CLEP College Algebra Practice Questions -- (Algebraic operations)

1. If $n \ne 0$ , $(2)^{5n}(8)^{7n}(32)^{3n}$
   
   
   1. $(32)^{15n}$
   2. $(8)^{15n}$
   3. $(2)^{5n}$
   4. $(2)^{41n}$
   5. $(2)^{21n}$
   
   
2. $\sqrt{32}+5\sqrt{50}-5\sqrt{2}$
   
   
   1. $24\sqrt{2}$
   2. $24\sqrt{8}$
   3. $20\sqrt{2}$
   4. $4\sqrt{2}$
   5. $24\sqrt{32}$
   
   
3. $\sqrt{1125}+7\sqrt{180}-5\sqrt{5}$
   
   
   1. $5\sqrt{5}$
   2. $-5\sqrt{5}$
   3. $62\sqrt{5}$
   4. $62\sqrt{15}$
   5. $62\sqrt{3}$
   
   
4. $\sqrt[3]{\frac{-54}{-2}}$
   
   
   1. $3$
   2. $-3$
   3. $8$
   4. $-\sqrt{3}$
   5. $\sqrt{3}$
   
   
5. $\sqrt{3} \div \sqrt[5]{3}$
   
   
   1. $3^{5}$
   2. $\sqrt{3}$
   3. $\sqrt[10]{3}$
   4. $\sqrt[5]{3}$
   5. $\sqrt[10]{27}$
   
   
6. Simplify $\frac{4a^{0}}{(4a)^{0}}$
   
   
7. Simplify $\frac{6x^{5}+12x^{4}}{3x^{3}}$
   
   1. $2x^{2}+x$
   2. $2x^{2}+4$
   3. $2x(x+2)$
   4. $2x+4$
   5. $2x^{2}-4x$
   
   
8. Simplify $\frac{x^{2}-3x}{x^{2}-9}+\frac{3}{x+3}$
   
   
   1. $x^{2}-4x+4$
   2. $x-4$
   3. $x+4$
   4. $1$
   5. $\frac{1}{4}$
   
   
9. Simplify $\frac{\sqrt[3]{x}}{\sqrt[6]{x}}$
   
   
   1. $\sqrt{x^{6}}$
   2. $\sqrt[3]{x}$
   3. $\sqrt[6]{x}$
   4. $x^{3}$
   5. $x^{6}$
   
   
10. Simplify $\frac{x^{4}-y^{4}}{x^{2}+y^{2}}$
    
    
    1. $x^{2}+y^{2}$
    2. $x^{2}-y^{2}$
    3. $x^{2}y^{2}$
    4. $0$
    5. $2\frac{x^{2}-y^{2}}{x^{2}+y^{2}}$
    
    

    Answer Key

    1	D
    2	A
    3	C
    4	A
    5	E
    6	4
    7	C
    8	D
    9	C
    10	B

CLEP College Algebra Practice Questions -- (Equations )

1. $\frac{9}{x+5}=\frac{3}{x+1}$
   
   
   1. $1$
   2. $3$
   3. $5$
   4. $9$
   5. $0$
   
   
2. $xy+5y=10$ and $x+2=7$, then $y=$
   
   
   1. $0$
   2. $1$
   3. $5$
   4. $7$
   5. $2$
   
   
3. $\frac{9x}{5}=(a^{7}-1)^{3}$ and $a=-1$, solve for $x$.
   
   
   1. $-40$
   2. $-\frac{40}{9}$
   3. $\frac{40}{9}$
   4. $\frac{35}{9}$
   5. $0$
   
   
4. $\frac{18}{x^{2}+6x+27}=1$
   
   
   1. $\{-3,3\}$
   2. $\{-3\}$
   3. $\{3\}$
   4. $\{-3,0\}$
   5. $\{-3,-3\}$
   
   
5. Find the solution of the following equation : $|5x-1|=9$
   
   
   1. $\{2\}$
   2. $\{-\frac{8}{5}\}$
   3. $\{-\frac{8}{5},2\}$
   4. $\{\frac{9}{5}\}$
   5. $\{\frac{1}{5}\}$
   
