## Full Length HiSET Mathematics Practice Test

Taking a full-length practice test of the HiSET math exam is not only preparation for your actual test, but also simulation of testing day. Not only will this help you to become familiar with the format and feel more confident on exam day, it will be an excellent way to measure your readiness for taking that professional level math certification.

It's essential to treat this practice test as a real one. By preparing everything you need and taking the test in one sitting, this will help you prepare your mind and body for the actual HiSET Math exam.

Take the following math practice test to simulate taking a real HiSET. After you finish, score your tests using the answer keys below.

Hope this helps with studying for that big day!

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## HiSET Mathematics Practice Test 3

50 questions
Total time: 90 Minutes
You may use a calculator for this test.
1- Solve for $$x$$:
$$2(x \ + \ 3) = 4(x \ − \ 6) \ + \ 22$$
(A) $$6$$
(B) $$4$$
(C) $$12$$
(D) $$8$$
2- In five successive hours, a car travels  $$20$$ km , $$25$$ km , $$15$$ km, $$30$$ km and $$35$$ km. In the next five hours, it travels with an average speed of $$30$$ km per hour. Find the total distance the car traveled in $$10$$  hours.
(A) $$450$$  km
(B) $$350$$   km
(C) $$250$$  km
(D) $$270$$  km
(E) $$275$$  km
3- What is the value of $$x$$ in the following figure?
(A) $$125$$
(B) $$115$$
(C) $$55$$
(D) $$130$$
(E) $$145$$
4- Right triangle ABC has two legs of lengths $$4$$ cm (AB) and $$3$$  cm (AC). What is the length of the third side (BC)?
(A) $$6$$  cm
(B) $$8$$  cm
(C) $$5$$  cm
(D) $$10$$   cm
5- $$(3 \ x \ + \ 2 \ y) \ (2\ x\ + \ 5 \ y) = ?$$
(A) $$6 \ x^2 \ + \ 19 \ x \ y \ + \ 10 \ y^2$$
(B) $$10 \ x^2 \ + \ 14 \ x \ y \ + \ 4 \ y^2$$
(C) $$4 \ x^2 \ + \ 10 \ x \ y \ + \ 4 \ y$$
(D) $$4 \ x \ + \ 8 \ x \ y \ + \ 4 \ y^2$$
(E) $$2 \ x \ + \ 4 \ x \ y \ + \ 2 \ y$$
6- $$45$$ is What percent of $$30$$?
(A) $$20\%$$
(B) $$25\%$$
(C) $$125\%$$
(D) $$150\%$$
(E) $$300\%$$
7- The marked price of a computer is D dollar. Its price decreased by $$10\%$$ in January and later increased by $$20\%$$ in February. What is the final price of the computer in D dollar
(A) $$0.80$$  D
(B) $$1.08$$  D
(C) $$0.90$$  D
(D) $$1.32$$  D
(E) $$1.40$$  D
8- If  $$y = 3\ a \ b \ - \ 4 \ b^2$$, what is $$y$$ when $$a = 3$$ and $$b = 2$$ ?
(A) $$2$$
(B) $$10$$
(C) $$8$$
(D) $$12$$
(E) $$14$$
9- What is $$4.5\%$$ of $$1,600$$ ?
(A) $$90$$
(B) $$65$$
(C) $$100$$
(D) $$300$$
(E) $$72$$
10- If  $$35\%$$ of a class are girls, and $$20\%$$ of girls play tennis, what percent of the class play tennis?
(A) $$15\%$$
(B) $$7\%$$
(C) $$25\%$$
(D) $$17\%$$
(E) $$10\%$$
11- How long does a $$670 \ –$$miles trip take moving at $$30$$ miles per hour (mph)?
(A) $$18$$ hours
(B) $$18$$ hours  and $$18$$ minutes
(C) $$22$$ hours  and $$20$$ minutes
(D) $$8$$ hours  and $$30$$ minutes
(E) $$20$$ hours  and $$30$$ minutes
12- A $$50$$ shirt now selling for $$38$$ is discounted by what percent?
(A) $$24\%$$
(B) $$20\%$$
(C) $$40\%$$
(D) $$60\%$$
(E) $$80\%$$
13- The radius of the following cylinder is $$6$$ inches and its height is $$11$$ inches. What is the surface area of the cylinder?
