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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. math exams: June 2011

Thursday, June 30, 2011

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

Wednesday, June 29, 2011

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

Tuesday, June 28, 2011

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$

Monday, June 27, 2011

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} $

Sunday, June 26, 2011

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}$








Saturday, June 25, 2011

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

Friday, June 24, 2011

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 $

Thursday, June 23, 2011

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.    
    3. $9x^{2}-1$
    4.    
    5. $9x^{2}+1$
    6.    
    7. $9x^{2}-6x+1$
    8.    
    9. $9x^{2}-3x+1$
  2.   
  3. Which of the following is a factor of $9-(x+y)^{2}$
         
    1. $(x+y)^{2}$
    2.    
    3. $(x+y)$
    4.    
    5. $3-x+y$
    6.    
    7. $3+x+y$
    8.    
    9. $9+x+y$
  4.   
  5. $3t(2t^{2}+1)-(4-2t^{3}+10t)+1$
         
    1. $8t^{2}+7t-3$
    2.    
    3. $8t^{2}+7t+1$
    4.    
    5. $8t^{2}-7t-3$
    6.    
    7. $8t^{2}-7t-4$
    8.    
    9. $2t^{3}-7t+4$
  6.   
  7. If $x+3=y$ What is the value of $|y-x|+|x-y|$
         
    1. $-6$
    2.    
    3. $0$
    4.    
    5. $3$
    6.    
    7. $6$
    8.    
    9. $-3$
  8.   
  9. $\frac{\frac{x^{2}-4}{x+1}}{\frac{x-2}{x-1}}$
         
    1. $\frac{x-1}{x+2}$
    2.    
    3. $\frac{(x-1)(x+2)}{x+1}$
    4.    
    5. $\frac{x^{2}-x-2}{x+1}$
    6.    
    7. $\frac{1}{(x-1)(x+1)}$
    8.    
    9. $\frac{x+2}{(x-1)(x+1)}$
  10.   
  11. Which of the following is a factor of $2x^{2}+4x-9$
         
    1. $x+\frac{2-\sqrt{22}}{2}$
    2.    
    3. $x-2-\frac{\sqrt{22}}{2}$
    4.    
    5. $x+2-\frac{\sqrt{22}}{2}$
    6.    
    7. $x-\frac{2+\sqrt{22}}{2}$
    8.    
    9. $x+2+\frac{\sqrt{22}}{2}$
  12.   
  13. $\frac{(n+2)!}{n+1}-n=$
         
    1. $0$
    2.    
    3. $2$
    4.    
    5. $n+2$
    6.    
    7. $(n+1)!$
    8.    
    9. $n+1$
  14.   
  15. Of the following which is greatest?
         
    1. $3^{(5^{7})}$
    2.    
    3. $(3^{5})^{7}$
    4.    
    5. $5^{(3^{7})}$
    6.    
    7. $(5^{3})^{7}$
    8.    
    9. $7^{(5^{3})}$
  16.   
  17. Which of the following gives all values of x for wich $|x-3| \leq 7$?
         
    1. $\{x/ -10 \leq x \leq 4 \}$
    2.    
    3. $\{x/ -7 \leq x \leq 3 \}$
    4.    
    5. $\{x/ -10 \leq x \leq -3 \}$
    6.    
    7. $\{x/ -10 \leq x \leq -4 \}$
    8.    
    9. $\{x/ -4 \leq x \leq -3 \}$
  18.   
  19. 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.    
    3. $-1+\frac{\sqrt{5}}{2}$ or  $-1-\frac{\sqrt{5}}{2}$
    4.    
    5. $\frac{1+\sqrt{5}}{2}$ or  $\frac{1-\sqrt{5}}{2}$
    6.    
    7. $1+\frac{\sqrt{5}}{2}$ or  $1-\frac{\sqrt{5}}{2}$
    8.    
    9. $\frac{1+i\sqrt{5}}{2}$ 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