Question 1

A paper boy collected \$7.55, part in nickels and part in dimes. If the number of nickels was 6 more than one- half the number of dimes, how many nickels were there?

Accepted Answer

A)  58 nickels 
B)  35 nickels 
C)  45 nickels 
D)  68 nickels 
A)  58 nickels 
B)  35 nickels 
C)  45 nickels 
D)  68 nickels

Question 2

When two linear equations are solved for $y$ and the slopes are different and the y-intercepts are different, the lines are ?

Accepted Answer

A)  Intersecting 
B)  One Graph 
C)  Parallel 
A)  Intersecting 
B)  One Graph 
C)  Parallel

Question 3

Solve the system by graphing. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number $x$.
-$x=y-6$
$6 x=3 y$

Accepted Answer

A)  $(12,6)$ 
B)  $(-6,0)$ 
C)  $(0,0)$ 
D)  $(6,12)$ 
A)  $(12,6)$ 
B)  $(-6,0)$ 
C)  $(0,0)$ 
D)  $(6,12)$

Question 4

Graph the system of inequalities.
-$\mathrm{x} \geq-4$
$x \leq 9$
$y<\frac{1}{5} x-3$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 5

A college student earned $\$ 6500$ during summer vacation working as a waiter in a popular restaurant. The student invested part of the money at $10 \%$ and the rest at $7 \%$. If he received a total of $\$ 569$ in interest at the end of the year, how much did he invest at $10 \%$ ?

Accepted Answer

A)  $\$ 2700$ 
B)  $\$ 3250$ 
C)  $\$ 928$ 
D)  $\$ 3800$ 
A)  $\$ 2700$ 
B)  $\$ 3250$ 
C)  $\$ 928$ 
D)  $\$ 3800$

Question 6

Solve by addition or substitution.
-$7 x+9 y=9$
$4 x+7 y=7$

Accepted Answer

A)  $(0,2)$ 
B)  $(0,1)$ 
C)  $(-1,2)$ 
D)  $\varnothing$ 
A)  $(0,2)$ 
B)  $(0,1)$ 
C)  $(-1,2)$ 
D)  $\varnothing$

Question 7

Graph the system of inequalities.
-$x+2 y \leq 2$
$x+y \geq 0$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 8

When two linear equations are solved for $y$ and the slopes are equal and the $y$ - intercepts are different, the lines are

Accepted Answer

A)  Intersecting 
B)  One Graph 
C)  Parallel 
A)  Intersecting 
B)  One Graph 
C)  Parallel

Question 9

$x-y+z=7$
$x+y+z=-3$
$\mathrm{x}+\mathrm{y}-\mathrm{z}=-11$

Accepted Answer

A)  $(4,-5,-2)$ 
B)  $(-2,-5,4)$ 
C)  $(4,-2,-5)$ 
D)  $(-2,4,-5)$ 
A)  $(4,-5,-2)$ 
B)  $(-2,-5,4)$ 
C)  $(4,-2,-5)$ 
D)  $(-2,4,-5)$

Question 10

Evaluate the determinant
-$\left|\begin{array}{rrr}9 & -1 & 7 \ 0 & 4 & 5 \ 0 & 0 & -8\end{array}\right|$

Accepted Answer

A)  288 
B)  283 
C)  -293 
D)  -288 
A)  288 
B)  283 
C)  -293 
D)  -288

Question 11

Solve the system of equations using matrices.
-$2 x-7 y=-19$
$-5 x+4 y=7$

Accepted Answer

A)  $(-1,3)$ 
B)  $(1,3)$ 
C)  $(-1,-3)$ 
D)  $(1,-3)$ 
A)  $(-1,3)$ 
B)  $(1,3)$ 
C)  $(-1,-3)$ 
D)  $(1,-3)$

Question 12

$9 x-8 y-z=43$
$x+4 y+8 z=60$
$4 \mathrm{x}+\mathrm{y}+\mathrm{z}=40$

Accepted Answer

A)  $(-8,3,16)$ 
B)  $(8,3,5)$ 
C)  $(8,5,3)$ 
D)  $(-8,5,3)$ 
A)  $(-8,3,16)$ 
B)  $(8,3,5)$ 
C)  $(8,5,3)$ 
D)  $(-8,5,3)$

Question 13

Helen Weller invested $\$ 14,000$ in an account that pays $12 \%$ APR. How much additional money must be invested in an aocount that pays an APR of $15 \%$ so that the total interest is equal to the interest on the two investments at the rate of $13 \%$ ?

