# Full-Length CLEP College Algebra Practice Test

Taking a Full-length CLEP College Algebra practice test is the best way to help you get familiar with the test format and feel more confident. Not only will this help you measure your exam readiness and solidify the concepts you’ve learned, but it is the best way to simulate test day.
To help you get the best out of this complete and realistic CLEP College Algebra practice test and prepare your mind and body for the actual test, we recommend that you treat this practice test as a real test. Prepare scratch papers, pencil, a timer, and a calculator and take the test in one sitting and follow the time limits to the minute.
Take the following full-length CLEP College Algebra practice test to simulate the test day experience. After you’ve finished, score your tests using the answer keys.
Good luck!

## The Absolute Best Book to Ace the CLEP College Algebra Test

Time to refine your Math skill with a practice test

Take an CLEP College Algebra test to simulate the test day experience. After you’ve finished,

Before You Start

• You’ll need a pencil, a calculator and a timer to take the test.
• For most multiple questions, there are five possible answers. Choose which one is best.
• It’s okay to guess. There is no penalty for wrong answers.
• Calculator is permitted for CLEP College Algebra Test.
• After you’ve finished the test, review the answer key to see where you went wrong.

Good Luck!

## CLEP College Algebra Practice Test

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

1- Which of the following is equivalent to $$(6m^2-4m-8)+(12m+5)$$?

☐A. $$6m^2+5$$

☐B. $$m^2+2$$

☐C. $$6m^2+8m-3$$

☐D. $$8m^2-8m+3$$

☐E. $$6m^2+16m$$

2- If $$x-y=2, 5x+3y=42$$, which of the following ordered pairs $$(x,y)$$ satisfies both equations?

☐A. $$(-2,1)$$

☐B. $$(1,2)$$

☐C. $$(2,5)$$

☐D. $$(4,8)$$

☐E. $$(6,4$$

3- If $$f(x)=x^2+8x+28$$ then $$f(-2x)=$$?

☐A. $$4(x+3)(x-4)$$

☐B. $$4(x-1)(x-7)$$

☐C. $$4x^2+18x-16$$

☐D. $$4x^2+16x+28$$

☐E. $$4x^2-16x+28$$

4- A line in the $$xy$$-plane passes through origin and has a slope of 3. Which of the following points lies on the line?

☐A. $$(-1, -2)$$

☐B. $$(0, 1)$$

☐C. $$(1, 3)$$

☐D. $$(2, -2)$$

☐E. $$(2, 2)$$

5- If $$6x-5=37$$, what is the value of $$3x+12$$?

☐A. 19

☐B. 24

☐C. 33

☐D. 39

☐E.43

6- Calculate $$f(2)$$ for the following function $$f$$.
$$f(x)=2x^2+4x-8$$

☐A. 4

☐B. 8

☐C. 12

☐D. 16

☐E. 30

7- If $$x≠-2$$ and $$x≠3$$, which of the following is equivalent to $$\frac{1}{(\frac{1}{x+2}+\frac{1}{x-3}}$$?

☐A. $$\frac{(x+2)(x-3)}{(x-3)+(x+2)}$$

☐B. $$\frac{(x+2)+(x-3)}{(x+2)(x-3)}$$

☐C. $$\frac{(x+3)(x-2)}{(x+3)-(x-2)}$$

☐D. $$\frac{(x-3)-(x+2)}{(x+2)(x-3)}$$

☐E. $$\frac{(x+2)(x-3)}{(x+2)(x-3)}$$

8- $$y>a+x , y<x+b$$
In the $$xy$$-plane, if (0, 0) is a solution to the system of inequalities above, which of the following relationships between a and b must be true?

☐A. $$a<b$$

☐B. $$a>b$$

☐C. $$a=b$$

☐D. $$a= b- a$$

☐E. $$a=3b$$

9- Which of the following points lies on the line that goes through the points (1,4) and (3,6)?

☐A. $$(-2,4)$$

☐B. $$(-1,0)$$

☐C. $$(0,0)$$

☐D. $$(1,4)$$

☐E.$$(4,1)$$

10- If $$(ax+2)(bx+6)=32x^2+cx+12$$ for all values of $$x$$ and $$a+b=12$$, what are the two possible values for c?

