AFOQT Math Knowledge

Examine (A), (B), and (C) and choose the best answer. (A) 0.5 (B) 5% (C) 1/5 a. (A) is greater than (B). b. (B) is greater than (A). c. (C) is greater than (A). d. (A) and (B) are equal. e. (B) times (A) is equal to (C).

A. (A) is greater than (B)

The number line- left is -5 then blank on the right and then center is 0 then blank on the right. What are the missing integers on this number line? a. -4 and 1 b. -6 and 1 c. -6 and -1 d. 4 and 9 e. 5 and 8

A. -4 and 1

The reciprocal of 10 is a. 0.1 b. 0.2 c. 0.5 d. 1.0 e. 2.0

A. 0.1

3/5= a. 0.60 b. 0.20 c. 0.50 d. 0.80 e. 0.90

A. 0.60

Find the circumference, in meters, of a circle with a radius of 25 centimeters. a. 1.57 m b. 157 m c. 15.7 cm d. 78.5 m e. 7.85 m

A. 1.57 m

**(means to what power) x-2/x(2)-6x+8 can be reduced to: A. 1/(x-4) B. 1/(x-2) C. (x-2)/(x+2) D. 1/(x+2) E. 1/(x+4)

A. 1/(x-4)

**[means to what power] Solve for x when: (2x)/7=2x[2] A. 1/7 B. 2/7 C. 2 D. 7 E. 14

A. 1/7

If x/54 = 2/9, then x is a. 12 b. 14 c. 18 d. 108 e. 118

A. 12

What number is 3 times 4% of 20? a. 2.4 b. 5.4 c. 24 d. 27 e. 32

A. 2.4

37.5 percent is equal to a. 3/8 b. 5/8 c. 4 3/4 d. 6 3/4 e. 3 7/5

A. 3/8

What is the probability of randomly drawing an odd number between 24 and 33 (inclusive)? A. 50% B. 66% C. 75% D. 80% E. 90%

A. 50%

Which of these is equivalent to 20°C? (F=9/5C+32) a. 68°F b. 95°F c. 45°F d. 19°F e. 70°F

A. 68°F

4 1/5 + 1 2/5 + 3 3/10 a. 8 9/10 b. 9 1/10 c. 8 4/5 d. 8 6/15 e. 9 5/10

A. 8 9/10

0.97 is equal to a. 97% b. 9.7% c. 0.97% d. 0.097% e. 0.0097%

A. 97%

**(means to what power) Simplify the following radical expression: Square root 3n(2) a. n square root 3 b. 9n c. n square root 9 d. square root 9 e. 3 square root n

A. n square root 3

Which of the following choices completes this number sentence? 5_____ = (10 × 2) + (5 × 3) a. ×(5+2) b. +(5+2) c. ×(5×2) d. +(5×2) e. +(5×3)

A. ×(5+2)

Examine (A), (B), and (C) and choose the best answer. (A) 2/5 of 100 (B) 1/2 of 80 (C) 1/8 of 160 a. (A) is less than (B) or (C). b. (A) and (B) are equal. c. (B) and (C) are equal. d. (B) is greater than (A) but less than (C). e. (B) times (A) is equal to (C).

B. (A) and (B) are equal

**(means to what power) Factor x(2)+7x+10 A. (2x+2)(x+5) B. (x+5)(x+2) C. (x+2)(2x+2) D. (2x+5)(x+5) E. (2x+)(x+10)

B. (x+5)(x+2)

The value in -1/9√(81) is equal to A. 0 B. -1 C. 1 D. -9 E. 9

B. -1

Which value of x will make the number sentence x + 32 ≤ 14 true? a. -16 b. -21 c. 12 d. 38 e. none of the above

B. -21

**(means to what power) 10(5) *10(6) *10(7)= A. 10(15) B. 10(18) C. 10(21) D. 10(24) E. 10(30)

B. 10(18)

How many inches are there in 3 1/3 yards? a. 126 b. 120 c. 160 d. 168 e. 313

B. 120

Solve 5/6+3/4+(3/2*9/21) A. 66/52 B. 187/84 C. 120/57 D. 66/145 E. 123/124

B. 187/84

0.15 is equal to a. 2/5 b. 3/20 c. 2/10 d. 1/20 e. 1.5/20

B. 3/20

What is the distance, in miles, around a circular course with a radius of 49 miles? (pi = 22/7) a. 154 miles b. 308 miles c. 462 miles d. 539 miles e. 616 miles

B. 308 miles

Find the circumference of a circle with a diameter of 10 centimeters. a. 3.14 cm b. 31.4 cm c. 62.8 cm d. 6.28 cm e. none of the above

