ASVAB - Arithmetic Reasoning / Mathematics Knowledge 2
Formula to solve (5^5)(5^3)
(a^x)(a^y) = a^(x+y)
the closed line of a circle-that is, the distance around the circle
(circles) circumference
is measured as a line passing through the center of the circle, from a point on one side of the circle all the way to a point on the other side of the circle
(circles) diameter
the measurement from the center of the circle to any point on the circumference of the circle
(circles) radius
Formula used to solve (6^3)^9
(x^a)^b = x^ab
an acute angle is more than ___° but less than ___°
0°, 90°
___ kilometer = 1000 meters
1
1 = 1.00 = 100%
1 to decimal to percent
1/10 = .10 = 10%
1/10 to decimal to percent
___ kilometers = 1 meter
1/1000
If the scale on a road map is 1inch=250 miles, how many inches would represent 1,250 miles?
1/250=m/1,250 (1,250×)1/250=m/1,250(×1,250) 1,250/250=m m=5
to find the area of a triangle
1/2bh or the ___ of a triangle is 1/2 the product of the base and the height
1/4 = .25 = 25%
1/4 to decimal to percent
___ decimeters = 1 meter
10
___ centimeters = 1 meter
100
___ millimeters = 1 meter
1000
a straight line is ___°
180°
1kg = ___ lbs
2.2
2/10 = 1/5 = .20 = 20%
2/10 (1/5) to decimal to percent
the fourth root of 16
2×2×2×2
3/10 = .30 = 30%
3/10 to decimal to percent
3/4 = .75 = 75%
3/4 to decimal to percent
a circle has ___ degrees
360°, any arc that isn't a complete circle measures less than 360°
the cube root of 27
3×3×3
4/10 = 2/5 = .40 = 40%
4/10 (2/5) to decimal to percent
5/10 = 1/2 = .5 = 50%
5/10 (1/2) to decimal to percent
6/10 = 3/5 = .60 = 60%
6/10 (3/5) to decimal to percent
7/10 = .7 = 70%
7/10 to decimal to percent
8/10 = 4/5 = .80 = 80%
8/10 to decimal to percent
9/10 = .9 = 90%
9/10 to decimal to percent
a right angle is exactly ___°
90°
an obtuse angle is more than ___° but less than ___°
90°, 180°
Although a total of 131 soldiers are authorized for an infantry company, B Company (Bulldogs), 3rd Battalion, 144th Infantry Regiment, has only 120 soldiers assigned, of whom 5% are officers. How many enlisted soldiers are assigned to the company? (A) 114 (B) 123 (C) 120 (D) 121
A
Danny is comparing the prices of tuxedos for his prom. A rental tuxedo costs $70, while a new tuxedo costs $120. Danny is thinking about having to have a tuxedo for next year's prom as well. Keeping this in mind, how much money will Danny save if he uses the same suit two years in a row? Assume that he will have to pay $4.50 to dry clean it before next year's prom. (A) $15.50 (B) $20.00 (C) $20.50 (D) $35.00
A
For a special mission, one soldier is to be chosen at random from among 3 infantrymen, 2 artillerymen, and 5 tank crewmen. What is the probability that an infantryman will be chosen? (A) 3/10 (B) 1/10 (C) 1/3 (D) 3/7
A
Simplify the expression [(x^2)y](2x - 3y) (A) 2(x^3)(y) - 3(x^2)(y^2) (B) 2(x^2)(y) - 2(x^3)(y^2) (C) 2(x^3)(y) - 2(x^2)(y^3) (D) 2(x^3)(y) + 3(x^3)(y^2)
A
Solve the following equation for y: ay - bx = 2 (A) (2 + bx) / a (B) 2 + bx - a (C) 2 / (a - bx) (D) (2 / a) - bx
A
Solve the following equation: (8 + 2 - 3)(7 - 9)^2 (A) 28 (B) -28 (C) 14 (D) -32
A
Solve the following equation: -6.1 * -8.05 (A) 49.105 (B) -56.35 (C) -49.105 (D) 51.85
A
What is the area of a circle whose diameter is 28 inches? Use 22/7 for the value of pi. (A) 616 square inches (B) 88 square inches (C) 44 square inches (D) 1,232 square inches
A
What is the maximum number of boxes, each measuring 3 inches by 4 inches by 5 inches, that can be packed into a storage space measuring 1 foot by 2 feet by 2 feet, 1 inch? (A) 120 (B) 60 (C) 75 (D) 98
A
Area of a Square
Area = (s)(s) or s^2
Area of a Triangle
Area = 1/2bh
Area of a Trapezoid
Area = 1/2h(b1 +b2), or h(b1+b2/2)
Area of a Parallelogram
Area = bh
Area of a Rectangle
Area = bh, or lw
Area of a Circle
Area = πr^2
