# Full-Length AFOQT Math Practice Test-Answers and Explanations

Did you take the AFOQT Math Practice Test? If so, then it’s time to review your results to see where you went wrong and what areas you need to improve.

## AFOQT Mathematical Reasoning Practice Test Answers and Explanations

1- Choice C is correct
$$\frac{198}{18} = 11$$

2- Choice A is correct
Area of a rectangle$$=$$ width $$×$$ length $$= 12 × 27 = 324$$

3- Choice C is correct
$$44 ÷ 4 = 11$$hours for one course, $$11 × 36 = 396 ⇒ 396$$

4- Choice A is correct
8 dozen of magazines are 96 magazines:$$8 × 12 = 96, 96 – 32 = 64$$

5- Choice A is correct
Michelle $$=$$ Karen $$– 6$$, Michelle $$=$$ David $$– 3$$, Karen $$+$$ Michelle $$+$$ David $$= 45$$ Karen $$=$$ Michelle $$+ 6$$, David $$=$$ Michelle $$+ 3$$, Karen $$+$$Michelle $$+$$ David$$= 45$$
Now, replace the ages of Karen and David by Michelle.
Then: Michelle $$+ 6 +$$ Michelle $$+$$ Michelle $$+ 3 = 45$$, 3Michelle $$+ 9 = 45 ⇒$$ 3Michelle $$= 45 – 9$$
3Michelle$$= 36$$, Michelle $$= 12$$

6- Choice D is correct
distance$$=$$speed $$×$$time ⇒time$$=\frac{distance}{speed}=\frac{900}{60}=15$$
(Round trip means that the distance is 900 miles)
The round trip takes 15 hours. Change hours to minutes, than: $$15×60=900$$

7- Choice A is correct
Write proportion and solve. $$\frac{1}{124} = \frac{19}{x} ⇒ x = 19 × 124 = 2,356$$

8- Choice A is correct
average$$=\frac{sum}{total}$$, Sum $$= 4 + 7 + 14 + 19 + 24 + 36 + 39 + 41 = 184$$ Total number of numbers $$= 8$$, average$$=\frac{184}{8} = 23$$

9- Choice C is correct
Each worker can walk 3 dogs: $$15 ÷ 5 = 3, 8$$ workers can walk 24 dogs. $$8 × 3 = 24$$

