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ASVAB-Mathematics-Knowledge ASVAB Section 6 : Mathematics Knowledge Study Guide |

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Exam Code: ASVAB-Mathematics-Knowledge ASVAB Section 6 : Mathematics Knowledge Study Guide January 2024 by team
ASVAB Section 6 : Mathematics Knowledge
Military Mathematics Study Guide

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ASVAB-Mathematics-Knowledge ASVAB Section 6 : Mathematics Knowledge
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ASVAB Section 6 : Mathematics Knowledge
Question: 223
What’s the mode of the following series of numbers?
4, 4, 8, 8, 8, 10, 10, 12, 12
A. 9
B. 8
C. 11
D. 10
Answer: B
The mode of a series of numbers is the number that appears in the series the most frequently. In this case, it’s 8.
Question: 224
If a = 4, then a3 ÷ a = __________.
A. 4
B. 12
C. 64
D. 16
Answer: D
(4 × 4 × 4) ÷ 4 = 64 ÷ 4 = 16
Question: 225
Which of the following is a prime number?
A. 27
B. 11
C. 8
D. 4
Answer: B
A prime number is a number that can be divided evenly by itself or by one, but not by any other number. Choices
27, 8 and 4 can all be divided evenly by other numbers.
Question: 226
(x + 4)(x + 2) =
A. x2 + 6x + 6
B. x2 + 8x + 8
C. x2 + 8x + 6
D. x2 + 6x + 8
Answer: D
Multiply the first variable in the first set of parentheses with the first variable in the second set of parentheses (x × x = x2).
Next, multiply the first variable in the first set of parentheses with the second number in the second set of parentheses (x × 2 = 2x). So far, the
results are x2+ 2x.
Now, multiply the second number in the first set of parentheses to the first variable in the second set of parentheses (4 × x = 4x).
Next, multiply the second variable in the first set of parentheses to the second number in the second set of parentheses (4 × 2 = 8). The solution is
x2+ 2x + 4x + 8. Combining the like terms results in x2+ 6x + 8.
Question: 227
1.5 × 103= __________.
A. 45
B. 150
C. 1,500
D. 15
Answer: C
1.5 × 103= 1.5 × (10 × 10 × 10) = 1.5 × 1,000 = 1,500.
Question: 228
(12 yards + 14 feet) ÷ 5 =
A. 12 feet
B. 51/5 feet
C. 10 feet
D. 21/2 yards
Answer: C
Convert 12 yards and 14 feet to feet:
(12 yards × 3 feet per yard) + 14 feet = 36 feet + 14 feet = 50 feet. Divide by 5 as instructed: 50 feet ÷ 5 = 10 feet.
Question: 229
x3 × x4 = __________.
A. x12
B. 2×7
C. 2×12
D. x7
Answer: D
If two powers have the same base, they can be multiplied by keeping the base and adding the powers together.
Question: 230
The fourth root of 16 is __________.
A. 4
B. 1
C. 3
D. 2
Answer: D
24 = 16; the fourth root of 16 is 2.
Question: 231
What’s the equation of a line that passes through points (0, – 1) and (2, 3)?
A. y = 2x – 1
B. y = 2x + 1
C. x = 2y – 1
D. x = 2y + 1
Answer: A
The slope of the line is equal to the change in y values divided by the change in x values. The change in y values is 4(3 – -1). The change in x
values is 2 (2 – 0). 4/2 = 2.
To find the intercept, substitute 0 for x in the equation y = 2x + b – 1 = 2(0) + b. Therefore, b = -1, so the equation is y = 2x – 1.
Question: 232
The cube of 5 is __________.
A. 125
B. 25
C. 15
D. 50
Answer: A
The cube of 5 = 5 × 5 × 5 = 125.
Question: 233
2.5 × 33 = __________.
A. 22.5
B. 75.0
C. 67.5
D. 675.0
Answer: C
2.5 × 33= 2.5 (3 × 3 × 3) = 2.5 × 27 = 67.50.
Question: 234
If x = 8, what’s the value of y in the equation: y = (x2 ÷ 4) – 2?
A. 1
B. 1
C. 1
D. 2
Answer: A
Explanation: y = (x2 ÷ 4)
– 2 y = (82 ÷ 4) – 2 y = (64
÷ 4) – 2 y = 16 – 2 = 14
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Military Mathematics Study Guide - BingNews Search results Military Mathematics Study Guide - BingNews Mathematics study guide 2023/24

Mathematics at Bristol

We provide a range of high quality teaching programmes. Our graduates go on to work in a wide variety of jobs in financial services, government statistical and security services, engineering and management consultancy, IT, accountancy, teaching and also in areas such as law, community work, sports coaching, civil service and filmmaking. All our academic staff are active in research, and we are one of the strongest mathematics schools in Europe in terms of research, as well as one of the top 5 mathematics departments in the UK (REF 2021). Our research is divided into five institutes: Applied Mathematics, Pure Mathematics, Mathematical Physics, Statistical Science and Probability, Analysis and Dynamics. We work with colleagues across philosophy and social sciences to physics, biology and medicine and collaborate with industry through both short and long-term research consultancies. Recent examples include Hewlett Packard, QinetiQ, LV, the Office for National Statistics and GSK.

Unit structure

The school offers many classes that are based in a single semester, and can therefore accept unit requests from Study Abroad students who want to join Bristol for just the autumn or spring semester.

Unit levels

The school offers units across all undergraduate levels of study – Year 1 (Level C/4), Year 2 (Level I/5), and Year 3 (Level H/6) – and selected postgraduate units (Level M/7). Level M/7 units are normally taken by students who have studied the subject for at least 3 years beforehand and are at an appropriate level of study to take postgraduate units.

Unit codes

Unit codes in the School of Mathematics begin with 'MATH'. This is followed by a number indicating the year (1, 2, 3). For example:

  • MATH10000 = year 1 unit
  • MATH20000 = year 2 unit
  • MATH30000 = year 3 unit.

For more information about each unit, check the University's unit catalogue for 2023/24. Applicants on all study abroad programmes must review the unit details on the catalogue before listing unit choices on their application form. This includes checking the format of assessment for each unit. The unit catalogue for 2023/24 is updated by April 2023.

Your unit choices cannot be guaranteed. Some units may not have capacity to accommodate all of the unit requests we receive. Registration on a unit also depends on whether you meet the pre-requisite conditions through prior study at your home university.

Study Abroad (Subject pathway)

If you have been nominated to Bristol on the Study Abroad (Subject pathway), you must take the majority of your credits in this department.

Units available on the study abroad programme in 2023/24

The following units from the School of Mathematics are open to inbound Study Abroad students.

Year 1 (level C/4)

Important note about Year 1 units: Mathematics Year 1 units cannot be taken in combination with Mathematics Years 2, 3, or 4 level units or with non-Mathematics units which involve exams. This is due to the scheduling of Mathematics Year 1 exams. Study Abroad students can choose to take all Year 1 Mathematics units or combine Mathematics Year 1 units with non-Mathematics units that involve no exams.


  • Applied Analysis A (TB1) - MATH10023


  • Applied Analysis B (TB2) - MATH10024


  • Algorithms and Programming in C(++) and R (TB4) - MATH10017
  • Analysis (TB4) - MATH10011
  • Introduction to Proofs and Group Theory (TB4) - MATH10010
  • Linear Algebra (TB4) - MATH10015
  • Matrix Algebra and Linear Models (TB4) - MATH10016
  • ODEs, Curves and Dynamics (TB4) - MATH10012
  • Probability and Statistics (TB4) - MATH10013

Year 2 (level I/5)


  • Algorithms and Machine Learning (TB1) - MATH20017
  • Linear Algebra 2 (TB1) - MATH21100
  • Metric Spaces (TB1) - MATH20006
  • Multivariable Calculus and Complex Functions (TB1) - MATH20015
  • Ordinary Differential Equations 2 (TB1) - MATH20101
  • Statistics 2 (TB1) - MATH20800


  • Advanced Linear Modelling and Classification (TB2) - MATH20016
  • Algebra 2 (TB2) - MATH21800
  • Applied Partial Differential Equations 2 (TB2) - MATH20402
  • Introduction to Geometry (TB2) - MATH20004
  • Mathematical Programming (TB2) - MATH20014
  • Mechanics 2 (TB2) - MATH21900
  • Probability 2 (TB2) - MATH20008


  • Perspectives in Data Science (TB4) - MATH20018

Year 3 (level H/6)


  • Combinatorics (TB1) - MATH30030
  • Complex Function Theory 3 (TB1) - MATH33000
  • Complex Networks (TB1) - MATH36201
  • Fields, Forms and Flows (TB1) - MATH30018
  • Financial Risk Management (TB1) - MATH30014
  • Fluid Dynamics (TB1) - MATH33200
  • Group Theory (TB1) - MATH33300
  • Linear and Generalised Linear Models (TB1) - MATH30013
  • Martingale Theory with Applications 3 (TB1) - MATH30027
  • Measure Theory and Integration (TB1) - MATH30007
  • Quantum Mechanics (TB1) - MATH35500
  • Set Theory (TB1) - MATH32000
  • Stochastic Optimisation (TB1) - MATH30021
  • Time Series Analysis (TB1) - MATH33800


  • Bayesian Modelling (TB2) - MATH30015
  • Dynamical Systems and Ergodic Theory 3 (TB2) - MATH36206
  • Financial Mathematics 3 (TB2) - MATH35400
  • Functional Analysis 3 (TB2) - MATH36202
  • Further Topics in Probability (TB2) - MATH30006
  • Information Theory (TB2) - MATH34600
  • Logic (TB2) - MATH30100
  • Mathematical Methods (TB2) - MATH30800
  • Number Theory (TB2) - MATH30200
  • Numerical Analysis (TB2) - MATH30029
  • Optimisation (TB2) - MATH30017
  • Quantum Information Theory (TB2) - MATH30031
  • Statistical Machine Learning (TB2) - MATH30028
  • Statistical Mechanics 3 (TB2) - MATH34300
  • Theory of Inference 3 (TB2) - MATH35600
  • Topics in Geometry and Discrete Mathematics (TB2) - MATH30034
  • Random Matrix Theory (TB2C) - MATH30016. This runs for half of the semester (weeks 13-18)


  • Perspectives in Mathematics (TB4) - MATH30024

Year 4 (level M/7)


  • Advanced Fluid Dynamics (TB1) - MATHM0600
  • Algebraic Topology (TB1) - MATHM1200
  • Axiomatic Set Theory (TB1) - MATHM1300
  • Complex Function Theory 34 (TB1) - MATHM3000
  • Complex Networks 4 (TB1) - MATHM6201
  • Data Science Toolbox (TB1) - MATHM0029
  • Fields, Forms and Flows (TB1) - MATHM0033
  • Geometry of Manifolds (TB1) - MATHM0037
  • Martingale Theory with Applications 4 (TB1) - MATHM0045
  • Representation Theory (TB1) - MATHM4600
  • Stochastic Optimisation (TB1) - MATHM0044
  • Anomaly Detection (TB1B) - MATHM0030. This runs for half of the semester (weeks 7-12)
  • Quantum Chaos (TB1B) - MATHM5700. This runs for half of the semester (weeks 7-12)


  • Algebraic Geometry (TB2) - MATHM0036
  • Algebraic Number Theory (TB2) - MATHM6205
  • Analytic Number Theory (TB2) - MATHM0007
  • Asymptotics (TB2) - MATHM4700
  • Dynamical Systems and Ergodic Theory 34 (TB2) - MATHM6206
  • Financial Mathematics 34 (TB2) - MATHM5400
  • Functional Analysis 34 (TB2) - MATHM6202
  • Further Topics in Probability (TB2) - MATHM0018
  • Galois Theory (TB2) - MATHM2700
  • Quantum Information Theory (TB2) - MATHM5610
  • Statistical Mechanics 34 (TB2) - MATHM4500
  • Theory of Inference 34 (TB2) - MATHM0019
  • Topics in Geometry and Discrete Mathematics (TB2) - MATHM0048
  • Advanced Quantum Theory (TB2C) - MATHM0013.
  • Monte Carlo Methods (TB2C) - MATHM6001. This runs for half of the semester (weeks 13-18)
  • Quantum Computation (TB2C) - MATHM0023. This runs for half of the semester (weeks 13-18)

Application queries

Contact the Centre for Study Abroad inbound team if you have any queries about the application process for the study abroad programmes:

Phone: +44 117 39 40207

Sat, 21 May 2022 09:15:00 -0500 en text/html
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Off-Campus Study

Sample Courses

Budapest Semesters in Mathematics Education (BSME)

Numerical Analysis (IES Cape Town, South Africa)

Introduction to Probability and Statistics (IES City University of London)

Calculus II (IES SKEMA, Nice, France)

Geometry (TEAN UWA, Perth, Australia)

Mon, 23 Sep 2019 14:15:00 -0500 en text/html
Troops do not have an extremism problem, but veterans do, study finds

Service members don’t participate in violent extremism at higher rates than the rest of the U.S. population, but former troops do — and their involvement is growing, according to research published at the end of December.

According to the report, which was commissioned by the Defense Department, anecdotal accounts of service members being involved in violent extremism create a false impression that it’s an outsized problem. Those accounts often fail to differentiate between current service members and former troops, a demographic found to participate in violent extremism at higher rates, the research states.