A naval task force is to be made up of a destroyer, a supply ship, and a submarine. If 4 destroyers, 2 supply ships, and 3 submarines are available, how many different combinations are possible for the task force? (A) 9 (B) 24 (C) 8 (D) 12
B
A pecan tree 36 feet high casts a shadow 8 feet long. At the same time of day, a nearby mesquite tree casts a shadow 6 feet long. How tall is the mesquite tree? (A) 30 feet (B) 27 feet (C) 24 feet (D) 32 feet
B
A private pilot needs to calculate how much fuel is needed for an upcoming trip of his vintage Waco biplane. The biplane's Jacobs B2M radial engine consumes about 15 gallons per hour at the aircraft's cruising speed of 120mph, and about 18 gallons per hour at speeds above 200mph. The plane will take off from Love Field General Aviation in Fort Worth, Texas, and fly 120 miles at cruising speed and then for 30 minutes near its top speed of 214mph. If the pilot must put in enough fuel for the trip plus an additional 5 gallons, how much fuel is needed? (A) 21.5 gallons (B) 29.0 gallons (C) 38.0 gallons (D) 48.5 gallons
B
A quadrilateral is a parallelogram only if (A) It has 4 equal sides and 4 right angles (B) Both of its 2 pairs of opposite sides are parallel (C) It has at least 1 pair of parallel sides (D) It has at least 2 right angles
B
Heather bought a rectangular Afghan rug with a perimeter that measures 36 feet. If the long sides measure 12 feet each, how long is each short side of the rug? (A) 4 feet (B) 6 feet (C) 10 feet (D) 12 feet
B
How many 4oz candy bars are there in a 3lb package of candy? (A) 9 (B) 12 (C) 16 (D) 24
B
Jolie Marie has a 25-year term life insurance policy for $100,000. The annual premium is $15.00 per thousand. What is the total premium paid for this policy every 6 months? (A) $600 (B) $750 (C) $1,200 (D) $1,500
B
Of 128 dogs at a dog show, 50% were female. Among these females, 3 out of 4 were over the age of 4. How many of the dogs were females 4 years old or older? (A) 64 (B) 48 (C) 16 (D) 32
B
One section of the front lawn of the Walker family's house is 21 feet wide and 39 feet long. How much will it cost to weed and feed it if Ace Gardening Service charges $0.40 per square yard for this treatment? (A) $109.20 (B) $36.40 (C) $327.60 (D) $24.00
B
Solve for z: 4z + 3 - 5z = 28 - 3z (A) z = -9 (B) z = 14 (C) z = -28 (D) z = 17
B
The base of a cylindrical can is a circle whose diameter is 2 inches, and whose height is 7 inches. How many cubic inches are there in the volume of the can? (Use 22/7 for the value of pi) (A) 12 4/7 cubic inches (B) 22 cubic inches (C) 44 cubic inches (D) 88 cubic inches
B
The fuel tank of a gasoline generator has enough capacity to operate the generator for an hour and 15 minutes. About how many times must the fuel tank be filled to run the generator from 6h15pm to 7h00am? (A) 9.4 (B) 10.2 (C) 10.8 (D) 11.5
B
The points A(2,7) and B(5,11) are plotted on coordinate graph paper. What is the distance from A to B? (A) 7 (B) 5 (C) 25 (D) 14^(1/2)
B
What is the fifth term of the series 2 5/6, 3 1/2, 4 1/6, 4 5/6, ...? (A) 5 1/6 (B) 5 1/2 (C) 5 5/6 (D) 6 1/6
B
A barrel with flat sides (i.e., a cylinder) has a height of 36 inches and a radius of 15 inches. About how many gallons of liquid can it hold? (There are 231 cubic inches in a gallon; use 3.14 for the value of pi.) (A) 7.3 gallons (B) 35 gallons (C) 110.1 gallons (D) 264.3 gallons
C
A floor is made up of hexagonal tiles, some of which are black and some of which are white. Every black tile is completely surrounded by white tiles. How many white tiles are there around each black tile? (A) 4 (B) 5 (C) 6 (D) 8
C
A postal carrier can deliver mail to about 900 addresses in one day. In the city of Hewitt, there are 26,942 residents. Workforce policies require hiring 5 percent more carriers than are estimated in order to compensate for vacation, sick days, and so on. About how many mail carriers must be hired to deliver mail to all of the Hewitt citizens each day? (A) 29 (B) 30 (C) 31 (D) 32
