11.8: Proficiency Exam

Last updated
Save as PDF

Page ID: 49416

$ \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } $ $ \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} $$\newcommand{\id}{\mathrm{id}}$ $ \newcommand{\Span}{\mathrm{span}}$ $ \newcommand{\kernel}{\mathrm{null}\,}$ $ \newcommand{\range}{\mathrm{range}\,}$ $ \newcommand{\RealPart}{\mathrm{Re}}$ $ \newcommand{\ImaginaryPart}{\mathrm{Im}}$ $ \newcommand{\Argument}{\mathrm{Arg}}$ $ \newcommand{\norm}[1]{\| #1 \|}$ $ \newcommand{\inner}[2]{\langle #1, #2 \rangle}$ $ \newcommand{\Span}{\mathrm{span}}$ $\newcommand{\id}{\mathrm{id}}$ $ \newcommand{\Span}{\mathrm{span}}$ $ \newcommand{\kernel}{\mathrm{null}\,}$ $ \newcommand{\range}{\mathrm{range}\,}$ $ \newcommand{\RealPart}{\mathrm{Re}}$ $ \newcommand{\ImaginaryPart}{\mathrm{Im}}$ $ \newcommand{\Argument}{\mathrm{Arg}}$ $ \newcommand{\norm}[1]{\| #1 \|}$ $ \newcommand{\inner}[2]{\langle #1, #2 \rangle}$ $ \newcommand{\Span}{\mathrm{span}}$$\newcommand{\AA}{\unicode[.8,0]{x212B}}$

Proficiency Exam

Exercise $\PageIndex{1}$

Solve using graphing:

$\left\{\begin{array}{r}
3x + 2y = 4\\
15x + 10y = -10
\end{array}\right.$

$An xy coordinate plane with gridlines, labeled negative five and five with increments of one unit for both axes.$

Answer

inconsistent

$A graph of two parallel lines. One line is labeled with the equation three x plus two y equals four and passes through the points zero, two and two, negative one. A second line is labeled with the equation fifteen x plus ten y equals negative ten and passes through the points zero, negative one and two, negative four.$

Exercise $\PageIndex{2}$

Solve using graphing:

$\left\{\begin{array}{r}
2x - 3y = 2\\
x + 2y = 8
\end{array}\right.$

$An xy coordinate plane with gridlines, labeled negative five and five with increments of one unit for both axes.$

Answer

(4,2)

$A graph of two lines intersecting at a point with coordinates four, two. One line is labeled with the equation x plus two y equals eight and passes through the points zero, four. A second line is labeled with the equation two x minus three y equals two and passes through the points zero, negative two over three and one, zero.$

Exercise $\PageIndex{3}$

Solve using substitution:

$\left\{\begin{array}{r}
2x + 6y = 16\\
x - 4y = -13
\end{array}\right.$

Answer: $(−1,3)$

Exercise $\PageIndex{4}$

Solve using addition:

$\left\{\begin{array}{r}
3x + 8y = -5\\
x - 2y = 3
\end{array}\right.$

Answer: $(1, -1)$

Exercise $\PageIndex{5}$

Solve using either substitution or addition:

$\left\{\begin{array}{r}
4x - 4y = 8\\
x - y = 5
\end{array}\right.$

Answer: inconsistent

Exercise $\PageIndex{6}$

Solve using either substitution or addition:

$\left\{\begin{array}{r}
9x + 3y = 12\\
3x - y = 4
\end{array}\right.$

Answer: $(\dfrac{4}{3}, 0)$

Exercise $\PageIndex{7}$

The sum of two numbers is 43 and the difference of the same two numbers is 7. What are the numbers?

Answer: 18 and 25

Exercise $\PageIndex{8}$

A chemist needs 80 ml of an 18% acid solution. She has two acid solutions, A and B, to mix together to form the 80-ml solution. Acid solution A is 15% acid and acid solution B is 20% acid. How much of each solution should be used?

Answer: 32 ml of solution A; 48 ml of solution B.

Exercise $\PageIndex{9}$

A parking meter contains 32 coins. If the meter contains only nickels and quarters, and the total value of the coins is $4.60, how many of each type of coin are there?

Answer: 17 nickels and 15 quarters

Exercise $\PageIndex{10}$

A person has $15,000 to invest. If he invests part at 8% and the rest at 12%, how much should he invest at each rate to produce the same return as if he had invested it all at 9%?

Answer: $11,250 at 8%; $3,750 at 12%

Search

Exercise \(\PageIndex{1}\)

Exercise \(\PageIndex{2}\)

Exercise \(\PageIndex{3}\)

Exercise \(\PageIndex{4}\)

Exercise \(\PageIndex{5}\)

Exercise \(\PageIndex{6}\)

Exercise \(\PageIndex{7}\)

Exercise \(\PageIndex{8}\)

Exercise \(\PageIndex{9}\)

Exercise \(\PageIndex{10}\)