ASVAB Word List September 18 2016 update

I think that a fluent speaker of American English uses a vocabulary of about 10,000 words.  I have created a list of words to help prepare for the Armed Services Vocational Aptitude Battery.  Some words have definitions which come from dictionaries no longer covered by copyright, or from my own spontaneous definition as I read the list.

Here is the list, which will be updated on a regular basis.

 

abandon  to give up
abated   past tense of abate, which means to bring down, reduce, diminish
abreast
absorption
abstain  keep from, restrain
abstract
abundance
abundant
abysmal      bottomless, pertaining to an abyss
accede          agree, assent, associate with others
accentuate  make prominent, emphasize
acclaim         applaud, as a noun:  receiving applause
accrue          increase, grow in number or value, such as bank account
interest accruing daily, quarterly
acquiesce      accept or agree to, but not with enthusiasm or strong
agreement
adept            skilled, proficient
adipose         related to animal fat, fat in cells of adipose tissue
adverse         acting against, contrary, unfavorable
aesthetic       related to senses such as sight
affectation     false display, artificial show
affinity        relationship,  attraction
affix           attach, annex, fix or fasten
affliction      distress, state of pain or grief; synonyms are calamity,
distress
aghast          terrified, amazed with a sense of horror or terror
agility         quality of being to move quickly and easily
aimless         without aim or purpose
alacrity cheerful readiness, eager brisk willingness
alias           another name by which a person or object is known
allay           pacify or appease,  alleviate, mitigate
allegiance
allele  [science]
allusion
aloof  no sympathy or regard a person without any favor or sympathy
altercation     a dispute that may involve verbal argument, but may
involve fighting
ambivalent
amicable friendly
amiss           astray, faulty, out of order
ampere [electronics]  the unit of electric current, one coulomb of
electrons passing a point in one second
ample  abundant, sufficient to satisfy a requirement for …
anachronistic erroneous, out of date
anarchy         confusion or disorder, absence of government
anion  an atom that has gained an electron and now has a negative
charge
anomie  feeling that one has no personal purpose in the world
antagonist      opponent, adversary
anthology      a collection
anxious
apathetic       indifferent, without any emotion
apparition       ghost, specter
appellation      word by which a person is known or called,  Mr.,
Corporal, etc.
appoint
approbation      the act of approving,  synonyms include approval,
consent
aptitude
archaic
arid
arrogant
articulate clear expression, distinctly spoken
artistic demonstration of imagination and skill in art, sensitive to art
and beauty
arsenal
ascertain       find out or learn for certain
ascetic         austere, severe
askew           awry, out of order, misplaced
assent
assert
assist  aid or support
atonement       making reparation , making amends
attentive
audition an appearance before a judge or judges who decide if the
person shall be chosen for a place or part
auger  a hand tool used for drilling holes, a machine that drills holes
augment         increase or enlarge in size or number
authentic genuine, original
autonomous      independent,, able to control its own action or
govern     itself
avarice           excessive desire for gain, greediness
average          in arithmetic, the sum of a set of numbers divided by the
total number of numbers
averse
avert           turn aside, ward off, prevent
Avogadro’s Law [science]
AWG = American Wire Guage
awl [shop tool]
baluster [shop]
banal            commonplace, trivial, trite
banish
barbarous       uncivilized, rude, being a barbarian
befell
beneficial
berth           nautical term for the place where a ship lies at anchor or at
a wharf
beseech  beg, plead
bestow
bevel rip  [shop tool]
binomial [mathematics]
biome  plants and animals that have common characteristics due to
similar climate
biscuit joiner [shop]  woodworking tool used to join two pieces of wood
together
bleak           colorless, desolate, cold and cutting
blemish  noun:  mark, deformity, imperfection; verb:  tarnish, defame,
deform
boisterous      synonyms are load, roaring, violent, rude
Boyle’s Law [science]
brace           a thing which holds something or supports it, also as a verb
brad            a thin nail
breach          noun or verb.  noun: a gap  common verb use: to break
through  in law breaking or infraction of obligation
breadboard [electronics]
brevity  concise, of few words
buoyancy
butane [science]
calamity
caliber         diameter of a cylindrical body, such as a bullet
caliper [shop and mechanical]  measuring instrument with two metal
legs that is used to measure distance between opposite sides
callow                  immature, boyish
cam
camaraderie  shared good feelings with others who have a common
bond
camber   In automotive use, the camber angle is the degrees the tire is
set off from perpendicular
camouflage  conceal, hide by covering or painting
camshaft                An engine shaft that one or more cams used in lifting
the valves of the engine
capacitor [electronics]
capacitive reactance  the measure of opposition to alternating current
capsize                 upset or overturn
caprice                 abrupt change in feeling, opinion, or action
caste                   a social ranking of a group of people compared with
others
catalyst  A chemical substance that modifies or increases the rate of
reaction, but is not in the reaction.
cation   an ion with a positive charge that will move toward a negative
electrode
cat’s paw [auto and shop]
caustic                 burning, corrosive
caution  to take care, to be on the watch, to warn, to be prudent
cautiously
cease  to stop, to end
censure         act of finding fault
centrifugal tending or causing to go out from the center
centripetal  tending or causing to go toward the center
cessation
chafe           wear by rubbing, to fret, to irritate
chamfer         verb in carpentry, to cut a furrow or groove in
Charles’s Law [science]
chasm           deep and wide opening
chisel [noun, verb; shop tool]
chuck  [shop tool noun, also verb]
circumference [of circle = 2[value of pi]]  the greek letter pi
civil
clash  interfere, oppose, strike against
cleft           space or opening made by splitting
clemency forgiveness,gentleness, usually granted by a judge or
authority with punishment power
cliche  a word or phrase which is used too frequently
coaxial
coefficient     mathematics:  the number before the letter in a formula,
in mathematics:   2x  2  is the coefficient
cog
commendable
complementary [mathematics, degrees of a complementary angle
added to degrees of adjacent angle = 180]
composure
concept
conciliatory acting to bring together, to reconcile
concoction        combinaton of different ingredients
conductance    The opposite of resistance.  The formula to measure
conductance is  G = A/pL
A is  the cross section area in cirular mils , p is the specific
resistance, and L is the length in feet.    The Siemens is the name
given to the unit of conductance.   R = 1/G    G = 1/R
conduction
configure     to arrange in a certain form, or to add specific equipment
to a device
confines
confound            to confuse
confront                oppose firmly
congruent  agreeing, accordant in geometry items that have all points
coinciding
conjecture          opinion or judgement made on a guess or presumptive
evidence
consensus       agreement, accord
console             as a verb  to cheer up, to alleviate grief
constant
constrict        make narrow, cause to shrink in diameter
consummate          adj.  complete, perfect
contemplate
contempt
