Mathematics Knowledge ASVAB, AVSAB Mathematics Knowledge

A cube has a volume of 64 cubic inches. What's its surface area? a.)16 sq in b.)64 sq in c.)96 sq in d.)32 sq in

c.)96 sq in *V=64 find the cube root of 64: 4^3 To find the surface area add 4+4=16 Multiply by 16 by 4=96

4!= a.)16 b.)40 c.)0 d.)24

d.)24 *4x3x2x1=24

Which of the following fractions is the largest? a.)2/3 b.)5/8 c.)11/16 d.)3/4

d.)3/4 *3/4=0.75

What's the product of _/36\ and _/49\? a.)1,764 b.)42 c.)13 d.)6

b.)42

Evaluate 3x + 7 when x = -3. A. -2 B. 10 C. 16 D. 30

A. -2 A. Substitute -3 for x. Then 3(-3) + 7 = -9 + 7 = -2.

(y^2)^3+y^2= a.)y^7 b.)y^6+y^2 c.)y^8+y^2 d.)3y^2

b.)y^6+y^2

(x^3)^3 a.)3x^3 b.)x^6 c.)x^9 d.)2x^6

c.)x^9

Which expression represents the volume of a cylinder whose height is equivalent to the length of the radius? A. pr2 B. pr3 C. (pr)2 D. (pr)3

B. pr3 B. The volume of a cylinder is given by the formula V = pr2h, where r is the radius of the circular base and h is the height. Since h = r, V = pr2r = pr3.

What is the area of the figure shown? A. 130 ft2 B. 145 ft2 C. 160 ft2 D. 175 ft2

B. 145 ft2 B. Divide the figure into a rectangle and triangle as shown. The area of the figure equals the area of the rectangle plus the area of the triangle. The rectangle = length × width or 10 × 13 = 130 ft2; the triangle = ? base × height or ? ?. Together, the area is 130 + 15 = 145 ft2.

At 3:00pm, the angle between the hands of the clock is? a.) 90 degrees b.) 180 degrees c.) 120 degrees d.) 360 degrees

b.) 180 degrees

Solve the inequality |x|<3 a.)3<x<3 b.)-3<x<3 c.)-3>x>-3 d.)-3>x<3

b.)-3<x<3

b.)x > 3

What inequality is represented by the number line seen in the figure? a.)x b.)x > 3 c.)x = 3 d.)x ≤ 3

(3 - 1)×7 - 12 ÷ 2 = A. 1 B. -2 C. 4 D. 8

D. 8 D. Following the correct order of operations produces: (3 - 1) × 7 - 12÷2 = 2 × 7 - (12÷2) = 14 - 6 = 8.

12 is 15% of what number? A. 0.0125 B. 1.8 C. 18 D. 80

D. 80 D. Let n represent the number. If 12 is 15% of n, then 12 = 0.15n. Divide both sides by 0.15. Therefore, n = 80.

Solve for m: 3m - 12 = -6 A. -6 B. 0 C. 2 D. 6

C. 2 C. 3m - 12 + 12 = -6 + 12; 3m = 6; Dividing both sides by 3 results in m = 2.

The slope of the line shown is A. -2/5 B. -5/2 C. 2/5 D. 5/2

C. 2/5 C. Slope is found by identifying two points on the line and finding the (change in y)/(change in x). The points (0, 0) and (5, 2) form the slope (2 - 0)/(5 - 0) = 2/5.

If a = 5/2 then 1/a = A. 2 B. 5 C. 2/5 D. 5/2

C. 2/5 C. Substitute 5/2 for a, giving you 1/a = 1/(5/2) = 1 x 2/5 = 2/5.

If 7p + 5q = -3, find q when p = 1. A. -1 B. -2 C. -1.142857143 D. -0.285714286

B. -2 B. Substitute 1 for p and solve for q. 7(1) + 5q = -3 and 7 + 5q = -3. 7 + 5q - 7 = -3 - 7 and 5q = -10. Dividing both sides by 5 results in q = -2.

The greatest common factor of 24 and 36 is A. 6 B. 12 C. 36 D. 72

B. 12 B. Factors of 24 are 2 × 2 × 2 × 3. Factors of 36 are 2 × 2 × 3 × 3. The greatest common factor is 2 × 2 × 3 = 12.

b.)8

In the circle seen below, what is the value of x. Where one section of the circle is 8? a.)4 b.)8 c.)10 d.)12

What angle is complementary to 47 degrees? a.)33 degrees b.)43 degrees c.)93 degrees d.)133 degrees

b.)43 degrees *Two angles are coplementary if they add up to 90 degrees. This means that the complementary angle to 47 degrees is equal to 90-47 = 43 degrees.