(A) $$204 \ π \ in^2$$
(B) $$190 \ π \ in^2$$
(C) $$300\ π \ in^2$$
(D) $$240 \ π \ in^2$$
(E) $$220 \ π \ in^2$$
14- Half of $$12$$ is equal to $$\frac{2}{3}$$ of what number?
(A) $$12$$
(B) $$18$$
(C) $$9$$
(D) $$8$$
(E) $$30$$
15- Which of the following expressions is equivalent to $$3x \ (2 \ + \ 5 \ y)$$ ?
(A) $$8 \ x \ y \ + \ 8 \ x$$
(B) $$2 \ x \ y \ + \ 5 \ x$$
(C) $$12 \ x \ y \ + \ 5 \ x$$
(D) $$15 \ x \ y \ + \ 6 \ x$$
(E) $$x \ y \ + \ x$$
16- What is the area of a square whose diagonal is $$4$$?
(A) $$16$$
(B) $$8$$
(C) $$10$$
(D) $$9$$
(E) $$18$$
17- A bank is offering $$2.5\%$$ simple interest on a savings account. If you deposit $$10,000$$, how much interest will you earn in four years?
(A) $$\ 400$$
(B) $$\ 750$$
(C) $$\ 1200$$
(D) $$\ 1000$$
(E) $$\ 800$$
18- If the height of a right pyramid is $$9$$ cm and its base is a square with side $$5$$ cm. What is its volume?
(A) $$108$$ cm$$^3$$
(B) $$155$$ cm$$^3$$
(C) $$105$$ cm$$^3$$
(D) $$104$$ cm$$^3$$
(E) $$75$$ cm$$^3$$
19- The price of a laptop is decreased by $$20\%$$ to $$400$$. What is its original price?
(A) $$\ 500$$
(B) $$\ 450$$
(C) $$\ 380$$
(D) $$\ 400$$
(E) $$\ 600$$
20- A chemical solution contains $$6\%$$ alcohol. If there is $$36$$ ml of alcohol, what is the volume of the solution?
(A) $$450$$ ml
(B) $$2000$$ ml
(C) $$2500$$ ml
(D) $$600$$ ml
(E) $$700$$ ml
21- What is the value of $$y$$ in the following system of equation?
$$2 \ x \ - \ 3 y= - \ 22$$
$$- \ x \ + \ 4 \ y= 16$$
(A) $$1$$
(B) $$- \ 1$$
(C) $$2$$
(D) $$- \ 2$$
(E) $$- \ 3$$
22- The perimeter of the trapezoid below is $$40$$. What is its area?
(A) $$62$$
(B) $$72$$
(C) $$85$$
(D) $$70$$
(E) $$36$$
23- The ratio of boys to girls in a school is $$3:4$$. If there are $$700$$ students in a school, how many boys are in the school?
(A) $$360$$
(B) $$450$$
(C) $$300$$
(D) $$250$$
(E) $$350$$
24- What is the median of these numbers? $$3 \ , \ 5 \ , \ 11 \ , \ 4 \ , \ 16 \ , \ 8 \ , \ 15$$
(A) $$11$$
(B) $$18$$
(C) $$15$$
(D) $$4$$
(E) $$8$$
25- The average of $$8 \ , \ 10 \ , \ 14$$ and $$x$$ is $$16$$. What is the value of $$x$$?
(A) $$32$$
(B) $$18$$
(C) $$64$$
(D) $$48$$
(E) $$30$$
26- A bank is offering $$2.5\%$$ simple interest on a savings account. If you deposit $$\ 6,000$$, how much interest will you earn in three years?
(A) $$\ 360$$
(B) $$\ 400$$
(C) $$\ 600$$
(D) $$\ 650$$
(E) $$\ 450$$
27- The price of a bed is decreased by $$25\%$$ to $$\ 540$$. What was its original price?
(A) $$540$$
(B) $$720$$
(C) $$450$$
(D) $$700$$
(E) $$500$$
28- The area of a circle is $$49\ π$$. What is the circumference of the circle?
(A) $$16 \ π$$
(B) $$24\ π$$
(C) $$14 \ π$$
(D) $$32 \ π$$
(E) $$120 \ π$$
29- Since last year, the price of gasoline has increased from $$\ 1.35$$ per gallon to $$\ 1.85$$ per gallon. The new price is what percent of the original price?