contrive            devise, invent, plan
convection
converse           commune, talk.  It can also be be used to describe a
statement in which the parts are reversed.
conveyed carried, transferred, passed from one person to another
copious         great quantity, abundant, plentify
corroborate
Coulomb [electronics]  quantity of electricity moving past a point when
one volt and one ohm, or one ampere in one second
counterpart a  part which has the same function in another thing, or a
person with the same job
courtesy
covalent [science]
covert
covet
cower           to quail, to sink down in fear
crankshaft a shaft with one or more cranks, which are parts on the
shaft which are attached to a moving piece, such as the piston
with    a  rod connecting
craving
creed
crevice
crimson
criterion standard measuring something, judging something
accordingto a standard
critical very important, absence of a condition, or a part failure may
cause damage and injury
CRT cathode ray tube
culminate
cure   [noun,  sometime used to describe a process]
curtail  stop, reduce, cut short
cytoplasm:  Living material inside the cell membrane, but outside the
nucleus and organelles.
dado blade [shop]
decennial               a ten year period;
deception  the act of deceiving or misleading; the state of being
deceived or misled
decibel [electronics]
decimation  the destruction of a considerable part of something or
some group,  such as 10% or more
deferred  delayed
deficiency
delete
delirious
deluge
denominator [numerator/denominator 7/8]
denote   mark , to point out
density
deplete   use up or seriously reduce the supply of a thing.
deplore
deportment  personal behavior
deride   to ridicule
desist  to stop, to cease
despair      hopelessness,  be the object of a feeling of hopelessness as a
person
despot
destitution  state of being without resources, state of being needy
deter
detest
deviate
dexterity  skill and ease in using the hands
diagnose  recognizing a condition, usually bad or confusing, which
affects a person or organization
diaphanous  transparent material, although sometimes used to
describe translucent material
diameter
die [shop]
dielectric  nonconductor
differential [automotive, mathematics]
diffident   lacking confidence, modest, bashful, hesitant
diffuse                 to spread out in all directions, such as adding a liquid
to another liquid
diligent
diminish
din
diode  [electronics]
disabuse                undeceive, set free from mistake, set right
discern   discriminate, distinguish
disconcerted  in disorder or confusion, disordered or confused
disconnect  sever, separate, dissolve a connection
disconsolate  sad, filled with grief, melancholy, cheerless
discovered  found, revealed, find something which was concealed or
secret
disingenuous  unworthy, not frank, lacking honor or dignity
disperse
dissension  disagreement of opinion, usually strong or heated, with
angry words spoken
disseminate     distribute, scatter,
dissipate  scatter, disperse, destroy by wasteful use
dissent
dissuade      persuade a person or organization to not do something, discourage
distort
doldrums                a state of listlissness, ennui.  Originally a part of the
ocean near the equator  with light winds or calm, or storm squalls
domain
drab
dreary
drizzle
drudgery  disagreeable or wearisome labor
droll   amusing, provoking laughter, comical, humorous
dubious
ecosystem     a system of interconnected organisms within their
environment
ecstatic  delighted,  an example of use is ecstatic bliss or joy
edge
electron [science, electronics]
electronegativity [science]
elementary
elevate
elite
eloquent
embark   to start up, to engage
enchanting
encode
encounter  face to face meeting, a sudden or incidental meeting, a
hostile meeting
endeavor
endoplasmic reticulum:
endothermic [science]    requires the absorption of heat
enduring
energy level [science]
engrossing
enigma   obscure saying, a riddle, some thing not satisfactorily
explained
enlightening
entente   agreement
enumerate
entice
entreaty  beseeching, petition, solicitation
equilateral [mathematics]
equivalent  equal to
equivocal               questionable
erratic
erect   raise, set upright, build or construct
evoke
exalt   elevate by praise, to glorify
excessive
exothermic [science]  a chemical reaction that generates heat
expendable
expedient
expertise
exploit
expressive
exult   be in high spirits, leap for joy, rejoice
facilitate
Farad [electronics]  A Farad is the storage of electrons producing a
voltage difference of one volt  across terminals while producing one
ampere per second.    This is a very large unit, and most capacitors
have  values measured in microfarads  (thousandths of a Farad)  or
picofarads.
fathom
feasible
feign
fertile
fervent        ardent, earnest, intense spirit for a thing or idea
fiasco
filibuster an obstructive tactic that is allowed by the rules of procedure
to prevent another action from being taken
fitful
flammbable    easily set on fire;  regulatory agencies have set 100
degrees F. or 37.8 degrees C. as the flash point .    Inflammable and
flammable mean the same thing, use nonflammable to describe
something that does not burn
flank
flaunt
flex
flexible
florid
flounder     move in awkward way or respond to questions in an
awkward way,  the fish known as the flounder lives on the bottom
and moves about by flopping
flout
flush
flux is a chemical that cleans the connection area.  Melted solder flows
easily and prevents oxidation.  Acid core      flux is used to solder
sheet metal.  Rosin flux is used in electrical and electronics work.
folio           A collection of examples of a person’s work
forgive
formidable
Forstner bit [shop]
fortnight  a time period of two weeks.
fractious
fret
furtive       action undertaken to avoid detection, done by stealth,  facial
expression and manners that attempt to conceal actions
garish
garnered
gaudy
gaunt
Gay-Lussac Law [science]
generic
germinate
ghastly
glare
glossy
grandeur
grate
grave
groan
guage
haphazard
haggard
hapless
harden
harmony
haughty
heave
heed
Henry [electronics]
Hertz [electronics]
heptagon [mathematics 128 degree angles] sometimes; septagon
hexagon [mathematics 120 degree internal angles] 6 sides
hinder
hoard
homozygote
hopeless
hub
hysterical
igneous  [science]
ignoble
immiscible
impair
impart
impartial
impassive
impedance [electronics]
impede       deter, slow
impenetrable
imperative vital requirement
imperious
imperturbability        not easily disturbed or activated
impetuous
implement
impose
impotent
improbable
imprudent
impunity
incense
incensed
incidental
incomprehensible
incredulous
indefatigable  not capable of being fatigued,  tireless
indignant
indispensable
indolent
induct
inductance    The opposition to changes in circuit current.  Unit of
measurement is the HENRY  H.  Inductance symbol is L.   An
inductor has one Henry of inductance if the electromotive force
current through the coil changes at one Ampere per second.
induction
inductive reactance  The opposition to alternating current by a coil of
wire.    X subL = 2<value of pi>fL   f is the frequency of alternating
current in hertz (example 60 hertz)
L = Inductance measured in Henry units
indulge
inert
inexorable
inexplicable
infer
infirm
inflammable     A language surprise.  It means the same as flammable.
Both terms refer to something that can easily catch fire and burn.
Use the word nonflammable when you seek a word to describe a
substance that does not burn or does not easily burn
inflict
inform
infraction violation
ingenious
inherent
iniquity
initiate
innate
inscribe
inscription
insolent
institute to establish
insubordination
insurmountable
insurrection
intensify
interior
interminable
intermittently
interpose
intimidate
intrusion
ionic
iridescent      surface colors that seem to change when viewed from
different angles.
ironic
irk
irrational
irregular
irresolute
isobutane [science, shop]