Accepted Answer

A)  $\$ 14,000$ 
B)  $\$ 10,000$ 
C)  $\$ 7000$ 
D)  $\$ 11,000$ 
A)  $\$ 14,000$ 
B)  $\$ 10,000$ 
C)  $\$ 7000$ 
D)  $\$ 11,000$

Question 14

In a basketball game, Will scored 36 points, consisting only of three-point shots and two-point shots. He made a total of 16 shots. How many shots of each type did he make?

Accepted Answer

A)  Two- point shots: 11; three- point shots: 5 
B)  Two- point shots: 13; three point shots: 3 
C)  Two- point shots: 12; three point shots: 4 
D)  Two- point shots: 4; three- point shots: 12 
A)  Two- point shots: 11; three- point shots: 5 
B)  Two- point shots: 13; three point shots: 3 
C)  Two- point shots: 12; three point shots: 4 
D)  Two- point shots: 4; three- point shots: 12

Question 15

In a chemistry class, 6 liters of a $4 \%$ - saline solution must be mixed with a $10 \%$ solution to get a $6 \%$ solution. How many liters of the $10 \%$ solution are needed?

Accepted Answer

A)  $6.0 \mathrm{~L}$ 
B)  $4.0 \mathrm{~L}$ 
C)  $2.0 \mathrm{~L}$ 
D)  $3.0 \mathrm{~L}$ 
A)  $6.0 \mathrm{~L}$ 
B)  $4.0 \mathrm{~L}$ 
C)  $2.0 \mathrm{~L}$ 
D)  $3.0 \mathrm{~L}$

Question 16

A college student earned $\$ 8800$ during summer vacation working as a waiter in a popular restaurant. The student invested part of the money at $8 \%$ and the rest at $6 \%$. If he received a total of $\$ 572$ in interest at the end of the year, how much did he invest at $8 \%$ ?

Accepted Answer

A)  $\$ 6600$ 
B)  $\$ 1466$ 
C)  $\$ 4400$ 
D)  $\$ 2200$ 
A)  $\$ 6600$ 
B)  $\$ 1466$ 
C)  $\$ 4400$ 
D)  $\$ 2200$

Question 17

Solve the system by graphing. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number $x$.
-$4 x+y=-14$
$x+4 y=-11$

Accepted Answer

A)  $(-4,2)$ 
B)  $(-3,-2)$ 
C)  $(-3,-4)$ 
D)  $(3,-2)$ 
A)  $(-4,2)$ 
B)  $(-3,-2)$ 
C)  $(-3,-4)$ 
D)  $(3,-2)$

Question 18

Solve the system by substitution. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number $x$.
-$4 \mathrm{x}-1=\mathrm{y}$
$y-4 x=1$

Accepted Answer

A)  $(0,0)$ 
B)  $(4,1)$ 
C)  Dependent, ( $x, 4 x-1)$ 
D)  Inconsistent, $\varnothing$ 
A)  $(0,0)$ 
B)  $(4,1)$ 
C)  Dependent, ( $x, 4 x-1)$ 
D)  Inconsistent, $\varnothing$

Question 19

A student was asked to find ordered pairs that solve the system of equations
$$\begin{gathered}
X+2 y=3 \
2 x+4 y=6
\end{gathered}$$
The student claims that $(1,1)$ and $(-1,2)$ are the only solutions. Is the student correct?

Accepted Answer

A) True 
 B)False

Question 20

A truck driver started for his destination at an average speed of 70 miles per hour. Once snow began to fall, he had to drop his speed to 40 miles per hour. It took the driver 14 hours to reach his destination, which was 707 miles away. How many hours after the driver started did the snow begin to fall?

Accepted Answer

A)  after $4.7 \mathrm{hr}$ 
B)  after $4.9 \mathrm{hr}$ 
C)  after $9.1 \mathrm{hr}$ 
D)  after $9.3 \mathrm{hr}$ 
A)  after $4.7 \mathrm{hr}$ 
B)  after $4.9 \mathrm{hr}$ 
C)  after $9.1 \mathrm{hr}$ 
D)  after $9.3 \mathrm{hr}$

A paper boy collected \$7.55, part in nickels and part in dimes. If the number of nickels was 6 more than one- half the number of dimes, how many nickels were there?

