Algebra
Expressions498
Classifications
A monomial contains one term, a binomial contains two terms, and a polynomial contains more than two terms. Linear expressions have no exponents. A quadratic expression contains variables that are squared (raised to the exponent of 2).
Operations Involving Monomials
You can only add or subtract monomials that have the same variable and the same exponent. However, you can multiply and divide monomials with unlike terms.
Multiplying Binomials
To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses.
Factoring Quadratics
To factor a quadratic expression, apply the FOIL (First, Outside, Inside, Last) method in reverse.
Solving Equations292
One Variable
An equation is two expressions separated by an equal sign. The key to solving equations is to repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.
Two Variables
When solving an equation with two variables, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)
Two Equations
When presented with two equations with two variables, evaluate the first equation in terms of the variable you're not solving for then insert that value into the second equation. For example, if you have x and y as variables and you're solving for x, evaluate one equation in terms of y and insert that value into the second equation then solve it for x.
Quadratic Equations
When solving quadratic equations, if the equation is not set equal to zero, first manipulate the equation so that it is set equal to zero: ax2 + bx + c = 0. Then, factor the quadratic and, because it's set to zero, you know that one of the factors must equal zero for the equation to equal zero. Finding the value that will make each factor, i.e. (x + ?), equal to zero will give you the possible value(s) of x.
Inequalities
Solving equations with an inequality (<, >) uses the same process as solving equations with an equal sign. Isolate the variable that you're solving for on one wide of the equation and put everything else on the other side. The only difference is that your answer will be expressed as an inequality (x > 5) and not as an equality (x = 5).
Geometry
Lines & Angles5214
Line Segment
A line segment is a portion of a line with a measurable length. The midpoint of a line segment is the point exactly halfway between the endpoints. The midpoint bisects (cuts in half) the line segment.
Right Angle
A right angle measures 90 degrees and is the intersection of two perpendicular lines. In diagrams, a right angle is indicated by a small box completing a square with the perpendicular lines.
Acute & Obtuse Angles
An acute angle measures less than 90°. An obtuse angle measures more than 90°.
Angles Around Lines & Points
Angles around a line add up to 180°. Angles around a point add up to 360°. When two lines intersect, adjacent angles are supplementary (they add up to 180°) and angles across from either other are vertical (they're equal).
Parallel Lines
Parallel lines are lines that share the same slope (steepness) and therefore never intersect. A transversal occurs when a set of parallel lines are crossed by another line. All of the angles formed by a transversal are called interior angles and angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°) and are called corresponding angles. Alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°) and all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other. Same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°).
Polygons81016
Triangle Geometry
A triangle is a three-sided polygon. It has three interior angles that add up to 180° (a + b + c = 180°). An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite (d = b + c). The perimeter of a triangle is equal to the sum of the lengths of its three sides, the height of a triangle is equal to the length from the base to the opposite vertex (angle) and the area equals one-half triangle base x height: a = ½ base x height.
Triangle Classification
An isosceles triangle has two sides of equal length. An equilateral triangle has three sides of equal length. In a right triangle, two sides meet at a right angle.
Pythagorean Theorem
The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c2) is equal to the sum of the two perpendicular sides squared (a2 + b2): c2 = a2 + b2 or, solved for c, \(c = \sqrt{a + b}\)
Quadrilateral
A quadrilateral is a shape with four sides. The perimeter of a quadrilateral is the sum of the lengths of its four sides (a + b + c + d).
Rectangle & Square
A rectangle is a parallelogram containing four right angles. Opposite sides (a = c, b = d) are equal and the perimeter is the sum of the lengths of all sides (a + b + c + d) or, comonly, 2 x length x width. The area of a rectangle is length x width. A square is a rectangle with four equal length sides. The perimeter of a square is 4 x length of one side (4s) and the area is the length of one side squared (s2).
Parallelogram
A parallelogram is a quadrilateral with two sets of parallel sides. Opposite sides (a = c, b = d) and angles (red = red, blue = blue) are equal. The area of a parallelogram is base x height and the perimeter is the sum of the lengths of all sides (a + b + c + d).
Rhombus
A rhombus has four equal-length sides with opposite sides parallel to each other. The perimiter is the sum of the lengths of all sides (a + b + c + d) or, because all sides are the same length, 4 x length of one side (4s).
Trapezoid
A trapezoid is a quadrilateral with one set of parallel sides. The area of a trapezoid is one-half the sum of the lengths of the parallel sides multiplied by the height. In this diagram, that becomes ½(b + d)(h).
Circles528
Dimensions
A circle is a figure in which each point around its perimeter is an equal distance from the center. The radius of a circle is the distance between the center and any point along its perimeter (AC, CB, CD). A chord is a line segment that connects any two points along its perimeter (AB, AD, BD). The diameter of a circle is the length of a chord that passes through the center of the circle (AB) and equals twice the circle's radius (2r).