isolation
isomer     (chemistry) a molecule with the same chemical formula as
another molecule, but a different structure.
isosceles [geometry]
itinerant
itinerary
jeopardize
Joule [electronics]
Joule’s Law  [electronics]
judiciary
judicious
juncture
jurisdiction
keen
kinetic
kerf [shop; width of the saw cut]  cut in wood made by a saw
laconic   short, brief, pithy, stern
lament
languid
lava (molten or solidified rock on the surface of the earth, see magma
for difference between lava and magma)
lax
leaden
LED light emitting diode
leer
legitimate
lethargic
lever, first class
lever, second class
lever, third class
lipid
liposome   a small sac within the cell.  Artificial liposomes can be
created in which compounds, vaccines, medicines can be put into a
cell
livid
lobe
logarithm  [mathematics]
loom
lucid
ludicrous
lull
lure
Lysosome:  A sac which controls the release of enzymes in the cell.
Lysosomes are the digestive system of a cell.  The  enzymes within a
lysosome can digest lipids, saccharides (sugars),  proteins, RNA,
and  DNA.  They digest obsolete parts   of a cell.
magma (molten rock below surface, lava is molten rock on or above
surface]
malice
malign
malleable
manic   frentic activity, wild excitement,  also refers to mania in
psychiatry
maxim   proverb, rule,
meager
meander
mechanical advantage  machine’s output force divided by the input
force.   For inclines,  the length is divided by the height of the  incline
median           middle value of a group of numbers
Megahertz [electronics]  1,000,000 hertz   1000 kilocycles = 1 megahertz
meiosis    cell division that reduces the number of chromosomes in
half,  in humans from 46 to 23.
menace
mercurial    unpredicatable,  having an angry temper
mesmerize  to bring the minds and thoughts of others under the
control of another, named after a Dr. Mesmer  of Vienna,  Austria in
the early 1700s
methodical
meticulous
miasma   infectious particles or germs in the air; noxious air, noxious
effluvia
micro     (ten to the minus 6 power)
mien
milieu   surroundings
mimesis   imitation, mimicry
mimic
mingle
mirth
misalign
miscible (see immiscible above)
mitochondrion:  Largest organelle within a cell.  It is involved with
respiration and is is the power station of the cell.
There are multiple mitochondria within a cell.
mitosis          cell division in which the cell divides in two, and both cells
have the same number of chromosomes
moderate (can be an adjective, noun, and verb)
modulate  [electronics; controlling the amplitude AM or transmitted
frequencies FM of a radio signal
molar [science]
mole [science]  mole (chemistry)   a chemical mass unit.
momentum
monera       prokaryotic organisms  no nuclear membrane, no
organelles except ribosomes.
monomial
monotonous
morbid
mortise [shop]
mourning
muffle
mundane
muse
muster
mutiny
mutualism
myriad
nadir
negligent
necessity
negate
neutron [science, electronics]
newton           force producing acceleration of one meter per second on
a mass of one kilogram
noisome
nomadic
nominal
notorious
novice
nucleus:  The control system of the cell. It contains the chromosomes
which have the genetic material of the cell.
obstinate
obtuse
occurrence  incident, event
octagon
Ohm’s Law [electronics]  Voltage = Amperes  times Resistance
omen
opinion
oppressed
optimal
option
opulence       a display of wealth, riches, affluent
orient
orientation
oscillate
oscilloscope       an electronic device that measures amplitude versus
time unit, such as frequency in hertz
ostracize
outfit
outlandish
pallid
palpable
paltry
panoply   tool, implement; a plural meaning can mean armor or
armament
pantheon
paragon   something against which other things are matched, held out
as an example of excellence
parallel [mathematics]
partake
pastoral
PCV positive crankcase ventilation [auto]
penance
pendulum
penitent
pensive
pentagon [mathematics, 108 degree angle] 5 sided
pensive
perception
peripheral
pernicious
perplexed
pert
phloem [biology, science]
photodiode [electronics]
picayune       paltry, petty
pier
pine
pinion [auto]
piqued
pizeoelectric [electronics]
pizeoelectric effect  some crystals such as quartz begin to vibrate when
electricity is applied to them.
placid
plaintive
plunge
polygon
pompous
ponder
portend   to warn before some event happens
portrayal
potentiometer      currently used to described a variable resistor
practical
precedent
precipitous
predecessor
predict
preferential
prerequisite
pretence
prevalent
previous
primeval
priority
profess
prolong
prominent
prone
propriety
prosecution
protist             They are one celled organisms
proton [science, electronics]
prototype
provocation
proximity
prudent
pulley
punctual
purport
quad- four
quadratic [mathematics]
quay
quint -five
quiver
rabbet  [auto, shop]
rabble
rack [auto, shop]
ramshackle
ratio
raucous   hoarse, loud, rough, also used for boisterous,
RC circuit [electronics]
reactance
reap
reckless
recluse
rectify   correct
recuperate
redress
redundant       superfluous, excess
reform
refute
reign
relish   a food, but also used as a verb such as to taste, savor, or enjoy
remorse
rendezvous
renounce
repress
reproof
requisite
reserved
reside
resolution  the act, operation, or process of resolving.  Also can mean a
decision made by a person or approved after discussion and a vote
by a group
resolve   finding a solution, a decision (He had a resolve to get a high
ASVAB score)
resound
respiration
respite
reticent
reverie
revolution   -ary  -ize
ribosome:  The site of protein synthesis within the cell.
right angle [mathematics, 90 degree angle]
rip blade [shop]
rivet
riveting
RMS  root mean square .707 of voltage [electronics]
rocker arm    an automotive term
rude
rudimentary   elementary, initial, primitive
rudiments
sage
salutary
sanctity
sanguine
sarcastic
scale
scanty
scarce
scatter
schematic [electronics]
scorn
scruple
sear
secondary
secret  -ive -ly
sediment
semiconductor
sequel
sequester
serene
sham
shear   cutting something, such as cloth or sheetmetal
shim [auto, shop]
slosh
small
smudge
sodden
solace
solemn
solenoid [electronics]
sordid
spartan
spite
spurious
staid
stalwart
steadfast
stealth
stench
stigma -tize
stochiometric [science]  In automotive gasoline engines, the
stoichiometric ratio is 1:12. something
stochiometric point [science]
strident  harsh, grating, shrill
strive
suduction
sublimate
sublimation
sublime
subduction’
subsume   take up into or under, include under something else
suffice
sufficient
sullen   usually used to describe a person who is ill-humored, morose, peevish, gloomy
sumptuous
superficial  shallow, not deep or profound
supposition
surmise
surreptitious
syntactic  putting together in order; related to the word syntax
tacit   silent, agreeing without saying yes or no
tactile
tantalize
tame
tapestry
taps [auto, shop]
telemetry  transmission by automatic instruments as in radio transmitters
tenacious
tenuous
terse
thwart  -ed
tout
trait
trance
transaxle         found in front wheel drive vehicles.
transducers             convert light,heat, sound, and pressure to
electricity.  A microphone is a transducer.
translate
transpire
transpiration
trapezoid [mathematics, 4 sides unequal length
tremulous
triangle [mathematics, internal angles add to 180]
trite
trivial
tumult
twisted
ubiquitous
umbrage   jealousy of another, resentment, feeling that one is
overshadowed by another
unanimity
uncouth
undertake  undertook   begin, attempt , promise to begin or attempt  underwrite
universal joint [auto]
urbanity  civility, courteous in manner, politeness
usurp
vacuum
variable
vascular [science]
vehement
verify
vernier calipers [shop]
versatile
vertex
vex
vexatious  aggravating, annoying
vigilant
vindictive
viscous
viscosity [the measure of how viscous a fluid is]
volition
volt [electronics]
voluntary
vortex
wary
Watt
wedge
whimsical
willful
wretched
xerophyte  using  little water
xylem     [biology, water ]

