## Full Length CLEP College Mathematics Practice Test

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60 questions Total time for this section: 90 Minutes   You can use a scientific calculator on this test.
1- If $$4\ n\ -\ 3\ ≥\ 1$$, what is the least possible value of $$4\ n\ +\ 3$$?
(A) $$3$$
(B) $$4$$
(C) $$7$$
(D) $$9$$
2- Simplify the expression.
$$(6\ x^3\ -\ 8\ x^2\ +\ 2\ x^4 )\ -\ (4\ x^2\ -\ 2\ x^4\ +\ 2\ x^3 )$$
(A) $$4\ x^4\ +\ 4x^3\ -\ 12\ x^2$$
(B) $$4\ x^3\ -\ 12\ x^2$$
(C) $$4\ x^4\ +\ 4\ x^3\ -\ 12\ x^2$$
(D) $$8\ x^3\ -\ 12\ x^2$$
3- In two successive years, the population of a town is increased by $$15\%$$ and $$20\%$$.
What percent of the population is increased after two years?
(A) $$32\%$$
(B) $$35\%$$
(C) $$38\%$$
(D) $$68\%$$
4- Which of the following graphs represents the compound inequality $$-\ 2\ \leq\ 2\ x\ -\ 4\ <\ 8$$ ?
(A)
(B)
(C)
(D)
5- What is the volume of a box with the following dimensions?
Hight $$= 4$$ cm                      Width $$= 5$$ cm                Length $$= 6$$ cm
(A) $$15$$ cm$$^3$$
(B) $$60$$ cm$$^3$$
(C) $$90$$ cm$$^3$$
(D) $$120$$ cm$$^3$$
6- Carlos family are choosing a menu for their reception. They have $$3$$ choices of appetizers,
$$5$$ choices of entrees, $$4$$ choices of cake. How many different menu combinations are possible for them to choose?
(A) $$12$$
(B) $$32$$
(C) $$60$$
(D) $$120$$
7- In a stadium the ratio of home fans to visiting fans in a crowd is $$5:7$$.
Which of the following could be the total number of fans in the stadium?
(A) $$12,324$$
(B) $$42,326$$
(C) $$44,566$$
(D) $$66,812$$
8- Last week $$24,000$$ fans attended a football match. This week three times as many bought tickets,
but one sixth of them cancelled their tickets. How many are attending this week?
(A) $$48,000$$
(B) $$54,000$$
(C) $$60,000$$
(D) $$72,000$$
9- What is the perimeter of a square in centimeters that has an area of $$595$$.$$36$$ cm$$^2$$ ?
(A) $$97.6$$
(B) $$96.2$$
(C) $$95.7$$
(D) $$92.6$$
10- Which of the following points lies on the line $$x\ +\ 2\ y=4$$ ?
(A) $$(-\ 2,\ 3)$$
(B) $$(1,\ 2)$$
(C) $$(-\ 1,\ 3)$$
(D) $$(-\ 3,\ 4)$$
11- The perimeter of a rectangular yard is $$60$$ meters. What is its length if its width is twice its length?
(A) $$10$$ meters
(B) $$18$$ meters
(C) $$20$$ meters
(D) $$24$$ meters
12- Which of the following shows the numbers in descending order?
$$\frac{2}{3},$$    $$0.68,$$      $$67\% ,$$    $$\frac{4}{5}$$
(A) $$67\%,\ 0.68,\ \frac{2}{3} ,\ \frac{4}{5}$$
(B) $$67\%,\ 0.68,\ \frac{4}{5},\ \frac{2}{3}$$
(C) $$0.68,\ 67\%,\ \frac{2}{3} ,\ \frac{4}{5}$$
(D) $$\frac{2}{3} ,\ 67\%,\ 0.68,\ \frac{4}{5}$$
13- The mean of $$50$$ test scores was calculated as $$88$$.
But, it turned out that one of the scores was misread as $$94$$ but it was $$69$$.
What is the correct mean of the test scores?
(A) $$85$$
(B) $$87$$
(C) $$87.5$$
(D) $$88.5$$
14- Two dice are thrown simultaneously, what is the probability of getting a sum of $$6$$ or $$9$$?
(A) $$\frac{1}{3}$$
(B) $$\frac{1}{4}$$
(C) $$\frac{1}{6}$$
(D) $$\frac{1}{12}$$
15- A swimming pool holds $$2,000$$ cubic feet of water. The swimming pool is $$25$$ feet long and $$10$$ feet wide.
How deep is the swimming pool?
(A) $$2$$
(B) $$4$$
(C) $$6$$
(D) $$8$$
16- What is the area of a square whose diagonal is $$8$$?
(A) $$16$$
(B) $$32$$
(C) $$36$$
(D) $$64$$
17- Anita’s trick–or–treat bag contains $$12$$ pieces of chocolate, $$18$$ suckers,
$$18$$ pieces of gum, $$24$$ pieces of licorice. If she randomly pulls a piece of candy from her bag,
what is the probability of her pulling out a piece of sucker?
(A) $$\frac{1}{3}$$
(B) $$\frac{1}{4}$$
(C) $$\frac{1}{6}$$
(D) $$\frac{1}{12}$$
18- The average of $$6$$ numbers is $$12$$. The average of $$4$$ of those numbers is $$10$$.
What is the average of the other two numbers.
(A) $$10$$
(B) $$12$$
(C) $$14$$
(D) $$16$$
19- What is the value of $$x$$ in the following system of equations?
$$2\ x\ +\ 5\ y=11\\ 4\ x\ -\ 2\ y=-\ 14$$
(A) $$-\ 1$$
(B) $$1$$
(C) $$-\ 2$$
(D) $$4$$
20- The perimeter of the trapezoid below is $$36$$ cm. What is its area?
(A) $$576$$ cm$$^2$$
(B) $$70$$ cm$$^2$$
(C) $$48$$ cm$$^2$$
(D) $$24$$ cm$$^2$$
21- If $$150\%$$ of a number is $$75$$, then what is the $$90\%$$ of that number?
(A) $$45$$
(B) $$50$$
(C) $$70$$
(D) $$85$$
22- If $$f(x) = 3\ x\ –\ 1$$ and $$g(x) = x\ 2\ –\ x$$, then find $$(\frac{f}{g})\ (x)$$.
(A) $$\frac{3\ x\ -\ 1}{x^2\ -\ x}$$
(B) $$\frac{x\ -\ 1}{x^2\ -\ x}$$
(C) $$\frac{x\ -\ 1}{x^2\ -\ 1}$$
(D) $$\frac{3\ x\ +\ 1}{x^2\ +\ x}$$
23- A card is drawn at random from a standard $$52\ –$$card deck, what is the probability that the card is of Hearts?
(The deck includes $$13$$ of each suit clubs, diamonds, hearts, and spades)
(A) $$\frac{1}{3}$$
(B) $$\frac{1}{4}$$
(C) $$\frac{1}{6}$$
(D) $$\frac{1}{52}$$
24- The average of five numbers is $$24$$. If a sixth number that is greater than $$42$$ is added,
then, which of the following could be the new average? (Select one or more answer choices)
(A) $$25$$
(B) $$26$$
(C) $$28$$
(D) $$27$$
25- The length of a rectangle is $$3$$ meters greater than $$4$$ times its width.
The perimeter of the rectangle is $$36$$ meters.  What is the area of the rectangle in meters?
(A) $$35$$
(B) $$45$$
(C) $$55$$
(D) $$65$$
26- Which of the following is equal to $$b^{\frac{3}{5}}$$?
(A) $$\sqrt{b^{\frac{5}{3}}}$$
(B) $$b^{\frac{5}{3}}$$
(C) $$\sqrt[5]{b^3}$$
(D) $$\sqrt[3]b^5$$
27- Jones saves $$2,500$$ out of his monthly family income of $$55,000$$.
What fractional part of his income does he save?
(A) $$\frac{1}{22}$$
(B) $$\frac{1}{11}$$
(C) $$\frac{3}{25}$$
(D) $$\frac{2}{15}$$
28- Jason needs an $$75\%$$ average in his writing class to pass. On his first $$4$$ exams,
he earned scores of $$68\%,\ 72\%,\ 85\%,$$ and $$90\%$$.
What is the minimum score Jason can earn on his fifth and final test to pass?
(A) $$375$$
(B) $$315$$
(C) $$90$$
(D) $$60$$

