Q: A chemist is mixing two solutions, one with 20% acid and one with 50% acid, to obtain 10 liters of a 30% acid solution. Let $$x be $$the amount (in liters) of the 20% solution used. Which system of equations models this scenario?

$$\begin{cases} x + y = 10 \\ 0.2x + 0.5y = 3 \end{cases}$$

Q: A company produces two types of widgets, A and B. Each widget A requires 2 hours of assembly and 1 hour of packaging. Each widget B requires 1 hour of assembly and 2 hours of packaging. If the company has 8 hours for assembly and 8 hours for packaging, which system of equations represents this situation?

$$\begin{cases} 2x + y = 8 \\ x + 2y = 8 \end{cases}$$

Question 1

In a graph, the solution of two linear equations is the ____.

Accepted Answer

intersecting point of the lines corresponding to the equations

Question 2

Solve the following system of equations:
$$
\begin{cases}
3x + 4y = 16 \
x = 6 - y
\end{cases}
$$

Accepted Answer

$$(x, y) = (4, 2)$$

Question 3

Solve the following system of equations:
$$
\begin{cases}
x + 3y = -2 \
3x + 9y = -6
\end{cases}
$$

Accepted Answer

Infinitely many solutions

Question 4

Solve the following system of equations:
$$
\begin{cases}
2x - 3y = -1 \
-3x + 2y = -6
\end{cases}
$$

Accepted Answer

$$(x, y) = (-2, 3)$$

Question 5

When solving systems of linear equations by substitution, we ____.

Accepted Answer

substitute one variable in terms of the other variable

Question 6

Jose sells cartons of soup and cartons of milk to raise funds for an event. He can sell up to 2 cartons of soup and up to 7 cartons of soup and cartons of milk total. Each carton of soup costs $$20 and each carton of milk costs 25. $$Jose writes the following system of linear inequalities to figure out how many cartons of soup ($$x) $$and cartons of milk ($$y) in $$order to earn at least $$100:
$$
\begin{cases}
20x + 25y \geq 100 \
0 \leq x + y \leq 7 \
0 \leq x \leq 2
\end{cases}
$
For which of the possibilities is he NOT able to afford to purchase?

Accepted Answer

4 cartons of milk only

Question 7

One number is 3 more than twice another. Their sum is 9. Find the two numbers.

Accepted Answer

2 and 7

Question 8

Which of the following expressions is NOT equivalent to the others?

Accepted Answer

$$a - 2r$$

Question 9

Which of the following expressions can NOT be computed as a real number?

Accepted Answer

$$(-16)^{1/4}$$

Question 10

Evaluate:
$$
\sqrt[3]{27} + \sqrt[4]{16} + \sqrt[3]{-125}
$$

Accepted Answer

$$0$$

Question 11

Simplify:
$$
\left( \frac{27b$$^{-6}$$}{8a$$^{-3}$$} \$$right)^{1/3}$$,\ a 
eq 0,\ b 
eq 0
$$

Accepted Answer

$$3a/2b^2$$

Question 12

Simplify:
$$
3\left( a$$^{2/3}$$ \$$right)^3$$,\ a 
eq 0
$$

Accepted Answer

$$3a^2$$

Question 13

Simplify:
$$
64$$^{-2/3}$$
$$

Accepted Answer

$$\frac{1}{16}$$

Question 14

Which of the following statements is true?
(I) $$(2a^3)^3$ = 2a$$^{27}$$
(II) 3$$^{1/2}$$ \cdot 3^0$ = 3$$^{1/2}$$
(III) 2x$$^{-2}$$ = \frac{1}{4x^2$}$

Accepted Answer

Only (II)

Question 15

Which of the following statements is true?
(I) $$(b-1)(b+1) - 2 = -2(b^2$-1)
(II$$) $$3a^3b$$ - $$6ab^3 = 3ab$
(III) (c-d)^2$ = c^2$ - d^2$

Accepted Answer

None of the above

Question 16

Subtract:
$$-(3x^2 + 3x + 3$$) - $$(2x^2 - 2x - 3$$)$$

Accepted Answer

$$-5x^2 - x$

Question 17

Expand:
$$(5x - 3)(2x^2$ + 3x + 5)$$

Accepted Answer

$$10x^3$$ + $$9x^2 + 16x - 15$

Question 18

A chemist is mixing two solutions, one with 20% acid and one with 50% acid, to obtain 10 liters of a 30% acid solution. Let $$x be $$the amount (in liters) of the 20% solution used. Which system of equations models this scenario?

Accepted Answer

$$\begin{cases} x + y = 10 \ 0.2x + 0.5y = 3 \end{cases}$$

Question 19

A company produces two types of widgets, A and B. Each widget A requires 2 hours of assembly and 1 hour of packaging. Each widget B requires 1 hour of assembly and 2 hours of packaging. If the company has 8 hours for assembly and 8 hours for packaging, which system of equations represents this situation?

Accepted Answer

$$\begin{cases} 2x + y = 8 \ x + 2y = 8 \end{cases}$$

Intermediate Algebra Practice Exam 2 – Guided Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards