 ## Full Length ASVAB Math Practice Test

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ASVAB Math Practice Test 3 CAT-ASVAB
Arithmetic Reasoning
16 questions
Total time for this section: 39 Minutes
Calculators are not allowed for this test.

1- If a rectangle is $$20$$ feet by $$35$$ feet, what is its area?
(A) $$750$$
(B) $$250$$
(C) $$700$$
(D) $$1240$$
2- Each year, a cyber café charges its customers a base rate of $$\ 25$$, with an additional $$\ 0.30$$ per visit for the first $$30$$ visits, and $$\ 0.15$$ for every visit after that. How much does the cyber café charge a customer for a year in which $$50$$ visits are made?
(A) $$\ 37$$
(B) $$\ 35$$
(C) $$\ 27$$
(D) $$\ 25$$
3- Amy was hired to teach three identical math courses, which entailed being present in the classroom $$45$$ hours altogether. At $$\ 20$$ per class hour, how much did Aria earn for teaching one course?
(A) $$\ 450$$
(B) $$\ 500$$
(C) $$\ 300$$
(D) $$\ 1500$$
4- Alex gives $$6$$ pieces of candy to each of his friends. If Alex gives all his candy away, which amount of candy could have been the amount he distributed?
(A) $$138$$
(B) $$218$$
(C) $$442$$
(D) $$213$$
5- If a vehicle is driven $$36$$ miles on Monday, $$30$$ miles on Tuesday, and $$24$$ miles on Wednesday, what is the average number of miles driven each day?
(A) $$32$$ miles
(B) $$28$$ miles
(C) $$21$$ miles
(D) $$30$$ miles
6- Ashly is $$14$$ years older than her sister Jennifer, and Jennifer is $$6$$ years younger than her brother John. If the sum of their ages is $$71$$, how old is Jennifer?
(A) $$25$$
(B) $$17$$
(C) $$32$$
(D) $$24$$
7- You are asked to chart the temperature during an $$6$$ hour period to give the average. These are your results:
$$5$$ am:$$3$$ degrees                $$6$$ am:$$8$$ degrees
$$7$$ am:$$15$$ degrees               $$8$$ am:$$22$$ degrees
$$9$$ am:$$24$$ degrees               $$9$$ am:$$30$$ degrees
What is the average temperature?
(A) $$25$$
(B) $$35$$
(C) $$42$$
(D) $$17$$
8- Mike is driving to visit his grandfather, who lives $$420$$ miles away. How long will the drive be, round−trip, if Mike drives at an average speed of $$70$$ mph?
(A) $$720$$ minutes
(B) $$542$$ minutes
(C) $$265$$ minutes
(D) $$360$$ minutes
9- Four co−workers contributed $$\ 12.25$$ , $$\ 14.25$$, $$\ 17.35$$, and $$\ 19.45$$ respectively to purchase a retirement gift for their boss. What is the maximum amount they can spend on a gift?
(A) $$\ 25.36$$
(B) $$\ 37.42$$
(C) $$\ 63.3$$
(D) $$\ 40.5$$
10- What is the prime factorization of $$280$$?
(A) $$2 \ × \ 2 \ × \ 2 \ × \ 5\ × \ 7$$
(B) $$2 \ × \ 2 \ × \ 2 \ × \ 2 \ × \ 5 \ × \ 7$$
(C) $$2 \ × \ 2 \ × \ 2 \ × \ 2 \ × \ 5$$
(D) $$2 \ × \ 2 \ × \ 7$$
11- While at work, David checks his email once every $$45$$ minutes. In $$6−$$hour, how many times does she check his email?
(A) $$25$$ Times
(B) $$3$$ Times
(C) $$8$$ Times
(D) $$18$$ Times
12- In the deck of cards, there are $$4$$ spades, $$6$$ hearts, $$7$$ clubs, and $$11$$ diamonds. What is the probability that John will pick out a spade?
(A) $$\frac{1}{7}$$
(B) $$\frac{1}{5}$$
(C) $$\frac{1}{4}$$
(D) $$\frac{1}{9}$$
13- A man goes to a casino with $$\ 200$$. He loses $$\ 50$$ on blackjack, then loses another $$\ 60$$ on roulette. How much money does he have left?
(A) $$\ 50$$
(B) $$\ 95$$
(C) $$\ 60$$
(D) $$\ 90$$
14- A family owns $$12$$ dozen of magazines. After donating $$64$$ magazines to the public library, how many magazines are still with the family?
(A) $$80$$
(B) $$25$$
(C) $$72$$
(D) $$45$$
15- A woman owns a dog walking business. If $$4$$ workers can walk $$12$$ dogs, how many dogs can $$6$$ workers walk?
(A) $$18$$
(B) $$8$$
(C) $$4$$
(D) $$5$$
16- Bob is driving a truck that can hold $$4$$ tons maximum. He has a shipment of food weighing $$24,000$$ pounds. How many trips will he need to make to deliver all of the food?
(A) $$5$$ Trips
(B) $$3$$ Trips
(C) $$7$$ Trips
(D) $$9$$ Trips

