3.8: Proficiency Exam
- Page ID
- 52133
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Exercise \(\PageIndex{1}\)
In the number \(8^5\), write the names used for the number 8 and the number 5.
- Answer
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base; exponent
Exercise \(\PageIndex{2}\)
Write using exponents. \(12 \times 12 \times 12 \times 12 \times 12 \times 12 \times 12\)
- Answer
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\(12^7\)
Exercise \(\PageIndex{3}\)
Expand \(9^4\).
- Answer
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\(9^4 = 9 \times 9 \times 9 \times 9 = 6,561\)
For problems 4-15, determine the value of each expression.
Exercise \(\PageIndex{4}\)
\(4^3\)
- Answer
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64
Exercise \(\PageIndex{5}\)
\(1^5\)
- Answer
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1
Exercise \(\PageIndex{6}\)
\(0^3\)
- Answer
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0
Exercise \(\PageIndex{7}\)
\(2^6\)
- Answer
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64
Exercise \(\PageIndex{8}\)
\(\sqrt{49}\)
- Answer
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7
Exercise \(\PageIndex{9}\)
\(\sqrt[3]{27}\)
- Answer
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3
Exercise \(\PageIndex{10}\)
\(\sqrt[8]{1}\)
- Answer
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1
Exercise \(\PageIndex{11}\)
\(16 + 2 \cdot (8 - 6)\)
- Answer
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20
Exercise \(\PageIndex{12}\)
\(5^3 - \sqrt{100} + 8 \cdot 2 - 20 \div 5\)
- Answer
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127
Exercise \(\PageIndex{13}\)
\(3 \cdot \dfrac{8^2 - 2 \cdot 3^2}{5^2 - 2} \cdot \dfrac{6^3 - 4 \cdot 5^2}{29}\)
- Answer
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24
Exercise \(\PageIndex{14}\)
\(\dfrac{20 + 2^4}{2^3 \cdot 2 - 5 \cdot 2} \cdot \dfrac{5 \cdot 7 - \sqrt{81}}{7 + 3 \cdot 2}\)
- Answer
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8
Exercise \(\PageIndex{15}\)
\([(8 - 3)^2 + (33 - 4 \sqrt{49})] - 2[(10 - 3^2) + 9] - 5\)
- Answer
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5
For problems 16-20, find the prime factorization of each whole number. If the number is prime, write "prime."
Exercise \(\PageIndex{15}\)
18
- Answer
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\(3^2 \cdot 2\)
Exercise \(\PageIndex{15}\)
68
- Answer
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\(2^2 \cdot 17\)
Exercise \(\PageIndex{15}\)
142
- Answer
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\(2 \cdot 71\)
Exercise \(\PageIndex{15}\)
151
- Answer
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prime
Exercise \(\PageIndex{15}\)
468
- Answer
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\(2^2 \cdot 3^2 \cdot 13\)
For problems 21 and 22, find the greatest common factor.
Exercise \(\PageIndex{21}\)
200 and 36
- Answer
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4
Exercise \(\PageIndex{22}\)
900 and 135
- Answer
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45
Exercise \(\PageIndex{23}\)
Write all the factors of 36.
- Answer
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1, 2, 3, 4, 6, 9, 12, 18, 36
Exercise \(\PageIndex{24}\)
Write all the divisors of 18.
- Answer
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1, 2, 3, 6, 9, 18
Exercise \(\PageIndex{25}\)
Does 7 divide into \(5^2 \cdot 6^3 \cdot 7^4 \cdot 8\)? Explain.
- Answer
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Yes, because one of the (prime) factors of the number is 7.
Exercise \(\PageIndex{26}\)
Is 3 a factor of \(2^6 \cdot 3^2 \cdot 5^3 \cdot 4^6\)? Explain.
- Answer
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Yes, because it is one of the factors of the number.
Exercise \(\PageIndex{27}\)
Does 13 divide into \(11^3 \cdot 12^4 \cdot 15^2\)? Explain.
- Answer
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No, because the prime 13 is not a factor any of the listed factors of the number.
For problems 28 and 29, find the least common multiple.
Exercise \(\PageIndex{28}\)
432 and 180
- Answer
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2,160
Exercise \(\PageIndex{29}\)
28, 40, and 95
- Answer
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5,320