sqrt{4^2 \times 2^2} = 4 \times 2 = 8$$.

###### Adding & Subtracting Radicals

To add or subtract radicals, the degree and radicand must be the same. For example, $$2\sqrt{3} + 3\sqrt{3} = 5\sqrt{3}$$ but $$2\sqrt{2} + 2\sqrt{3}$$ cannot be added because they have different radicands.

###### Multiplying & Dividing Radicals

To multiply or divide radicals, multiply or divide the coefficients and radicands separately: $$x\sqrt{a} \times y\sqrt{b} = xy\sqrt{ab}$$ and $${x\sqrt{a} \over y\sqrt{b}} = {x \over y}\sqrt{a \over b}$$

###### Square Root of a Fraction

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately. For example, $$\sqrt{9 \over 16}$$ = $${\sqrt{9}} \over {\sqrt{16}}$$ = $${3 \over 4}$$

##### Miscellaneous
###### Scientific Notation

Scientific notation is a method of writing very small or very large numbers. The first part will be a number between one and ten (typically a decimal) and the second part will be a power of 10. For example, 98,760 in scientific notation is 9.876 x 104 with the 4 indicating the number of places the decimal point was moved to the left. A power of 10 with a negative exponent indicates that the decimal point was moved to the right. For example, 0.0123 in scientific notation is 1.23 x 10-2.

###### Factorials

A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

### Applications

##### Order of Operations
###### PEMDAS

Arithmetic operations must be performed in the following specific order:

1. Parentheses
2. Exponents
3. Multiplication and Division (from L to R)
4. Addition and Subtraction (from L to R)

The acronym PEMDAS can help remind you of the order.

###### Distributive Property - Multiplication

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

###### Distributive Property - Division

The distributive property for division helps in solving expressions like $${b + c \over a}$$. It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: $${b + c \over a} = {b \over a} + {c \over a}$$. For example, $${a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6$$.

###### Commutative Property

The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.

##### Ratios
###### Ratios

Ratios relate one quantity to another and are presented using a colon or as a fraction. For example, 2:3 or $${2 \over 3}$$ would be the ratio of red to green marbles if a jar contained two red marbles for every three green marbles.

###### Proportions

A proportion is a statement that two ratios are equal: a:b = c:d, $${a \over b} = {c \over d}$$. To solve proportions with a variable term, cross-multiply: $${a \over 8} = {3 \over 6}$$, 6a = 24, a = 4.

###### Rates

A rate is a ratio that compares two related quantities. Common rates are speed = $${distance \over time}$$, flow = $${amount \over time}$$, and defect = $${errors \over units}$$.

###### Percentages

Percentages are ratios of an amount compared to 100. The percent change of an old to new value is equal to 100% x $${ new - old \over old }$$.

##### Statistics
###### Averages

The average (or mean) of a group of terms is the sum of the terms divided by the number of terms. Average = $${a_1 + a_2 + ... + a_n \over n}$$

###### Sequence

A sequence is a group of ordered numbers. An arithmetic sequence is a sequence in which each successive number is equal to the number before it plus some constant number.

###### Probability

Probability is the numerical likelihood that a specific outcome will occur. Probability = $${ \text{outcomes of interest} \over \text{possible outcomes}}$$. To find the probability that two events will occur, find the probability of each and multiply them together.

##### Word Problems
###### Practice

Many of the arithmetic reasoning problems on the ASVAB will be in the form of word problems that will test not only the concepts in this study guide but those in Math Knowledge as well. Practice these word problems to get comfortable with translating the text into math equations and then solving those equations.