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29- What is the value of $$x$$ in the following equation?
$$\frac{2}{3}\ x\ +\ \frac{1}{6}= \frac{1}{3}$$
(A) $$6$$
(B) $$\frac{1}{2}$$
(C) $$\frac{1}{3}$$
(D) $$\frac{1}{4}$$
30- What is the surface area of the cylinder below?
(A) $$48\ π$$ in$$^2$$
(B) $$57\ π$$ in$$^2$$
(C) $$66\ π$$ in$$^2$$
(D) $$288\ π$$ in$$^2$$
31- The square of a number is  $$\frac{25}{64}$$. What is the cube of that number?
(A) $$\frac{5}{8}$$
(B) $$\frac{25}{254}$$
(C) $$\frac{125}{512}$$
(D) $$\frac{125}{64}$$
32- What is the median of these numbers? $$2,\ 27,\ 28,\ 19,\ 67,\ 44,\ 35$$
(A) $$19$$
(B) $$28$$
(C) $$44$$
(D) $$35$$
33- Right triangle $$A\ B\ C$$ has two legs of lengths $$6$$ cm $$(A\ B)$$ and 8 cm $$(A\ C)$$.
What is the length of the third side $$(B\ C)$$?
(A) $$4$$ cm
(B) $$6$$ cm
(C) $$8$$ cm
(D) $$10$$ cm
34- What is the equivalent temperature of $$104^\circ \ F$$ in Celsius?
(A) $$32$$
(B) $$40$$
(C) $$48$$
(D) $$52$$
35- If $$40\%$$ of a number is $$4$$, what is the number?
(A) $$4$$
(B) $$8$$
(C) $$10$$
(D) $$12$$
36- The circle graph below shows all Mr. Green’s expenses for last month.
If he spent $$660$$ on his car, how much did he spend for his rent?
(A) $$700$$
(B) $$740$$
(C) $$780$$
(D) $$810$$
37- Jason is $$9$$ miles ahead of Joe running at $$5.5$$ miles per hour and Joe is running at the speed of $$7$$ miles per hour.
How long does it take Joe to catch Jason?
(A) $$3$$ hours
(B) $$4$$ hours
(C) $$6$$ hours
(D) $$8$$ hours
38- $$55$$ students took an exam and $$11$$ of them failed.
What percent of the students passed the exam?
(A) $$20\%$$
(B) $$40\%$$
(C) $$60\%$$
(D) $$80\%$$
39- A bank is offering $$3.5\%$$ simple interest on a savings account. If you deposit $$12,000$$, how much interest will you earn in two years?
(A) $$420$$
(B) $$840$$
(C) $$4200$$
(D) $$8400$$
40- Simplify $$6\ x^2\ y^3\ (2\ x^2\ y)^3=$$
(A) $$12\ x^4\ y^6$$
(B) $$12\ x^8\ y^6$$
(C) $$48\ x^4\ y^6$$
(D) $$48\ x^8\ y^6$$
41- The table above shows some values of linear function . Which of the following defines ?
 $$x$$ $$1$$ $$2$$ $$3$$ $$g(x)$$ $$-\ 1$$ $$-\ 3$$ $$-\ 5$$
(A) $$g(x)=2\ x\ +\ 1$$
(B) $$g(x)=2\ x\ -\ 1$$
(C) $$g(x)=-\ 2\ x\ +\ 1$$
(D) $$g(x)=x\ +\ 2$$
42- Which of the following expressions is equal to $$\sqrt{\frac{x^2}{2}\ +\ \frac{x^2}{16}}$$ ?
(A) $$x$$
(B) $$\frac{3\ x}{4}$$
(C) $$x\ \sqrt{x}$$
(D) $$\frac{x\ \sqrt{x}}{4}$$
43- What is the $$y\ -$$intercept of the line with the equation $$x\ -\ 3\ y=12$$ ?
(A) $$1$$
(B) $$-\ 2$$
(C) $$3$$
(D) $$-\ 4$$
44- If $$4\ a\ -\ 3=14$$ what is the value of $$6\ a$$ ?
(A) $$5$$
(B) $$15$$
(C) $$30$$
(D) $$45$$
45- If $$x≠0$$ and $$x=x^{-\ 6}$$, what is the value of $$x$$?
(A) $$-\ 2$$
(B) $$1$$
(C) $$2$$
(D) $$3$$
46- Which of the following is equal to expression $$\frac{5}{x^2}\ +\ \frac{7\ x\ -\ 3}{x^3}$$  ?
(A) $$\frac{6\ x\ +\ 1}{x^3}$$
(B) $$\frac{10\ x\ +\ 6}{x^3}$$
(C) $$\frac{12\ x\ +\ 1}{x^3}$$
(D) $$\frac{13\ x\ +\ 2}{x^3}$$
47- Which of the following is the equation of a quadratic graph with a vertex $$(3,\ -\ 3)$$?