When two linear equations are solved for $y$ and the slopes are different and the y-intercepts are different, the lines are ?

Solve the system by graphing. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number $x$ . - $x=y-6$ $6 x=3 y$

Graph the system of inequalities. - $\mathrm{x} \geq-4$ $x \leq 9$ $y<\frac{1}{5} x-3$ $Graph the system of inequalities. - \mathrm{x} \geq-4 x \leq 9 y<\frac{1}{5} x-3$

A college student earned $\$ 6500$ during summer vacation working as a waiter in a popular restaurant. The student invested part of the money at $10 \%$ and the rest at $7 \%$ . If he received a total of $\$ 569$ in interest at the end of the year, how much did he invest at $10 \%$ ?

Solve by addition or substitution. - $7 x+9 y=9$ $4 x+7 y=7$

Graph the system of inequalities. - $x+2 y \leq 2$ $x+y \geq 0$ $Graph the system of inequalities. - x+2 y \leq 2 x+y \geq 0$

When two linear equations are solved for $y$ and the slopes are equal and the $y$ - intercepts are different, the lines are

$x-y+z=7$ $x+y+z=-3$ $\mathrm{x}+\mathrm{y}-\mathrm{z}=-11$

Evaluate the determinant - $\left|\begin{array}{rrr}9 & -1 & 7 \\ 0 & 4 & 5 \\ 0 & 0 & -8\end{array}\right|$

Solve the system of equations using matrices. - $2 x-7 y=-19$ $-5 x+4 y=7$

$9 x-8 y-z=43$ $x+4 y+8 z=60$ $4 \mathrm{x}+\mathrm{y}+\mathrm{z}=40$

Helen Weller invested $\$ 14,000$ in an account that pays $12 \%$ APR. How much additional money must be invested in an aocount that pays an APR of $15 \%$ so that the total interest is equal to the interest on the two investments at the rate of $13 \%$ ?

In a basketball game, Will scored 36 points, consisting only of three-point shots and two-point shots. He made a total of 16 shots. How many shots of each type did he make?

In a chemistry class, 6 liters of a $4 \%$ - saline solution must be mixed with a $10 \%$ solution to get a $6 \%$ solution. How many liters of the $10 \%$ solution are needed?

A college student earned $\$ 8800$ during summer vacation working as a waiter in a popular restaurant. The student invested part of the money at $8 \%$ and the rest at $6 \%$ . If he received a total of $\$ 572$ in interest at the end of the year, how much did he invest at $8 \%$ ?

Solve the system by graphing. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number $x$ . - $4 x+y=-14$ $x+4 y=-11$

Solve the system by substitution. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number $x$ . - $4 \mathrm{x}-1=\mathrm{y}$ $y-4 x=1$

A student was asked to find ordered pairs that solve the system of equations X+2y=3 2x+4y=6 The student claims that $(1,1)$ and $(-1,2)$ are the only solutions. Is the student correct?

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Exponents, Polynomials, and Factoring Polynomials

Rational Expressions and Equations

Radical Expressions and Equations

Quadratic Equations

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 4: Systems of Equations

A paper boy collected \$7.55, part in nickels and part in dimes. If the number of nickels was 6 more than one- half the number of dimes, how many nickels were there?

When two linear equations are solved for yyy and the slopes are different and the y-intercepts are different, the lines are ?

Solve the system by graphing. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number xxx . - x=y−6x=y-6x=y−6 6x=3y6 x=3 y6x=3y

Graph the system of inequalities. - x≥−4\mathrm{x} \geq-4x≥−4 x≤9x \leq 9x≤9 y<15x−3y<\frac{1}{5} x-3y<51​x−3

Solve by addition or substitution. - 7x+9y=97 x+9 y=97x+9y=9 4x+7y=74 x+7 y=74x+7y=7

Graph the system of inequalities. - x+2y≤2x+2 y \leq 2x+2y≤2 x+y≥0x+y \geq 0x+y≥0

When two linear equations are solved for yyy and the slopes are equal and the yyy - intercepts are different, the lines are

x−y+z=7x-y+z=7x−y+z=7 x+y+z=−3x+y+z=-3x+y+z=−3 x+y−z=−11\mathrm{x}+\mathrm{y}-\mathrm{z}=-11x+y−z=−11