If 2b+3=1/8, b= A. -6 B. -3 C. 0 D. 2

A. -6 A. 1/8=1/23=2-3 so 2b+3=2-3 and b + 3 = -3. Therefore, b + 3 - 3 = -3 - 3 = -6.

How many minutes are there in 1 week? A. 10,080 B. 1,440 C. 420 D. 168

A. 10,080 A. There are 60 minutes in 1 hour, 24 hours in 1 day, and 7 days in 1 week. So 1 week = ? = 7 × 24 × 60 = 10,080 minutes.

If x is a positive integer, solve x2 + 6x = 16. A. 2 B. 4 C. 8 D. 10

A. 2 A. Set the equation equal to 0 and factor. x2 + 6x - 16 = 0 and (x + 8)(x - 2) = 0. Then, either x + 8 = 0 or x - 2 = 0, so x = -8 or x = 2. Since x is positive, x = 2 only.

If the area of a square is 400, what is the length of its side? A. 20 B. 40 C. 100 D. 200

A. 20 A. The area of a square is s2 where s is a side of the square. If s2 = 400, then s = √400 = 20.

Subtract (2x3-3x+1)-(x2-3x-2) A. 2x3-x2+3 B. 2x3-x2-6x-1 C. x3-6x-1 D. x2+3

A. 2x3-x2+3 A. Subtraction can be changed to addition by changing the signs in the entire term being subtracted. (2x3 -3x +1) - (x2-3x-2)=(2x3-3x+1) + (-x2+3x+2).. Combine like terms: 2x3-x2-3x+3x+1+2=2x3-x2+3.

The value of x if the angles are 140 degrees, 40 degrees and 70 degrees. A. 70° B. 110° C. 140° D. 210°

B. 110° B. The angle adjacent to the 140° angle is 40° since supplementary angles add to 180°. The angles of a triangle add to 180° so the angle adjacent to angle x is 180° - 70° - 40° = 70°. Angle x and 70° are supplementary, so x = 180° - 70° = 110°.

How many distinct prime factors are there in 120? A. 2 B. 3 C. 4 D. 5

B. 3 B. Prime factors of 120 are 2 × 2 × 2 × 3 × 5. Distinct factors are 2, 3, and 5. Therefore, there are three distinct prime factors.

Find the diagonal of a square whose area is 36. A. 6 B. 6√2 C. 9 D. 9 √2

B. 6√2 B. The area of a square is s2 where s is a side of the square. If s2 = 36, then s = 6. The diagonal of a square forms two right triangles; d is the hypotenuse and the two legs are 6 units long. Using the Pythagorean theorem, d2 = 62 + 62 = 36 + 36 = 72. Therefore, d = √72 = 6√2.

In a standard deck of playing cards, a king of hearts is drawn and not replaced. What is the probability of drawing another king from the deck? A. 1/4 B. 1/13 C. 1/17 D. 3/52

C. 1/17 C Probability is ?. Since one king was drawn and not replaced, three kings remain in the deck of 51 cards. So the probability of drawing another king is ?.

What percent of 3/4 is 1/8? A. 9.38% B. 12% C. 16.67% D. 25%

C. 16.67% C. Let p represent the unknown percent. p×3/4=1/8. Solve for p by multiplying both sides by the reciprocal of 3/4. p×3/4×4/3=1/8×4/3=4/24=1/6. As a percent, 1/6 is 16 2/3%.

If a + b = 6, what is the value of 3a + 3b? A. 9 B. 12 C. 18 D. 24

C. 18 C. 3a + 3b = 3(a + b). Since a + b = 6, 3a + 3b = 3(6) = 18.

Seven more than 3 times a number is equal to 70. Find the number. A. 10 B. 17 C. 21 D. 30

C. 21 C. Translate to a mathematical expression and solve. 3x + 7 = 70 so 3x + 7 - 7 = 70 - 7 and 3x = 63. Divide both sides by 3. Therefore, x = 21.

Simplify (9x2y3z-12xy2z2)/3yz A. 3xy2z2 - 4xyz B. 3xy2z - 12xyz C. 3x2y2 - 4xyz D. 3y2 - 4xy2z2

C. 3x2y2 - 4xyz C. (9x2y3z - 12xy2z2)/3yz = 9x2y3z/3yz - 12xy2z2/3yz = 3x2y2 - 4xyz

The angles of a triangle are in the ratio 3:4:5. What is the measure of the smallest angle? A. 15° B. 30° C. 45° D. 75°

C. 45° C. Angles in a triangle add to 180°. So 3x + 4x + 5x = 180° and 12x = 180°. Dividing both sides by 12 results in x = 15°. The smallest angle is represented by 3x = 3(15°) = 45°.