(A) $$y=3\ x^2\ -\ 3$$
(B) $$y=-\ 3\ x^2\ +\ 3$$
(C) $$y=x^2\ +\ 3\ x\ -\ 3$$
(D) $$y=4\ (x\ -\ 3)^2\ -\ 3$$
48- What is the average of $$4\ x\ +\ 2,\ -\ 6\ x\ -\ 5$$ and $$8\ x\ +\ 2$$?
(A) $$3\ x\ +\ 2$$
(B) $$3\ x\ -\ 2$$
(C) $$2\ x\ +\ 1$$
(D) $$2\ x\ -\ \frac{1}{3}$$
49- What is the slope of a line that is perpendicular to the line
$$4\ x\ -\ 2\ y=12$$?
(A) $$-\ 2$$
(B) $$-\frac{1}{2}$$
(C) $$4$$
(D) $$12$$
50- In a coordinate plane, triangle $$A\ B\ C$$ has coordinates: $$(−\ 1,\ 6),\ (−\ 2 ,\ 5)$$,
and $$(5,\ 8)$$. If triangle $$A\ B\ C$$ is reflected over the $$y\ -\ a\ x$$ is,
what are the coordinates of the new image?
(A) $$(−\ 1,\ −\ 6),\ (−\ 2,\ −\ 5),\ (−\ 5,\ −\ 8)$$
(B) $$(−\ 1,\ −\ 6),\ (−\ 2,\ −\ 5),\ (5,\ − \ 8)$$
(C) $$(1,\ 6),\ (2,\ 5),\ (5,\ 8)$$
(D) $$(1,\ 6),\ (2,\ 5),\ (−\ 5,\ 8)$$
51- What is the difference in area between a $$9$$ cm by $$4$$ cm rectangle and a circle with diameter of $$10$$ cm? $$(π=3)$$
(A) $$49$$
(B) $$39$$
(C) $$6$$
(D) $$4$$
52- If $$f(x)=2\ x^3\ +\ 2$$ and $$(x)=\frac{1}{x}$$ , what is the value of $$f(g(x))$$?
(A) $$\frac{1}{2\ x^3\ +2}$$
(B) $$\frac{2}{x^3}$$
(C) $$\frac{1}{2\ x}$$
(D) $$\frac{2}{x^3}\ +\ 2$$
53- What is the value of $$x$$ in the following equation?
$$6^x=1296$$
(A) $$3$$
(B) $$4$$
(C) $$5$$
(D) $$6$$
54- $$A$$cruise line ship left Port $$A$$ and traveled $$80$$ miles due west and then $$150$$ miles
due north. At this point, what is the shortest distance from the cruise to port $$A$$?
(A) $$70$$ miles
(B) $$80$$ miles
(C) $$150$$ miles
(D) $$170$$ miles
55- The length of a rectangle is $$3$$ meters greater than $$4$$ times its width.
The perimeter of the rectangle is $$36$$ meters.  What is the area of the rectangle?
(A) $$12$$ m$$^2$$
(B) $$27$$ m$$^2$$
(C) $$36$$ m$$^2$$
(D) $$45$$ m$$^2$$
56- Tickets to a movie cost $$12.50$$ for adults and $$7.50$$ for students. $$A$$ group
of $$12$$ friends purchased tickets for $$125$$. How many student tickets did they buy?
(A) $$3$$
(B) $$5$$
(C) $$7$$
(D) $$8$$
57- If the ratio of $$5\ a$$ to $$2\ b$$ is $$\frac{1}{10}$$, what is the ratio of $$a$$ to $$b$$?
(A) $$10$$
(B) $$25$$
(C) $$\frac{1}{25}$$
(D) $$\frac{1}{20}$$
58- If $$x=9$$, what is the value of $$y$$ in the following equation?
$$2\ y = \frac{2\ x^2}{3}\ +\ 6$$
(A) $$30$$
(B) $$45$$
(C) $$60$$
(D) $$120$$
59- A plant grows at a linear rate. After five weeks, the plant is $$40$$ cm tall.
Which of the following functions represents the relationship between the height $$(y)$$
of the plant and number of weeks of growth $$(x)$$?
(A) $$1.085\ (3\ p)\ +\ 6$$
(B) $$6\ p\ +\ 3$$
(C) $$91.085\ (6\ p)\ +\ 3$$
(D) $$3\ p\ +\ 6$$
60- Sara orders a box of pen for $$3$$ per box.
$$A$$ tax of $$8.5\%$$ is added to the cost of the pens before a flat shipping
fee of $$6$$ closest out the transaction.
Which of the following represents total cost of boxes of pens in dollars?
(A) $$y(x)=40\ x\ +\ 8$$
(B) $$y(x)=8\ x\ +\ 40$$
(C) $$y(x)=40\ x$$
(D) $$y(x)=8\ x$$
1- Choice C is correct

