5.11: Proficiency Exam
- Page ID
- 58543
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Proficiency Exam
Solve the equations and inequalities for the following problems.
\(x+8=14\)
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\(x=6\)
\(6a+3=−10\)
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\(a = \dfrac{-13}{6}\)
\(\dfrac{-3a}{8} = 6\)
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\(a=−16\)
\(\dfrac{x}{-2} + 16 = 11\)
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\(x=10\)
\(\dfrac{y-9}{4} + 6 = 3\)
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\(y=−3\)
\(5b−8=7b+12\)
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\(b=−10\)
\(3(2a+4)=2(a+3)\)
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\(a = -\dfrac{3}{2}\)
\(5(y+3)−(2y−1)=−5\)
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\(y=−7\)
\(\dfrac{-(4x+3-5x)}{3} = 2\)
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\(x=9\)
Solve \(2p−6q+1=−2\) for \(p\).
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\(p = \dfrac{6q-3}{2}\)
Solve \(p = \dfrac{nRT}{V}\) for \(T\)
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\(T = \dfrac{Vp}{nR}\)
\(a−8≥4\)
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\(a≥12\)
\(−3a+1<−5\)
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\(a>2\)
\(−2(a+6)≤−a+11\)
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\(a≥−23\)
\(\dfrac{-4x-3}{3} > -9\)
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\(x<6\)
Translate the phrases or sentences into mathematical expressions or equations for the following problems.
Three added to twice a number.
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\(3+2a\)
Eight less than two thirds of a number.
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\(\dfrac{2}{3}x - 8\)
Two more than four times a number.
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\(2+4x\)
A number is added to itself and this result is multiplied by the original number cubed. The result is twelve.
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\(2x(x^3) = 12\)
A number is decreased by five and that result is divided by ten more than the original number. The result is six times the original number.
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\(\dfrac{x-5}{x+10} = 6x\)
Solve the following problems.
Eight percent of a number is 1.2. What is the number?
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\(x=15\)
Three consecutive odd integers sum to 38. What are they?
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There are no three consecutive odd integers that add to 38.
Five more than three times a number is strictly less than seventeen. What is the number?
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\(x<4\)
Solve \(y=8x−11\) for \(y\) if \(x=3\), and write the solution as an ordered pair.
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\((3,13)\)