ASVAB Math Practice Test 3  CAT-ASVAB
Mathematics Knowledge
Total time for this section: 18 Minutes
16 questions
Calculators are not allowed for this test

17- If $$a = 6$$ , what is the value of b in this equation?
$$b =\frac{a^2}{6} \ + \ 6$$
(A) $$15$$
(B) $$20$$
(C) $$8$$
(D) $$12$$
18- A circle has a radius of $$3$$  inches. What is its approximate area? $$(π = 3.14)$$
(A) $$22.5$$ square inches
(B) $$16.26$$ square inches
(C) $$28.26$$ square inches
(D) $$32$$ square inches
19- In the following diagram, what is the value of $$x$$? (A) $$65^\circ$$
(B) $$70^\circ$$
(C) $$35^\circ$$
(D)  $$45^\circ$$
20- The eighth root of $$256$$ is:
(A) $$2$$
(B) $$5$$
(C) $$4$$
(D) $$6$$

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21- If $$- \ 9 \ a = 81$$, then a = ___
(A) $$6$$
(B) $$- \ 8$$
(C) $$- \ 9$$
(D) $$12$$
22- $$4(a \ + \ 5)=24$$, what is the value of $$a$$?
(A) $$5$$
(B) $$1.5$$
(C) $$1$$
(D) $$3$$
23- In the following right triangle, what is the value of rounded to the nearest hundredth? (A) $$6.27$$
(B) $$8.27$$
(C) $$9.219$$
(D) $$23$$
24- Which of the following is an obtuse angle?
(A) $$160^\circ$$
(B) $$45^\circ$$
(C) $$35^\circ$$
(D) $$80^\circ$$
25- If $$3^{21}=3^7 \ × \ 3^x$$, what is the value of $$x$$ ?
(A) $$14$$
(B) $$25$$
(C) $$2.5$$
(D) $$7$$
26- Factor this expression: $$x^2 \ + \ 6x \ - \ 7$$
(A) $$x^2 \ (x \ + 6)$$
(B) $$x (x \ + \ 6 \ - \ 7)$$
(C) $$(x + 7) \ (x \ - \ 1)$$
(D) $$(x \ + \ 7) \ (x \ + \ 1)$$
27- Which of the following is not equal to $$6^2$$?
(A) the squared of $$6$$
(B) $$6$$ cubed
(C) $$6$$ to the second power
(D) $$6$$ squared
28- Find the slope of the line running through the points $$(4 \ , \ 5)$$ and $$(5 \ , \ 8)$$.
(A) $$3$$
(B) $$- \ 4$$
(C) $$- \ 2$$
(D) $$\frac{1} {2}$$
29- What is $$854,320$$ in scientific notation?
(A) $$85.432$$
(B) $$0.85432 × 10^6$$
(C) $$8.5432 × 10^5$$
(D) $$8.5432$$
30- What is the value of $$\sqrt{81} \ × \sqrt {25}$$ ?
(A) $$\sqrt{45}$$
(B) $$\sqrt{145}$$
(C) $$45$$
(D) $$130$$
31- The cube root of $$2,197$$ is?
(A) $$13$$
(B) $$121$$
(C) $$25.6$$
(D) $$2.6$$
32- $$(2 \ x \ + \ 3) \ (3 \ x \ + \ 4)$$ =  ?
(A) $$6 \ x^2 \ + \ 17 \ x \ + \ 12$$
(B) $$6 \ x^2 \ + \ 5 \ x \ + \ 6$$
(C) $$6 \ x^2 \ + \ 5 \ x$$
(D) $$6 \ x \ + \ 5 \ x$$
 1- Choice C is correct The correct answer is $$700$$Area of a rectangle = width × length = $$20 \ × \ 35 =700$$ 2- Choice A is correct The correct answer is $$\ 37$$The base rate is $$\ 25$$.The fee for the first $$30$$ visits is:$$30 \ × \ 0.30=9$$The fee for the visits $$31$$ to $$50$$ is: $$20 \ × \ 0.15=3$$Total charge: $$25 \ + \ 9 \ + \ 3 = 37$$ 3- Choice C is correct The corrrect answer is $$\ 300$$$$45 \ ÷ \ 3 = 15$$ hours for one course$$15 \ × \ 20 = 300 ⇒ \ 300$$ 4- Choice A is correct The correct answer is $$138$$Since Alex gives $$6$$ pieces of candy to each of his friends, then number of pieces of candies must be divisible by $$6$$.