zener diode  [electronics]

How many words do you need to recognize and understand their meanings to get high ASVAB scores?

I have been looking at word lists in ASVAB study guides, core lists of 3000 words from several dictionary publishers, and other sources of information about word frequency.  I do not have THE ANSWER.

My opinion is that a person should be familiar with all the words in core list of 3000 words, such as from learnersdictionary.com,  the Longman Communication 3000, the manythings.org word list, the oxfordlearnersdictionaries.com 3000 words lists,  AND, all the words that appear in word lists in ASVAB study guides.  This would be about 4500 words.

I would pay particular attention to the word lists in ASVAB study guides.  I do not know how the authors chose those words, but it may from studying official word lists, information provided by past ASVAB takers, and their own careful research.   I compared one author’s list with a 3000 core word list, and found less than 10 % of the words in the ASVAB study guide author’s word list in the core word list.

I once heard a speaker say that the English language has about 600,000 words, and that German has only about 180,000 words.  Hmm,  it makes me wonder what types of examinations German students who want to enter THEIR military services must successfully pass!

 

A set of ASVAB like mathematics knowledge and arithmetic reasoning Questions

I am trying to create a set of arithmetic and mathematical knowledge questions that are similar to those that are found in study guides for the Armed Services Vocational Aptitude Battery.  All the questions are original, I did not copy a question from another source and mix up the names or numbers.  ASVAB test questions have a variety of styles for each subtest.  I am guessing that the test creators examine the responses from all test takers and try to improve the questions to eliminate those that are too easy and those that take too long to answer.

ASVAB_Tom_Lindsey_Original_Arithmetic_Mathematical-Knowledge_August_23_2016
These problems are my original creations.  I looked at test questions from other sample tests, but have created
original problems.
Arithmetic 1.  The reciprocal of 2 10/12  (Two and ten-twelths) is
A.  24/90  B. 32/12  c. 12/20  D.  12/34  Correct Answer D  2 time 12/12 = 24/12  24 + 10 =34  The reciprocal is the number
that is multiplied by the original number number to equal 1.0   34/12 times 12/34 = 408/408 = 1
Arithmetic 2.  Jeff finds a closeout on 9 inch square floor tiles .  How many 9 inch square tiles are needed to lay down in a
corridor that is 6 feet wide by 12 feet 9 inches long.
A. 120  B. 136  C. 140  D. 144   6 feet = 12 inches x 6 feet = 72 inches.  12 feet 9 inches = (12 x 12) + 9 inches= 153
72 divided by 9  = 8  153 divided by 9 = 17  8 x 17 = 136
Mathematics 3.  The value of xy – yz  (xy minus yz, divided by xy)  x = 2 y = 3 z = 4
_______
xy
(2 x 3) – (3 x 4) / (2 x 3)  = 6 – 12 / 6   -6 / 6 = – 1  (minus one)
Mathematics 4.   A triangle has two sides with lengths  4 and 6
     An isoceles triangle has two equal length sides,  in this case either 4 or 6   Two angles are the same degrees.
     A right triangle.  If the hypotenuse the side opposite the right angle were length 6, the other two sides would be
length 4 and [square root of 20, a number between integers 4 and 5]. 4 x 4 + [square root 20][square root 20 = 6 x6
If 6 and 4 were the sides that formed the right angle, the hypotenuse would be [square root of 52].
     An obtuse triangle with sides 4 and 6, forming an angle greater than 90 degrees, will have a third side longer
than 6 but less than 10.  If the third side was length 10, it would equal the length of the other two sides.
The angle of the two sides length 4 and 6  would be 180 degrees.  A triangle is three intersecting lines with internal angles
equal to 180 degrees.
     A scalene triangle has no angles equal to another angle.
     An equilateral triangle has three sides of equal length.  Each interior angle is 60 degrees.
Arithmetic 5.  What percent of 500 is 975? Divide 975 by 500  900/500 = 195 %
Arithmetic 6.  Sean must read 14 pages from his economics textbook, 2 short stories of 22 pages length from English, a 12 page
chapter in his U.S. History book, and a 24 page chapter from the chemistry book. He has completed 1/3 of the reading.
How many pages has he read.  14 + 22 + 12 +  24 = 72    72 x 1/3 = 24
Arithmetic 7.  A helicopter makes a cross-country flight of 750 miles in 6 hours.  If it flew at a constant speed during
the trip,    how many miles per hour did it fly?  750/ 6 = 125
Mathematics 8.  Petty cash is used to buy office supplies and equipment with a price of $ 49.99 or less, plus sales tax of 8.25 %
    Purchases costing $ 50.00 to $ 499.99, employees use a company credit card that is kept by department managers.
    Purchases that cost $ 500.00 or more are made by the purchasing department.
    A company credit card was used to purchase some equipment.   Which of these choices MIGHT be true?
    A.  The equipment cost $ 39.99 plus sales tax.
B.  The item was purchased by the purchasing department.
C.  The equipment cost $ 119.99 plus sales tax.
D.  An employee bought the equipment with her own money, and was reimbursed when she came back to the office.
Arithmetic 9.  The tallest player on the school basketball team is 6 feet 5 inches tall.  The shortest player on the hockey
team is 5 feet 7 inches.   How much taller is the basketball player than the hockey player?    8 inches
Mathematics 10.  Tom rented an apartment for $ 900 a month.  He has to pay non-refundable $ 270 fee to keep his dog Ollie at
the apartment.  What fraction of one month’s rent is the dog fee?  270/900  9 x 30 / 9 x 100 = 3 / 10
Mathematics 11.  Brian has a part-time job signing visitors in and out of an office building.  He will start September 1 for 15 weeks
for 15 hours per week.  The building is closed to everyone on Labor Day, Columbus Day, Thanksgiving Day, and
the Friday after Thanksgiving Day.  His hourly pay is $ 8.00 per hour.  How many hours will he work?
213 hours  15 weeks but 4 unpaid days = 14 weeks plus 1 day  (14 weeks x 15 hours) + (1 day x 3 hours)
Mathematics 12.  The phrase “Triple the sum of three and three divided by five”  is the same as  A. 9 3/5 B. 10 4/5 C. 10 3/5  D. 9 4/5
Mathematics 13.  A pint is 1/8 of a gallon.  How many pints are found in 4 2/3 gallons?  Mulitply the two denominators 8 and 3
to get the product number 24.  If there are 24/24ths in a gallon, a pint (1/8th of a gallon) must be 3/24th of a
gallon.  2/3 = 16/24   4 gallons x 24/24 = 96/24 + 16/24 = 112/24   112 divided by 3 = 37, and a remainder of 1.
There are 37 and 1/3 pints [1/3 pint = 1/24 gallon] in 4 2/3 gallons.
     Rounding down, there are 37 pints in 4 2/3 gallons
Mathematics 14.  Aurora Cam Company inventoried older equipment and is sending some to auction. The inventory is:
One lathe, estimated auction value of 1000 dollars
Two drill presses, estimated value     450 dollars
Three equipment lockers 25 dollars each
Box of wrenches                         35 dollars
An auctioneer commission of 15 percent is charged for each item auctioned.  What is the estimated charge? $ 234
Mathematics15.  A triangle has a base of 10 inches, with the other two sides 6 inches and 8 inches meeting at the peak.
What is the area of the triangle?
A.  [square root of 11, divided by 10] plus [square root of 39, divided by 2]
B.  [square root of 22, divided by 5]  (originally, square root of 11 times square root of 32 , divided by 20)
C.  2 times [square root of 11] / divided by 10 times [square root of 39]
D.  24
The answer is 24.  This is a right angle triangle, with the hypotenuse side lying flat
     6 x 6  plus 8 x 8 = 10 x 10   Instead of trying to figure out the height of the triangle with the side 10 on the
base, imagine that it is tilted so that either the 6 or 8 length side is the base.  1/2 b X h  1/2 (6×8) = 24
If a picture were shown, it might seem as if the perpendicular line intersects the base at 5 inches on either side.
Arithmetic  16.  Gretchen was shocked to get a natural gas bill of $ 150.00 for the month of January.  She has gotten notices
in the past about a “Balanced Billing Program”.  The three highest bills and the three lowest bills of the past 12 bills are
added together, and an average billing amount is calculated.  The average is changed with each September bill.
Gretchen’s three high and three low bills were 150, 100, 90, 45, 39, and 32 dollars.  If she chose balanced billing,
how much would she be billed each month?  456 dollars divided by 6 = 76
Arithmetic:  17.  The Franklin Community Association is creating a fenced outdoor park where owners can let their dogs
exercise without being leashed.   Three condemned homes were razed so that the lots can be joined together to make
the park.  Each lot was 120 feet deep  with 60 feet width.  What length of fencing is needed to surround the park.?  600 feet
Mathematics: 18:  The Franklin Community Association is creating a fenced outdoor park where owners can let their dogs
exercise.  The design plan calls for the use of prefabricated fence panels  on posts that are eight feet long and
seven feet high.  If the perimeter of the lot is six hundred feet, how many fence panels need to be purchased? 75
Mathematics:  19.  Which of these numbers equals the internal angle of two sides of an octagon?
108  120 135 144        135  An octagon has 8 points.  Lines from a center point can be drawn to points
A, B, C, D, E, F, G, H on the corners of the octagon.  Eight triangles are formed inside the octagon.
360 degrees divided by 8 = 45 degrees.  The interior angles of a triangle total 180 degrees. The other angles
are 135 degrees divided by 2 or 67.5 on each corner.  Add the angles on each side of the line together.
     108 = pentagon, 120 = hexagon,  135 = octagon, 144 = 10 sided figure,