☐A. 24,36

☐B. 36,42

☐C. 40,56

☐D. 58,60

☐E. 60,65

11- What is the solution of the following inequality?
$$|2x+6|≤2$$

☐A. $$-4≤x≤2$$

☐B. $$2≤x≤4$$

☐C. $$x≥-2$$

☐D. $$-4≤x≤-2$$

☐E. Set of real numbers

12- If $$\frac{7}{2x}=\frac{8}{2x+1}$$ what is the value of $$2x$$?

☐A. $$\frac{2}{7}$$

☐B. $$\frac{7}{2}$$

☐C. $$-2$$

☐D. 2

☐E. 7

13- Which of the following is an equation of a circle in the $$xy$$-plane with center $$(2,-1)$$ and a radius with endpoint $$(4,-1)$$?

☐A. $$(x+2)^2+(y-1)^2=4$$

☐B. $$2x^2+(y+4)^2=2$$

☐C. $$(x-2)^2+(y+1)^2=4$$

☐D. $$x^2+(y-2)^2=2$$

☐E. $$2x^2+(y-1)^2=4$$

14- What is the equation of the graph?

☐A. $$-4x^2+16x+1$$

☐B. $$4x^2+8x+4$$

☐C. $$-2x^2-16x+1$$

☐D. $$2x^2+8x+2$$

☐E. $$4x^2+4x+16$$

15- John buys a pepper plant that is 8 inches tall. With regular watering the plant grows 5 inches a year. Writing John’s plant’s height as a function of time, what does the $$y$$-intercept represent?

☐A. The $$y$$-intercept represents the rate of grows of the plant which is 5 inches

☐B. The $$y$$-intercept represents the starting height of 8 inches

☐C. The$$y$$-intercept represents the rate of growth of plant which is 3 inches per year

☐D. There is no $$y$$-intercept

16- If $$x^2-10x-r$$ factors into $$(x + 5)(x- p)$$, and r and p are constants, what is the value of r?

☐A. 15

☐B. 25

☐C. 40

☐D. 55

☐E. 75

17- If $$6n+4≥2$$, what is the least possible value of $$6n-2$$ ?

☐A. $$-4$$

☐B. $$-2$$

☐C. 2

☐D. 4

☐E. 6

18- A ladder leans against a wall forming a 60$$^\circ$$ angle between the ground and the ladder. If the bottom of the ladder is 40 feet away from the wall, how long is the ladder?

☐A. 30 feet

☐B. 40 feet

☐C. 60 feet

☐D. 80 feet

☐E. 110 feet

19- If A$$={1,3,6,9,12,15 }$$ and B$$={1,5,10,15,20}$$, how many elements are in A$$∩$$B

☐A. 1

☐B. 2

☐C. 3

☐D. 4

☐E. 5

20- If A$$={1,2,3,4,5,6 }$$, B$$={2,4,6,8,10,12 }$$, and C$$={1,3,5,7,9,11 }$$, then which of the following set is (A$$∩$$B)$$∪$$C

☐A. {2,4,6,7,9,11}

☐B. {1,2,3,4,5,6,7,9,11 }

☐C. {1,3,5,7,8,10,12}

☐D. {8,9,10,11,12 }

☐E. {1,2,3,4,5}

21- For what value of $$x$$ is $$|x+6|+6$$ equal to 0?

☐A. $$-2$$

☐B. $$-1$$

☐C. no value of $$x$$

☐D. 1

☐E. 2

22- Two cars are 220 miles apart. They both drive in a straight line toward each other. If Car A drives at 68 mph and Car B drives at 76 mph, then how many miles apart will they be exactly 40 minutes before they meet?

☐A. 66

☐B. 72

☐C. 86

☐D. 96

☐E. 110

23- What is the ratio of the minimum value to the maximum value of the following function?
$$f(x)=-x^2+3x-4$$
$$-1≤x≤4$$

☐A. $$-2$$

☐B. $$\frac{12}{7}$$

☐C. $$\frac{32}{7}$$

☐D. 2

☐E. 3

24- The equation $$2x^2=x-3$$ has how many distinct real solutions?

☐A. 0

☐B. 1

☐C. 2

☐D. 3

☐E. 4

25- Simplify.
$$x^2+6x^4-7y^3+4z^2-4x^4+5y^3-4z^2-z+y^2$$

☐A. $$2x^2-2y^3+x^4+z$$

☐B. $$2x^4+2y^3-2z^2+x^2$$

☐C. $$x^2+2x^4+3y^3+7z^2$$

☐D. $$x^2+2x^4-2y^3+y^2-z$$

☐E. $$x^2+2y^3-2z^2+z$$

26- If$$x$$ is a real number, and if $$x^3+18=130$$ , then $$x$$ lies between which two consecutive integers?