Calculations
The circumference of a circle is the distance around its perimeter and equals π (approx. 3.14159) x diameter: c = π d. The area of a circle is π x (radius)2 : a = π r2.
Solids245
Cubes
A cube is a rectangular solid box with a height (h), length (l), and width (w). The volume is h x l x w and the surface area is 2lw x 2wh + 2lh.
Cylinders
A cylinder is a solid figure with straight parallel sides and a circular or oval cross section with a radius (r) and a height (h). The volume of a cylinder is π r2h and the surface area is 2(π r2) + 2π rh.
Coordinate Geometry222
Coordinate Grid
The coordinate grid is composed of a horizontal x-axis and a vertical y-axis. The center of the grid, where the x-axis and y-axis meet, is called the origin.
Slope-Intercept Equation
A line on the coordinate grid can be defined by a slope-intercept equation: y = mx + b. For a given value of x, the value of y can be determined given the slope (m) and y-intercept (b) of the line. The slope of a line is change in y over change in x, \({\Delta y \over \Delta x}\), and the y-intercept is the y-coordinate where the line crosses the vertical y-axis.
FAQs
Is the Coast Guard ASVAB test hard? ›
The Coast Guard is the most challenging branch of the military to enter. A minimum ASVAB score of 36 is required to enlist.
What ASVAB score do you need for Coast Guard? ›What is the qualifying ASVAB score for the Coast Guard? In order to join the Coast Guard, you must achieve a minimum overall qualifying ASVAB score of 40 if you are a high school senior or have a high school diploma, and 50 if you are a GED holder.
How do you become a marine science technician in the Coast Guard? ›Prospective MSTs must meet Armed Services Vocational Aptitude Battery (ASVAB) score requirements of 114 in Verbal Ability plus Arithmetic Reasoning (VE+AR), and a minimum Mathematics Knowledge (MK) score of 56. Training for the rating is accomplished through a 12-week course at USCG Training Center Yorktown, VA.
What score on the ASVAB do I need to be in the Marines? ›The Armed Service Vocational Aptitude Battery (ASVAB) test is a multiple-choice test taken by all who aspire to become Marines. To pass the test, aspiring Marines must achieve a score of 31 or higher, and those with nontraditional degrees or a GED must score at least a 50.
How fast do you have to run a mile in the Coast Guard? ›| Event | Male | Female |
|---|---|---|
| Push-ups (60 sec) | 29 | 15 |
| Sit-ups (60 sec) | 38 | 32 |
| Run (1.5 mile) | 12:51 | 15.26 |
| Sit and reach* | 16.50 " | 19.29" |
Your AFQT score is very important.
This percentile is based on the number of questions that you answered correctly compared to others that have taken the ASVAB. If you receive a percentile score of 90, that simply means that you have scored as well or better than 90% of other test-takers.
With ASVAB Standard scores, the majority of students score between 30 and 70. This means that a standard score of 50 is an average score, and a score of 60 would be an above-average score.
Is Coast Guard the hardest bootcamp? ›While the Coast Guard might be considered the easiest military branch in terms of physical fitness, it is by far the hardest to join.
How many recruits fail Coast Guard boot camp? ›Every wet-behind-the-ears recruit is scared of failing Coast Guard Boot Camp – and for good reason – last I heard the attrition rate is over 10% nowadays. BUT that's not what this is about. That's just a harsh fact that you have to swallow.
How long is MST a school USCG? ›Marine Science Technician "A" (MST) Course
The course is 9 weeks long and is open to qualified active and reserve enlisted personnel. The training topics covered include Pollution Investigation, Pollution Response, Occupational Safety and Health, Facility Inspections and Vessel Boardings.
Is marine technician a good career? ›
Is a boat mechanic a good career? Boat mechanics and service technicians can get many job roles with excellent prospects of a high salary. Along with decent wages, boat mechanics have immense growth and learning opportunities. Earn your degree in marine tech from NEIT and begin your new career path today!
What is a Marines salary? ›While ZipRecruiter is seeing annual salaries as high as $121,500 and as low as $11,500, the majority of salaries within the Marine Corps jobs category currently range between $37,500 (25th percentile) to $73,000 (75th percentile) with top earners (90th percentile) making $104,000 annually across the United States.
Which branch has the easiest ASVAB? ›At the ASVAB stage, the easiest military branch to join is the Army or Air Force. At the basic training stage, the easiest military branch to join is the Air Force.
What is the hardest part of the ASVAB? ›According to recent research, the mathematics knowledge test is considered to be the hardest ASVAB subtest. To get a well understanding as well as tips and tricks to get the highest ASVAB Scores in this section, read more information on our free ASVAB Math study guide!