The correct answer is $$7$$
Adding $$6$$ to each side of the inequality $$4\ n\ -\ 3\ ≥\ 1$$ yields the inequality $$4\ n\ +\ 3\ ≥\ 7$$.
Therefore, the least possible value of $$4\ n\ +\ 3$$ is $$7$$.

2- Choice A is correct

The correct answer is $$4\ x^4\ +\ 4x^3\ -\ 12\ x^2$$
Simplify and combine like terms. $$(6\ x^3\ -\ 8\ x^2\ +\ 2\ x^4 )\ -\ (4\ x^2\ -\ 2\ x^4\ +\ 2\ x^3 )$$ ⇒
$$(6\ x^3\ -\ 8\ x^2\ +\ 2\ x^4 )\ -\ 4\ x^2\ +\ 2\ x^4\ -\ 2\ x^3\ ⇒\ 4\ x^4\ +\ 4\ x^3\ -\ 12\ x^2$$

3- Choice C is correct

The correct answer is $$38\%$$
The population is increased by $$15\%$$ and $$20\%$$. $$15\%$$ increase changes the population to $$115\%$$ of original population.
For the second increase, multiply the result by $$120\%$$. $$(1.15)\ ×\ (1.20)=1.38=138\%$$
$$38$$ percent of the population is increased after two years.

4- Choice D is correct

Solve for $$x$$. $$-\ 2\ ≤\ 2\ x\ -\ 4\ <\ 8\ ⇒$$ (add $$4$$ all sides) $$-\ 2\ +\ 4\ ≤\ 2\ x\ -\ 4\ + \ 4\ <\ 8\ +\ 4 ⇒$$
$$2\ ≤\ 2\ x\ <\ 12 ⇒$$ (divide all sides by $$2$$) $$1\ ≤\ x\ <\ 6$$
$$x$$ is between $$1$$ and $$6$$. Choice $$D$$ represent this inequality.

5- Choice D is correct

The correct answer is $$120$$ cm$$^3$$
Volume of a box $$=$$ length $$×$$ width $$×$$ height $$=4\ ×\ 5\ ×\ 6=120$$

6- Choice C is correct

The correct answer is $$60$$
To find the number of possible outfit combinations, multiply number of options for each factor: $$3\ ×\ 5\ ×\ 4=60$$

7- Choice A is correct

The correct answer is $$12,324$$
In the stadium the ratio of home fans to visiting fans in a crowd is $$5:7$$. Therefore,
total number of fans must be divisible by $$12: 5\ +\ 7 = 12$$.
Let’s review the choices:
A. $$12,324:$$          $$12,324\ ÷\ 12=1,027$$
B. $$42,326$$           $$42,326\ ÷\ 12=3,527.166$$
C. $$44,566$$           $$44,566\ ÷\ 12=3,713.833$$
D. $$66,812$$           $$66,812\ ÷\ 12=5,567.666$$
Only choice $$A$$ when divided by $$12$$ results a whole number.

8- Choice C is correct

The correct answer is $$60,000$$
Three times of $$24,000$$ is $$72,000$$. One sixth of them cancelled their tickets.
One sixth of $$72,000$$ equals $$12,000\ (\frac{1}{6}\ ×\ 72000 = 12000)$$.
$$60,000\ (72,000\ –\ 12,000=60,000)$$ fans are attending this week

9- Choice A is correct

The correct answer is $$97.6$$
The area of the square is $$595.36$$. Therefore, the side of the square is square root of the area. $$\sqrt{595.36}=24.4$$
Four times the side of the square is the perimeter: $$4\ ×\ 24.4=97.6$$

10- Choice A is correct

The correct answer is $$(-\ 2,\ 3)$$
$$x\ +\ 2\ y=4$$. Plug in the values of $$x$$ and $$y$$ from choices provided. Then:
A.             $$(-\ 2,\ 3)$$ $$x\ +\ 2\ y=4\ →\ -\ 2\ +\ 2\ (3)=4\ →\ -\ 2\ +\ 6=4$$                This is true!
B.             $$(1,\ 2)$$ $$x\ +\ 2\ y=4\ →\ 1\ +\ 2\ (2)=4\ →\ 1\ +\ 4 =4$$ This is                   NOT true!
C.             $$(-\ 1,\ 3)$$ $$x\ +\ 2\ y = 4\ →\ -\ 1\ +\ 2\ (3)=4\ →\ -\ 1\ +\ 6=4$$               This is NOT true!
D.             $$(-\ 3,\ 4)$$ $$x\ +\ 2\ y=4\ →\ -\ 3\ +\ 2\ (4)=4\ →\ -\ 3\ +\ 8=4$$                 This is NOT true!

11- Choice A is correct

The correct answer is $$10$$ meters
The width of the rectangle is twice its length. Let $$x$$ be the length. Then, width$$=2\ x$$
Perimeter of the rectangle is $$2$$ (width $$+$$ length) $$= 2\ (2\ x\ +\ x)=60\ ⇒\ 6\ x=60\ ⇒\ x=10$$
Length of the rectangle is $$10$$ meters.

