Question 1

Find the next three terms of the arithmetic sequence.
-Find the 25 th term of the arithmetic sequence with first term $- 3$ and common difference $- 4$.

Accepted Answer

A)  93 
B)  97 
C)  $- 99$ 
D)  $- 103$ 
A)  93 
B)  97 
C)  $- 99$ 
D)  $- 103$

Question 2

Use the given feasible region determined by the constraint inequalities to find the maximum possible value of the
objective function.
-$$\begin{aligned}
f = & 3 x + 11 y \text { subject to the constraints } \
& \left\{ \begin{array} { l } 
5 x + 4 y \leq 180 \
x + 2 y \leq 66 \
x \geq 0 , y \geq 0
\end{array} \right.
\end{aligned}$$

Accepted Answer

A)  343 
B)  383 
C)  363 
D)  323 
A)  343 
B)  383 
C)  363 
D)  323

Question 3

Express the function in terms of x.
-If $f ( u ) = u ^ { 4 / 3 }$ and $u = x ^ { 7 } - 3$, then express $\frac { 4 } { 3 } u ^ { 1 / 3 } \cdot 7 x ^ { 6 }$ in terms of $x$ alone.

Accepted Answer

A)  $\frac { 28 } { 3 } \sqrt [ 3 ] { x ^ { 6 } - 3 }$ 
B)  $\left(\frac{28}{3} x\right)^{63} \sqrt{x^{7}-3}$ 
C)  $\frac { 4 } { 3 } x \sqrt [ 3 ] { 7 x ^ { 7 } - 3 }$ 
D)  $\frac { 28 } { 3 } x ^ { 6 } \sqrt [ 3 ] { x ^ { 7 } - 3 }$ 
A)  $\frac { 28 } { 3 } \sqrt [ 3 ] { x ^ { 6 } - 3 }$ 
B)  $\left(\frac{28}{3} x\right)^{63} \sqrt{x^{7}-3}$ 
C)  $\frac { 4 } { 3 } x \sqrt [ 3 ] { 7 x ^ { 7 } - 3 }$ 
D)  $\frac { 28 } { 3 } x ^ { 6 } \sqrt [ 3 ] { x ^ { 7 } - 3 }$

Question 4

Graph the inequality.
-$5 x+y \leq 4$

Accepted Answer

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

Question 5

A radio telescope has a parabolic surface. If it is 1 meter(s) deep and 20 meters wide, how far is the focus from the vertex?

Accepted Answer

A)  25 m 
B)  5 m 
C)  1 m 
D)  100 m 
A)  25 m 
B)  5 m 
C)  1 m 
D)  100 m

Question 6

Write four additional terms of the geometric sequence.
-Find the first six terms of the sequence with first term 3 and nth term $a _ { n } = 1 - \frac { 1 } { a _ { n } - 1 }$.

Accepted Answer

A)  $3 , - \frac { 2 } { 3 } , \frac { 5 } { 2 } , \frac { 3 } { 5 } , - \frac { 2 } { 3 } , \frac { 5 } { 3 }$ 
B)  $3 , \frac { 2 } { 3 } , \frac { 1 } { 2 } , - 1,2 , \frac { 1 } { 2 }$ 
C)  $3 , \frac { 2 } { 3 } , - \frac { 1 } { 2 } , 3 , \frac { 2 } { 3 } , - \frac { 1 } { 2 }$ 
D)  $3 , \frac { 2 } { 3 } , - \frac { 1 } { 2 } , - 3 , \frac { 4 } { 3 } , \frac { 1 } { 4 }$ 
A)  $3 , - \frac { 2 } { 3 } , \frac { 5 } { 2 } , \frac { 3 } { 5 } , - \frac { 2 } { 3 } , \frac { 5 } { 3 }$ 
B)  $3 , \frac { 2 } { 3 } , \frac { 1 } { 2 } , - 1,2 , \frac { 1 } { 2 }$ 
C)  $3 , \frac { 2 } { 3 } , - \frac { 1 } { 2 } , 3 , \frac { 2 } { 3 } , - \frac { 1 } { 2 }$ 
D)  $3 , \frac { 2 } { 3 } , - \frac { 1 } { 2 } , - 3 , \frac { 4 } { 3 } , \frac { 1 } { 4 }$