What percent of recruits fail basic training? ›Yes, it is possible to fail basic training. You could go through the trouble of leaving your home, job, family and friends and come back a failure. In fact, this happens to about 15% of recruits who join the military every year.
Can you have your phone in Coast Guard boot camp? ›Family Communication During Coast Guard Boot Camp
You are allowed to bring your cell phone, but you may not receive or make personal phone calls for granted liberty on Sunday of the final two weeks of training. Any future phone calls you make while in boot camp will be at the discretion of your Company Commander.
TWO- “At least your spouse gets ?to come home every night.” The reality is that Coast Guard missions are often away from home. CG members do not get to go home every night. Depending on their unit, they may be gone from a couple of days to upwards of a year.
Is a 70% good on the practice ASVAB? ›With ASVAB Standard scores, the majority of students score between 30 and 70. This means that a standard score of 50 is an average score, and a score of 60 would be an above-average score.
How far in advance should I study for the ASVAB? ›To study effectively for the ASVAB, you really need to begin studying at least two months before you plan to take the test, if not more! Here are some basic steps to take: Find a comfortable, quiet area to study. Gather paper, pens and pencils, a calculator and other tools.
How likely is it to fail the ASVAB? ›There is no pass or fail on the ASVAB. You cannot "ace" the ASVAB or "flunk" it! Your scores reflect your own abilities! You will want to do your best so that you will be eligible for the military skill specialty that matches your ability and interests.
What is the easiest way to pass the ASVAB test? ›
The easiest way to pass the ASVAB is by taking practice exams. You can use these practice exams to become more familiar with the exam in terms of content, topics, and the timing aspect. You can use the practice exams to narrow down the subjects you need the most help in.
How many questions can I miss on the ASVAB? ›You will not be penalized for incorrect answers, but you will be penalized for questions that are left blank, as these will count as incorrect answers. Each question is 1 point, so if you leave 15 questions blank, you will automatically reduce your ASVAB score to 85.
What parts of the ASVAB matter the most? ›Four of these sections- Arithmetic Reasoning, Mathematics Knowledge, Paragraph Comprehension, and Word Knowledge- make up your AFQT score. This score is the most important as it determines if you can enlist in the military at all.
What is the easiest military branch? ›The Air Force is reported to be the “easiest” branch when it comes to physical challenges and difficulties. Next to the Coast Guard, Air Force members are among the least likely to see combat. Deployments in the Air Force are not as common as the Army, Navy, or Marine Corps, and they are generally shorter in duration.
What branch has hardest boot camp? ›The military branch with the toughest basic training is the Marine Corps. The hardest military branch for non-males because of exclusivity and male dominance is the Marine Corps.
Is the Navy or Coast Guard harder? ›Navy probably trains harder only because Coast Guard doesn't have as much time to train. CG is involved in a ton a search and rescue as well as law enforcement. They are the basically the national fire and police of the waterways. Navy serves a different purpose as they are national defense.
What happens if you cry during basic training? ›With all the pressure that comes with boot camp, it's no wonder people cry. Crying isn't looked at as a bad thing, though some drill instructors give the recruit grief if they think he's just feeling sorry for himself. But in most cases, you are not considered less of a marine if you cry.
Can a drill sergeant hit you? ›The military's drill sergeants and instructors are prohibited from hitting their recruits.
Where is MST stationed? ›MSTs are stationed at Sectors, and Marine Safety Units and Detachments.
Is MST secondary to PTSD? ›Posttraumatic stress disorder (PTSD) is one of the most common mental health diagnoses among MST survivors. Other mental health diagnoses that are frequently related to MST include depression and other mood disorders and substance use disorders.
What is the hardest marine job? ›
One of the military's most dangerous jobs is explosive ordnance disposal technician. These troops risk life and limb responding to IEDs and other explosive threats. Two seasoned Marine Corps EOD techs recently told Insider about the challenges of the job.
How long does it take to be a marine technician? ›How Long Does It Take to Become a Marine Mechanic? Once you graduate high school, completing a certificate course will require about one year, while an associate's degree can take up to two years. Apprenticeship programs for marine mechanics can span over four years.
What does a marine science technician do in the Coast Guard? ›Coast Guard: Marine Science Technician
From protecting U.S. waters and the public from oil and hazardous material responses to conducting safety and security inspections, an MST plays the essential role of enforcing regulations for the safety of the marine environment and the security of the port.
Our current retirement system consists of a 20 year cliff vested annuity (a defined benefit plan). This means that if you enter the Marine Corps and serve for at least 20 years, you will earn a monthly retirement annuity for the remainder of your life.
What rank do most Marines retire at? ›...
O-5 Lieutenant Colonel - U.S. Marine Corps Ranks.
| Class | Field Officer |
|---|---|
| Basic Pay | $6,112/mo |
There is no military spouse pay or stipend, but the military offers a number of benefits to help service members and their families. Your first stop after the wedding should be the nearest military ID card issuing facility to enroll in DEERS, the Defense Enrollment Eligibility Reporting System.