C
Amanda is working as a hostess at a local restaurant until she graduates from college. She receives an equal cut of a 10% tip share (calculated on total sales) split on an hourly basis between the hostesses and busboys. Amanda also receives her hourly wage of $3.13 an hour. The restaurant sale's were $7,874 for a 7-hour shift that 3 hostesses and 2 busboys all worked from open to close. How much tip share did the busboys receive together on their shift? (A) $157.48 (B) $179.39 (C) $314.96 (D) $472.44
C
During 1 season, a college football quarterback attempted 439 passes and completed 267 of them for a total of 3,217 yards. What is his completion percentage? (A) 13.6% (B) 54.2% (C) 60.8% (D) 62.8%
C
Express 6/4 as a percentage (A) 50% (B) 75% (C) 150% (D) 225%
C
If 1 pound of mesquite-smoked, deli-sliced turkey breast cost $7.98 at the second-largest grocery store in town, and each slide is about 1 ounce, what is the cost of 5 slices?
C
If 2x -3 = 37, what is the value of x? (A) 17 (B) 38 (C) 20 (D) 80
C
If x^2 + x = 6, what is the value of x (A) 6 or -1 (B) 1 or -6 (C) 2 or -3 (D) 3 or -2
C
In a steakhouse, a guest orders a small steak entree with vegetables for $12.50, dessert for $3.50, and coffee for $1.49. If the tax on meals is 8.25%, what tax should be added to his check? (A) $1.03 (B) $1.40 (C) $1.44 (D) $1.74
C
Jonathan spent 4 hours studying, 1 hour raking leaves, 30 minutes doing laundry, and 2 hours watching TV. What percentage of his time was spent studying? (A) 46.6% (B) 50.0% (C) 53.3% (D) 57.1%
C
Jonathan wants to find the average number of miles traveled per day on his 3-day road trip. Since he is an engineer, he decides to set up the problem algebraically. If he drove A miles the first day, B miles the second day, and C miles the third day, what is the formula for the average number of miles driven per day? (A) 3abc (B) 3(a+b+c) (C) (a+b+c)/3 (D) (a+b+c)^3
C
June found a pair of red heels regularly priced at $120. The ones she found were priced at $54, while all of the other boxes of the same shoes were sale priced at $67. Since June is going to buy this particular pair of shoes, she wants to calculate the extra amount that she saved compared to the correct sale price. What is the difference between her mispriced shoes and the sale price of the shoes? (A) 44.2% (B) 55.0% (C) 10.8% (D) 14.0%
C
Over the course of the 6-week grading period, Jaycie took 5 tests for her Social Studies class; the teacher told her that her average for all 5 tests was 91. That night at home, she could remember only her 1st 4 scores: 88, 86, 94, and 96. What was her score on the 5th test? (A) 88 (B) 90 (C) 91 (D) 92
C
The value of 8^0 is (A) 8 (B) 0 (C) 1 (D) 1/8
C
Travis invests $5,000 at 4% annual interest. How much more must he invest at the same rate to insure that his annual income from both investments exceeds $700? (A) $9,750 (B) $10,000 (C) $12,500 (D) $14,750
C
Which of the following is a binomial? Example 1: 2(x^4) + 7(x^3) Example 2: 2 + 3 Example 3: 3x - 2 Example 4: 4ab - 5(a^3)(b^2) (A) Example 1 (B) Examples 1 and 4 (C) Examples 1, 3, and 4 (D) All examples are binomials
C
Circumference of a Circle
Circumference = 2πr, or πd
(5+3) * (2+1) * (10/20) + 5 = ? (A) 48 (B) 53 (C) 12 (D) 17
D
A cylindrical post has a cross-section that is a circle with a radius of 3 inches. A piece of cord can be wound around it exactly 7 times. How long is the piece of cord? (Use 22/7 as the value of pi) (A) 66 inches (B) 42 inches (C) 198 inches (D) 132 inches
D
A girls' softball team won 70% of the 40 games it played. How many games did it lose? (A) 28 (B) 30 (C) 22 (D) 12
D