180 sided figure. 2 degrees at top, 89 degree angles on the sides, 178 degrees of angle of points A,B,C
of the 180 side points.

Mathematics:  20  Which equation is incorrect? A. [square root of 3] + [square root of 4] = [square root of 5]

B. [square root of 3] times [square root of 4] = [square root of 12]
C. [square root of 5] divided by [square root of 4] = [square root of 5] / 2
D. [square root of 27] divided by the cube root of 8] = 3[square root of 3] / 2  or 1.5 times [square root of 2]
Mathematics:  21.  Which integers will make this equation true?
A  > 4   but A < 11
A. 4,5,6,7,8,9,10
B. 5,6,7,8,9,10,11
C. 7,8,9,10,11
D.5,6,7,8,9,10    D.  the > sign is for greater than, the < is less than  The characters with a bar underneath them
are “equal to or greater than”   and “less than or equal to”   / with an equal sign through it
means that the number is not equal the next number.
Mathematics:  22:  Which is a simplification of 2 “x squared” – 12x – 14 ?      (2x + 2)(x – 7)
Mathematics:  Parallel lines:  same distance apart throughout the length of the line
Mathematics: 23:  One angle, known as the supplementary angle measures 75 degrees.  The other angle is complementary and
measures  ____ degrees?
Mathematics: 24. A triangle has sides with lengths that are consecutive odd numbers.  The perimeter is 27.  What is the value
of the longest side?   Answer 11    The average length of the three sides is 27/3 or 9.  9 is probably one of the
three numbers.  5 + 7 + 9 = 25  7 + 9 + 11 = 27  9 + 11 + 13 =33 .

 

How many words should a person know to have success in passing the ASVAB??

Posted by Thomas Lindsey,  mos96b@yahoo.com

The ASVAB test seems to be testing the intelligence level of a prospect, breadth of knowledge, willingness to read and learn more information, and a unique “talent”.  Military life has times when its servicemembers find them themselves in “chaotic situations” when the person must rapidly assess the situation, choose a course of action, respond to the commands of others in the same situation, and take action.

The “chaotic situation” could be gunfire, explosion, fire, chemical hazards, collision, crash, equipment failure, electrocution, flooding by water, other people’s behaviors, or any other abnormal situation.  Is the prospect likely to be shocked and not able to respond.  Will the prospect respond quickly?

The work knowledge and paragraph comprehension subtests are written to see if the prospect has a broad vocabulary to recognize the meaning of words, and can quickly comprehend messages, instructions, and orders.  At least, this is what I think they are intended to test.

How much vocabulary knowledge is enough.  500 words?  1500 words?  3000 words? 5000 words?

The Voice of America broadcasting and internet-based news service of our government broadcasts programs in “Special English” to help people who are learning English.  The vocabulary list has changed a little over 70 years, but has about 1,500 words.  English language dictionary editors, such as the Merriam-Webster Dictionary company, think that everyone should know about 3,000 words.

Here are internet addresses for the VOA and Merriam-Webster lists, with definitions and a spoken voice.

Special English  http://docs.voanews.eu/en-US-LEARN/2014/02/15/7f8de955-596b-437c-ba40-a68ed754c348.pdf

Merriam-Webster Dictionary  Learners Dictionary 3000 words  http://learnersdictionaries.com/3000-words

Other dictionary publishers have prepared their own lists of 3000 words

A Corpus of American Spoken English prepared by a professor at Brigham Young University can be viewed.  A list of the 5000 most frequently used words can be downloaded for individual use, but not posted online.

Books and CDs with vocabulary lists

There are not many CDs available and the costs are usually more than $ 30.00 for a CD set.

Vocabulary word books can be found at public libraries.  The Dewey Decimal Classification  is 428.1  .

A common library catalog subject heading is:   Vocabulary–Problems, Exercises

Books at bookstores, new and used books

Ask for books in the Vocabulary/Spelling section.  This may be near handbooks for writers .

These books may contain from 250 to 1500 words.  Choose one with the greatest number of words.

An ASVAB study guide may have a chapter with words, prefixes, suffixes, word roots, and other information.

—————————————————————————–

If you cannot find a vocabulary word book, look for test books for the SAT, ACT, or civil service exam study guides.

Some of these books may have a word list and study guide to help increase vocabulary.

Physical bookstores are declining in number.  Many stores selling used and rare books do not stock the ASVAB test books.

This an alphabetical list of SOME of the online book selling websites that stock back copies of ASVAB study guides.

Which guide should a person buy at a store or from an online book selling website.  It is a difficult task, as about 20 different book publishers offer study guides.  I have a preference for two publisher’s guides, but I always look at other publisher’s guides for diagnostic and practice tests with different problems, different advice about how to mentally and physically prepare oneself for taking the ASVAB.

A cataloging record service known as Worldcat, from OCLC, Inc., is used by thousands of libraries worldwide to find catalog records to put into local catalogs, and to offer catalog records created by a library staff for use by other libraries.

One of the features of the catalog record display is that there is a line with a phrase like

“1 of 6 libraries of  nnn libraries using this record.”  The number of times a title, or an edition of a title,  has been purchased by libraries, has guided me in my choice of ASVAB study guides.  I also go to a nearby book store to see what titles they carry in stock, and look through each different title.

Purchasing online:  I have located these websites and have listed them in alphabetical order

http://www.abebooks.com

http://www.alibris.com

http://www.amazon.com

http://www.thriftbooks.com

There are other websites and stores with online websites.  As for myself,  I am looking for used copies of ASVAB study guides published 2010 and later.   .  Fair condition is fine, as long as pages are not missing. or a prior user has filled out the answer block pages.

 

There are a large number of webpages and subscription sites that will help with the ASVAB. There are professional tutors of the ASVAB test.

 

I like these guides because they test my knowledge and skills in different ways that are unlike the SAT test, GRE, or other tests.   They are great ways to pass the time, and learn something while waiting in line or a reception area for an appointment.   Thomas Lindsey  mos96b@yahoo.com

 

 

 

 

 

 

 

 

 

New Post trying to consolidate all the Mathematical Info material

I THINK THAT THIS POSTING COMBINES ALL POSTINGS FROM JULY 2016 and the one before this one into one message about ASVAB Mathematics.