10- Choice B is correct
The base rate is $12. The fee for the first 30 visits is: $$30×0.15=4.5$$ The fee for the visits 31 to 45 is: $$15×0.10=1.5$$, Total charge: $$12 + 4.5 + 1.5 = 18$$ 11- Choice C is correct average$$=\frac{sum}{total}=\frac{45+33+27}{3}=\frac{105}{3}=35$$ 12- Choice A is correct The amount they have $$= 9.85 + 15.45 + 12.75 = 38.05$$ 13- Choice D is correct Change 8 hours to minutes, then:$$8 × 60 = 480$$ minutes, $$\frac{480}{40}= 12$$ 14- Choice C is correct Since Julie gives 6 pieces of candy to each of her friends, then, the number of pieces of candies must be divisible by 6. A. $$98 ÷ 6 = 16.33$$ B. $$128 ÷ 6 = 21.33$$ C. $$210 ÷ 6 = 35$$ D. $$385 ÷ 6 = 64.166$$ Only choice C gives a whole number 15- Choice D is correct probability$$=\frac{desired outcomes}{possible outcomes}=\frac{5}{5+3+10+7}=\frac{5}{25}=\frac{1}{5}$$ 16- Choice B is correct 1 ton $$= 2,000$$ pounds, 10 ton $$= 20,000$$ pounds, $$\frac{27,000}{10,000} = 2.7$$ William needs to make at least 3 trips to deliver all of the food. 17- Choice A is correct $$145 – 30 – 40 = 75$$ 18- Choice B is correct 3 weeks $$= 21$$ days, $$21 × 5 = 105$$ hours, $$105 × 60 = 6,300$$ minutes 19- Choice B is correct Find the value of each choice: A. $$2 × 2 × 3 × 7 = 84$$ B. $$2 × 3 × 3 × 3 × 7 = 378$$ C. $$2 × 3 × 5 × 5 × 7 = 1,050$$ D. $$3 × 3 × 5 × 7 × 7 = 1,960$$ 20- Choice D is correct $$25\% × 80 = \frac{25}{100} × 80 = 20$$, The coupon has $$20$$ value. Then, the selling price of the sweater is $$60$$. $$80 – 20 = 60$$, Add $$9\%$$ tax, then: $$\frac{9}{100} × 60 = 5.4$$ for tax, Total: $$60 + 5.4 = 65.4$$ ## The Absolute Best Book to Ace the AFOQT Math Test 21- Choice C is correct 1 quart $$= 0.25$$ gallon, 28 quarts $$= 28 × 0.25 = 7$$ gallons, then: $$\frac{7}{2} = 3.5$$ weeks 22- Choice D is correct The difference of the file added, and the file deleted is: $$487,236 – 397,756 = 89,480, 987,345 + 89,480 = 1,076,825$$ 23- Choice C is correct 40 students did not have to go to summer school. $$50 – 10 = 40, \frac{40}{50} = \frac{4}{5}$$ 24- Choice B is correct Diameter $$= 2r ⇒4 = 2r⇒r = 2$$, Circumference $$= 2πr ⇒ C = 2π (2) ⇒ C = 4π$$ 25- Choice D is correct Write a proportion and solve. $$\frac{\frac{1}{4}}{1}= \frac{60}{x}$$ $$x = \frac{60}{\frac{1}{4}} = 240$$ 26- Choice A is correct All angles in a triable add up to 180 degrees. $$90^\circ + 60^\circ = 150^\circ ⇒ x = 180^\circ − 150^\circ = 30^\circ$$ 27- Choice C is correct $$\sqrt{81} = 9, \sqrt{49} = 7, 9 × 7 = 63$$ 28- Choice D is correct If $$a = 5$$ then: $$b = \frac{a^3}{5} -2 ⇒ b = \frac{5^3}{5} -2 = 25 -2 = 23$$ 29- Choice B is correct An obtuse angle is an angle of greater than 90 degrees and less than 180 degrees. Only choice A is an obtuse angle. 30- Choice D is correct Only choice D is not equal to $$3^2$$ 31- Choice B is correct $$\sqrt[4]{625} = 5, (5^4=5×5×5×5=625)$$ 32- Choice B is correct ($$r =$$ radius) Area of a circle $$= πr^2 = π × (4)^2 = 3.14 × 16 = 50.26$$ 33- Choice D is correct Volume $$=$$ length $$×$$ width $$×$$height, Volume $$= 8 × 3 × 4$$, Volume $$= 96$$ cm$$^3$$ 34- Choice A is correct $$-9a = 81 ⇒ a = \frac{81}{-9}= – 9$$ 35- Choice C is correct Area of a square $$=$$ (one side)$$^2 ⇒ A = (8)^2 ⇒ A = 64$$ 36- Choice B is correct Use Pythagorean Theorem: $$a^2 + b^2 = c^2 ⇒ (6)^2 + (3)^2 = c^2 ⇒36 + 9 = 45 = C^2⇒C =\sqrt{45} = 6.708$$ 37- Choice B is correct Use FOIL (first, out, in, last) method. $$(-3x +7) (3x-4) = -9x^2 + 12x + 21x – 28 = -9x^2 + 33x – 28$$ 38- Choice D is correct $$3(a–7)=34 ⇒ 3a-21=34 ⇒3a=34+21=45 , ⇒ 3a=45⇒a=\frac{45}{3}=15$$ 39- Choice C is correct Use exponent multiplication rule: $$x^a. x^b = x^{a + b}$$ Then:$$2^{18}=2^5× 2^x=2^{5+x}⇒ 18 = 5 + x ⇒x=18-5=13$$ 40- Choice C is correct To factor the expression $$x^2 + 4x –21$$, we need to find two numbers whose sum is 4 and their product is $$-21$$. Those numbers are 7 and $$-3$$. Then:$$x^2+4x-21=(x+7)(x-3)$$ ## Best AFOQT Math Prep Resource for 2022 41- Choice B is correct Slope of a line:$$\frac{y_2- y_1}{x_2 – x_1 } = \frac{rise}{run}, \frac{y_2- y_1}{x_2 – x_1 } = \frac{1- 4}{7 – 4} = \frac{-3}{3} = -1$$ 42- Choice B is correct $$\sqrt[3]{4,913} = 17$$ 43- Choice C is correct In scientific notation form, numbers are written with one whole number times 10 to the power of a whole number. Number 87,456 has 5 digits. Write the number and after the first digit put the decimal point. Then, multiply the number by 10 to the power of 4 (number of remaining digits). Then: $$87,456 = 8.7456 × 10^4$$ 44- Choice B is correct The area of the non-shaded region is equal to the area of the bigger rectangle subtracted by the area of the smaller rectangle. Area of the bigger rectangle $$= 5 × 7 = 35$$ Area of the smaller rectangle $$= 5 × 3 = 15$$ Area of the non-shaded region $$= 35 – 15 = 20$$ 45- Choice B is correct Diameter $$= 2r ⇒ 7 = 2r⇒r = 3.5$$, Circumference $$= 2πr ⇒ C = 2π (3.5) ⇒ C = 7π$$ 46- Choice A is correct average$$=\frac{sum}{total}=\frac{270}{45} = 6$$ 47- Choice A is correct Factor of $$56: {1, 2, 4, 7, 8, 14, 28, 56}$$ Factor of $$18: {1, 2, 3, 6, 9, 18}$$, Then, factors they have in common is $${1, 2}$$ 48- Choice C is correct Diameter$$= 2r ⇒ 10 = 2r ⇒r = 5$$, Circumference $$= 2πr ⇒ C = 2π (5) ⇒ C = 10 × 3.14 = 31.4$$ 49- Choice C is correct The straight line is 180 degrees. Then: $$a = 180^\circ – 45^\circ = 135^\circ$$ 50- Choice C is correct $$\sqrt{49x^4 }=\sqrt{49}×\sqrt{x^4 }=7×x^2=7x^2$$ ## The Best Booksto Ace the AFOQT Math Test ## More from Effortless Math for AFOQT Test … ### What tips you should follow to prevent failure again AFOQT? By following the tips provided here: Top 10 Tips You MUST Know to Retake the AFOQT Math ### Want to review the most common AFOQT Math formulas? Here is our complete list of AFOQT Math formulas. ### Here are some tips to help you make the most of your test day:AFOQT Math-Test Day Tips ## The Perfect Prep Booksfor the AFOQT Math Test ## Have any questions about the AFOQT Test? Write your questions about the AFOQT or any other topics below and we’ll reply! ## Related to "Full-Length AFOQT Math Practice Test-Answers and Explanations" ### More math articles ### What people say about "Full-Length AFOQT Math Practice Test-Answers and Explanations"? No one replied yet. X 52% OFF Huge Discount! 52% OFF SAVE$40

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