In the drawing below, which angles are alternate interior angles, and are they congruent? (A) Angles 1 and 4 and angles 5 and 8; yes (B) Angles 2 and 3 and angles 6 and 7; yes (C) Angles 3 and 5 and angles 4 and 6; no (D) Angles 3 and 6 and angles 4 and 5; yes
D
June found a chandelier for the dining room for $1,399. However, since the model has been discontinued and the display had no factory packaging material, the store manager discounted the price to $1,149. What was the percentage of the reduction? (A) 10.8% (B) 12.9% (C) 14.1% (D) 17.9%
D
Multiply 7a^3b^2c by 3a^2b^4c^2 (A) 10a^5b^6c^3 (B) 21a^5b^6c^2 (C) 21a^6b^8c^2 (D) 21a^5b^6c^3
D
The value of 164^(1/2) to the nearest integer is (A) 18 (B) 42 (C) 26 (D) 13
D
What is the value of the expression x^2 - 5xy + 2y if x=3 and y=-2? (A) -25 (B) -27 (C) 32 (D) 35
D
What is the volume of a camping trailer that is 23 feet long, 15 feet wide, and 11 feet high? (A) 2,530 square feet (B) 2,950 cubic feet (C) 3,295 square feet (D) 3,795 cubic feet
D
Which of these is an example of similar figures in the geometric sense? (A) A soccer ball and a football (B) A right triangle and an isosceles triangle (C) A bicycle and a tricycle (D) A sailing ship and a scale model of that ship
D
Perimeter of a Parallelogram
Perimeter = 2(l + w), or 2l + 2w
Perimeter of a Trapezoid
Perimeter = b1 + b2 + s1 + s2
Surface area of a Cube
Surface area = (s)(s)(6)
Surface area of a Rectangular Prism
Surface area = 2(lw) + 2(lh) + 2(wh)
Volume of a Cube
Volume = (s)(s)(s) = s^3
Volume of a Rectangular Prism
Volume = lwh
a shape with four sides, has angles that add up to 360°
a quadrilateral
to find the perimeter of a triangle
add together the lengths of the three sides
sum, total, in all, perimeter, increased by, combined, added
addition clue words
0, and, when added to any number will result in that number; example 7⁺0=0
additive identity
is the negative of that number. when a number is added to its additive inverse, the answer is 0; example 4 ⁺ −4 = 0
additive inverse
to find the diameter of a a circle
always twice as long as the radius or 2r
a=pi*r^2
area of a circle
a=lw
area of a rectangle
a=s^2
area of a square
a=.5bh
area of a triangle
that regrouping numbers being added or multiplied will NOT affect the sum
associative property
a number that's used as a factor at least two times-its a number raised to an exponent. for example the base of 4³ is 4
base
c=2*pi*r
circumference of a circle
that reversing the order of addition or multiplication will NOT affect the sum.
commutative property
two angles that equal 90° when added together
complementary angles are
a whole number that can be divided evenly by itself and by 1, as well as by one or more other whole numbers
composite number
arcs of a circle and angles are measured in
degrees and (not very often) minutes or even seconds, 1 degree equals 60 minutes, and 1 minute equals 60 seconds
d=squareroot of 2l+2w
diagonal of a rectangle
d=s*squareroot of 2
diagonal of a square
when you subtract, all that remains is a
difference
rate (speed) × time
distance formula
a × (b ⁺ c) = ab ⁺ ac
distributive property of multiplication over addition
the same thing as multiplying it by the inverse (reciprocal) of that number
dividing a fraction
how do you figure out your gas mileage
dividing the number of miles by the amount of gas
share, distribute, ratio, quotient, average, per, out of, percent
division clue words
is, was, are, were, amounts to
equals clue words
has three equal sides, each of the angles measures 60°
equilateral triangle
a shorthand method of indicating repeated multiplication, for example 15×15 can also be expressed as 15²
exponent
integers (whole numbers) that can be divided evenly into another integer, To factor a number, you simply determine the numbers that you can divide into it.