   
6. If $a=(b+5)^{2}$ and $b=-5$, what is $a$?
   
   
   1. $-5$
   2. $5$
   3. $0$
   4. $1$
   5. $2$
   
   
7. Solve $x^{2}+2x+11=0$
   
   
   1. $-1+\sqrt{10}$ or $-1-\sqrt{10}$
   2. $1+i\sqrt{10}$ or $-1-i\sqrt{10}$
   3. or $-1-i\sqrt{10}$
   4. $-1+i\sqrt{10}$ or $-1-i\sqrt{10}$
   5. $-1+i\sqrt{10}$
   
   
8. If $\frac{a}{b}=5$ then $a^{2}-25b^{2}+7=$
   
   
   1. $0$
   2. $7$
   3. $-1$
   4. $25$
   5. $5$
   
   
9. Solve $9x-6 \leq 5x+2$
   
   
   1. $x \leq 2$
   2. $x \geq 2$
   3. $x \leq -2$
   4. $x \geq -2$
   5. $x < 2$
   
   
   
10. Solve $\frac{3}{x}=\frac{2}{x-1}$
    
    
    1. $-3$
    2. $2$
    3. $-2$
    4. $3$
    5. There is no solution

Answer Key

1	A
2	B
3	B
4	E
5	C
6	C
7	D
8	B
9	A
10	D

CLEP College Algebra Practice Questions - 5

1. Find the indicated root $\sqrt[3]{-64}$
   
   1. $-4$
   2. $-16$
   3. $16$
   4. $4$
   5. Cannot be evaluated
   
   
2. $3^{3x}=9^{x-1}$
   
   
   1. $2$
   2. $-2$
   3. $\frac{1}{2}$
   4. $\frac{1}{3}$
   5. $3$
   
   
   
3. $3\sqrt{20}+6\sqrt{45}$
   
   
   1. $24\sqrt{5}$
   2. $9\sqrt{65}$
   3. $3\sqrt{5}$
   4. $20\sqrt{5}$
   5. $18\sqrt{5}$
   
   
4. $2a^{2}-3(b-c)^{2}$
   
   
   1. $[\sqrt{2}a-\sqrt{3}b+\sqrt{3}c][\sqrt{2}a+\sqrt{3}b-\sqrt{3}c]$
   2. $[\sqrt{2}a-\sqrt{3}b+\sqrt{3}c][\sqrt{2}a-\sqrt{3}b+\sqrt{3}c]$
   3. $[\sqrt{2}a-\sqrt{3}b.\sqrt{3}c][\sqrt{2}a+\sqrt{3}b.\sqrt{3}c]$
   4. $[2a-3b+3c][2a+3b-3c]$
   5. $[\sqrt{2}a+\sqrt{3}b+\sqrt{3}c][\sqrt{2}a+\sqrt{3}b+\sqrt{3}c]$
   
   
5. $(2\sqrt{5}+5\sqrt{2})(5\sqrt{5}-2\sqrt{2})$
   
   
   1. $30-21\sqrt{10}$
   2. $30+21\sqrt{10}$
   3. $-30+21\sqrt{10}$
   4. $-10$
   5. $+10$
   
   
6. $x^{3}-36x=0$
   
   
   1. $-6$ and $6$
   2. $-3$, $0$ and $3$
   3. $-6$, $0$ and $6$
   4. $36$
   5. $6$
   
   
7. $g(x)=-2x^{2}+5x-1$
   
   $g(-5)$
   
   
8. $log_{25}(\frac{1}{125})=$
   
   
   1. $\frac{-3}{2}$
   2. $\frac{2}{3}$
   3. $\frac{3}{2}$
   4. $-3$
   5. $2$
   
   
9. If $log_{b}(5)=0.81$ and $log_{b}(3)=0.13$ find $log_{b}(15)$
   
   
   1. $0.1053$
   2. $0.94$
   3. $0.10$
   4. $0.9$
   5. $0.95$
   
   
10. If $log_{5}N=2$, find $N$
    
    
    1. $\frac{5}{2}$
    2. $10$
    3. $\frac{2}{5}$
    4. $log_{2}5$
    5. $25$
    
    