Find the length of the radius in the following figure. A. 3 B. 4 C. 5 D. 10

C. 5 C. The hypotenuse of the triangle is the diameter of the circle. By the Pythagorean theorem, d2 = 62 + 82= 36 + 64 = 100. So d = √100 = 10 and the radius is 10/2=5.

The reciprocal of 1/6 is a.)1 b.)3 c.)6 d.)1/3

a.)1 *multiply 1/6 by 6= 1

Solve for x: 2x-3=x+7 a.)10 b.)6 c.)21 d.)-10

a.)10

The surface area of a rectangular prism with sides 3 x 5 x 5 inches is: a.)110 square inches b.)140 square inches c.)72 square inches d.)85 square inches

a.)110 square inches *The area of each of the three unique sides are 15, 15, and 25. We need to double (by 5) this area because each side is mirrored in a rectangular solid. This gives us a total surface area of 110 square inches.

What is the value of YZ If XY is 4 and XZ is 5? a.)3 b.)2 c.)6 d.)5

a.)3 *a^2+b^2=c^2 4^2+b^2=5^2 16+b^2=25 b^2=9 b=_/9\ b=3

If a rectangle has a perimeter of 36 feet and is 4 feet wide, what's its area? a.)56 sq ft b.)128 sq ft c.)112 sq ft d.)16 sq ft

a.)56 sq ft *A=lw P=2l+2w =36-2(4)-36-8=28 Divide the answer by the 2 to determine the length of one side 28/2=14 Multiply the area by the with A=14x4= 56

A circle has a radius of 5 inches. What's its approximate area? a.)78.5 in b.)70 in c.)314 in d.)25 in

a.)78.5 in *A=pi(r)^2 =3.14(5)^2 =3.14(25) 78.5

Find the area and the perimeter of the triangle if the sides are 10in, 8in, base is 13in and the height is 6in high. a.)A=39in^2;P=31in b.)A=45in^2;P=56in c.)A=23in^2;P=44in d.)A=88in^2;P=36in

a.)A=39in^2;P=31in *A=1/2bh A=1/2(13)(6) A=3(13) A=39in^2 P=s1+s2+b P=10+8+13 P=31in

Solve by factoring x^4-16=0 a.)x=_+2 b.)x=_+4 c.)x=_+5 d.)x=_+8

a.)x=_+2

x^2(x^4) a.)x^6 b.)x^8 c.)2x^6 d.)2x^8

a.)x^6

Solve for x: -x^2-x+30=0 a.)4,-8 b.)-6,5 c.)-4,5 d.)6,-3

b.)-6,5 *-x^2-x+30=0 -(x^2+x-30)=0 -(x+6)(x-5)=0 x=-6,5

A tube has a radius of 3 inches and a height of 5 inches. What's its approximate volume? a.)34 cubic inches b.)141 cubic inches c.)565 cubic inches d.)45 cubic inches

b.)141 cubic inches V=pi(r)^3(h) =3.14(3)^3(5) =3.14(9)(5) =141

A square box has a volume of 64, cubic inches. What's the perimeter of one of its faces? a.)8 in b.)16 in c.)64 in d.)32 in

b.)16 in *V=64 find the cube root of 64: 4^3 Add the 4 sides of the square 4+4+4+=16

In any triangle, the sum of the interior angles add up to how many degrees? a.)90 b.)180 c.)270 d.)360

b.)180

Solve for x in the equation (x-7)^2-4=(x+1)^2 a.)2 1/2 b.)2 3/4 c.)4 1/2 d.)4 3/4

b.)2 3/4 *(x-7)(x-7)-4=(x+1)(x+1) x^2-14x+49-4=x^2+2x+1 x^2-14x+45=x^2+2x+1 -14x+45=2x+1 44=16x 2 3/4=x