(A) $$158\%$$
(B) $$150\%$$
(C) $$137\%$$
(D) $$148\%$$
(E) $$175\%$$
30- What are the zeros of the function: $$f(x)=x^3 \ + \ 3 \ x^2 \ + \ 2 \ x$$?
(A) $$- \ 2 \ , \ 2$$
(B) $$- \ 1 \ , \ 2$$
(C) $$- \ 1 \ , \ - \ 1$$
(D) $$0 \ , \ - \ 2 \ , \ - \ 1$$
(E) $$0$$

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31- In 1999, the average worker's income increased $$\ 15,000$$ per year starting from $$\ 20,000$$ annual salary. Which equation represents income greater than average? (I = income,  = number of years after 1999)
(A) $$I > 15000 \ x \ + \ 20000$$
(B) $$I > 15000 \ x \ - \ 20000$$
(C) $$I < 15000 \ x \ - \ 20000$$
(D) $$I < 15000 \ x \ + \ 20000$$
(E) $$I < \ - \ 15000 \ x \ + \ 20000$$
32- Which of the following could be the product of two consecutive prime numbers?
(A) $$4$$
(B) $$16$$
(C) $$10$$
(D) $$18$$
(E) $$35$$
33- The score of Amy was half that of Kevin and the score of Jennifer was twice that of Kevin. If the score of Jennifer was $$72$$, what is the score of Amy?
(A) $$35$$
(B) $$15$$
(C) $$18$$
(D) $$20$$
(E) $$10$$
34- The average of five consecutive numbers is $$54$$. What is the smallest number?
(A) $$52$$
(B) $$22$$
(C) $$35$$
(D) $$30$$
(E) $$14$$
35- A ladder leans against a wall forming a $$60^ᵒ$$ angle between the ground and the ladder. If the bottom of the ladder is $$25$$ feet away from the wall, how long is the ladder?
(A) $$110$$ feet
(B) $$60$$ feet
(C) $$30$$ feet
(D) $$25$$ feet
(E) $$50$$ feet
36- If $$40\%$$ of A is$$10\%$$  of B, then B is what percent of A?
(A) $$400\%$$
(B) $$4\%$$
(C) $$300\%$$
(D) $$30\%$$
(E) $$40\%$$
37- When a number is subtracted from $$35$$ and the difference is divided by that number, the result is $$4$$. What is the value of the number?
(A) $$4$$
(B) $$2$$
(C) $$6$$
(D) $$5$$
(E) $$7$$
38- How many possible outfit combinations come from four shirts, five slacks, and two ties?
(A) $$90$$
(B) $$60$$
(C) $$25$$
(D) $$11$$
(E) $$40$$
39- An angle is equal to one-fourth of its supplement. What is the measure of that angle?
(A) $$40$$
(B) $$20$$
(C) $$65$$
(D) $$36$$
(E) $$90$$
40- How many tiles of $$7$$ cm$$^2$$ are needed to cover a floor of dimension $$4$$ cm by $$28$$ cm?
(A) $$9$$
(B) $$16$$
(C) $$22$$
(D) $$14$$
(E) $$20$$
41- Calculate the value of $$x$$ for the right triangle shown below.
(A) $$25$$ ft
(B) $$45$$ ft
(C) $$60$$ ft
(D) $$22.8$$ ft
(E) $$16$$ ft
42- If the height of a right pyramid is $$15$$ cm and its base is a square with side $$7$$ cm. What is its volume?
(A) $$245$$ cm$$^3$$
(B) $$250$$ cm$$^3$$
(C) $$132$$ cm$$^3$$
(D) $$268$$ cm$$^3$$
(E) $$365$$ cm$$^3$$
43- The price of a cellphone is decreased by $$20\%$$ to $$\ 400$$. What is its original price?
(A) $$\ 300$$
(B) $$\ 320$$
(C) $$\ 500$$
(D) $$\ 450$$
(E) $$\ 400$$
44- A rope weighs $$500$$ grams per meter of length. What is the weight in kilograms of $$10.5$$  meters of this rope? ($$1$$ kilograms $$= 1000$$ grams)
(A) $$4.25$$
(B) $$0.25$$
(C) $$0.525$$
(D) $$5.25$$
(E) $$5.025$$
45- The average weight of $$24$$ girls in a class is $$70$$ kg and the average weight of $$36$$ boys in the same class is $$72$$ kg. What is the average weight of all the $$60$$ students in that class?
