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

Branch | Air Force |

MOS | 3P031 |

Title | Security Forces |

Description | Leads, manages, supervises, and performs security force (SF) activities, including installation, weapon system, and resource security; antiterrorism; law enforcement and investigations; military working dog function; air base defense; armament and equipment; training; pass and registration; information security; and combat arms. Shredouts: A- Military Working Dog handler B- Combat Arms experience in leading and directing SF activities. Leads, manages, supervises, and performs force protection duties, including use of deadly force to protect personnel and resources. Protects nuclear and conventional weapons systems and other resources. Performs air base defense functions contributing to the force protection mission. Controls and secures terrain inside and outside military installations. Defends personnel, equipment, and resources from hostile forces. Operates in various field environments, performs individual, and team patrol movements, both mounted and dismounted, tactical drills, battle procedures, convoys, military operations other than war, antiterrorism duties, and other special duties. Operates communications equipment, vehicles, intrusion detection equipment, crew-served weapons, and other special purpose equipment. Applies self-aid buddy care, life saving procedures, including cardiopulmonary resuscitation, as first responder to accident and disaster scenes. 2.2. Provides armed response and controls entry. Detects and reports presence of unauthorized personnel and activities. Implements security reporting and alerting system. Enforces standards of conduct, discipline, and adherence to laws and directives. Directs vehicle and pedestrian traffic. Investigates motor vehicle accidents, minor crimes, and incidents. Operates speed measuring, drug and alcohol, and breath test devices. Apprehends and detains suspects. Searches persons and property. Secures crime and incident scenes. Collects, seizes, and preserves evidence. Conducts interviews of witnesses and suspects. Obtains statements and testifies in official judicial proceedings. Responds to disaster and relief operations. Participates in contingencies. 2.3. Develops plans, policies, procedures, and detailed instructions to implement SF programs. Plans, organizes, and schedules SF activities. Provides oversight, guidance, and assistance to commanders with the application of information, personnel, and industrial security programs. Operates pass and registration activities. Supervises and trains SF augmentees. Provides on-scene supervision for security forces. Inspects and evaluates effectiveness of SF personnel and activities. Analyzes reports and statistics. 2.4. Provides guidance on employment and utilization of military working dog teams. Ensures proficiency training and certification standards are maintained. Employs military working dogs to support worldwide security force operations and executive agency requirements. Ensures health and welfare of military working dogs. Trains handlers and military working dogs on all aspects of military working dog training. Acts as an intruder in dog bite and hold training. Reports and reacts to dog alerts. Maintains dog training and usage records. Responsible for storage, handling, and security of drug and explosive training aids. 2.5. Leads, manages, supervises, and implements ground weapons training programs. Operates SF armories. Controls and safeguards arms, ammunition, and equipment. Instructs ground weapons qualification training. Provides guidance on weapons placement to security forces and ground defense force commanders. Inspects ground weapons and replaces unserviceable parts. Analyzes malfunctions by inspection and serviceability testing. Uses precision gauges, testing instruments, and special tools to adjust parts and operating mechanisms. Function-fires weapons for accuracy and serviceability. Controls and operates firing ranges and associated facilities to include supervising construction and rehabilitation. experience in SF functions such as weaponry; controlling entry into and providing internal control within installations and restricted areas; response force tactics; air base defense concepts and procedures; terrorist threat response techniques; alarm monitor duties; control center duties; traffic control; patrolling; or accident investigation. Also, experience in functions such as SF weaponry, maintaining dog handling equipment, caring for and training military working dogs, and reacting to dog alerts. experience supervising or performing functions such as weapon systems and resource security, air base defense, law enforcement, military working dog functions, or combat arms functions. |

Subtests | Arithmetic Reasoning, Paragraph Comprehension, Word Knowledge |

- 13 Questions
- 54 Problems
- 36 Flash Cards

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

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.

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).

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, ...

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

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

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.

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).

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.

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.

An exponent (cb^{e}) 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 (b^{1} = b) and a base with an exponent of 0 equals 1 ( (b^{0} = 1).

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, 3x^{2} + 2x^{2} = 5x^{2} and 3x^{2} - 2x^{2} = x^{2} but x^{2} + x^{4} and x^{4} - x^{2} cannot be combined.

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, 3x^{2} x 2x^{2} = 6x^{4} and \({8x^5 \over 4x^2} \) = 2x^{(5-2)} = 2x^{3}.

To raise a term with an exponent to another exponent, retain the base and multiply the exponents: (x^{2})^{3} = x^{(2x3)} = x^{6}

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, \(3^{-2} = {1 \over 3^2} = {1 \over 9}\)

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**).

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, \(\sqrt{64} = \sqrt{16 \times 4} = \sqrt{4^2 \times 2^2} = 4 \times 2 = 8\).

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.

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

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, \(\sqrt{9 \over 16}\) = \({\sqrt{9}} \over {\sqrt{16}}\) = \({3 \over 4}\)

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 10^{4} 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}.

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.

Arithmetic operations must be performed in the following specific order:

**P**arentheses**E**xponents**M**ultiplication and**D**ivision (from L to R)**A**ddition and**S**ubtraction (from L to R)

The acronym **PEMDAS** can help remind you of the order.

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.

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, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

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 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.

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.

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

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

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 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.

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.