Evaluate the determinant - ∣9−1704500−8∣\left|\begin{array}{rrr}9 & -1 & 7 \\ 0 & 4 & 5 \\ 0 & 0 & -8\end{array}\right|​900​−140​75−8​​

Solve the system of equations using matrices. - 2x−7y=−192 x-7 y=-192x−7y=−19 −5x+4y=7-5 x+4 y=7−5x+4y=7

9x−8y−z=439 x-8 y-z=439x−8y−z=43 x+4y+8z=60x+4 y+8 z=60x+4y+8z=60 4x+y+z=404 \mathrm{x}+\mathrm{y}+\mathrm{z}=404x+y+z=40

Helen Weller invested $14,000\$ 14,000$14,000 in an account that pays 12%12 \%12% APR. How much additional money must be invested in an aocount that pays an APR of 15%15 \%15% so that the total interest is equal to the interest on the two investments at the rate of 13%13 \%13% ?

In a basketball game, Will scored 36 points, consisting only of three-point shots and two-point shots. He made a total of 16 shots. How many shots of each type did he make?

In a chemistry class, 6 liters of a 4%4 \%4% - saline solution must be mixed with a 10%10 \%10% solution to get a 6%6 \%6% solution. How many liters of the 10%10 \%10% solution are needed?

Solve the system by graphing. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number xxx . - 4x+y=−144 x+y=-144x+y=−14 x+4y=−11x+4 y=-11x+4y=−11

Solve the system by substitution. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number xxx . - 4x−1=y4 \mathrm{x}-1=\mathrm{y}4x−1=y y−4x=1y-4 x=1y−4x=1

A student was asked to find ordered pairs that solve the system of equations X+2y=3 2x+4y=6 The student claims that (1,1)(1,1)(1,1) and (−1,2)(-1,2)(−1,2) are the only solutions. Is the student correct?

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Exponents, Polynomials, and Factoring Polynomials

Rational Expressions and Equations

Radical Expressions and Equations

Quadratic Equations

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

When two linear equations are solved for $y$ and the slopes are different and the y-intercepts are different, the lines are ?

Solve the system by graphing. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number $x$ . - $x=y-6$ $6 x=3 y$

Graph the system of inequalities. - $\mathrm{x} \geq-4$ $x \leq 9$ $y<\frac{1}{5} x-3$ $Graph the system of inequalities. - \mathrm{x} \geq-4 x \leq 9 y<\frac{1}{5} x-3$

Solve by addition or substitution. - $7 x+9 y=9$ $4 x+7 y=7$

Graph the system of inequalities. - $x+2 y \leq 2$ $x+y \geq 0$ $Graph the system of inequalities. - x+2 y \leq 2 x+y \geq 0$

When two linear equations are solved for $y$ and the slopes are equal and the $y$ - intercepts are different, the lines are

$x-y+z=7$ $x+y+z=-3$ $\mathrm{x}+\mathrm{y}-\mathrm{z}=-11$

Evaluate the determinant - $\left|\begin{array}{rrr}9 & -1 & 7 \\ 0 & 4 & 5 \\ 0 & 0 & -8\end{array}\right|$

Solve the system of equations using matrices. - $2 x-7 y=-19$ $-5 x+4 y=7$

$9 x-8 y-z=43$ $x+4 y+8 z=60$ $4 \mathrm{x}+\mathrm{y}+\mathrm{z}=40$

Helen Weller invested $\$ 14,000$ in an account that pays $12 \%$ APR. How much additional money must be invested in an aocount that pays an APR of $15 \%$ so that the total interest is equal to the interest on the two investments at the rate of $13 \%$ ?

In a chemistry class, 6 liters of a $4 \%$ - saline solution must be mixed with a $10 \%$ solution to get a $6 \%$ solution. How many liters of the $10 \%$ solution are needed?

Solve the system by graphing. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number $x$ . - $4 x+y=-14$ $x+4 y=-11$

Solve the system by substitution. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number $x$ . - $4 \mathrm{x}-1=\mathrm{y}$ $y-4 x=1$

A student was asked to find ordered pairs that solve the system of equations X+2y=3 2x+4y=6 The student claims that $(1,1)$ and $(-1,2)$ are the only solutions. Is the student correct?