(A) $$71.2$$
(B) $$70.2$$
(C) $$70$$
(D) $$0.70$$
(E) $$0.7$$
46- Alex  traveled $$240$$ km in $$8$$ hours and Mary traveled $$270$$ km in $$6$$ hours. What is the ratio of the average speed of Alex to average speed of Mary?
(A) $$9 : 6$$
(B) $$4 : 5$$
(C) $$3 : 2$$
(D) $$2 : 3$$
(E) $$2 : 9$$
47- The width of a box is one-third of its length. The height of the box is one-third of its width. If the length of the box is $$36$$ cm, what is the volume of the box?
(A) $$726$$ cm$$^3$$
(B) $$250$$ cm$$^3$$
(C) $$1320$$ cm$$^3$$
(D) $$1728$$ cm$$^3$$
(E) $$172$$ cm$$^3$$
48- The price of a car was $$\ 20,000$$ in 2014, $$\ 16,000$$ in 2015 and $$\ 12800$$ in 2016. What is the rate of depreciation of the price of car per year?
(A) $$20\%$$
(B) $$15\%$$
(C) $$35\%$$
(D) $$40\%$$
(E) $$50\%$$
49- In a coordinate plane, triangle ABC has coordinates: $$( -\ 2 \ , \ 5)$$, $$(− \ 1 \ , \ 4)$$, and $$(3 \ , \ 7)$$. If triangle ABC is reflected over the $$y-$$axis, what are the coordinates of the new image?
(A) $$(2 \ , \ 5) , (1 \ , \ 4) , (- \ 3 \ , \ 7)$$
(B) $$(2 \ , \ - \ 5) , (- \ 1 \ , \ 4) , (- \ 3 \ , \ 7)$$
(C) $$(2 \ , \ 5) , (- \ 1 \ , \ - \ 4) , (- \ 3 \ , \ 7)$$
(D) $$(2 \ , \ 5) , (- \ 1 \ , \ - \ 4) , (- \ 3 \ , \ - \ 7)$$
(E) $$(2 \ , \ 5) , ( 1 \ , \ - \ 4) , (- \ 3 \ , \ - \ 7)$$
50- Multiply and write the product in scientific notation:
$$(4.2 \ × \ 10^5) \ × \ (1.5 \ × \ 10^{-4})$$
(A) $$- \ 6.3 \ × \ 10^1$$
(B) $$- \ 6.32\ × \ 10^3$$
(C) $$6.3 \ × \ 10$$
(D) $$632 \ × \ 10$$
(E) $$632 \ × \ 10^2$$
 1- Choice B is correct The correct answer is $$4$$Simplify:$$2(x \ + \ 3) \ = \ 4(x \ − \ 6) \ + \ 22 \ ⇒ \ 2x \ + 6 = 4x \ − \ 24 \ + \ 22 \ ⇒ \ 2x \ + \ 6 \ = \ 4x \ – \ 2$$Subtract $$2x$$ from both sides:$$6 \ = \ 2x \ – \ 2$$, Add $$2$$ to both sides:$$8 \ = \ 2x \ ⇒ \ 4 \ = \ x$$ 2- Choice E is correct The corret answer is $$275$$Add the first $$5$$ numbers. $$20 \ + \ 25 \ + \ 15 \ + \ 30 \ + \ 35 = 125$$To find the distance traveled in the next $$5$$ hours, multiply the average by number of hours.Distance = Average × Rate $$= 30 \ × \ 5 = 150$$, Add both numbers.$$125 \ + \ 150 = 275$$ 3- Choice A is correct The correct answer is $$125$$$$x=100 \ + \ 25=125$$ 4- Choice C is correct The correct answer is $$5$$Use Pythagorean Theorem: $$a^2 \ + \ b^2 \ = \ c^2 \ ⇒ \ 4^2 \ + \ 3^2 \ = \ c^2 \ ⇒ \ 25 = c^2 ⇒ c = 5$$ 5- Choice A is correct The correct answer is $$6 \ x^2 \ + \ 19 \ x \ y \ + \ 10\ y^2$$Use FOIL (First, Out, In, Last)$$(3x \ + \ 2y) \ (2x \ + \ 5y) \ = \ 6x^2 \ + \ 15xy \ + \ 4xy \ + \ 10y^2 \ = \ 6x^2 \ + \ 19xy \ + \ 10y^2$$ 6- Choice D is correct The correct answer is $$150$$Use percent formula:part $$=\frac{ percent}{100}×$$whole$$45= \frac{percent}{100} \ × \ 30 ⇒ 45 = \frac{percent \ × \ 30}{100}⇒45 = \frac{percent × \ 3}{10}$$, multiply both sides by $$10$$.