CLEP College Algebra Practice Questions - 4

1. $(3x-5)^{2}=$
   
   
   1. $9x^{2}-30x-25$
   2. $9x^{2}+30x+25$
   3. $39x-25$
   4. $9x^{2}-25$
   5. $9x^{2}-30x+25$
   
   
2. $5^{x+1}=25^{3x+1}$, then $x=$
   
   
   1. $\frac{1}{5}$
   2. $5$
   3. $-\frac{1}{5}$
   4. $0$
   5. $\frac{1}{3}$
   
   
3. $log_{3}(x+5)=3$
   
   
   1. $10$
   2. $22$
   3. $27$
   4. $30$
   5. $32$
   
   
4. $f(x)=7-3x^{3}$
   
   
   1. $\sqrt[3]{\frac{7-x}{3}}$
   2. $\frac{\sqrt[3]{7-x}}{3}$
   3. $\sqrt[3]{\frac{x-7}{3}}$
   4. $\frac{1}{7-3x^{3}}$
   5. $7x^{3}+3$
   
   
5. $f(x)=3x+1$ and $g(x)=5x-1$
   
   
   1. $15x+2$
   2. $15x$
   3. $15x^{2}+x+2$
   4. $15x+4$
   5. $15x-2$
   
   
6. Which quadrants of the xy-plane contain points of the graph of $3x-y>1$
   
   
   1. $I$, $II$ and $III$ only
   2. $I$, $II$ and $IV$ only
   3. $I$, $III$ and $IV$ only
   4. $II$ $III$ and $IV$ only
   5. $I$, $II$, $III$ and $III$ only
   
   
7. $(\sqrt{3}i)^{4}=$
   
   
   1. $9$
   2. $-9$
   3. $9i$
   4. $-9i$
   5. $-\sqrt{3}$
   
   
8. What are all real values of $x$ for which $\frac{2}{5-x}=\frac{1}{5}-\frac{1}{x}$
   
   
   1. $x=-5$ only
   2. $x=5$ only
   3. $x=-5$
   4. $x=-5$ and $x=0$
   5. $x=-5$ and $x=-5$
   
   
9. When $\frac{5+6i}{1+i}$ is expressed in the form $a+bi$, what is the value of $a$.
   
   
10. If $x$, $2x+1$ and $7x+5$ are the first three terms of an arithmetic progression, then $x=$
    
    
    1. $-\frac{3}{4}$
    2. $-3$
    3. $0$
    4. $\frac{7}{5}$
    5. $\frac{1}{5}$
    
    

CLEP College Algebra Practice Questions - 3

1. The reduced form of $\sqrt{162x^{11}y^{17}}$ is:
   
   
   1. $18x^{5}y^{8}\sqrt{2xy}$
   2. $9x^{5}y^{8}\sqrt{2}$
   3. $3x^{5}y^{8}\sqrt{2xy}$
   4. $9x^{4}y^{4}\sqrt{2xy}$
   5. $9x^{5}y^{8}\sqrt{2xy}$
   
   
2. $\frac{2\sqrt{x}-\sqrt{y}}{\sqrt{x}+\sqrt{y}}$ is equal to:
   
   
   1. $-2$
   2. $1$
   3. $\frac{2x-y}{x-y}$
   4. $\frac{2x-\sqrt{xy}+y}{x-y}$
   5. $\frac{2x-3\sqrt{xy}+y}{x-y}$
   
   
3. Solve the equation: $2x^{6}+52x^{3}-54=0$
   
   
   1. $-27$, $1$
   2. $+3$, $-1$
   3. $-3$
   4. $1$, $27$
   5. $-3$
   
   
4. The reduced form of $\frac{\frac{1}{x+y}-\frac{1}{y}}{x}$ is
   
   
   1. $0$
   2. $1$
   3. $\frac{1}{xy+y^{2}}$
   4. $-\frac{1}{xy+y^{2}}$
   5. $xy+y^{2}$
   