B. 31.4 cm

What number plus 2 times the same number equals 99? a. 16 b. 33 c. 66 d. 297 e. 365

B. 33

Find the volume of a pyramid with four congruent base sides. The length of each base side and the prism's height measure 2.4 feet. a. 46 cubic feet b. 4.6 cubic feet c. 4.8 cubic feet d. 48 cubic feet e. 1.2 cubic feet

B. 4.6 cubic feet

The hypotenuse of a right triangle whose legs are 3 feet and 4 feet is A. 4 B. 5 C. 6 D. 7 E. 8

B. 5

The sum of the interior angles of a pentagon is A. 360 degrees B. 540 degrees C. 720 degrees D. 900 degrees E. 1180 degrees

B. 540 degrees

**(means to what power) If 2(n)=8, what is the value of 3(n+1)? A. 70 B. 81 C. 95 D. 102 E. None of the above

B. 81

76 1/2 + 11 5/6 = a. 87 1/2 b. 88 1/3 c. 88 2/3 d. 88 5/6 e. 89

B. 88 1/3

The figure is an X. O is the center. In this figure, angle POS measures 90°. What is the measure of angle ROQ? a. 45° b. 90° c. 180° d. 270° e. 360°

B. 90°

Roberta draws two similar pentagons. The perimeter of the larger pentagon is 93 feet; one of its sides measures 24 feet. If the perimeter of the smaller pentagon equals 31 feet, then the corresponding side of the smaller pentagon measures a. 5s = 31 b. 93s = 24 × 31 c. 93 × 24 = 31s d. 5 × 31 = s e. 31 × 24 = s

B. 93s = 24 × 31

5v-u=-2 and -v+9u=18, then the simultaneous solution of the given equation is: A. u=3, v=9 B. u=2, v=0 C. u=1, v=-9 D.u=-2, v=-36 E.u=3, v=-15

B. u=2, v=0

√(28) - √(7) reduces to A. √(4) B. √(7) C. 3√(7) D. √(21) E. -√(35)

B. √(7)

Examine (A), (B), and (C) and choose the best answer. **(means to what power) (A) 7(2) (B) 4(3) (C) 3(2) + 6 a. (A) and (B) are equal. b. (A) is greater than (B). c. (B) minus (A) is equal to (C). d. (B) and (C) are equal to (A). e. (B) times (A) is equal to (C).

C. (B) minus (A) is equal to (C)

2/3*3/4*4/5*5/6*6/7*7/8= A. 1/16 B. 1/8 C. ¼ D. ½ E. None of the above

C. 1/4

17/20 + 6/100 + 15/50 is equal to A. 43/50 B. 111/100 C. 121/100 D. 83/50 E. 289/25

C. 121/100

What number is 42 less than 1/5 of 820? a. 98 b. 112 c. 122 d. 210 e. 222

C. 122

What is the length of a rectangle if its width is 6 feet and its area is 108 square feet? a. 1.8 feet b. 10.5 feet c. 18 feet d. 16 feet e. 68 feet

C. 18 feet

The sum of the interior angles of a triangle is always A. 90 degrees B. 120 degrees C. 180 degrees D. 320 degrees E. 360 degrees

C. 180 degrees

Which of the following is equivalent to 202,436? a. 20,000 + 2,000 + 400 + 30 + 6 b. 2,000 + 40 + 300 + 6 c. 200,000 + 2,000 + 400 + 30 + 6 d. 200,000 + 2,000 + 4,000 + 300 + 6 e. 200,000 + 12,000 + 4,000 + 300 + 6

C. 200,000 + 2,000 + 400 + 30 + 6

The first digit of the square root of 112,092 is a. 1 b. 2 c. 3 d. 4 e. 5

C. 3

Solve for x using the following two equations: 2x+4y=10 and 9x-4y=20 A. x=21/15 B. x=40/21 C. x=30/11 D. x=8/9 E. x=29/13

C. 30/11

If w=4c then (3/4)w= A. 3/ c B. 4/3c C. 3c D. c/3 E. c/4

C. 3c

What number is 6 less than 2/5 of 25? a. -4 b. 1 c. 4 d. 9 e. 12

C. 4

Look at this series: 1/6, 1/3, 1/2, 2/3, . . . What number should come next? a. 1 b. 4/6 c. 5/6 d. 8/9 e. 7/12

C. 5/6

What is another way to write 7.25 ×10(3)? **(means to what power) a. 72.5 b. 725 c. 7,250 d. 72,500 e. 720,500

C. 7,250

In a triangle, angle A is 70 degrees and angle B is 30 degrees. What is the measure of angle C? a. 90 degrees b. 70 degrees c. 80 degrees d. 100 degrees e. 120 degrees