$$450 = percent \ × \ 3$$, divide both sides by $$3$$ ⇒ $$150=$$ percent 7- Choice B is correct The correct answer is $$108\%$$To find the discount, multiply the number by ($$100 \% \ –$$ rate of discount).Therefore, for the first discount we get: (D)  $$(100\% \ – \ 10\%) =$$ (D)   $$(0.90) = 0.90$$ DFor increase of $$20\%: (0.90 D) \ (100\% \ + \ 20\%) = (0.90 D) \ (1.20) = 1.08 D = 108\%$$ of D 8- Choice A is correct The correct answer is $$2$$$$y = 3\ a \ b \ - \ 4 \ b^2$$Plug in the values of $$a$$ and $$b$$ in the equation: $$a = 3$$ and $$b = 2$$$$y = 3 \ (3) \ (2) \ - \ 4 \ (2)^2 = 18 \ - \ 4 \ (4) = 18 \ - \ 16 = 2$$ 9- Choice E is correct The correct answer is $$72$$$$4.5\%$$ of $$1,600 = 0.045 \ × \ 1600 = 72$$ 10- Choice B is correct The correct answer is $$7$$The percent of girls playing tennis is: $$35\% ×20\% = 0.35 \ × \ 0.20 = 0.07 = 7\%$$ 11- Choice C is correct The correct answer is $$22$$ hours and $$20$$ minutesUse distance formula:Distance = Rate × time ⇒ $$670 = 30 × T$$, divide both sides by $$30$$ ⇒$$\frac{670}{30} = T$$ ⇒ $$T = 22.33$$ hours.Change hours to minutes for the decimal part. $$0.33$$ hours $$= 0.33 \ × \ 60 = 20$$ 12- Choice A is correct The correct answer is $$24\%$$Use the formula for Percent of Change: $$\frac{New \ Value \ - \ Old \ Value}{Old \ Value} \ × \ 100\%$$$$\frac{38 \ - \ 50}{50} \ × \ 100\% = – \ 24\%$$ (negative sign here means that the new price is less than old price). 13- Choice A is correct The correct answer is $$204 \ π \ in^2$$Surface Area of a cylinder  $$= 2 \ π \ r \ (r \ + \ h)$$,The radius of the cylinder is $$6$$ inches and its height is $$11$$ inches.Surface Area of a cylinder $$= 2 \ (π) \ (6) \ (6 \ + \ 11) = 204 \ π$$ 14- Choice C is correct The correct answer is $$9$$Let $$x$$ be the number. Write the equation and solve for $$x$$.$$\frac{1}{2} \ × \ 12 \ = \ \frac {2}{3} \ x \ ⇒ \ \frac{1 \ × \ 12}{2}=\frac{2 \ x}{3}$$use cross multiplication to solve for $$x$$. $$12 \ \times \ 3 \ = \ 2x \ \times \ 2 \ ⇒ \ 36 \ = \ 4x \ ⇒ \ x \ = \ 9$$ 15- Choice D is correct The correct answer is $$15 \ x \ y \ + \ 6 \ x$$Use distributive property: $$3x(2 \ + \ 5y) \ = \ 6x \ + \ 15xy \ = \ 15xy \ + \ 6x$$ 16- Choice B is correct The correct answer is $$8$$The diagonal of the square is $$4$$. Let $$x$$ be the side. Use Pythagorean Theorem: $$a^2 \ + \ b^2 = c^2$$$$x^2 \ + \ x^2 \ = \ 4^2 \ ⇒ \ 2x^2 \ = \ 4^2 \ ⇒ \ 2x^2 \ = \ 16 \ ⇒ \ x^2 \ = \ 8 \ ⇒ \ x= \ \sqrt{8}$$The area of the square is:$$\sqrt{8} \times \sqrt{8} \ = \ 8$$ 17- Choice D is correct The correct answer is $$1000$$Use simple interest formula: (I = interest, p = principal, r = rate, t = time)$$I \ = \ (1000) \times (0.025) \times (4) = 1000$$ 18- Choice E is correct The correct answer is $$75$$ cm$$^3$$The formula of the volume of pyramid is: V $$= \frac{l \ \times \ w \ \times \ h}{3}$$The length and width of the pyramid are $$5$$ cm and its height is $$9$$ cm.Therefore:V $$= \frac{5 \ \times \ 5 \ \times \ 9}{3}=75$$cm$$^3$$ 19- Choice A is correct The correct answer is $$500$$Let $$x$$ be the original price. If the price of a laptop is decreased by $$20\%$$ to $$400$$, then: $$80\%$$ of $$x \ = \ 400 \ ⇒ \ 0.80x \ = \ 400 \ ⇒ \ x \ = \ 400 \ ÷ \ 0.80 \ = \ 500$$ 20- Choice D is correct The correct answer is $$600$$ ml$$6\%$$ of the volume of the solution is alcohol.Let $$x$$ be the volume of the solution. Then: $$6\%$$ of $$x \ = \ 36$$ ml $$⇒ \ 0.06x \ = \ 36 \ ⇒ \ x \ = \ 36 \div 0.06 \ = \ 600$$ 21- Choice C is correct The correct answer is $$2$$Solving Systems of Equations by Elimination$$2 \ x \ - \ 3 \ y = - \ 22$$$$- \ x \ + \ 4 \ y =16$$Multiply the second equation by $$2$$, then add it to the first equation.$$2 \ x \ - \ 3 \ y = - \ 22$$$$2 (- \ x \ + \ 4 \ y =16)⇒ \ -2 \ x \ + \ 8 \ y = 32$$   $$⇒ \ 5 \ y= 10 \ ⇒ \ y = 2$$ 22- Choice B is correct The correct answer is $$72$$The perimeter of the trapezoid is $$40$$.So, the missing side (height) is $$= 40 \ – \ 14 \ – \ 8 \ – \ 10 = 8$$Area of the trapezoid:A $$=\frac{1}{2} \ h \ (b_1 \ + \ b_2) = \frac{1}{2} (8) \ (10 \ + \ 8) = 72$$ 23- Choice C is correct The correct answer is $$300$$The ratio of boys to girls is $$3:4$$. Therefore, there are $$3$$ boys out of $$7$$ students. To find the answer, first, divide the total number of students by $$7$$, then multiply the result by $$3$$. $$700 \ ÷ \ 7 = 100 ⇒ 100 × 3 = 300$$ 24- Choice E is correct The correct answer is $$8$$Write the numbers in order:   $$3 \ , \ 4 \ , \ 5 \ , \ 8 \ , \ 11 \ , \ 15 \ , \ 16$$Since we have $$7$$ numbers ($$7$$ is odd),then the median is the number in the middle, which is $$8$$. 25- Choice A is correct The correct answer is $$32$$average $$= \frac{sum \ of \ terms}{number \ of \ terms}⇒ 16 = \frac{10 \ + \ 14 \ + \ 8 \ + \ x}{4 }⇒ 64 = 32 \ + \ x ⇒ x = 32$$ 26- Choice E is correct The correct answer is $$\ 450$$Use simple interest formula: (I = interest, p = principal, r = rate, t = time)$$I=(6,000) \ (0.025) \ (3)=450$$ 27- Choice B is correct The correct answer is $$720$$Let $$x$$ be the original price. If the price of the bed is decreased by $$25\%$$ to $$\ 540$$,then: $$75\%$$ of $$x=540 ⇒ 0.75 \ x = 540 ⇒ x =540 \ ÷ \ 0.75=720$$ 28- Choice C is correct The correct answer is $$14 \ π$$Use the formula of areas of circles.Area $$= π \ r^2 ⇒49 \ π = π \ r^2⇒ 49 = r^2 ⇒ r = 7$$Radius of the circle is $$7$$.Now, use the circumference formula:Circumference $$= 2 \ π \ r = 2 \ π (7)= 14 \ π$$ 29- Choice C is correct The correct answer is $$137$$The question is this:$$1.85$$ is what percent of $$1.35$$?Use percent formula:part $$= \frac{percent}{100} \ ×$$ whole$$1.85 = \frac{percent}{100} \ × \ 1.35 ⇒1.85 = \frac{percent \ × \ 1.35}{100} ⇒ 185 = percent \ × \ 1.35$$ ⇒$$percent = \frac{185}{1.35} = 137$$ 30- Choice D is correct The correct answer is $$0 \ , \ - \ 2 \ , \ - \ 1$$ First factor the function:$$x \ (x \ + \ 2) \ (x \ + \ 1)$$To find the zeros, $$f(x)$$ should be zero.