   
5. Solve the equation: $\frac{1}{x-2}+\frac{1}{x+2}=\frac{1}{x^{2}-4}$
   
   
   1. $-\frac{1}{2}$
   2. $\frac{1}{2}$
   3. $\frac{1}{4}$
   4. $2$
   5. $1$
   
   
6. Which factors $5x^{3}-3x^{2}-20x+12$ completely?
   
   
   1. $(5x+3)(x+2)^{2}$
   2. $(5x-3)(x+4)(x-1)$
   3. $(5x+3)(x^{2}-4)$
   4. $(5x^{2}+3)(x-4)$
   5. $(5x-3)(x^{2}+4)$
   
   
7. Reduced $(\frac{7a^{-5}}{5c^{\frac{1}{2}}})^{-1}$
   
   
   1. $\sqrt{\frac{7a^{5}}{5c}}$
   2. $\frac{-14a^{5}}{5c}$
   3. $\frac{7a^{5}\sqrt{c}}{5}$
   4. $\frac{5a^{5}}{7\sqrt{c}}$
   5. $\frac{5}{7}a^{5}\sqrt{c}$
   
   
   
   
   
   
   
   
   

CLEP College Algebra Practice Questions - 2

1. Determine the range of the following function : $f(x)=-x^{4}+5$
   
   
   1. $y \geq 5$
   2. $y \geq -5$
   3. $y \geq 4$
   4. $y \leq -4$
   5. $y \leq 5$
   
   
2. Solve the equation : $3(6x+2)=2x$
   
   
   1. $x=- \frac{3}{8}$
   2. $x=\frac{3}{8}$
   3. $x=\frac{8}{3}$
   4. $x=-\frac{8}{3}$
   5. $x=-3$
   
   
3. What is the multiplicative inverse of $-7$?
   
   
   1. $\frac{1}{7}$
   2. $-\frac{1}{7}$
   3. $0$
   4. $7$
   5. $-7$
4. Simplify : $\sqrt{169}.\sqrt{81}.\sqrt{196}$
   
   
   1. $13689$
   2. $21294$
   3. $1638$
   4. $1764$
   5. $12356$
5. Factor: $b^{2}-121$
   
   
   1. $(b-11)(b+11)$
   2. $(b^{2}-11)(b^{2}+11)$
   3. $(b^{2}+11)(b^{2}+11)$
   4. $(b-11)(b-11)$
   5. $(b+11)(b+11)$
6. Solve: $1+\frac{1}{x}=\frac{12}{x^{2}}$
   
   
   1. $x=-4$ or $x=3$
   2. $x= 4$ or $x=-3$
   3. $x=-4$ or $x=-4$
   4. $x=-3$ or $x=3$
   5. $x= 6$ or $x=-2$
7. Factor the following equation: $a^{2}-2a-35$
   
   
   1. $(a-7)(a+5)$
   2. $(a+7)(a+5)$
   3. $(a-5)(a-7)$
   4. $(a-1)(a+35)$
   5. $(a-35)(a+1)$
8. Solve the following inequality: $9(6-2x) \leq -12$
   
   
   1. $x\geq 11$
   2. $x \leq \frac{11}{3}$
   3. $x \geq \frac{11}{3}$
   4. $x\geq$ 3
   5. $x \leq$ -11
9. Determine the x-intercepts of the following parabola: $y=3x^{2}+x-14$
   
   
   1. $(2,0)$ and $(-\frac{7}{3},0)$
   2. $(2,0)$ and $(-3,0)$
   3. $(-\frac{3}{7},0)$ and $(-4,0)$
   4. $(0,2)$ and $(0,-\frac{7}{3})$
   5. $(0,-\frac{7}{3})$ and $(2,0)$
   
   
10. A Graph of $x^{2} + y^{2} = 9$ is a
    
    
    1. Parabola
    2. Hyperbola
    3. Circle
    4. Line
    5. ellipse
    
    