☐A. 1 and 2

☐B. 2 and 3

☐C. 3 and 4

☐D. 4 and 5

☐E. 5 and 6

27- In the triangle below, if the measure of angle A is 42 degrees, then what is the value of $$y$$? (figure is NOT drawn to scale)

☐A. 39

☐B. 48

☐C. 51

☐D. 62

☐E. 73

28- Four years ago, Amy was two times as old as Mike was. If Mike is 12 years old now, how old is Amy?

☐A. 12

☐B. 16

☐C. 20

☐D. 24

☐E. 28

29- A chemical solution contains $$8\%$$ alcohol. If there is 36 ml of alcohol, what is the volume of the solution?

☐A. 280 ml

☐B. 320 ml

☐C. 450 ml

☐D. 500 ml

☐E. 620 ml

30- If $$|a|<1$$, then which of the following is true? ($$b>0$$)?
I. $$–b<ba <b$$
II. $$-a<a^2<a$$ if $$a<0$$
III. $$-1<3a-2<1$$

☐A. I only

☐B. II only

☐C. I and III only

☐D. III only

☐E. I, II and III

31- Which of the following numbers is NOT a solution of the inequality $$4x+2≥5x-4$$?

☐A. 1

☐B. 2

☐C. 4

☐D. 6

☐E. 8

32- If $$(x+2)^4=256$$ which of the following could be the value of $$(x+5)(x-1)$$?

☐A. 3

☐B. 5

☐C. 7

☐D. 9

☐E. 11

33- Simplify $$(2+4i)(3-3i),$$

☐A. $$6-4i$$

☐B. $$6+2i$$

☐C. $$18-6i$$

☐D. $$18+6i$$

☐E. $$18+2i$$

34- If $$y=nx-3$$, where n is a constant, and when$$x=3, y=9$$, what is the value of $$y$$ when$$x=2$$?

☐A. 5

☐B. 7

☐C. 9

☐D. 11

☐E. 13

35- If $$\frac{4x}{15}=\frac{x-3}{5}, x=$$

☐A. $$-9$$

☐B. $$-7$$

☐C. 7

☐D. 9

☐E. 11

36- In 2010, the average worker’s income increased $12,000 per year starting from$36,000 annual salary. Which equation represents income greater than average? (I = income, $$x$$ = number of years after 2010)

☐A. $$I>12000x+36000$$

☐B. $$I>-12000x+36000$$

☐C. $$I<-12000x+36000$$

☐D. $$I<12000x-36000$$

☐E. $$I<36,000x+12000$$

37- If $$\sqrt{3m-2}=m$$, what is (are) the value(s) of n?

☐A. 0

☐B. $$-1,-2$$

☐C. $$-1,2$$

☐D. $$1,-2$$

☐E. $$1,2$$

38- If $$\frac{8}{3} y=\frac{16}{12}$$, what is the value of $$y$$?

☐A. $$\frac{1}{4}$$

☐B. $$\frac{1}{2}$$

☐C. $$\frac{3}{4}$$

☐D. $$\frac{5}{6}$$

☐E. $$\frac{7}{3}$$

39- The length of a rectangle is 3 meters greater than 2 times its width. The perimeter of the rectangle is 24 meters. What is the area of the rectangle in meters?

☐A. 15

☐B. 18

☐C. 27

☐D. 32

☐E. 36

40- If the following equations are true, what is the value of $$x$$?
$$a=\sqrt{7}$$
$$5a=\sqrt{5x}$$

☐A. 10

☐B. 15

☐C. 25

☐D. 30

☐E. 35

41- If the function $$g(x)$$ has three distinct zeros, which of the following could represent the graph of $$g(x)$$?

☐A.

☐B.

☐C.

☐D.

42- If $$f(x)=2^x$$ and $$g(x)=log_2 x$$, which of the following expressions is equal to $$f(2g(p))$$?

☐A. $$\frac{p}{2}$$

☐B. $$p^2$$

☐C. $$p^4$$

☐D. $$2^p$$

☐E. $$4^p$$

43- In the $$xy$$-plane, the point $$(2,-1)$$ and (4,2) are on line A. Which of the following equations of lines is parallel to line A?