“[The] review found no evidence that the number of violent extremists in the military is disproportionate to the number of violent extremists in the United States as a whole,” the research says. “Extremism in the veterans’ community has peaks and valleys over recent decades, and currently appears to be on the increase.”

While the study found there were not more violent extremists in the military than in the overall population, researchers did highlight racism and sexism as ongoing problems in the Armed Forces. Moreover, researchers said that even a single incident of violent extremism carried out by a service member can lead to “significant negative repercussions” for the nation as a whole.

Because of the effect that even a small number of incidents can create, researchers urged the Pentagon to hold a zero-tolerance policy on troops’ advocacy of violent extremism and take steps to ensure “core military values prevail over fringe beliefs.”

The Pentagon approved the release of the study last week. The Defense Department first commissioned the research in 2021 to investigate extremism among the Armed Forces. Defense Secretary Lloyd Austin called for the study based on a recommendation from the Countering Extremism Working Group, which was established after the Jan. 6, 2021, attack on the Capitol.

The nonprofit Institute for Defense Analyses conducted research for the study from June 2021 to June 2022. It was approved for release after Christmas, about 18 months after the working group said it would be made available. The delay prompted anti-extremism advocacy groups and DOD watchdogs last year to question the report’s whereabouts.

At the end of the 262-page report, the Institute for Defense Analyses listed out 18 recommendations for the Pentagon. In light of the growing number of violent extremists among the veteran population, the institute called on the Defense Department to bolster the resources made available for service members as they exit the military. The Department of Veterans Affairs should also play a role, researchers said.

“For the Veterans’ community in particular, loss of military identity appears to have a strong association with difficult adjustments to civilian life that can in turn contribute to negative behaviors,” the report states.

Some service members told researchers that they were confused about the definitions and standards regarding prohibited extremist behaviors and activities. That confusion could lead to polarization and division in the ranks, researchers warned. Researchers suggested the Pentagon could present the information in a less divisive way by focusing on the military’s values, such as loyalty, respect, duty and honor, and explain how extremist activities work against those principles.

To combat division in the ranks, the Defense Department should also try to mentor and counsel service members before doling out punishments for prohibited extremist activities, researchers recommended.

Other recommendations asked that the Pentagon more uniformly flag cases of extremism, and that it add questions about prohibited extremist activities in its process for awarding security clearances. Researchers warned against any plans by the Defense Department to monitor troops’ social media activity to identify their links to extremism. Those efforts could be seen as overly intrusive and may alienate service members, the report states.

“Many of the recommendations in this report call for comprehensive cultural change that cannot be accomplished through a single action but will require a concerted effort over a period of time,” researchers wrote. “As the Department responds to such events, it should remain cognizant of the fact that violent extremism does not appear to be any more prevalent among service members than it is in American society as a whole, and avoid steps that risk unnecessary polarization or division in the ranks.”

This story was produced in partnership with Military Veterans in Journalism. Please send tips to

Nikki Wentling covers disinformation and extremism for Military Times. She's reported on veterans and military communities for eight years and has also covered technology, politics, health care and crime. Her work has earned multiple honors from the National Coalition for Homeless Veterans, the Arkansas Associated Press Managing Editors and others.

Fri, 05 Jan 2024 05:08:00 -0600 en text/html
Why Study Math?

Mathematicians and statisticians have diverse opportunities, from analyzing data and applying mathematical and statistical techniques to solving real-world problems in business, engineering, healthcare, or other fields. Read more about all the reasons to study math.

Wed, 15 Nov 2017 08:52:00 -0600 en text/html
Maths Study Adviser

The Mathematics Study Adviser for the Department’s undergraduate students is Laurence O'Toole. As a Study Adviser, he can help with issues surrounding transition to university, getting to grips with abstract mathematics and academic insecurities, and any initial concerns you may have about studying at LSE.

Laurence works closely with the Student Wellbeing Service to make sure students get the help they need, as well as with the Academic Mentors who can refer you to the MSA for support.

The appointments are individual but you can bring someone else for support if you need to.

To book an appointment, please email

You are at LSE because you are good at mathematics, and you have good A-Level results to show this. However, your study skills from school will not get you the best results at university.  The three books listed below may help you start to think differently:

There are lots of websites where you can find study skills advice you might like to try on the links below. We also have our own website about Study Skills for Mathematics, which we would recommend reading.

  • Success in Mathematics - this is an American website which contains lots of good advice specifically for mathematics.
  • Maths Centre - if you struggle remembering the actual mathematics you need help with. You can choose a resource with fits how you like to learn. You can also find a recap of what you should know from A-Level.