Question 7

Graph the circle.
-$$( x - 2 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 9$$

Accepted Answer

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

Question 8

Graph.
-$$\frac { ( x - 5 ) ^ { 2 } } { 16 } - \frac { ( y + 4 ) ^ { 2 } } { 4 } = 1$$

Accepted Answer

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

Question 9

An auditorium has 30 rows, with 10 seats in the first row, 12 in the second row, 14 in the third row, and so forth. How many seats are in the auditorium?

Accepted Answer

A)  1230 
B)  600 
C)  1170 
D)  735 
A)  1230 
B)  600 
C)  1170 
D)  735

Question 10

Write four additional terms of the geometric sequence.
-Find the 6 th term of the geometric sequence with first term $\frac { 1 } { 2 }$ and common ratio $\frac { 1 } { 4 }$.

Accepted Answer

A)  $\frac { 1 } { 512 }$ 
B)  $\frac { 1 } { 8192 }$ 
C)  $\frac { 1 } { 128 }$ 
D)  $\frac { 1 } { 2048 }$ 
A)  $\frac { 1 } { 512 }$ 
B)  $\frac { 1 } { 8192 }$ 
C)  $\frac { 1 } { 128 }$ 
D)  $\frac { 1 } { 2048 }$

Question 11

The circle that is tangent to the x-axis at the point (8, 0) and passes through the point (0, -4)

Accepted Answer

A)  $( x + 8 ) ^ { 2 } + ( y - 10 ) ^ { 2 } = - 10$ 
B)  $( x + 10 ) ^ { 2 } + ( y - 8 ) ^ { 2 } = 100$ 
C)  $( x - 8 ) ^ { 2 } + ( y + 10 ) ^ { 2 } = - 10$ 
D)  $( x - 8 ) ^ { 2 } + ( y + 10 ) ^ { 2 } = 100$ 
A)  $( x + 8 ) ^ { 2 } + ( y - 10 ) ^ { 2 } = - 10$ 
B)  $( x + 10 ) ^ { 2 } + ( y - 8 ) ^ { 2 } = 100$ 
C)  $( x - 8 ) ^ { 2 } + ( y + 10 ) ^ { 2 } = - 10$ 
D)  $( x - 8 ) ^ { 2 } + ( y + 10 ) ^ { 2 } = 100$

Question 12

Find the sum of the series, if possible.
-$$3 + 12 + 48 + 192 + 768 + \ldots$$

Accepted Answer

A)  Not possible 
B)  13,023 
C)  1023 
D)  1,000,001,023 
A)  Not possible 
B)  13,023 
C)  1023 
D)  1,000,001,023

Question 13

The vertex of a parabola occurs where the derivative of its equation is 0, so an equation associated with the equation of a
parabola can be solved to find the x-coordinate of the vertex. Find the vertex of the parabola, given the equation of the
parabola and its associated equation.
-Equation of parabola: $f ( x ) = - \left( 7 + 8 x + 3 x ^ { 2 } \right)$; associated equation: $0 = - 8 - 6 x$

Accepted Answer

A)  $\left( - \frac { 4 } { 3 } , \frac { 37 } { 3 } \right)$ 
B)  $\left( - \frac { 4 } { 3 } , \frac { 10 } { 3 } \right)$ 
C)  $\left( - \frac { 4 } { 3 } , - \frac { 5 } { 3 } \right)$ 
D)  $\left( - \frac { 4 } { 3 } , - 46 \right)$ 
A)  $\left( - \frac { 4 } { 3 } , \frac { 37 } { 3 } \right)$ 
B)  $\left( - \frac { 4 } { 3 } , \frac { 10 } { 3 } \right)$ 
C)  $\left( - \frac { 4 } { 3 } , - \frac { 5 } { 3 } \right)$ 
D)  $\left( - \frac { 4 } { 3 } , - 46 \right)$

