8.7: Proficiency Exam
- Page ID
- 53041
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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
For problems 1 - 16, estimate each value. After you have made an estimate, find the exact value. Results may vary.
Exercise \(\PageIndex{1}\)
\(3,716 + 6,789\)
- Answer
-
10,500 (10,505)
Exercise \(\PageIndex{2}\)
\(8,821 + 9,217\)
- Answer
-
18,000 (18,038)
Exercise \(\PageIndex{3}\)
\(7,316 - 2,305\)
- Answer
-
5,000 (5,011)
Exercise \(\PageIndex{4}\)
\(110,812 - 83,406\)
- Answer
-
28,000 (27,406)
Exercise \(\PageIndex{5}\)
\(82 \cdot 38\)
- Answer
-
3,200 (3,116)
Exercise \(\PageIndex{6}\)
\(51 \cdot 92\)
- Answer
-
4,500 (4,692)
Exercise \(\PageIndex{7}\)
\(48 \cdot 6,012\)
- Answer
-
300,000 (288,576)
Exercise \(\PageIndex{8}\)
\(238 \div 17\)
- Answer
-
12 (14)
Exercise \(\PageIndex{9}\)
\(2,660 \div 28\)
- Answer
-
90 (95)
Exercise \(\PageIndex{10}\)
\(43.06 + 37.94\)
- Answer
-
81 (81.00)
Exercise \(\PageIndex{11}\)
\(307.006 + 198.0005\)
- Answer
-
505 (505.0065)
Exercise \(\PageIndex{12}\)
\((47.2)(92.8)\)
- Answer
-
4,371 (4,380.16)
Exercise \(\PageIndex{13}\)
\(58 + 91 + 61 + 88\)
- Answer
-
\(2(60) + 2(90) = 300\) (298)
Exercise \(\PageIndex{14}\)
\(43 + 39 + 89 + 92\)
- Answer
-
\(2(40) + 2(90) = 260\) (263)
Exercise \(\PageIndex{15}\)
\(81 + 78 + 27 + 79\)
- Answer
-
\(30 + 3(80) = 270\) (265)
Exercise \(\PageIndex{16}\)
\(804 + 612 + 801 + 795 + 606\)
- Answer
-
\(3(800) + 2(600) = 3,600\) (3,618)
For problems 17-21, use the distributive property to obtain the exact result.
Exercise \(\PageIndex{17}\)
\(25 \cdot 14\)
- Answer
-
\(25 (10 + 4) = 250 + 100 = 350\)
Exercise \(\PageIndex{18}\)
\(15 \cdot 83\)
- Answer
-
\(15 (80 + 3) = 1,200 + 45 = 1,245\)
Exercise \(\PageIndex{19}\)
\(65 \cdot 98\)
- Answer
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\(65 (100 - 2) = 6,500 - 130 = 6,370\)
Exercise \(\PageIndex{20}\)
\(80 \cdot 107\)
- Answer
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\(80 (100 + 7) = 8,000 + 560 = 8,560\)
Exercise \(\PageIndex{21}\)
\(400 \cdot 215\)
- Answer
-
\(400 (200 + 15) = 80,000 + 6,000 = 86,000\)
For problems 22-25, estimate each value. After you have made an estimate, find the exact value. Results may vary.
Exercise \(\PageIndex{22}\)
\(\dfrac{15}{16} + \dfrac{5}{8}\)
- Answer
-
\(1 + \dfrac{1}{2} = 1 \dfrac{1}{2}\) (\(1 \dfrac{9}{16}\))
Exercise \(\PageIndex{23}\)
\(\dfrac{1}{25} + \dfrac{11}{20} + \dfrac{17}{30}\)
- Answer
-
\(0 + \dfrac{1}{2} + \dfrac{1}{2} = 1\) (\(1 \dfrac{47}{300}\))
Exercise \(\PageIndex{24}\)
\(8 \dfrac{9}{16} + 14 \dfrac{1}{12}\)
- Answer
-
\(8 \dfrac{1}{2} + 14 = 22 \dfrac{1}{2}\) (\(22 \dfrac{31}{48}\))
Exercise \(\PageIndex{25}\)
\(5 \dfrac{4}{9} + 1 \dfrac{17}{36} + 6 \dfrac{5}{12}\)
- Answer
-
\(5 \dfrac{1}{2} + 1 \dfrac{1}{2} + 6 \dfrac{1}{2} = 13 \dfrac{1}{2}\) (\(13 \dfrac{1}{3}\))