12- Choice D is correct

The correct answer is $$\frac{2}{3} ,\ 67\%,\ 0.68,\ \frac{4}{5}$$
Change the numbers to decimal and then compare. $$\frac{2}{3}=0.666$$… $$67\%=0.67$$
$$\frac{4}{5}=0.80$$ Then: $$\frac{2}{3}\ <\ 67\%\ <\ 0.68\ <\ \frac{4}{5}$$

13- Choice C is correct

The correct answer is $$87.5$$
average (mean)$$= \frac{sum\ of\ terms}{number\ of\ terms}\ ⇒\ 88= \frac{sum\ of\ terms}{50}\ ⇒$$ sum$$=88\ ×\ 50=4400$$
The difference of $$94$$ and $$69$$ is $$25$$. Therefore, $$25$$ should be subtracted from the sum.
$$4400\ –\ 25=4375$$, mean$$= \frac{sum\ of\ terms}{number\ of\ terms}\ ⇒$$ mean$$=\frac{4375}{50}=87.5$$

14- Choice B is correct

The correct answer is $$\frac{1}{4}$$
To get a sum of $$6$$ for two dice, we can get $$5$$ different options: $$(5,\ 1),\ (4,\ 2),\ (3,\ 3),\ (2,\ 4),\ (1,\ 5)$$
To get a sum of $$9$$ for two dice, we can get $$4$$ different options: $$(6,\ 3),\ (5,\ 4),\ (4,\ 5),\ (3,\ 6)$$
Therefore, there are $$9$$ options to get the sum of 6 or $$9$$. Since, we have $$6\ ×\ 6 = 36$$ total options,
the probability of getting a sum of $$6$$ and $$9$$ is $$9$$ out of $$36$$ or $$\frac{1}{4}$$.

15- Choice D is correct

The correct answer is $$8$$
Use formula of rectangle prism volume. $$V=$$(length) (width) (height) $$⇒ 2000=(25)\ (10)$$ (height) $$⇒$$ height$$=2000\ ÷\ 250=8$$

16- Choice B is correct

The correct answer is $$32$$
The diagonal of the square is $$8$$. Let $$x$$ be the side.
Use Pythagorean Theorem: $$a^2\ +\ b^2=c^2$$
$$x^2\ +\ x^2=8^2\ ⇒\ 2\ x^2 = 82\ ⇒\ 2\ x^2 = 64\ ⇒\ x^2 = 32\ ⇒\ x= \sqrt{32}$$
The area of the square is: $$\sqrt{32}\ ×\ \sqrt{32}=32$$

17- Choice B is correct

The correct answer is $$\frac{1}{4}$$
Probability$$=\frac{number\ of\ desired\ outcomes}{number\ of\ total\ outcomes} = \frac{18}{12\ +\ 18\ +\ 18\ +\ 24} = \frac{18}{72} =\frac{1}{4}$$

18- Choice D is correct

The correct answer is $$16$$
average $$=\frac{sum\ of\ terms}{number\ of\ terms}\ ⇒$$ (average of $$6$$ numbers) $$12 = \frac{sum\ of\ numbers}{6}\ ⇒$$ sum of $$6$$ numbers is $$12\ ×\ 6 = 72$$
(average of $$4$$ numbers) $$10 = \frac{sum\ of\ numbers}{4}\ ⇒$$ sum of $$4$$ numbers is $$10\ ×\ 4 = 40$$
sum of $$6$$ numbers $$–$$ sum of $$4$$ numbers $$=$$ sum of $$2$$ numbers $$72\ –\ 40 = 32$$
average of $$2$$ numbers $$= \frac{32}{2}=16$$

19- Choice C is correct

The correct answer is $$-\ 2$$
Solving systems of Equations by Elimination
Multiply the first equation by ($$-\ 2$$), then add it to the second equation
$$\underline{-\ 2\ (2\ x\ +\ 5\ y=11)\\ 4\ x\ -\ 2\ y =-\ 14}$$ $$\Rightarrow$$ $$- \ 4\ x\ -\ 10\ y= -\ 22\\ 4\ x\ -\ 2\ y= -\ 14$$ $$\Rightarrow$$ $$-\ 12\ y=-\ 36 \Rightarrow \ y=3$$
Plug in the value of $$y$$ into one of the equations and solve for $$x$$.
$$2\ x\ +\ 5\ (3)= 11\ ⇒ \ 2\ x\ +\ 15= 11\ ⇒\ 2\ x= -\ 4\ ⇒\ x= -\ 2$$

20- Choice B is correct

The correct answer is $$70$$ cm$$^2$$
The perimeter of the trapezoid is $$36$$ cm. Therefore, the missing side (height) is $$= 36\ –\ 8\ –\ 12\ –\ 6=10$$.
Area of a trapezoid: $$A=\frac{1}{2}\ h\ (b_1\ +\ b_2)= \frac{1}{2}\ (10)\ (6\ +\ 8)=70$$

21- Choice A is correct

The correct answer is $$45$$
First, find the number. Let $$x$$ be the number. Write the equation and solve for $$x$$.
$$150\%$$ of a number is $$75$$, then: $$1.5\ ×\ x=75\ ⇒\ x=75\ ÷\ 1.5=50$$
$$90\%$$ of $$50$$ is: $$0.9\ ×\ 50=45$$

22- Choice A is correct

The correct answer is $$\frac{3\ x\ -\ 1}{x^2\ -\ x}$$
$$(\frac{f}{g})\ (x) = \frac{f\ (x)}{g\ (x)} = \frac{3\ x\ –\ 1}{x^2\ -\ x}$$

23- Choice B is correct

The correct answer is $$\frac{1}{4}$$
The probability of choosing a Hearts is $$\frac{13}{52}=\frac{1}{4}$$

24- Choice D is correct

The correct answer is $$27$$
First, find the sum of five numbers.
average $$=\frac{sum\ of\ terms}{number\ of\ terms}\ ⇒\ 24 = \frac{sum\ of\ 5\ numbers}{5}\ ⇒$$ sum of $$5$$ numbers $$= 24\ ×\ 5 = 120$$
The sum of $$5$$ numbers is $$120$$. If a sixth number that is greater than $$42$$ is added to these numbers,
then the sum of $$6$$ numbers must be greater than $$162$$. $$120\ +\ 42 = 162$$
If the number was $$42$$, then the average of the numbers is:
average $$=\frac{sum\ of\ terms}{number\ of\ terms}=\frac{162}{6}=27$$
Since the number is bigger than $$42$$. Then, the average of six numbers must be greater than $$27$$. Choice $$D$$ is greater than $$27$$.