$$f(x)=x \ (x \ + \ 2) \ (x \ + \ 1)=0$$Therefore, the zeros are:$$x=0$$, $$(x \ + \ 2)=0 ⇒x= - \ 2$$ , $$(x \ + \ 1)=0 ⇒x= - \ 1$$ 31- Choice A is correct The correct answer is $$I > 15000 \ x \ + \ 20000$$Let $$x$$ be the number of years. Therefore, $$\ 15,000$$ per year equals $$15000 \ x$$. starting from $$\ 20,000$$ annual salary means you should add that amount to $$15000 \ x$$. Income more than that is:$$I > 15000 \ x \ + \ 20000$$ 32- Choice E is correct The correct answer is $$35$$Some of prime numbers are: $$2 \ , \ 3 \ , \ 5 \ , \ 7 \ , \ 11 \ , \ 13$$Find the product of two consecutive prime numbers:$$2 \ × \ 3 = 6$$ (not in the options)$$3 \ × \ 5 = 15$$(not in the options),$$5 \ × \ 7 = 35$$ (bingo!) 33- Choice C is correct The correct answer is $$18$$If the score of Jennifer was $$72$$, therefore the score of Kevin is $$36$$.Since the score of Amy was half that of Kevin,therefore, the score of Amy is $$18$$. 34- Choice A is correct The correct answer is $$52$$Let $$x$$ be the smallest number. Then, these are the numbers: $$x \ , \ x \ + \ 1 \ , \ x \ + \ 2 \ , \ x \ + \ 3 \ , \ x \ + \ 4$$average $$=\frac {sum \ of \ terms}{number \ of \ terms}⇒ 54 =\frac { x \ + \ (x \ + \ 1) \ + \ (x \ + \ 2) \ + \ (x \ + \ 3)\ + \ (x \ + \ 4)}{5} ⇒$$$$54=\frac {5 \ x \ + \ 10}{5} ⇒ 270 = 5 \ x \ + \ 10 ⇒ 260 = 5 \ x ⇒ x=52$$ 35- Choice E is correct The correct answer is $$50$$ feetThe relationship among all sides of a special right triangle $$30^° \ - \ 60^° \ - \ 90^°$$ is provided in this triangle: In this triangle, the opposite side of the $$30^°$$ angle is half of the hypotenuse. Draw the shape of this question: The latter is the hypotenuse. Therefore, the ladder is $$50$$ ft. 36- Choice A is correct The correct answer is $$400\%$$Write the equation and solve for B$$:0.40$$ A $$= 0.10$$ B, divide both sides by $$0.10$$ , then you will have $$\frac{0.40}{0.10}$$ A = B,therefore: B $$= 4$$ A, and B is $$4$$ times of A or it’s $$400\%$$ of A. 37- Choice E is correct The correct answer is $$7$$Let $$x$$ be the number. Write the equation and solve for $$x$$. $$(35 \ – \ x) \ ÷ \ x= 4$$Multiply both sides by $$x$$.$$(35 \ – \ x) = 4 \ x$$,then add $$x$$ both sides. $$35 = 5 \ x$$,now divide both sides by $$5$$ ⇒ $$x = 7$$ 38- Choice E is correct The correct answer is $$40$$To find the number of possible outfit combinations, multiply the number of options for each factor:$$4 \ × \ 5 \ × \ 2 =40$$ 39- Choice D is correct The correct answer is $$36$$The sum of supplement angles is $$180$$. Let $$x$$ be that angle.Therefore, $$x = \frac{1}{4}(180 \ - \ x) ⇒ x \ + \ 4 \ x = 180 ⇒$$$$5x \ = \ 180$$ , divide both sides by $$5$$ : $$x = 36$$ 40- Choice B is correct The correct answer is $$16$$The area of the floor is: $$4 \ cm \ × \ 28 \ cm = 112$$ cm,The