# Air Force 1C231 Combat Control ASVAB Study Guide

 Branch Air Force MOS 1C231 Title Combat Control Description Provides command, control, communications, intelligence, surveillance and reconnaissance (C3ISR) to assist, control and enable the application of manned and unmanned, lethal and non-lethal airpower in all geographic and environmental conditions across the full spectrum of military operations. Includes terminal control (air traffic control [ATC]) and targeting, and control of air strikes (including close air support [CAS]) and use of visual and electronic aids to control airheads and enable precision navigation. Provides long-range voice and data command and control and communications. Performs tactical level surveillance and reconnaissance functions, fusing organic and remote controlled technologies and manned platforms to build the common operating picture (COP).experience in reconnaissance, terminal control, and combat enabling tasks. Also, experience performing or supervising duties involving reconnaissance, and terminal control and enabling tasks.Plans, coordinates, and conducts reconnaissance and surveillance of potential assault zones, targets and areas of interest. Operates advanced technologies, including ground based sensors and unmanned aerial systems (UAS) to support reconnaissance and target identification. Surveys runways, assault zones (drop, landing, forward area refueling points [FARP]) and other areas critical to aviation and records data for inclusion in mission plans. Reports current battlefield information. Plans, organizes, supervises, and establishes ATC in the target area. Initiates, coordinates, and issues ATC clearances, holding instructions, and advisories to maintain aircraft separation and promote safe, orderly, and expeditious flow of traffic under visual and conventional approach control flight rules. Operates and monitors portable and mobile communications equipment and terminal and tactical navigational aids required to control and support air traffic in forward areas. Evaluates and relays status of airfields and assault zones to inbound aircraft and higher headquarters. Provides limited weather observations, including surface and altitude wind data, temperature, and cloud heights. Prepares and issues advisories to pilots, ATC and other agencies concerning weather, notice-to-airmen information, air traffic flow control measures, and wake turbulence. Provides flight assistance and emergency service to air traffic. Records weather and ATC data. Controls vehicular traffic on the airport movement area. Identifies, assesses, and marks assault zones with visual and electronic navigational aids for day and night air-land and airdrop operations. Coordinates clearances, instructions, advisories, and air traffic movement with forward and rear area commanders. Uses ground-to-air communications equipment in conjunction with visual and electronic systems to control and expedite the movement of en route, arriving, and departing air traffic. Directs actions to handle aircraft emergencies or mishaps. Coordinates casualty and patient evacuation between aviation and medical personnel. Provides airlift operations support that cannot be provided by combat communications groups or other agencies. Operates global positioning systems (GPS) equipment for targeting, navigation, and for the location, assessment and establishment of assault zones. Coordinates airfield ground support (crash/fire/rescue, sweep). Targets and controls fires. Plans, coordinates, and conducts fires to accomplish supported commander objectives. Includes CAS and supporting arms for surface elements and C3ISR in support of combined forces air component commander (CFACC) assets. Employs visual and electronic navigation and marking equipment to direct aviation assets to target. Issues weapons release clearance. Deploys into semi- and non-permissive forward areas and forward operating locations by land (mounted, special purpose vehicle or dismounted), sea (surface or subsurface naval vessel, small watercraft, self contained underwater breathing apparatus [SCUBA], or surface swim) or air (parachute, airmobile, air-land) to participate in the full spectrum of military operations to include air expeditionary force (AEF), force projection, direct action (DA), counterterrorism (CT), counter-proliferation (CP), foreign internal defense (FID), humanitarian assistance (HA), special reconnaissance (SR), personnel recovery (PR), noncombatant evacuation operations (NEO), integrated survey program (ISP), counter narcotic (CN), operational preparation of the environment (OPE), advanced force operations (AFO) and fire support operations. Uses demolitions to remove obstacles affecting safe air traffic flow in the target area. Maintains qualification on primary assigned weapons.Experience managing operations involving reconnaissance, and terminal control and combat control enabling tasks. 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).

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).

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

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 $${x\sqrt{a} \over y\sqrt{b}} = {x \over y}\sqrt{a \over b}$$

###### 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.