25- Choice B is correct

The correct answer is $$45$$
Let $$L$$ be the length of the rectangular and $$W$$ be the with of the rectangular. Then, $$L=4\ W\ +\ 3$$
The perimeter of the rectangle is $$36$$ meters. Therefore: $$2\ L\ +\ 2\ W=36$$ $$L\ +\ W=18$$
Replace the value of $$L$$ from the first equation into the second equation and solve for $$W$$:
$$(4\ W\ +\ 3)\ +\ W=18\ →\ 5\ W\ +\ 3=18\ →\ 5\ W=15\ →\ W=3$$
The width of the rectangle is $$3$$ meters and its length is: $$L=4\ W\ +\ 3=4\ (3)\ +\ 3=15$$
The area of the rectangle is: length $$×$$ width $$= 3\ ×\ 15 = 45$$

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26- Choice C is correct

The correct answer is $$\sqrt[5]{b^3}$$
$$b^{\frac{m}{n}}=\sqrt[n]{b^m}$$ For any positive integers $$m$$ and $$n$$. Thus, $$b^{\frac{3}{5}}=\sqrt[5]{b^3}$$.

27- Choice A is correct

The correct answer is $$\frac{1}{22}$$
$$2,500$$ out of $$55,000$$ equals to $$\frac{2500}{55000}=\frac{25}{550}=\frac{1}{22}$$

28- Choice D is correct

The correct answer is $$60$$
Jason needs an $$75\%$$ average to pass for five exams. Therefore, the sum of $$5$$ exams must be at lease $$5\ ×\ 75 = 375$$.
The sum of $$4$$ exams is: $$68\ +\ 72\ +\ 85\ +\ 90=315$$
The minimum score Jason can earn on his fifth and final test to pass is: $$375\ –\ 315=60$$

29- Choice D is correct

The correct answer is $$\frac{1}{4}$$
Isolate and solve for $$x$$. $$\frac{2}{3}\ x\ +\ \frac{1}{6}= \frac{1}{3}\ ⇒\ \frac{2}{3}\ x= \frac{1}{3}\ -\ \frac{1}{6} = \frac{1}{6}\ ⇒\ \frac{2}{3}\ x= \frac{1}{6}$$
Multiply both sides by the reciprocal of the coefficient of $$x$$. $$(\frac{3}{2})\ \frac{2}{3}\ x=\frac{1}{6}$$ $$(\frac{3}{2})\ ⇒\ x= \frac{3}{12}=\frac{1}{4}$$

30- Choice C is correct

The correct answer is $$66\ π$$ in$$^2$$
Surface Area of a cylinder $$= 2\ π\ r\ (r\ +\ h)$$, The radius of the cylinder is $$3\ (6\ ÷\ 2)$$ inches and its height is $$8$$ inches.
Therefore, Surface Area of a cylinder $$= 2\ π\ (3)\ (3\ +\ 8) = 66\ π$$

31- Choice C is correct

The correct answer is $$\frac{125}{512}$$
The square of a number is $$\frac{25}{64}$$, then the number is the square root of $$\frac{25}{64}$$ $$\sqrt{\frac{25}{64}}= \frac{5}{8}$$
The cube of the number is: $$(\frac{5}{8})^3 = \frac{125}{512}$$

32- Choice B is correct

The correct answer is $$28$$
Write the numbers in order: $$2,\ 19,\ 27,\ 28,\ 35,\ 44,\ 67$$
Median is the number in the middle. So, the median is $$28$$.

33- Choice D is correct

The correct answer is $$10$$
Use Pythagorean Theorem: $$a^2\ +\ b^2= c^2$$                $$6^2\ +\ 8^2= c^2\ ⇒\ 100= c^2 \ ⇒\ c=10$$

34- Choice B is correct

The correct answer is $$40$$
Plug in $$104$$ for $$F$$ and then solve for $$C$$. $$C= \frac{5}{9}\ (F\ –\ 32)\ ⇒\ C= \frac{5}{9}\ (104\ –\ 32)\ ⇒ C= \frac{5}{9}\ (72)=40$$

35- Choice C is correct

The correct answer is $$10$$
Let $$x$$ be the number. Write the equation and solve for $$x$$.
$$40\%$$ of $$x=4\ ⇒\ 0.40\ x=4 \ ⇒\ x=4\ ÷\ 0.40=10$$

36- Choice D is correct

The correct answer is $$810$$
Let $$x$$ be all expenses, then $$\frac{22}{100}\ x=660\ →\ x=\frac{100\ ×\ 660}{22}=3,000$$
He spent for his rent: $$\frac{27}{100}\ ×\ 3,000=810$$

37- Choice C is correct

The correct answer is $$6$$ hours
The distance between Jason and Joe is $$9$$ miles.
Jason running at $$5.5$$ miles per hour and Joe is running at the speed of $$7$$ miles per hour.
Therefore, every hour the distance is $$1.5$$ miles less. $$9\ ÷\ 1.5=6$$

38- Choice D is correct

The correct answer is $$80\%$$
The failing rate is $$11$$ out of $$55 = \frac{11}{55}$$. Change the fraction to percent: $$\frac{11}{55}\ ×\ 100\%=20\%$$
$$20$$ percent of students failed. Therefore, $$80$$ percent of students passed the exam.