We encourage you to find a study buddy or study group to give mutual support.

Mon, 03 Oct 2022 09:23:00 -0500 en-GB text/html
Why Study Mathematics?

"The study of mathematics, like the Nile, begins in minuteness but ends in magnificence.”
– Charles Caleb Colt

Mathematics is a demanding intellectual pursuit, but one that can be interesting, exciting and challenging. People like its clarity and the satisfaction of knowing when you have the right answer to a problem. Further, a math degree requires sound analytical skills and the ability to work in a problem-solving environment. This proves to be an advantage when considering careers in fields other than math. Suppose you love mathematics, but ultimately see yourself pursuing a career as a doctor, lawyer, or in business. You should be aware that professional graduate schools in medicine, law, and business think mathematics is a great major and that their entrance tests support this bias; the more math you know the better you will do on their exams.

The National Institute of Education conducted a study comparing the scores of 550,000 college students who took the Law School Admission Test (LSAT) and Graduate Management Admission Test (GMAT), with data collected over the previous eighteen years. The study showed that students majoring in mathematics received scores substantially higher than the average on each of the tests.

"But I'm not interested in a grad degree! After being a college student for four years I need to make some money!"

Not to worry! Did you know mathematicians are some of the best paid professionals in the country?

If you want to take your bachelor degree straight to the job market, math will serve you well, when considering potential salaries. Among bachelor's degree graduates from the Class of 2018, those from the STEM disciplines are expected to receive the highest starting salaries, according to results of NACE's Winter 2018 Salary Survey. Further, the top three projected salaries are for engineering, computer sciences, and math and sciences graduates. The following chart was extracted from the National Association of Colleges and Employers helps emphasize this:

  • Engineering degrees - Overall, the average salary for bachelor's degree graduates is projected to be $64,891, almost the same as the 2017 projection.

  • Computer science fields - Overall starting salary projected at $66,005. Two of the three reported computer science disciplines also top the $60,000 mark, while the third- information science and systems falls just below that mark ($59,810).

  • Mathematics and Science - Graduates in these fields are expected to average $61,867, an increase of 4.2% over 2017.  Those earning physics degrees will see the largest salary bump, $69,000

  • Business - Majors land in the fourth spot, with a projected starting average salary of $56,720.

  • Among the remaining broad categories on the list, Business, Social Science and Humanities all average about $56,700.  AG and Natural Resources average $53,565 and Communication majors average $51,488.


“If you stop at general math, then you will only make general money.”
– Snoop Dogg

Sun, 12 Nov 2023 07:33:00 -0600 en text/html
Study reveals the unique mathematics of snowflakes

Aside from being cold, snowflakes are well-known for their unique shapes. New research illuminates how these lovely crystals fall to the ground. When the air is still snowflakes gently drift to the surface, but on other occasions they get violently tossed about by wind and other forms of precipitation. While this can be beautiful to observe, it also adds an element of the unpredictable to snowstorms — although a group of researchers at the University of Utah may have helped change that forever.

According to a recent study published in the journal Physics of Fluids, scientists can actually anticipate how snowflakes will fall during different types of air turbulence, something that atmospheric modelers previously struggled to do. After much research, the scientists found that they simply had to use the Stokes number for the snowflakes. A Stokes number is a dimensionless figure that determines the behavior of particles suspended in a fluid flow. Such a straightforward solution may seem counterintuitive because, as the authors noted, snowflakes come in so many individual shapes and sizes.

"Despite the complexity of snowflake structures and the non-uniform nature of the turbulence, we find that mean snowflake acceleration distributions can be uniquely determined from the value of [Stokes numbers]," the authors explain. While this information does not immediately help scientists better predict the timing, length and severity of snowstorms, it paves the path toward that outcome.

"If that is the case and we can show in the future that this really is supported, that could lead to quite significant improvements in storm modeling," study co-author Tim Garrett, a University of Utah professor of atmospheric scientists, told "Right now, one of the biggest challenges weather models have is predicting the types of snowflakes that form in clouds. Our results hint that some of the difficulties ... may actually end up being (less complicated)."

Wed, 27 Dec 2023 10:00:00 -0600 en-US text/html
Study reveals the unique mathematics of snowflakes No result found, try new keyword!According to a recent study published in the journal Physics of Fluids, scientists can actually anticipate how snowflakes will fall during different types of air turbulence, something that ... Wed, 27 Dec 2023 20:50:00 -0600 en-us text/html

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