Who fights more Army or Marines? ›The Army has a force of roughly 500,00 active duty Soldiers, while the active duty Marine Corps is under 200,000. . The Army is composed of multiple subgroups, including the Infantry, Special Forces and the Army Rangers.
Is the Coast Guard hard to get into? ›The acceptance rate at United States Coast Guard Academy is 14.2%. For every 100 applicants, only 14 are admitted. This means the school is extremely selective. Meeting their GPA requirements and SAT/ACT requirements is very important to getting past their first round of filters and proving your academic preparation.
What branch needs the highest ASVAB score? ›To join the Air Force as an enlisted member, you must get a decent score on the Armed Services Vocational Aptitude Battery (ASVAB) test. In fact, the Air Force requires the highest score of any branch of the service for admission. Jobs in the Air Force are called Air Force Specialty Code (AFSC).
How many times can you fail the ASVAB? ›Retest Policy
If you take the test once and don't do well, you can retake it after just one month. If you fail to perform well on this second attempt, you can retake it again after another month. Your fourth attempt, and any subsequent attempt, requires a six-month wait from the previous test.
What is the best study material for the ASVAB? ›
- Mometrix ASVAB Study Guide 2021-2022: ASVAB Test Prep Secrets (5th Edition) ...
- Kaplan ASVAB Prep Plus 2022–2023. ...
- Kaplan ASVAB Total Prep 2022–2023. ...
- 2021/2022 ASVAB For Dummies. ...
- Newstone Test Prep ASVAB Exam Prep 2021-2022.
What kind of math is on the ASVAB? There are two ASVAB math tests: Arithmetic Reasoning and Math Knowledge. The Arithmetic Reasoning test covers word problems that involve arithmetic. The Math Knowledge test covers high school math skills.
What if I don't score high enough on the ASVAB? ›The Army will allow a retest only if the applicant's previous ASVAB test has expired, or the applicant failed to achieve an AFQT score high enough to qualify for enlistment, or when unusual circumstances occur, such as if an applicant, through no fault of their own, is unable to complete the test.
What job can you get with a 31 on the ASVAB? ›To join the Army as an enlisted member, you usually must take the Armed Services Vocational Aptitude Battery (ASVAB) test and get a good score. The maximum ASVAB score is 99. For enlistment into the Army, you must get a minimum ASVAB score of 31.
Is Coast Guard the hardest to get into? ›The Coast Guard is one of the more difficult branches to join because it accepts far fewer new recruits than the other branches of the military, and qualifying requirements are strict. In addition to basic citizenship and physical fitness prerequisites, the Coast Guard sets academic standards as will.
What is the hardest ASVAB test? ›According to recent research, the mathematics knowledge test is considered to be the hardest ASVAB subtest. To get a well understanding as well as tips and tricks to get the highest ASVAB Scores in this section, read more information on our free ASVAB Math study guide!
Is Coast Guard basic hard? ›As with any military service, your journey begins at basic training. Basic training is tough. You'll be challenged every day, both mentally and physically. You'll be pushed, tested and worked harder than you ever thought possible.
What is the failure rate of Coast Guard boot camp? ›Every wet-behind-the-ears recruit is scared of failing Coast Guard Boot Camp – and for good reason – last I heard the attrition rate is over 10% nowadays.
What is the most elite Coast Guard unit? ›Maritime Security Response Teams (Coast Guard)
The MSRTs are the Coast Guard's elite. They specialize in maritime counterterrorism and high-risk maritime law enforcement. Like Navy SEALs, they also excel at Visit, Board, Search, and Seizure (VBSS) operations and often deploy outside the US.
At the ASVAB stage, the easiest military branch to join is the Army or Air Force. At the basic training stage, the easiest military branch to join is the Air Force.
What's the lowest ASVAB score ever? ›
An AFQT score is a percentile score. This means a person can receive a score from 0-99, and the score means "You have scored higher than X% of test takers". The lowest score a person can get is 0 - they did not score higher than anyone on the grading curve.
What is the safest branch of the military? ›Today's article will look at “safety” in terms of man-to-man combat and machine-to-machine accidents and give you this answer: THE SPACE FORCE is the safest military branch. But, since there are different jobs within a branch, it is also worth considering the degree of safety at the job level.
What GPA do you need for Coast Guard? ›Average GPA: 3.81
With a GPA of 3.81, United States Coast Guard Academy requires you to be near the top of your class, and well above average. You'll need mostly A's, ideally with several AP or IB classes to help show your preparation at a college level.
Counting the half-week you spend in forming (in-processing), you'll spend a total of seven-and-a-half weeks in Coast Guard basic training at Cape May, (N.J.,) the shortest basic training of all the services.