$$138 \ ÷ \ 6 =23$$$$218 \ ÷ \ 6 = 36.33$$$$442 \ ÷ \ 6 = 73.66$$$$213 \ ÷ \ 6 = 35.5$$Only choice a gives a whole number. 5- Choice D is correct The correct answer is $$30$$ miles$$average=\frac{sum}{total}=\frac{36 \ + \ 30 \ + \ 24}{3}=\frac{90}{3}=30$$ 6- Choice B is correct The correct answer is $$17$$Jennifer= Ashly $$– \ 14$$Jennifer= John $$– \ 6$$Ashly  +  Jennifer  +  John $$= 71$$Ashly $$- \ 14 =$$ Jennifer        ⇒Ashly = Jennifer $$+ \ 14$$Ashly + Jennifer + John $$= 71$$Now, replace the ages of Ashly and John by Jennifer. Then:Jennifer $$+ \ 14 \ +$$ Jennifer + Jennifer $$+ \ 6 = 71$$$$3$$ Jennifer $$+ \ 20= 71$$ ⇒ $$3$$ Jennifer $$= 71 \ – \ 20$$$$3$$ Jennifer $$= 51$$Jennifer $$= 17$$ 7- Choice D is correct The correct answer is $$17$$average =$$\frac{sum}{total}$$sum$$=3 \ + \ 15 \ + \ 24 \ + \ 8 \ + 22 \ + \ 30 =102$$Total number of numbers = $$6$$average = $$\frac {102}{6} =17$$ 8- Choice A is correct The correct answer is $$720$$ minutesdistance=speed ×time ⇒$$time=\frac{distanc}{speed}=\frac{840}{70}=12$$(Round trip means that the distance is $$840$$ miles)The round trip takes $$12$$ hours. Change hours to minutes, then:$$12 \ × \ 60=720$$ minutes 9- Choice C is correct The correct answer is $$\ 63.3$$The amount they have = $$\ 12.25 \ + \ \ 14.25 \ + \ \ 17.35 \ + \ \ 19.45 = \ 63.3$$ 10- Choice A is correct The correct answer is $$2 \ × \ 2 \ × \ 2 \ × \ 5 \ × \ 7$$Find the value of each choice$$2 \ × \ 2 \ × \ 2 \ × \ 5 \ × \ 7=280$$$$2 \ × \ 2 \ × \ 2 \ × \ 2 \ × \ 5 \ × \ 7=560$$$$2 \ × \ 2 \ × \ 2 \ × \ 2 \ × \ 5=80$$$$2 \ × \ 2 \ × \ 7=28$$ 11- Choice C is correct The correct answer is  $$8$$ TimesChange $$6$$ hours to minutes, then: $$6 \ × \ 60 = 360$$ minutes$$\frac{360}{45}= 8$$ 12- Choice A is correct The correcst answer is $$\frac{1}{7}$$probability=$$\frac{desird \ outcomes}{possible \ outcomes}=\frac{4}{3 \ + \ 6 \ + \ 8 \ + \ 11}=\frac{4}{28}=\frac{1}{7}$$ 13- Choice D is correct The correct answer is $$\ 90$$$$200 \ - \ 50 \ - \ 60 =90$$ 14- Choice A is correct The correct answer is $$80$$$$12$$ dozen of magazines are $$144$$ magazines: $$12 \ × \ 12 = 144$$$$144 \ – \ 64 = 80$$ 15- Choice A is correct The  correct answer is $$18$$Each worker can walk $$3$$ dogs: $$12 \ ÷ \ 4 = 3$$$$6$$ workers can walk $$18$$ dogs.$$6 \ × \ 3 = 18$$ 16- Choice B is correct The correct answer is $$3$$ Trips$$1$$ ton = $$2,000$$ pounds$$4$$  ton = $$8,000$$ pounds$$\frac{24000}{8000}= 3$$Bob  needs to make at least $$3$$ trips to deliver all of the food. 16- Choice B is correct The correct answer is $$3$$ Trips$$1$$ ton = $$2,000$$ pounds$$4$$  ton = $$8,000$$ pounds$$\frac{24000}{8000}= 3$$Bob  needs to make at least $$3$$ trips to deliver all of the food. 17- Choice D is correct The correct answer is $$12$$If $$a = 6$$ then:$$b =\frac{a^2}{6}+ \ 6$$⇒ $$b =\frac{6^2}{6} \ + \ 6 = 