Free Full Length CLEP College Mathematics Practice Test

Full Length CLEP College Mathematics Practice Test

If you want to prepare for the CLEP College Mathematics Practice Test? It’s time to taking a Full-length CLEP College Mathematics Practice Test. It is the best way to simulate test day. To challenge your skills and simulate the full length CLEP College Mathematics Practice Test day experience, score your tests using the answer keys.

The Most Comprehensive CLEP College Math Preparation Bundle

~~$76.99~~ $36.99

52% Off*

Includes CLEP College Math Prep Books, Workbooks, and Practice Tests

eBook (PDF Format)

Download

60 questions Total time for this section: 90 Minutes You can use a scientific calculator on this test.

If $4\ n\ -\ 3\ ≥\ 1$, what is the least possible value of $4\ n\ +\ 3$?

(A)

$3$

(B)

$4$

(C)

$7$

(D)

$9$

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)

$8\ x^3\ -\ 12\ x^2$

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)

$68\%$

Which of the following graphs represents the compound inequality $-\ 2\ \leq\ 2\ x\ -\ 4\ <\ 8$ ?

(A)

(B)

(C)

(D)

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$^3$

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)

$120$

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)

$66,812$

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)

$72,000$

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?
College Mathematic4

(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)

$60$

CLEP College Math for Beginners 2022

~~$24.99~~ $14.99

40% Off*

The Ultimate Step by Step Guide to Preparing for the CLEP College Math Test

eBook (PDF Format)
All Available Formats & Editions

Download

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?
College Mathematic5

(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?
College Mathematic6

(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)

$y(x)=8\ x$

CLEP College Mathematics Practice Test Answers and Explanations

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 $= 3\ ×\ 15 = 45$

The Most Comprehensive CLEP College Math Preparation Bundle

~~$76.99~~ $36.99

52% Off*

Includes CLEP College Math Prep Books, Workbooks, and Practice Tests

eBook (PDF Format)

Download

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: $y(x)=8\ x$