 

I have tried to consolidate all my notes and ideas about doing arithmetic, algebra, and geometry on a test like the Armed Services Vocational Aptitude Battery.   I came upon a document in the ERIC collection eric.ed.gov from an organization known as the Education Trust.  30 % of high school graduates are not able to pass the ASVAB and be eligible to enter the military if they wish.  Whatever opinions each person may have about serving in the U.S. military services, they are a great source of training  after high school for young people.

It is a shame that our school systems seem to be failing 30 % of the students that they graduate.  Many of these students are not considering enrolling in college regardless of how much financial aid they might be offered.

I suspect that most students studying for college admission tests are not taking any type of ASVAB exam.  I wonder what the failure rate on an ASVAB test would be if all students took the exam.

Here are my consolidated mathematics notes.   I may have copied part of this material several times, I am editing it.

I _THINK_  that I have eliminated all the duplication.

ORDER OF PRECEDENCE IN DOING MATHEMATICAL CALCULATIONS
The acronym PEMDAS, often appearing with the  next sentence gives the order.
Please Excuse My Dear Aunt Sally
Do arithmetic work within parentheses first.  Then work on exponents.
Multiplication is next.  Then do Division work.  Addition work.  Subtraction work is next.
——————————————————————————
ALGEBRA
Find common factors that are part of each part of the equation and remove them outside the common area.
2x[squared] + 12x + 18   is the same as 2(x[squared] + 6x + 9)  The part within parentheses looks like
an (x + y)[squared] type quadratic equation.     The formula could be rewritten as 2(x + 3)[squared]
 [squared] is meant to represent an exponent, shown on a page with a number raised 1/2 space above the line.
Locate any common factors that are part of each part of the equation and remove them outside the common area.
2x[squared] + 12x + 18   is the same as 2(x[squared] + 6x + 9)  The part within parentheses looks like
an (x + y)[squared] type quadratic equation.     The formula could be rewritten as 2(x + 3)[squared]
 [squared] is meant to represent an exponent, shown on a page with a number raised 1/2 space above the line.
Three common quadratics
(x + y)(x-y)  =  x [squared] – y [squared]  “squared” means the number 2 appears one half line above the typed x and y
(x + y) [squared] = x [squared] + 2xy + y [squared]
(x-y) [squared] = x [squared] -2xy + y [squared]
A perfect square number such as 4, 16, 25, 36, 49, 64, 81 in front of the x[squared] or y[squared] in a quadratic equation. means
that it is probably one of the three common quadratics.

Locate any common factors that are part of each part of the equation and remove them outside the common area.
2x[squared] + 12x + 18   is the same as 2(x[squared] + 6x + 9)  The part within parentheses looks like
an (x + y)[squared] type quadratic equation.     The formula could be rewritten as 2(x + 3)[squared]
 [squared] is meant to represent an exponent, shown on a page with a number raised 1/2 space above the line.
———————————————————————–
The capital letter X is used as the symbol for multiplication.
F is for First, O is Outside, I is for Inside, and L is for Last.
Multiplying (4 + 2x) times (5 + 6y) using FOIL  (4 + 2x) X (5 + 6y)    or (4 + 2x)(5 + 6y)
Multiply the FIRST part of the term inside each parentheses.  4 X 5 = 20  F for First
Multiply the OUTSIDE part of the term inside each parentheses.  4 X 6y = 24 y O for Outside
Multiply the INSIDE part of of the term inside each parentheses 2x X 5 = 10x  I for Inside
Multiply the LAST part of the term inside each parentheses 2x X 6y = 12xy  L for Last
Add all the terms together to get 20 + 24y + 10x + 12xy
If the terms inside parentheses had been (4 + 2x)(5 + 6x), the sum would be 20 + 34x + 12x[squared]  x with a  raised 2
—————————————————————————
Mathematical Knowledge  One Variable Equation
Multiply the OUTSIDE part of each term)  4 X 6 y  = 24y  O for Outside
Multiply the INSIDE or second part of each term  2x  X  5 = 10x
Multiply the Last part of each term  2x X 6y  = 12xy
Add the result of each multiplication   20 + 24y + 10x + 12xy
It is easier to work with positive values on both sides of the = sign when it possible.
Let’s use  15a  = 45  .  Divide both side of the equation by the number 15 .  15a/15 = 45/15
a = 3      Mathematics check  12(3) +9 = 45.
Linear equations where one or more sides have a fraction.
2x + 7 =  x/4      .    The first step is to remove the fraction.
4 X (2x+ 7) = 4 X  (x/4)       8x + 28 = x   .  Move the number or the 8x to one side.
8x – x  = – 28   7x  = -28    7x/7 = -28/7     x = -4
————————————————————————-
Mathematical Knowledge  Prime Numbers, Factoring Numbers, Inequality
PRIME NUMBERS
A prime number is an integer that cannot be separated by two numbers multiplied together.
1, 2, 3,  5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 are prime numbers in the range 1 to 50
Numbers ending with 0, 2, 4, 6, 8 can be divided by the number 2 .
Numbers 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 44, 48 can be divided by the number 3.
Numbers ending with a 5 or 0 can be divided by 5, and other numbers depending upon the number.
Number 49 can be divided by the number 7.  7 X 7 = 49
FACTORIALS
These numbers are an integer followed by the exclamation point sign , such as 9!
9!  is 9 X 8 X 7  X 6 X 5 X 4 X 3 X 2 X 1     504 X 120 X 6 = 362,880
4! is 4 X 3 X 2 X 1  = 24
     ASVAB problems that use factorials may appear with statements such as:
     Tom, Dick, Harry, and Jane have are standing in a line.  If they change places so that each of them
is at the front of the line, how many lines are possible?
4!  4 factorial number of lines        4 x 3 x 2 1 = 24
 TDHJ, TDJH, THDJ, THJD, TJDH, TJHD              Tom in front of 6 lines
DTJH, DTHJ, DJTH, DJHT, DHJT, DHTJ               Dick
HTDJ, HTJD, HJTD, HJDT, HDJT, HDTJ               Harry
JTDH, JTHD, JHDT, JHTD, JDTH, JDHT               Jane
 It took many minutes to figure out the chart of letters.  This shows why factorials are so handy.
 INEQUALITY, LESS THAN OR EQUAL TO, GREATER THAN OR EQUAL TO
<  is used to represent two numbers or variables  when one is less than the other.  a  <  b  , a < 8
> is used to represent two numbers or variables when one is greater than the other.  a > b , a > 8
 LESS THAN OR EQUAL TO, GREATER THAN OR EQUAL TO
  The < and > signs are used, but a bar appears under the character.  <_        and   >_
   (I am not sure how to create these symbols in this Word Press system, probably by typing multiple keys simultaneously.
Another mathematical symbol is for “not equal to” . It is an equal sign  =  with a slash through it.  /=
  n /= 2    means that the variable n is not equal to 2.
  SQUARE ROOT AND CUBE ROOT SYMBOLS
 The root sign is a symbol that looks like a check mark with a line at the top of the check mark.
The square of 2 is 4, the square root of 4 is 2. square of 3 is 9, the square root of 9 is 3, square of 4 is 16, square root of 16 is 4
Squares 2, 4 ;  3, 9; 4, 16; 5, 25; 6, 36; 7, 49; 8, 64; 9, 81; 10, 100; 15, 225; 20, 400;  25, 625; 30, 900
The squares of numbers in between have a value of:   a( squared) + 2ab + b (squared)
The square of 13,  when a = 10 and b = 3 is:  (10 X 10) + 2(10)(3) + (3 X 3)     100 + 60 + 9 = 169
Square root of 4=2; 25=5; 36=6; 49=7; 64=8;  81=9; 100=10; 225=15; 400=20; 625=25; 900=30 .
  What if the value to be squared has a decimal part in the number, such as 1.5?
This is a list of squares from 1.4 to 9.5
Known length angle side length[squared] + unknown length  right angle side[squared] = hypotenuse side[squared]
SCALENE TRIANGLE: No interior angles of the triangle equal 90 degrees, and all angles have different values.
ISOSCELES TRIANGLE:  Two sides of the triangle have the same length.  The angles formed when the equal length side  cross the third side are of equal value.
OBTUSE TRIANGLE:  One angle has a value greater than 90 degrees. The values of all angles add up to 180 degrees.
 EOMETRY, PARALLEL LINES, CIRCLES, AREA OF GEOMETRIC FIGURES AND CIRCLES
 PARALLEL LINES  ____________   Two or more lines are the same distance apart.
____________
                  a     /  b
_______/____    The lines to the left are a set of slash marks and a set of underline characters.
/         Assume that the slash marks are an unbroken line.   The underline characters
c          d    can be known as an angle of 180 degrees.  Angle a and Angle B = 180 degrees.
Angle c and Angle d = 180 degreees.
Angle a value is equal to the value of angle d.  Angle b  value is equal to the value of angle c.
 Some ASVAB mathematics may give values for two angles such a and c, or a and d, and you must determine the
value of angle of another angle.  a + b = 180 , and a + c= 180.  Using subtraction, the value of the other
angles can be calculated.
CIRCLES and VOLUME.
Radius of A circule is from the middle point of the circle to the edge.  The Diameter is 2 times the radius.
The CIRCUMFERENCE or length of a circle if it were cut apart and laid straight in a line, is
2 times the number PI.  PI is an irrational number with no end of its decimal portion.
For simple calculation, the value of PI is given as 3.14
 Area of a circle is PI times Radius times Radius  or PI times r[squared]  r X r .
        Area of a triangle is 1/2 times length of base times length of height.
There are many mathematics help sites.  The United States Coast Guard Recruit Training Center Cape May, New Jersey
has list of web addresses for sites.  Some URLs are not operational at this time, and need to be corrected.
 http://uscg.mil/hq/capemay/AdminServices/asvab.asp     My favorite of the list is math2.org
        One of my favorite sites not on the list is a site created by a mathematics professor, last name Perez, at
Saddleback College in Mission Viejo, California [near San Diego].http://www.saddleback.edu/faculty/lperez/Algebra2Go    It has instruction information from arithmetic
through the first two semesters of calculus [5th year mathematics in high school or freshman mathematics for
college science majors.]
Tom Lindsey, mos96b@yahoo.com  August 1, 2016