39- Choice B is correct

The correct answer is $$840$$
Use simple interest formula: $$I=$$ prt ($$I =$$ interest, $$p =$$ principal, $$r =$$ rate, $$t =$$ time)
$$I=(12000)\ (0.035)\ (2)=840$$

40- Choice D is correct

The correct answer is $$48\ x^8\ y^6$$
Simplify. $$6\ x^2\ y^3\ (2\ x^2\ y)^3= 6\ x^2\ y^3\ (8\ x^6\ y^3 ) = 48\ x^8\ y^6$$

41- Choice C is correct

The correct answer is $$g(x)=-\ 2\ x\ +\ 1$$
Plugin the values of $$x$$ in the choices provided. The points are $$(1,\ -\ 1),\ (2,\ -\ 3)$$,and $$(3,\ - \ 5)$$
For $$(1,\ -\ 1)$$ check the options provided:
A.              $$g(x)=2\ x\ +\ 1\ →\ -\ 1=2\ (1)\ +\ 1\ →\ -\ 1=3$$                  This is NOT true.
B.              $$g(x)=2\ x\ -\ 1\ →\ -\ 1=2\ (1)\ -\ 1=1$$                                 This is NOT true.
C.              $$g(x)=-\ 2\ x\ +\ 1\ →\ -\ 1=2\ (-\ 1)\ +\ 1\ →\ -\ 1=-\ 1$$       This is true.
D.              $$g(x)=x\ +\ 2\ →\ -\ 1=1\ +\ 2\ →\ -\ 1=3$$                            This is NOT true.
From the choices provided, only choice C is correct.

42- Choice B is correct

The correct answer is $$\frac{3\ x}{4}$$
$$\sqrt{\frac{x^2}{2}\ +\ \frac{x^2}{16}}=\sqrt{\frac{8\ x^2}{16}\ +\ \frac{x^2}{16}}=\sqrt{\frac{9\ x^2}{16}}=\sqrt{\frac{9}{16}\ x^2} =\sqrt{\frac{9}{16}}\ ×\ \sqrt{x^2}=\frac{3}{4}\ ×\ x=\frac{3\ x}{4}$$

43- Choice D is correct

The correct answer is $$-\ 4$$
To find the y-intercept of a line from its equation, put the equation in slope-intercept form:
$$x\ -\ 3\ y=12$$,       $$-\ 3\ y=-\ x\ +\ 12$$,             $$3\ y=x\ -\ 12$$,              $$y=\frac{1}{3}\ x\ -\ 4$$
The $$y\ -$$intercept is what comes after the $$x$$. Thus, the $$y\ -$$intercept of the line is $$-\ 4$$.

44- Choice C is correct

The correct answer is $$30$$
Adding both side of $$4\ a\ -\ 3=17$$ by $$3$$ gives $$4\ a=20$$
Divide both side of $$4\ a=20$$ by $$4$$ gives $$a=5$$, then $$6\ a=6\ (5)=30$$

45- Choice B is correct

The correct answer is $$1$$
The easiest way to solve this one is to plug the answers into the equation.
When you do this, you will see the only time $$x=x^{-\ 6}$$ is when $$x=1$$ or $$x=0$$.
Only x=1 is provided in the choices.

46- Choice C is correct

The correct answer is $$\frac{12\ x\ +\ 1}{x^3}$$
First find a common denominator for both of the fractions in the expression $$\frac{5}{x^2}\ +\frac{7\ x\ -\ 3}{x^3}$$ .
of $$x^3$$, we can combine like terms into a single numerator over the denominator:
$$\frac{5\ x\ +\ 4}{x^3}\ +\ \frac{7\ x\ -\ 3}{x^3} =\frac{(5\ x\ +\ 4)\ +\ (7\ x\ -\ 3)}{x^3} =\frac{12\ x\ +\ 1}{x^3}$$

47- Choice D is correct

The correct answer is $$y=4\ (x\ -\ 3)^2\ -\ 3$$
Let’s find the vertex of each choice provided:
A.                    $$y=3\ x^2\ -\ 3$$                    The vertex is: $$(0,\ -\ 3)$$
B.                    $$y=-\ 3\ x^2\ +\ 3$$                The vertex is: $$(0,\ 3)$$
C.                    $$y=x^2\ +\ 3\ x\ -\ 3$$
The value of $$x$$ of the vertex in the equation of a quadratic in standard form is: $$x=\frac{-\ b}{2\ a}=\frac{-\ 3}{2}$$
(The standard equation of a quadratic is: $$a\ x^2\ +\ b\ x\ +\ c=0)$$
The value of $$x$$ in the vertex is $$3$$ not $$\frac{-\ 3}{2}$$.
D.                     $$y=4\ (x\ -\ 3)^2\ -\ 3$$
Vertex form of a parabola equation is in form of $$y=a\ (x\ -\ h)^2\ +\ k$$, where $$(h,\ k)$$ is the vertex. Then $$h=3$$ and $$k=-\ 3$$. (This is the answer)

48- Choice D is correct

The correct answer is $$2\ x\ -\ \frac{1}{3}$$
To find the average of three numbers even if they’re algebraic expressions, add them up and divide by $$3$$. Thus, the average equals: $$\frac{(4\ x\ +\ 2)\ +\ (-\ 6\ x\ -\ 5)\ +\ (8\ x\ +\ 2)}{3}=\frac{6\ x\ -\ 1}{3}=2\ x\ -\frac{1}{3}$$