C. 80 degrees

What are the next two choices following the below pattern? A R C S E T G ___ ___ A. UH B. HI C. UI D. IU E. IH

C. UI

**(means to what power) n(5)/n(2) = a. n7 b. n2 c. n3 d. 2n3 e. 7n

C. n3

What is another way to write 4×4×4? a.3×4 b.8×4 c.4 3 d.3 4 e.8 3

C.4 3

What is the volume of a pyramid that has a rectangular base 5 feet by 3 feet and a height of 8 feet? (V = 1/3 lwh) **(means to what power) a .16 feet(3) b. 30 feet(3) c. 40 feet(3) d. 120 feet(3) e. 220 feet(3)

C.40 feet(3)

Examine (A), (B), and (C) and choose the best answer. **(means to what power) (A) n × n (B) n(2) (C) n(n) a. (A) plus (C) equals (B). b. (B) is greater than (C) but less than (A). c. (A) is less than (C). d. (A), (B), and (C) are all equal. e. (B) times (A) is equal to (C).

D. (A), (B), and (C) are all equal

**(means to what power) (-3)(3)= A. 9 B. -9 C. 27 D. -27 E. None of the above

D. -27

**(means to what power) 12.687x10(-4) is equal to A. 1.2687 B. .12687 C. .012687 D. .0012687 E. .00012687

D. .0012687

What is the decimal equivalent of 1/6 rounded to the nearest thousandth? a. 0.165 b. 0.666 c. 0.123 d. 0.167 e. 0.176

D. 0.167

What is 3/8 equal to? a. 0.25 b. 0.333 c. 0.60 d. 0.375 e. 3.80

D. 0.375

1/6 + 7/12 + 2/ 3 = a. 10/24 b. 2 1/6 c. 1 5/6 d. 1 5/12 e. 2 5/6

D. 1 5/12

1 1/2 is equal to a. 0.50 b. 1.25 c. 2.50 d. 1.50 e. 0.150

D. 1.50

**(means to what power) 10(y)/10(z) equals A. 10(y/z) B. 10(yz) C. 10(y+z) D. 10(y-z) E. None of the above

D. 10(y-z)

Which of the following is divisible by both 7 and by 8? a. 63 b. 106 c. 114 d. 112 e. 78

D. 112

The expression 5 factorial equals a. 1/4 b. 16 c. 50 d. 120 e. 500

D. 120

What number added to 15% of 30 equals 20? a. -25 b. 4.5 c. 12 d. 15.5 e. 25.5

D. 15.5

**(means to what power) 8xy(2)/2xy = a. 2xy b. 4x(2) c. 16y d. 4y e. 4y(2)

D. 4y

Which measurement uses the largest increment? a. perimeter b. area c. surface area d. volume e. They all use the same size increment.

D. Volume

Isadora wants to know the perimeter of the face of a building; however, she does not have a ladder. She knows that the building's rectangular facade casts a 36-foot shadow at noon, while a nearby mailbox casts a 12-foot shadow at noon. The mailbox is 4.5-feet tall. If the length of the façade is 54 feet, what is the measure of the façade's perimeter? a. p = 13.5 × 4 b. p = 54 × 4 c. p = 4.5(2) + 12(2) d. p = 13.5(2) + 54(2) e. p = 13.5 + 4

D. p = 13.5(2) + 54(2)

Which of the following statements is false? A triangle can have A. three equal angles B. one obtuse angle C. three equal sides D. two right angles E. three acute angles

D. two right angles

**(means to what power) The factors of 30x(2)-30 are A. (5x-6), (6x+5) B. (15x+5), (2x-6) C. (5x-6), (6x-5) D. (30x-5), (x+6) E. (5x+5), (6x-6)

E. (5x+5), (6x-6)

Simplify the following radical expression: 2 square root 7 - 3 square root 28 a. -6 square root 7 b. 5 square root 196 c. -5 square root 196 d. square root 7 e. -4 square root 7

E. -4 square root 7

3/4 is equal to a. 0.25 b. 0.30 c. 0.34 d. 0.50 e. 0.75

E. 0.75

Which of the measures represents an obtuse angle? a. 45° b. 60° c. 85° d. 90° e. 105°

E. 105°

What is the next logical choice following the below pattern? 2 4 12 48 ____ A. 96 B. 144 C. 192 D. 204 E. 240

E. 240

**(means to what power) The volume of a cylinder with radius b and height w is A. pie bw B. 2pie bw C. 2pie b(2)w D. 4pie b(2)w E. None of the above

E. None of the above