Question 14

Determine whether the graph of the equation is a circle or an ellipse.
-$$9 x ^ { 2 } + 90 x + 25 y ^ { 2 } - 50 y + 25 = 0$$

Accepted Answer

A)  Circle 
B)  Ellipse 
A)  Circle 
B)  Ellipse

Question 15

Find the sum of the series, if possible.
-$$\sum _ { i = 1 } ^ { \infty } \left( \frac { 3 } { 5 } \right) ^ { i }$$

Accepted Answer

A)  $- \frac { 3 } { 2 }$ 
B)  $\frac { 3 } { 2 }$ 
C)  Not possible, infinite 
D)  $\frac { 5 } { 2 }$ 
A)  $- \frac { 3 } { 2 }$ 
B)  $\frac { 3 } { 2 }$ 
C)  Not possible, infinite 
D)  $\frac { 5 } { 2 }$

Question 16

A stack of poles has 21 poles in the bottom row, 20 poles in the next row, and so on, with 10 poles in the top row. How many poles are there in the stack?

Accepted Answer

A)  176 
B)  186 
C)  196 
D)  160 
A)  176 
B)  186 
C)  196 
D)  160

Question 17

Graph the inequality.
-$-2 x-4 y \leq 8$

Accepted Answer

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

Question 18

The vertex of a parabola occurs where the derivative of its equation is 0, so an equation associated with the equation of a
parabola can be solved to find the x-coordinate of the vertex. Find the vertex of the parabola, given the equation of the
parabola and its associated equation.
-Between $x = 0$ and $x = 8$, the largest value of the expression $y = x ^ { 3 } - 15 x ^ { 2 } + 63 x + 18$ occurs where $3 x ^ { 2 } - 30 x + 63 = 0$. Of the values of $x$ that satisfy $3 x ^ { 2 } - 30 x + 63 = 0$, which gives the maximum value of $y = x ^ { 3 } - 15 x ^ { 2 } + 63 x + 18 ?$

Accepted Answer

A)  $x = 2$ 
B)  $x = 3$ 
C)  $x = 6$ 
D)  $x = 7$ 
A)  $x = 2$ 
B)  $x = 3$ 
C)  $x = 6$ 
D)  $x = 7$

Question 19

Suppose a plumber charges $160 for the first hour plus $70 for each additional hour. Write an expression for the cost (in dollars) of a job lasting n hours.

Accepted Answer

A)  $160 + 70 n$ 
B)  $160 + 70 ( n - 1 )$ 
C)  $160 \cdot 70 ^ { \mathrm { n } - 1 }$ 
D)  $230 \mathrm { n }$ 
A)  $160 + 70 n$ 
B)  $160 + 70 ( n - 1 )$ 
C)  $160 \cdot 70 ^ { \mathrm { n } - 1 }$ 
D)  $230 \mathrm { n }$

Question 20

Graph the inequality.
-$x+2 y \geq 1$

Accepted Answer

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

Find the next three terms of the arithmetic sequence. -Find the 25 th term of the arithmetic sequence with first term $- 3$ and common difference $- 4$ .

Express the function in terms of x. -If $f ( u ) = u ^ { 4 / 3 }$ and $u = x ^ { 7 } - 3$ , then express $\frac { 4 } { 3 } u ^ { 1 / 3 } \cdot 7 x ^ { 6 }$ in terms of $x$ alone.

Graph the inequality. - $5 x+y \leq 4$ $Graph the inequality. - 5 x+y \leq 4$

A radio telescope has a parabolic surface. If it is 1 meter(s) deep and 20 meters wide, how far is the focus from the vertex?