Geometry, Angles, Parallel Lines, and Figure Shapes

A triangle has three lines. Each line intersects or touches the end of two other lines.

The interior angles of a triangle add up to 180 degrees.

An equilateral triangle has three sides of equal length.  the interior angle of each angle is

60 degrees.

An equilateral triangle has two lines of equal length that touch at one point and cross a

line at the bottom the two lines.  The interior angles at the intersection of the bottom line are

equal in value.

A SCALENE triangle has 3 interior angles of different values.  All the angles are less than 90 degrees.

An OBTUSE triangle has one angle that is greater than 90 degrees but less than 180 degrees.

A RIGHT ANGLE triangle has two lines that interest with a 90 degree angle at intersection.

The long side opposite the 90 degree angle is called the hypotenuse.  When right angle

length 1 is squared, and length 2 is squared, the sum of the numbers is equal to the square of the side opposite the right angle   That side is called the hypotenuse.

(a X a) + (b X b) = (c X c)

 

PARALLEL LINES

Parallel lines have the same distance between each point on the line for the length of each line.    The pound sign on the keyboard  # has two horizontal parallel lines and two diagonal lines.   A website with geometry information such as  math2.org or Algebra2Go ,

http://www.saddleback.edu/faculty/lperez/Algebra2GO  or other websites with geometry explanations have pictures of parallel lines and the relationship of angles.

In geometry, a line  is an angle of 180 degrees.  Cutting a diagonal  across a line creates two angles.  Two complementary angles are equal to 90 degrees.  Two supplementary angles are  equal to 180 degrees.    Check a geometry textbook or website to confirm or correct this definition of complementary and supplementary angles.

POLYGONS  Polygons are enclosed areas with 4 or more sides.  A square, trapezoid, rectangle, and any area enclosed by four sides is a polygon.

Polygons usually begin with 5 sides, the pentagon.  the six sided polygon is the hexagon, the rarely seen seven sided figure is the heptagon, the eight sided figure is the octagon, and the 10 sided figure is the decagon.  The interior angle of a pentagon is 108 degrees, an octagon is 135 degreees, and a decagon is 144 degrees.

 

 

 

 

 

Squares , Square Roots, and Cube Roots

The root sign is a symbol that looks like a check mark with a line at the top of the check mark. –

The square of 2 is 4, the square root of 4 is 2. square of 3 is 9, the square root of 9 is 3, square of 4 is 16, square root of 16 is 4

Squares 2, 4 ;  3, 9; 4, 16; 5, 25; 6, 36; 7, 49; 8, 64; 9, 81; 10, 100; 15, 225; 20, 400;  25, 625; 30, 900

The squares of numbers in between have a value of:   a( squared) + 2ab + b (squared)

The square of 13 is  (10 X 10) + 2(10)(3) + (3 X 3)   when a = 10 and b = 3

100 + 60 + 9 = 169

Square roots  4=2; 25=5; 36=6; 49=7; 64=8;  81=9; 100=10; 225=15; 400=20; 625=25; 900=30 .

A cube root will have the root sign with a number 3 above it or in the pocket of the check mark.

What if the value to be squared has a decimal part in the number, such as 1.5?

This is a list of squares from 1.5 to 9.5

SQUARED Value of

1.4 = 1.96

1.5 = 2.25;

2.0 = 4      2.5 = 6.25

3.0= 9      3.5 = 12.25

4.0= 16    4.5 = 20.25

5.0 = 25   5.5 = 30.25 ;

6.0= 36.0 6.5 = 42.25

7.0=49.0  7.5 = 56.25

8.0=64     8.5 = 72.25

9.0=81     9.5 = 90.25

Calculating 9.5 squared using the FOIL method, separating 9.5 into 9.0 and 0.5

( 9.0 + 0.5)((9.0 + 0.5)  = 81.0  + 4.5 + 4.5 + 0.25 = 90.25

Some ASVAB mathematics questions may ask for the square root of a number that is not a perfect square.    It may ask for the square root of 19 , or 23,  or 32,  and provide 4 choices.

From the table above, we see that 4.5 squared = 20.25.  The square root of 19 is a number

between 4.0 and 4.5 .   The square root of 23 is between 4.5  squared (20.25) and 5 squared

= 25, so the root is between 4.5 and 5.0

The square root of 32  is the same as “”square root of 2” X “square root of 16”.

The square root of 16 is 4, so the square root of 32 is the same as 16 X “square root of 2”.

The number value is something higher than 16 X 1.4 =,  or higher than 22.4 , but less than

16 X 1.5=  or less than 24.0   .

CUBES AND CUBE ROOTS

The symbol for a Cube Root is the root sign with the number 3 above the check mark.

The cubes of integers 1 to 10 are  1, 8, 27, 64, 125, 216, 343, 512, 729, and 1000.

 

 

Mathematical Knowledge Prime Numbers, Factoring Numbers, Inequality Signs

PRIME NUMBERS

A prime number is an integer that cannot be separated by two numbers multiplied together.