49- Choice B is correct

The correct answer is $$-\frac{1}{2}$$
The equation of a line in slope intercept form is: $$y=m\ x\ +\ b$$.
Solve for $$y$$. $$4\ x\ -\ 2\ y=12\ ⇒\ -\ 2\ y=12\ -\ 4\ x\ ⇒\ y=(12\ -\ 4\ x)\ ÷\ (-\ 2)\ ⇒\ y=2\ x\ -\ 6$$. The slope is $$2$$.
The slope of the line perpendicular to this line is: $$m\ 1\ ×\ m\ 2 = -\ 1\ ⇒\ 2\ ×\ m\ 2 = -\ 1\ ⇒\ m\ 2=-\ \frac{1}{2}$$

50- Choice D is correct

The correct answer is $$(1,\ 6),\ (2,\ 5),\ (−\ 5,\ 8)$$
Since the triangle $$A\ B\ C$$ is reflected over the $$y\ -$$ axis,
then all values of y’s of the points don’t change and 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 when a point is reflected over the $$x\ -$$axis, the value of $$x$$ does not change).
Therefore: $$(−\ 1,\ 6)$$ changes to $$(1,\ 6)$$. $$(−\ 2,\ 5)$$ changes to $$(2,\ 5)$$. $$(5,\ 8)$$ changes to $$(−\ 5,\ 8)$$

51- Choice B is correct

The correct answer is $$39$$
The area of rectangle is:$$9\ ×\ 4=36$$ cm$$^2$$.
The area of circle is: $$π\ r^2=π\ ×(\frac{10}{2})^2=3\ ×\ 25=75$$ cm$$^2$$. Difference of areas is: $$75\ -\ 36=39$$

52- Choice D is correct

The correct answer is $$\frac{2}{x^3}\ +\ 2$$
$$f(g(x) )=2\ ×(\frac{1}{x})^3\ +\ 2=\frac{2}{x^3}\ +\ 2$$

53- Choice B is correct

The correct answer is $$4$$
$$1269=6^4$$ $$→\ 6^x=6^4\ →\ x=4$$

54- Choice D is correct

The correct answer is $$170$$ miles
Use the information provided in the question to draw the shape.
Use Pythagorean Theorem: $$a^2\ +\ b^2 = c^2$$
$$80^2\ +\ 150^2 = c^2\ ⇒\ 6400\ +\ 22500 = c^2\ ⇒\ 28900 = c^2\ ⇒ c = 170$$

55- Choice D is correct

The correct answer is $$45$$ m$$^2$$
Let $$L$$ be the length of the rectangular and $$W$$ be the with of the rectangular. Then, $$L=4\ W\ +\ 3$$
The perimeter of the rectangle is $$36$$ meters. Therefore: $$2\ L\ +\ 2\ W=36$$          $$L\ +\ W=18$$
Replace the value of $$L$$ from the first equation into the second equation and solve for $$W$$:
$$(4\ W\ +\ 3)\ +\ W=18\ →\ 5\ W\ +\ 3=18\ →\ 5\ W=15\ →\ W=3$$
The width of the rectangle is $$3$$ meters and its length is: $$L=4\ W\ +\ 3=4\ (3)\ +\ 3=15$$
The area of the rectangle is: length $$×$$ width $$= 3\ ×\ 15 = 45$$

56- Choice B is correct

The correct answer is $$5$$
Let $$x$$ be the number of adult tickets and $$y$$ be the number of student tickets. Then:
$$x\ +\ y=12$$,                  $$12.50\ x\ +\ 7.50\ y=125$$
Use elimination method to solve this system of equation. Multiply the first equation by $$-\ 7$$.$$5$$ and add it to the second equation.                                   $$-\ 7.5\ (x\ +\ y=12)$$,                        $$-\ 7.5\ x\ -\ 7.5\ y=-\ 90$$,                       $$12.50\ x\ +\ 7.50\ y=125$$.                         $$5\ x=35$$, $$x=7$$
There are $$7$$ adult tickets and $$5$$ student tickets.

57- Choice C is correct

The correct answer is $$\frac{1}{25}$$
Write the ratio of $$5\ a$$ to $$2\ b$$. $$\frac{5\ a}{2\ b}=\frac{1}{10}$$
Use cross multiplication and then simplify. $$5\ a\ ×\ 10=2\ b\ ×\ 1\ →\ 50\ a=2\ b\ →\ a=\frac{2\ b}{50}=\frac{b}{25}$$
Now, find the ratio of $$a$$ to $$b$$. $$\frac{a}{b}=\frac{\frac{b}{25}}{b}\ →\ \frac{b}{25}\ ÷\ b=\frac{b}{25}\ ×\ \frac{1}{b}=\frac{b}{25\ b}=\frac{1}{25}$$

58- Choice A is correct

The correct answer is $$30$$
Plug in the value of $$x$$ in the equation and solve for $$y$$.
$$2\ y=\frac{ 2\ x^2}{3}\ +\ 6\ →\ 2\ y = \frac{2\ (9)^2}{3}\ +\ 6\ →\ 2\ y=\frac{2\ (81)}{3}\ +\ 6\ →\ 2\ y= 54\ +\ 6=60$$
$$2\ y = 60\ →\ y=30$$

59- Choice A is correct

The correct answer is $$1.085\ (3\ p)\ +\ 6$$
Since a box of pen costs $$3$$, then $$3\ p$$ Represents the cost of $$p$$ boxes of pen.
Multiplying this number times $$1.085$$ will increase the cost by the $$8.5\%$$ for tax.
Then add the $$6$$ shipping fee for the total: $$1.085\ (3\ p)\ +\ 6$$

60- Choice D is correct

The correct answer is $$y(x)=8\ x$$
Rate of change (growth or $$x$$) is $$8$$ per week. $$40\ ÷\ 5=8$$
Since the plant grows at a linear rate,
then the relationship between the height $$(y)$$ of the plant and number of weeks of growth $$(x)$$ can be written as: $$y(x)=8\ x$$

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