factor
is represented by an exclamation point, you calculate a factorial by finding the product of (multiplying) a whole number and all the whole numbers less than it down to 1, so 6 factorial is 6×5×4×3×2×1
factorial
the side opposite the right angle which is the longest side of a right triangle
hypotenuse
any positive or negative whole number or zero, such as −6, 0, 27
integer
whole numbers that have square roots that are decimals that go on forever and have no pattern that repeats
irrational numbers
formula to find the volume of boxes
length × width × height or lwh
product, total, area, cubic, times, multiplied by, of
multiplication clue words
1, and when multiplied by any number, will result in that number; example 7 ×1 = 7
multiplicative identity
is the reciprocal of that number (one divided by that number). when a number is multiplied by its multiplicative inverse, the answer is 1
multiplicative inverse
area of a triangle and/or square
multiply length times width or lw
parentheses take precedence, you should do everything contained in parentheses first
order of operations step 1
exponents come next
order of operations step 2
multiplication and division
order of operations step 3
addition and subtraction are last
order of operations step 4
a quadrilateral that has opposite sides that are parallel, and their opposite sides and angles are equal. the angles don't have to be right angles.
parallelogram
p=2l+2w
perimeter of a rectangle
p=4s
perimeter of a square
p=s1+s2+s3
perimeter of a triangle
to measure the circumference of a circle, use the number ___
pi
formula to find the volume of cylinders
pi × the radius squared × height or (pi)r²h
formula to find the circumference of a circle
pie × diameter or (pi)d
formula to find the area of a circle
pie × the square of the radius or (pi)r²
a whole number that can be divided evenly by itself and by 1 but not by any other number
prime number
when you multiply, you come up with a
product
if you know the lengths of two sides of a right triangle, you can determine the length of the thrid side using the formula a² ⁺ b² = c², where a and b represent the legs and c is the hypotenuse
pythagorean theorem
an equation that includes the square of a variable
quadratic equation
when you divide, you're left with a
quotient
r=.5d
radius of a circle
a fixed quantity,a 5% interest rate for example
rate
distance ÷ time
rate formula
shows a relationship between two things, if Margaret invested in her tattoo parlor at a 2:1 ratio to her partner Julie, then Margaret put in $2 for every $1 that Julie put in
ratio
the number by which another number can be multiplied to produce 1, if you have a fraction its reciprocal is that fraction turned upside down
reciprocal
a quadrilateral that have all right angles
rectangle
a quadrilateral that has four sides of equal length, but the angles don't have to be right angles
rhombuse
has one right angle, therefore the remaining two angles are complementary
right triangle
formula to find the volume of a cube
side × side × side or s³
principle (the initial amount invested) × rate × time
simple interest formula
a quadrilateral with four sides of equal length, and all the angles are right angles
square
the factor of a number that when multiplied by itself produces the number
square root
the number that, when multiplied by itself equals the original number, for example the square root of 36 is 6, if you square 6 or multiply it by itself you produce 36
square root
difference, how much more, exceed, less than, fewer than, decreased
subtraction clue words
when you add two numbers together, you arrive at a
sum
two angles that equal 180° when added together
supplementary angles are
sa=6s^2
surface area of a cube
sa=2lw+2wh+2lh
surface area of a rectangular box
move the decimal point two spaces to the right and add a percent sign, for example 0.6 becomes 60%
to change a decimal into a percent
divide the numerator by the denominator
to change a fraction into a decimal
drop the percent sign and move the decimal point two places to the left, adding zeros as needed.
to change a percent to a decimal
a quadrilateral that has exactly two sides that are parallel
trapezoid
consists of three straight side whose three angles always add up to 180°
triangle
perimeter of a rectangle
two times the length plus the width or 2(l⁺w)
the space a solid shape takes up, measured in cubic units
volume
v=s^3
volume of a cube
v=pi*r^2*h
volume of a cylinder
v=lwh
volume of a rectangular box
Formula to solve (3)^-2
x^-a = 1/x^a
Formula used to solve 10^-3 / 10^-6
x^a / x^b = x^a-b = answer (note: must have same base)
square root: radical sign
√