☐A. $$y=\frac{1}{2} x+2$$

☐B. $$y=\frac{3}{2} x-5$$

☐C. $$y=2x+3$$

☐D. $$y=4x$$

☐E. $$y=5x-1$$

44- In the following equation when z is divided by 4, what is the effect on x?
$$\frac{\frac{8y+r}{r+1}}{\frac{6}{z}}$$

☐A. $$x$$ is divided by 2

☐B. $$x$$ is divided by 4

☐C. $$x$$ does not change

☐D. $$x$$ is multiplied by 2

☐E. $$x$$ is multiplied by 4

45- A boat sails 5 miles south and then 12 miles east. How far is the boat from its start point?

☐A. 13 miles

☐B. 16 miles

☐C. 18 miles

☐D. 25 miles

☐E. 28 miles

46- For what real value of $$x$$ is the equation below true?
$$x^3-7x^2+4x-28=0$$

☐A. 3

☐B. 5

☐C. 7

☐D. 9

☐E. 10

47- If $$50\%$$ of $$x$$ equal to $$25\%$$ of 38, then what is the value of $$(x-3)^3$$?

☐A. 2980

☐B. 3450

☐C. 3850

☐D. 4096

☐E. 4671

48- A function $$g(2)=4$$and $$g(4)=6$$. A function $$f(4)=-2$$ and $$f(6)=5$$. What is the value of $$f(g(4))$$?

☐A. $$-2$$

☐B. 4

☐C. 5

☐D. 6

☐E. 8

49- Mary’s average score after 5 tests is 80. What score on the 5th test would bring Mary’s average up to exactly 85?

☐A. 100

☐B. 105

☐C. 110

☐D. 112

☐E. 114

50- The equation $$2x^2=7x-3$$ has how many distinct real solutions?

☐A. 0

☐B. 1

☐C. 2

☐D. 3

☐E. 4

51- If $$y = 5a^2 b – 3ab+4b^2$$, what is y when $$a=2$$ and $$b=-2$$ ?

☐A. $$-16$$

☐B. $$-12$$

☐C. 10

☐D. 12

☐E. 1

52- If $$f(x)= 2x-8$$ and $$g(x) = x^2+3x-9$$ then find $$(f-2g)(x)$$?

☐A. $$2x^2+4x-10$$

☐B. $$-2x^2+4x-10$$

☐C. $$2x^2-4x+10$$

☐D. $$-2x^2-4x+10$$

☐E. $$-2x^2-4x-10$$

53- $$x$$ is $$y\%$$ of what number?

☐A. $$\frac{100x}{y}$$

☐B. $$\frac{100y}{x}$$

☐C. $$\frac{x}{100y}$$

☐D. $$\frac{y}{100x}$$

☐E. $$\frac{xy}{100}$$

54- In the $$xy$$-plane, the line determined by the points (8,m) and (m,18) passes through the origin. Which of the following could be the value of m?

☐A. 8

☐B. 10

☐C. 12

☐D. 14

☐E. 16

55- The cost of using a car is \$1.23 per minutes. Which of the following equations represents the total cost c, in dollars, for h hours of using the car?

☐A. $$c=\frac{1.23}{60h}$$

☐B. $$c=\frac{60h}{1.23}$$

☐C. $$c=1.23h+60$$

☐D. $$c=60h+1.23$$

☐E. $$c=1.23(60h)$$

56- Which of the following points lies on the line $$6x-3y=12$$?

☐A. ($$-$$1, 2)

☐B. (0, 3)

☐C. (1, 4)

☐D. (3, 2)

☐E. (4, 1)

57- Point A lies on the line with equation $$y-4=3(x+6)$$. If the $$x$$-coordinate of A is 8, what is the $$y$$-coordinate of A?

☐A. 28

☐B. 34

☐C. 46

☐D. 50

☐E. 54

58- If $$|a|<1$$, then which of the following is true? $$(b>0)$$?
I. $$–b<ba <b$$
II. $$-a<a^2<a$$ if $$a<0$$
III. $$-6<4a-2<2$$

☐A. I only

☐B. III only

☐C. I and III only

☐D. I, II and III

☐E. None of the above

59- $$\frac{c-d}{c}=a$$
In the equation above, if c is negative and d is positive, which of the following must be true?

☐A. $$a<1$$

☐B. $$a=0$$

☐C. $$a>1$$

☐D. $$a<-1$$

☐E. $$a<-2$$

60- If $$f(x)=-x^3+4x^2-8x+2$$, and $$g(x)=2$$, what is the value of $$f(g(x))$$?

☐A. $$-12$$

☐B. $$-6$$

☐C. 0

☐D. 6

☐E. 12

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