What's the prime factorization of 90? a.)2*3*5 b.)2*3^2*5 c.)2^2*3^2 d.)2*3*5^2

b.)2*3^2*5

One complementary angle is 62 degrees. What is measure of the other angle? a.)158 degrees b.)28 degrees c.)62 degrees d.)26 degrees

b.)28 degrees *complementary angle are always 90 degrees Subtract 90-62=28

What's the sum of the integers from 1 to 300? a.)38,243 b.)45,150 c.)49,923 d.)52,024

b.)45,150 *S=n/2(a+b) =300/2(1+300) =150(301) 45,150

If a^3+b^3=a^3+x^3, then b= a.)b^3-a^3 b.)x c.)a^3-b^3 d.)a

b.)x *a^3+b^3=a^3+x^3 b^3=x^3 3_/b^3\=3_/x^3\ b=x

A circle has a radius of 15 feet. What's most nearly its circumference? a.)30 ft b.) 225 ft c.) 94 ft d.) 150 ft

c.) 94 ft add the radius twice 15+15=30 Multiply 30 by 3.14 3.14x30=94

If I=Prt, and P=$1,000, r=7% and t=1. What does I equal? a.)$35 b.)$1,000 c.)$700 d.)$70

c.)$700 *I=Prt =1,000(0.07)(1) 700

Simplify 8x^2-3x+4xy-9x^2-5x-20xy a.)5x^2+9xy b.)8x-9x^2 c.)-x^2-8x-16xy d.)8x+9x^2

c.)-x^2-8x-16xy

What is the area of the trapezoid? If AB is 7cm, AE is 10cm and DEC is 15 a.)32 cm^2 b.)157 cm^2 c.)110 cm^2 d.) 220 cm^2

c.)110 cm^2 *A=h(base1+base2/2) A=10(7+15/2) A=10(22/2) A=10(11) A=110cm^2

Solve (4*3)*3-6*(9/3) a.)54 b.)14 c.)18 d.)28

c.)18

A pizza with an 18-inch diameter is cut into 12 equal slices. What is the area of each slice? How many linear inches of crust does each one have? What is the total perimeter of each slice? a.)A=37/5in^2;C=1 1/2piin;P=6+2piin b.)A=89/3in^2;C=1 3/4piin;P=4+9.7piin c.)A=27/4piin^2;C=1 1/2piin;P=18+1.5piin d.)A=65/2piin^2;C=1 2/9piin;P=19+2.7piin

c.)A=27/4piin^2;C=1 1/2piin;P=18+1.5piin *A=pir^2 half of 18 is 9. 9 is the radius A=pi(9)^2 =81piin^2 A=81piin^2/12= 27/4piin^2 C=pid =pi(18) =18piin =18piin/12= 6/4 = 1 1/2piin P=s1+s2+b =1.5+9+9 =18+1.5piin

Solve the inequality 5-3x-3x+2/4<12 a.)x<2 b.)x>2 c.)x>-2 d.)x<-2

c.)x>-2 *5-3x-3x+2/4<12 20-12x-(3x+2)<48 20-12x-3x-2<48 -15x+18<48 -15x<30 x>-2

Solve: 7 1/7 + 3 3/14 a.)64/52 b.)1 5/8 c.)9 d.)2 2/9

d.)2 2/9 *7 1/7 + 3 3/14 =7*7+1/7 + 3*14+3/14 =50/7 +45/14(flip it into a proper faction) =50/7* 14/45 =50/5/7+7 * 14/7/45/5 =10*2/1*9 =20/9 2 2/9

Find the area and circumference of the following circle in terms of pi and round to the nearest tenth. The diameter is 22cm. a.)A=290.5cm^2;C=55.2cm b.)A=477.6cm^2;C=89.7cm c.)A=150.4cm^2;C=45.2cm d.)380.1cm^2;C=69.1cm

d.)380.1cm^2;C=69.1cm *r=1/2d r=1/2(22) r=11 A=pi*r^2 =pi(11)^2 =121picm^2 Multiply 121 by 3.14 and round it to the nearest tenth A=380.1cm^2 C=pid =pi(22cm) =22picm C=69.1cm

Find the volume of a cube that has only 4in. a.)56in^3 b.)89in^3 c.)24in^3 d.)64in^3

d.)64in^3 *V=s^3 =(4)^3 =64in^3

The angle shown here is a(n) a.)complementary angle b.)supplementary angle c.)acute angle d.)obtuse angle

d.)obtuse angle

The following figure is what type of quadrilateral? a.)square b.)rhombus c.)trapezoid d.)parallelogram

d.)parallelogram

Solve the following inequality 2/3(6x-9)+4>5x+1 a.)x>6 b.)x<6 c.)x>-3 d.)x<-3

d.)x<-3 *2/3(6x-9)+4>5x+1 4x-6+4>5x+1 4x-2>5x+1 -x>3 x<-3