Write four additional terms of the geometric sequence. -Find the first six terms of the sequence with first term 3 and nth term $a _ { n } = 1 - \frac { 1 } { a _ { n } - 1 }$ .

Graph the circle. - $( x - 2 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 9$ $Graph the circle. - ( x - 2 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 9$

Graph. - $\frac { ( x - 5 ) ^ { 2 } } { 16 } - \frac { ( y + 4 ) ^ { 2 } } { 4 } = 1$ $Graph. - \frac { ( x - 5 ) ^ { 2 } } { 16 } - \frac { ( y + 4 ) ^ { 2 } } { 4 } = 1$

An auditorium has 30 rows, with 10 seats in the first row, 12 in the second row, 14 in the third row, and so forth. How many seats are in the auditorium?

Write four additional terms of the geometric sequence. -Find the 6 th term of the geometric sequence with first term $\frac { 1 } { 2 }$ and common ratio $\frac { 1 } { 4 }$ .

The circle that is tangent to the x-axis at the point (8, 0) and passes through the point (0, -4)

Find the sum of the series, if possible. - $3 + 12 + 48 + 192 + 768 + \ldots$

Determine whether the graph of the equation is a circle or an ellipse. - $9 x ^ { 2 } + 90 x + 25 y ^ { 2 } - 50 y + 25 = 0$

Find the sum of the series, if possible. - $\sum _ { i = 1 } ^ { \infty } \left( \frac { 3 } { 5 } \right) ^ { i }$

A stack of poles has 21 poles in the bottom row, 20 poles in the next row, and so on, with 10 poles in the top row. How many poles are there in the stack?

Graph the inequality. - $-2 x-4 y \leq 8$ $Graph the inequality. - -2 x-4 y \leq 8$

Suppose a plumber charges $160 for the first hour plus $70 for each additional hour. Write an expression for the cost (in dollars) of a job lasting n hours.

Graph the inequality. - $x+2 y \geq 1$ $Graph the inequality. - x+2 y \geq 1$

Functions, Graphs, and Models; Linear Functions

Linear Models, Equations, and Inequalities

Quadratic, Piecewise-Defined, and Power Functions

Additional Topics With Functions

Exponential and Logarithmic Functions

Higher-Degree Polynomial and Rational Functions

Systems of Equations and Matrices

Filters

Exam 8: Special Topics in Algebra

Find the next three terms of the arithmetic sequence. -Find the 25 th term of the arithmetic sequence with first term −3- 3−3 and common difference −4- 4−4 .

Use the given feasible region determined by the constraint inequalities to find the maximum possible value of the objective function. - f= 3x+11y subject to the constraints 5x+4y\leq180 x+2y\leq66 x\geq0,y\geq0

Express the function in terms of x. -If f(u)=u4/3f ( u ) = u ^ { 4 / 3 }f(u)=u4/3 and u=x7−3u = x ^ { 7 } - 3u=x7−3 , then express 43u1/3⋅7x6\frac { 4 } { 3 } u ^ { 1 / 3 } \cdot 7 x ^ { 6 }34​u1/3⋅7x6 in terms of xxx alone.

Graph the inequality. - 5x+y≤45 x+y \leq 45x+y≤4

A radio telescope has a parabolic surface. If it is 1 meter(s) deep and 20 meters wide, how far is the focus from the vertex?

Write four additional terms of the geometric sequence. -Find the first six terms of the sequence with first term 3 and nth term an=1−1an−1a _ { n } = 1 - \frac { 1 } { a _ { n } - 1 }an​=1−an​−11​ .

Graph the circle. - (x−2)2+(y+4)2=9( x - 2 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 9(x−2)2+(y+4)2=9

Graph. - (x−5)216−(y+4)24=1\frac { ( x - 5 ) ^ { 2 } } { 16 } - \frac { ( y + 4 ) ^ { 2 } } { 4 } = 116(x−5)2​−4(y+4)2​=1

An auditorium has 30 rows, with 10 seats in the first row, 12 in the second row, 14 in the third row, and so forth. How many seats are in the auditorium?

