10.9: Proficiency Exam
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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
Exercise \(\PageIndex{1}\)
Write all integers that are strictly between –8 and –3.
- Answer
-
{-7, -6, -5, -4}
Exercise \(\PageIndex{2}\)
Write all integers that are between and including –2 and 1.
- Answer
-
{-2, -1, 0, 1}
For problems 3-5, write the appropriate symbol (<, >, =) in place of the □ for each pair of numbers.
Exercise \(\PageIndex{3}\)
–1 □ –1
- Answer
-
=
Exercise \(\PageIndex{4}\)
0 □ 3
- Answer
-
<
Exercise \(\PageIndex{5}\)
–1 □ –2
- Answer
-
>
For problems 6 and 7, what numbers can replace \(x\) so that the statement is true?
Exercise \(\PageIndex{6}\)
\(-3 \le x < 0\), \(x\) is an integer.
- Answer
-
{-3, -2, -1}
Exercise \(\PageIndex{7}\)
\(-4 \le x \le 0\), \(x\) is a natural number.
- Answer
-
{1, 2}
Exercise \(\PageIndex{8}\)
How many units are there between –3 and 2?
- Answer
-
5
For problems 9-20, find each value.
Exercise \(\PageIndex{9}\)
|-16|
- Answer
-
16
Exercise \(\PageIndex{10}\)
-|-2|
- Answer
-
-2
Exercise \(\PageIndex{11}\)
\(-(-|-4|^2)\)
- Answer
-
16
Exercise \(\PageIndex{12}\)
|-5| + |-10|
- Answer
-
15
Exercise \(\PageIndex{13}\)
-8 + 6
- Answer
-
-2
Exercise \(\PageIndex{14}\)
-3 + (-8)
- Answer
-
-11
Exercise \(\PageIndex{15}\)
0 - 16
- Answer
-
-16
Exercise \(\PageIndex{16}\)
\((-14) \cdot (-3)\)
- Answer
-
42
Exercise \(\PageIndex{17}\)
\((-5 - 6)^2\)
- Answer
-
121
Exercise \(\PageIndex{18}\)
\((-51) \div (-7)\)
- Answer
-
\(\dfrac{51}{7}\) or \(7 \dfrac{2}{7}\)
Exercise \(\PageIndex{19}\)
\(\dfrac{-42}{-7}\)
- Answer
-
6
Exercise \(\PageIndex{20}\)
\(|\dfrac{-32}{8} - \dfrac{-15 - 5}{5}|\)
- Answer
-
0