number is tiles needed $$= 112 \ ÷ \ 7 = 16$$ 41- Choice D is correct The correct answer is $$22.8$$ ftUse Pythagorean theorem: $$a^2 \ + \ b^2 = c^2$$ , $$14^2 \ + \ 18^2= x^2$$ , $$196 \ + \ 324 = x^2$$$$520 = x^2$$ ⇒ $$x = 22.8$$ 42- Choice A is correct The correct answer is $$245$$ cm$$^3$$The formula of the volume of a pyramid is:V$$=\frac {l \times w \times h}{3}$$The length and width of the pyramid are $$7$$ cm and its height is $$14$$ cm. Therefore:V $$= \frac{7 \ \times \ 7 \ \times \ 15}{3} = 245$$ cm$$^3$$ 43- Choice C is correct The correct answer is $$\ 500$$Let $$x$$ be the original price.If the price of a laptop is decreased by $$20\%$$ to $$\ 400$$ , then: $$80\%$$  of  $$x= 400 \ ⇒ \ 0.80x \ = \ 400 ⇒ x = 400 \ ÷ \ 0.80 \ = \ 500$$ 44- Choice D is correct The correct answer is $$5.25$$The weight of $$10.5$$ meters of this rope is: $$10.5 \ × \ 500 \ g = 5250$$ g1 kg $$= 1000$$ g,therefore, $$5250$$ g $$÷ \ 1000 = 5.25$$ kg 45- Choice A is correct The correct answer is $$71.2$$average $$= \frac{sum \ of \ terms }{number \ of \ terms}$$The sum of the weight of all girls is: $$24 \ × \ 70 = 1680$$ kgThe sum of the weight of all boys is: $$36 \ × \ 72 =2592$$ kgThe sum of the weight of all students is: $$1680 \ + \ 2592 =4272$$ kgaverage $$= \frac{4272}{60}= 71.2$$ 46- Choice D is correct The correct answer is $$2 : 3$$The average speed of john is: $$240 \ ÷ \ 8 = 30$$The average speed of Alice is: $$270 \ ÷ \ 6 = 45$$Write the ratio and simplify. $$30 : 45 ⇒ 2 : 3$$ 47- Choice D is correct The correct answer is $$1728$$ cm$$^3$$If the length of the box is $$36$$, then the width of the box is one-third of it, $$12$$, and the height of the box is $$4$$ (one-third of the width). The volume of the box is: $$V = l \ w \ h = (36) \ (12) \ (4) =1728$$ cm$$^3$$ 48- Choice A is correct The corrrect answer is $$20\%$$Use this formula: Percent of Change $$=\frac{New \ Value \ - \ Old \ Value}{Old Value} \ × \ 100\%$$$$\frac{16000 \ - \ 20000}{20000} \ × \ 100\% = 20\%$$ and $$\frac{12800 \ - \ 16000}{16000} \ × \ 100\% = 20\%$$ 49- Choice A is correct The correct answer is $$(2 \ , \ 5)$$ , $$(1 \ , \ 4)$$ , $$(- \ 3 \ , \ 7)$$Since the triangle ABC is reflected over the $$y-$$axis, then all values of $$y$$’s of the points don’t changeand the sign of all$$x$$’s change.(remember that when a point is reflected over the $$y-$$axis, the value of $$y$$ does not change and whena point is reflected over the $$x-$$axis, the value of $$x$$  does not change).Therefore:$$(− \ 2,5)$$ changes to $$(2 \ , \ 5)$$$$(− \ 1 \ , \ 4)$$ changes to $$(1 \ , \ 4)$$$$(3 \ , \ 7)$$ changes to$$(− \ 3 \ , \ 7)$$ 50- Choice C is correct The correct answer is $$6.3 \ × \ 10^1$$$$(4.2 \ × \ 10^5) \ × \ (1.5 \ × \ 10^{−4}) = (4.2 \ × \ 1.5) \ × \ (10^5 \ × \ 10^{−4}) = 6.3 \ × \ (10^{5 + (−4)} ) =$$$$6.3 \ × \ 10^1$$

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