Write four additional terms of the geometric sequence. -Find the 6 th term of the geometric sequence with first term 12\frac { 1 } { 2 }21​ and common ratio 14\frac { 1 } { 4 }41​ .

The circle that is tangent to the x-axis at the point (8, 0) and passes through the point (0, -4)

Find the sum of the series, if possible. - 3+12+48+192+768+…3 + 12 + 48 + 192 + 768 + \ldots3+12+48+192+768+…

Determine whether the graph of the equation is a circle or an ellipse. - 9x2+90x+25y2−50y+25=09 x ^ { 2 } + 90 x + 25 y ^ { 2 } - 50 y + 25 = 09x2+90x+25y2−50y+25=0

Find the sum of the series, if possible. - ∑i=1∞(35)i\sum _ { i = 1 } ^ { \infty } \left( \frac { 3 } { 5 } \right) ^ { i }∑i=1∞​(53​)i

A stack of poles has 21 poles in the bottom row, 20 poles in the next row, and so on, with 10 poles in the top row. How many poles are there in the stack?

Graph the inequality. - −2x−4y≤8-2 x-4 y \leq 8−2x−4y≤8

Suppose a plumber charges $160 for the first hour plus $70 for each additional hour. Write an expression for the cost (in dollars) of a job lasting n hours.

Graph the inequality. - x+2y≥1x+2 y \geq 1x+2y≥1

Functions, Graphs, and Models; Linear Functions

Linear Models, Equations, and Inequalities

Quadratic, Piecewise-Defined, and Power Functions

Additional Topics With Functions

Exponential and Logarithmic Functions

Higher-Degree Polynomial and Rational Functions

Systems of Equations and Matrices

Filters

Find the next three terms of the arithmetic sequence. -Find the 25 th term of the arithmetic sequence with first term $- 3$ and common difference $- 4$ .

Express the function in terms of x. -If $f ( u ) = u ^ { 4 / 3 }$ and $u = x ^ { 7 } - 3$ , then express $\frac { 4 } { 3 } u ^ { 1 / 3 } \cdot 7 x ^ { 6 }$ in terms of $x$ alone.

Graph the inequality. - $5 x+y \leq 4$ $Graph the inequality. - 5 x+y \leq 4$

Write four additional terms of the geometric sequence. -Find the first six terms of the sequence with first term 3 and nth term $a _ { n } = 1 - \frac { 1 } { a _ { n } - 1 }$ .

Graph the circle. - $( x - 2 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 9$ $Graph the circle. - ( x - 2 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 9$

Graph. - $\frac { ( x - 5 ) ^ { 2 } } { 16 } - \frac { ( y + 4 ) ^ { 2 } } { 4 } = 1$ $Graph. - \frac { ( x - 5 ) ^ { 2 } } { 16 } - \frac { ( y + 4 ) ^ { 2 } } { 4 } = 1$

Write four additional terms of the geometric sequence. -Find the 6 th term of the geometric sequence with first term $\frac { 1 } { 2 }$ and common ratio $\frac { 1 } { 4 }$ .

Find the sum of the series, if possible. - $3 + 12 + 48 + 192 + 768 + \ldots$

Determine whether the graph of the equation is a circle or an ellipse. - $9 x ^ { 2 } + 90 x + 25 y ^ { 2 } - 50 y + 25 = 0$

Find the sum of the series, if possible. - $\sum _ { i = 1 } ^ { \infty } \left( \frac { 3 } { 5 } \right) ^ { i }$

Graph the inequality. - $-2 x-4 y \leq 8$ $Graph the inequality. - -2 x-4 y \leq 8$

Graph the inequality. - $x+2 y \geq 1$ $Graph the inequality. - x+2 y \geq 1$