6 \ + \ 6 = 12$$ 18- Choice C is correct The correct answer is $$28.26$$ square inches(r = radius)Area of a circle = $$π \ r^2 = π \ × \ (3)^2 = 3.14 \ × \ 9 = 28.26$$ 19- Choice D is correct The correct answer is $$45^\circ$$All angles in a triangle add up to $$180$$ degrees. $$90^\circ \ + \ 45^\circ = 135^\circ$$$$x = 180^\circ \ − \ 135^\circ = 45^\circ$$ 20- Choice A is correct The correct answer is $$2$$$$\sqrt{256} = 2$$ $$2^8=2 \ × \ 2 \ × \ 2 \ × \ 2 \ × \ 2 \ × \ 2 \ × \ 2 \ × \ 2=256$$ 21- Choice C is correct The correct answer is $$- \ 9$$$$- \ 9 \ a = 81$$ ⇒ $$a = \frac{81}{- \ 9}= - \ 9$$ 22- Choice C is correct The correct answer is $$1$$$$4 \ (a \ + \ 5)=24 ⇒ 4 \ a \ + \ 20=24 ⇒4 \ a=24 \ - \ 20=4$$⇒$$4 \ a=4⇒a=\frac{4}{4}=1$$ 23- Choice C is correct The correct answer is $$9.219$$Use Pythagorean Theorem: $$a^2 \ + \ b^2 = c^2$$$$(6)^2 \ + \ (7)^2 = c^2$$ ⇒ $$36 \ + \ 49 = 85 = C^2$$ $$C =\sqrt{85} = 9.219$$ 24- Choice A is correct The correct answer is $$160^\circ$$An obtuse angle is an angle of greater than $$90$$ degrees and less than $$180$$ degrees. Only choice A is an obtuse angle. 25- Choice A is correct The correct answer is $$14$$Use exponent multiplication rule:$$x^a . x^b = x^{a \ + \ b}$$Then;$$3^{21}=3^7 \ × \ 3^ \ x=3^{7 \ + \ x}$$$$21 = 7 \ + \ x ⇒x=21 \ - \ 7=14$$ 26- Choice C is correct The correct answer is $$(x \ + 7) \ (x \ - \ 1)$$To factor the expression $$x^2 \ + \ 6x \ – \ 7$$, we need to find two numbers whose sum is $$6$$ and their product is $$- \ 7$$.Those numbers are $$7$$ and $$- \ 1$$. Then:$$x^2 \ + \ 6x \ - \ 7=(x \ + \ 7) \ (x \ - \ 1)$$ 27- Choice B is correct The correct answer is $$6$$ cubedOnly choice b is not equal to $$6^2$$$$6$$ cubed $$=$$ $$6^3$$ 28- Choice A is correct The correct answer is $$3$$Slope of a line:$$\frac{y_2 \ - \ y_1}{x_2 \ - \ x_1}=\frac{rise}{run}$$$$\frac{y_2\ - \ y_1}{x_2 \ - \ x_1}=\frac{8 \ - \ 5}{5 \ - \ 4}=\frac{3}{1}= 3$$ 29- Choice C is correct The correct answer is $$8.5432 × 10^5$$In scientific notation form, numbers are written with one whole number times $$10$$ to the power of a whole number.Number $$854,320$$ has $$6$$ digits.Write the number and after the first digit put the decimal point.Then, multiply the number by $$10$$ to the power of $$5$$ (number of remaining digits). Then:$$854,320 = 8.5432 \ × \ 10^5$$ 30- Choice C is correct The correct answer is $$45$$$$\sqrt{81} =9$$$$\sqrt{25} = 5$$$$9 \ × \ 5 =45$$ 31- Choice A is correct The correct answer is $$13$$$$\sqrt{2,197} = 13$$ 32- Choice A is correct The correct answer is $$6 \ x^2 \ + \ 17 \ x \ + \ 12$$Use FOIL (first, out, in, last) method.$$(2 \ x \ + \ 3) \ (3 \ x \ + \ 4) = 6 \ x^2 \ + \ 8 \ x \ + \ 9 \ x \ + \ 12 = 6 \ x^2 \ + \ 17 \ x \ + \ 12$$

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### Practice Test 1

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