1, 2, 3,  5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 are prime numbers in the range 1 to 50

Numbers ending with 0, 2, 4, 6, 8 can be divided by the number 2 .

Numbers 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 44, 48 can be divided by the number 3.

Numbers ending with a 5 or 0 can be divided by 5 and other numbers depending upon the number.

Number 49 can be divided by the number 7.  7 X 7 = 49

 

FACTORIAL NUMBERS

These numbers are an integer followed by the exclamation point sign , such as 9!

9!  is 9 X 8 X 7  X 6 X 5 X 4 X 3 X 2 X 1     504 X 120 X 6 = 362,880

4! is 4 X 3 X 2 X 1  = 24

 

INEQUALITY  , LESS THAN OR EQUAL TO, GREATER THAN OR EQUAL TO

<  is used to represent two numbers or variables one less than the other  a  <  b  , a < 8

> is used to represent two numbers or variables one greater than the other  a > b , a > 8

These are used to represent situations where the variable is to be less than or greater than a number

Less than or equal to, or greater than or equal to

The < and > signs are used, but a bar appears under the character.

<_        and   >_     (I am not sure how to create these symbols in this Word Press system, but it is probably a typing multiple keys simultaneously.

Another mathematical symbol is for “not equal to” . It is an equal sign  =  with a slash through it.

/=     n /= 2    means that the variable n is not equal to 2.

 

Mathematical Knowledge Equations with two variables

These equations have two letters for variables, such as a and b,  p and q, x and y.

An equation might be 5x + y +9  or a formula such as 5a[superscript 3, a X a X a ]  + 5xy

Arithmetic uses a system with the acronym PEMDAS for the order of calculations in a series of addition, subtraction, multiplication, division, and exponent power actions.  A frequently used phrase to recall the PEMDAS order is

1. Please Excuse My Dear Aunt Sally

2.  A phonetic alphabet phrase is Papa Echo Mike Delta Alpha Sierra

Number 1 is most frequently used in textbooks and study guides.

P  Parentheses  (  )  Perform the mathematical actions with the parentheses.

E Exponents   with a number raised one half line above the letter.  The number may be positive or       negative.

M  Multiplication

D  Division

A  Addition

S  Subtraction

What is the value of 5a(x + y) when a = 4,  x = 2,  and y = 7

Parentheses first (x + y) = 2 + 7 = 9  .  Add the two numbers together.  If there had been three variables between the parentheses,  add the numbers on either side of the + sign, and then subtract that number from the number on the other side of the  –   sign.

Exponents   there are no exponents in this equation, such as a X a  or ” a squared “.

Multiplication  Multiply 5 X a  to get 5 X 4 = 20

Division   there are no division actions for this equation.

Addition/Substraction  There are no additional actions to be done within the equation.

5a(x + y) when a = 4, x = 2, and y = 7  is  5(4)(2 + 7) = 5(4)(9) = 180

 

 

 

ASVAVB and similar tests study help websites

Internet Sources that I think are useful for preparation to take the Arithmetic and Mathematics Knowledge Parts of the Armed  Services Vocational Aptitude Battery
It is my understanding that these portions of the ASVAB are the ones with the highest failure rate.
I have been looking for internet accessible study help.  I have found two groups of sources
Internet web pages and web sites.
Youtube videos.
I have looked at sample GED Tests and sample ASVAB Tests.  I think that success in completing GED type questions will help a  a person succeed in completing the Arithmetic and Mathematics segments of the ASVAB.
The ASVAB  has many questions that are based on algebra or geometry.  The following lists of website addresses (URLs) are some  I think will help a person.  There are many other sites with good instruction.  I chose to limit my list to websites  that usually have a domain ending in:  edu  , k12, or org.
There are many study guides available.  I found books by 7 different publishers at a bookstore.  Public libraries may have  “Test Book Section” with a variety of study guides for civil service, military service, undergraduate, and professional  education programs.  Used book stores may have copies of older editions of study guides.  A major change in the GED test  system was made in 2014, so only GED guides with copyright dates of 2014 or later should be purchased or borrowed.
ALGEBRA
     Professor Perez
http://saddleback.edu/faculty/lperez/algebra2go/prealgebra/index.html  .
This site was started by Professor Perez of Saddleback Community College, Mission Viejo, California.
The segments begin with pre-algebra mathematics, but continue up through algebra, and perhaps even into calculus.
Web pages are available in English AND in Spanish.   The file formats are in several different programs,  including .wmv, and Youtube videos.
     Khan Academy
http:// www.khanacademy.org
The Khan Academy was started by by Salman Khan in 2006 to provide free, high-quality instruction to anyone with access  to a computer.  Broad area of education include Mathematics, Science and Engineering, Arts and Humanities, Computing, and  Test Preparation.
The segments with videos to help those preparing for the ASVAB include Arithmetic, Algebra, Geometry, and Probability and Statistics.
A typical URL begins with https://www.khanacademy.org/math/algebra-home/     and one of  these words  algebra , arithmetic , geometry , probability   .
There are subtopics for each of the words.  I recommend getting an ASVAB study guide, using it, and then looking at the Kahanacademy video listings to find    the video or videos that are most likely to match the study guide topic.  (New study guides may have a CD disc or password card included within which will provide links to the publisher’s own help site.  Take advantage of this material if it is in the guide.)
GEOMETRY
https://www.saddleback.edu/faculty/lperez/algebra2go/    The sections that show up on the left hand side of the web page under Courses,  Math 351 down through Intermediate Algebra may be useful to prepare for examinations.
http://dummies.com  The publishers of the “Dummies” book series have web pages about the concepts of geometry and use of geometry.
 Some of the websites that I found are:
  dummies.com/how-to/content/geometry-formulas-you-should-know.html
                                                         /adding-and-subtracting-segments-and-angles.html
/getting-to-know-angles.html
/how-to-measure-line-segments.html
/getting-to-know-points.html
                                                     /bisecting-and-trisecting-segments.html
 While scanning Youtube,  I came upon a video titled  “Most missed GED Math Test Problem”  .
I have not checked my ASVAB Test Guides to see if this problem type is also used in the ASVAB test, but I have a hunch that this problem type does appear in the ASVAB.
 http://youtube.com/watch?v=4kEpzeCDL_K   (I hope that I have the letters and numbers correct in capitalization.)
Khanacademy.org has videos offering instruction in geometry.  I think that a person studying for an exam with a pre-examination information sheet, or a common study guide, should look at the sheet or guide and the list of Khan Academy videos to see which ones will help them prepare for that specific examination.
 There is a free website  http://www.GEDMathlessons.com  which may be helpful in studying the types of problems on that exam that are probably similar to those found on the ASVAB test.   The author of this site offers a larger, pay for use, site for the total GED.
You may not need to subscribe to it unless you do not have a high school diploma.  GED certificate holders must receive a higher score on the AFQT and ASVAB test to be considered enlistment.
If you have a chance to get a high school diploma OR go for a GED, get the diploma./
Studying  for the GED test in SPANISH.
I found three sites that offer preparation material to take the Spanish language GED examination.  The ASVAB is an English language test.  If you feel more
comfortable learning the arithmetic and mathematics in Spanish, you might try these sites.
Spanish GED  www.spanishged365.com
GED EN  ESPANOL
Khanlatinoamericano  (Khan Academy)
I located a set of 11 lessons for geometry in Khanlatinoamericano  when I searched Youtube.com  Geometrica 1   ….. Geometrica 11
There may be a set of lessons for algebra    The English and spanish spellings of algebra are the same except for the accent over the a.
The master webpage for Khanlatinoamericano may have a table of contents list similar to the ones of the English language web site.
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