CLEP College Mathematics Practice Questions - 1

1. Simplify the following expression : $8x+3-3x-7$
   
   1. $5x-4$
   2. $5x+4$
   3. $11x-4$
   4. $10x-4$
   5. $-5x-4$
   
   
2. Determine the mean of the numbers : 20, 34, 36, 52, 60.
   
   1. $35$
   2. $40.1$
   3. $40.4$
   4. $40.6$
   5. $50$
   
   
3. What is the rule of $f+g$ if $f(x)=10x+7$ and $g(x)=3x$
   
   1. $30x+7$
   2. $30x+21$
   3. $7x+7$
   4. $10x-7$
   5. $13x+7$
   
   
4. What percent of 30 is 13
   
   
   1. $43.33$
   2. $43$
   3. $80$
   4. $72.3$
   5. $35$
   
   
5. Find the inverse of the function $f(x)=-\frac{9}{5}x+1$
   
   
   1. $b=-\frac{9}{5}a+5$
   2. $a=\frac{9}{5}b-1$
   3. $b=-\frac{9}{5}(a-1)$
   4. $b=-\frac{9}{5}a-\frac{9}{5}$
   5. $a=-\frac{9}{5}b-1$
   
   
6. What is the name give to two angles that add up to 180
   
   
   1. $Complemtary$
   2. $Adjacent$
   3. $straight$
   4. $right$
   5. $supplementary$
   
   
7. Determine the mode of the following numbers : 6,7,7,5,5,5,9
   
   
   1. $5$
   2. $5.5$
   3. $6.29$
   4. $7$
   5. $7.5$
   
   
8. Which of the following expressions is the same as $\frac{a^{-7}b^{2}}{a^{-3}}$
   
   
   1. $\frac{a^{-4}}{b^{2}}$
   2. $\frac{b^{2}}{a^{4}}$
   3. $\frac{b^{2}}{a^{-4}}$
   4. $b^{2}a^{-4}$
   5. $a^{4}b^{2}$
   
   
9. Determine the range of the following set : 5.6, 10.2, 7.3, 9.9, 8.1, 9.7
   
   
   1. $2.9$
   2. $4.3$
   3. $10.2$
   4. $2.1$
   5. $4.6$
10. If $f(x)=x^{5}$ and $g(x)=x^{2}-1$, what is the domain restriction on $f.g$
    
    
    1. $x \leq 11$
    2. $x \neq 1$
    3. $x \geq 1$
    4. There is no restriction
    5. $x\leq 5$

GMAT Besic Equations

1. $3(x-2)+6=2x$
2. $\frac{1}{3}x-1=\frac{5}{6}+\frac{7}{2}$
3. $\frac{7x-3}{7}=x+2$
4. $0.16x+1.1=0.2x+0.96$

SAT Practice Questions - 1

1. $2(5x-5)+5(2x+2)=$
   
   1. $0$
   2. $20x$
   3. $20x-10$
   4. $20x+10$
   5. $10x^{2}+20+x+20$
   
   
2. If $x=a+2$, and $y=-8-a$ then $x+y=$
   
   
   1. $6$
   2. $10$
   3. $2a-6$
   4. $-10$
   5. $-6$
   
   
3. If $x \ne -5$, then $\frac{x^{2}+3x-10}{x+5}-(x-2)=$
   
   
4. If $(a-\frac{1}{a})^{2}=8$, then $a^{2}+\frac{1}{a^{2}}=$
   
   
   1. $8$
   2. $6$
   3. $10$
   4. $12$
   5. $100$
   
   
5. $(x+y)^{2}=16$, and $x^{2}+y^{2}=6$ then $xy=$
   
   
   1. $5$
   2. $10$
   3. $6$
   4. $4$
   5. $16$
   
   
6. $(x+y)=6$, and $x^{2}-y^{2}=2$ then $x-y=$
   
   
   1. $12$
   2. $4$
   3. $6$
   4. $\frac{1}{3}$
   5. $3$
   
   
7. $\frac{15y+3}{3}-5y=$
   
   
   1. $1$
   2. $0$
   3. $10y+1$
   4. $3$
   5. $3y+1$
   
   
   
8. if $b^{2}-a^{2}=9$ then $5(a-b)(a+b)=$
   
   
   1. $45$
   2. $\frac{9}{5}$
   3. $4$
   4. $50$
   5. $-45$
   
   
9. When $c \ne 3$, then $\frac{c^{2}-9}{c-3}=$
   
   
   1. $c-3$
   2. $1$
   3. $c+3$
   4. $3-c$
   5. $o$
   
   
10. If $b>0$, and $b^{2}-1=10 \times 12$, then $b=$
    
    
    1. $9$
    2. $1$
    3. $12$
    4. $10$
    5. $11$
    
    
    

    Answer Key

    1	B
    2	E
    3	0
    4	C
    5	A
    6	D
    7	A
    8	E
    9	C
    10	E

CLEP College Algebra Practice Questions - 1

 

1. $(3x-1)^{2}$
   
      
   1. $3x^{2}+1$
      
   2. $9x^{2}-1$
      
   3. $9x^{2}+1$
      
   4. $9x^{2}-6x+1$
      
   5. $9x^{2}-3x+1$
  
2. Which of the following is a factor of $9-(x+y)^{2}$
   
      
   1. $(x+y)^{2}$
      
   2. $(x+y)$
      
   3. $3-x+y$
      
   4. $3+x+y$
      
   5. $9+x+y$
  
3. $3t(2t^{2}+1)-(4-2t^{3}+10t)+1$
   
      
   1. $8t^{2}+7t-3$
      
   2. $8t^{2}+7t+1$
      
   3. $8t^{2}-7t-3$
      
   4. $8t^{2}-7t-4$
      
   5. $2t^{3}-7t+4$
  
4. If $x+3=y$ What is the value of $|y-x|+|x-y|$
   
      
   1. $-6$
      
   2. $0$
      
   3. $3$
      
   4. $6$
      
   5. $-3$
  
5. $\frac{\frac{x^{2}-4}{x+1}}{\frac{x-2}{x-1}}$
   
      
   1. $\frac{x-1}{x+2}$
      
   2. $\frac{(x-1)(x+2)}{x+1}$
      
   3. $\frac{x^{2}-x-2}{x+1}$
      
   4. $\frac{1}{(x-1)(x+1)}$
      
   5. $\frac{x+2}{(x-1)(x+1)}$
  
6. Which of the following is a factor of $2x^{2}+4x-9$
   
      
   1. $x+\frac{2-\sqrt{22}}{2}$
      
   2. $x-2-\frac{\sqrt{22}}{2}$
      
   3. $x+2-\frac{\sqrt{22}}{2}$
      
   4. $x-\frac{2+\sqrt{22}}{2}$
      
   5. $x+2+\frac{\sqrt{22}}{2}$
  
7. $\frac{(n+2)!}{n+1}-n=$
   
      
   1. $0$
      
   2. $2$
      
   3. $n+2$
      
   4. $(n+1)!$
      
   5. $n+1$
  
8. Of the following which is greatest?
   
      
   1. $3^{(5^{7})}$
      
   2. $(3^{5})^{7}$
      
   3. $5^{(3^{7})}$
      
   4. $(5^{3})^{7}$
      
   5. $7^{(5^{3})}$
  
9. Which of the following gives all values of x for wich $|x-3| \leq 7$?
   
      
   1. $\{x/ -10 \leq x \leq 4 \}$
      
   2. $\{x/ -7 \leq x \leq 3 \}$
      
   3. $\{x/ -10 \leq x \leq -3 \}$
      
   4. $\{x/ -10 \leq x \leq -4 \}$
      
   5. $\{x/ -4 \leq x \leq -3 \}$
  
10. Which of the following are the solutions of the equation  $x^{2}-x-1=0$ ?
    
        
    1. $\frac{-1+\sqrt{5}}{2}$ or  $\frac{-1-\sqrt{5}}{2}$
       
    2. $-1+\frac{\sqrt{5}}{2}$ or  $-1-\frac{\sqrt{5}}{2}$
       
    3. $\frac{1+\sqrt{5}}{2}$ or  $\frac{1-\sqrt{5}}{2}$
       
    4. $1+\frac{\sqrt{5}}{2}$ or  $1-\frac{\sqrt{5}}{2}$
       
    5. $\frac{1+i\sqrt{5}}{2}$ or  $\frac{1-i\sqrt{5}}{2}$

Answer Key

1	D
2	D
3	C
4	D
5	B
6	D
7	B
8	A
9	C
10	C