Question 1

Write the equation for the shape described.
-The circle with endpoints of a diameter at $( - 1,4 )$ and $( - 1 , - 4 )$

Accepted Answer

A)  $( x - 4 ) ^ { 2 } + y ^ { 2 } = 1$ 
B)  $( x + 1 ) ^ { 2 } + y ^ { 2 } = 4$ 
C)  $x ^ { 2 } + ( y - 4 ) ^ { 2 } = 1$ 
D)  $( x + 1 ) ^ { 2 } + y ^ { 2 } = 16$ 
A)  $( x - 4 ) ^ { 2 } + y ^ { 2 } = 1$ 
B)  $( x + 1 ) ^ { 2 } + y ^ { 2 } = 4$ 
C)  $x ^ { 2 } + ( y - 4 ) ^ { 2 } = 1$ 
D)  $( x + 1 ) ^ { 2 } + y ^ { 2 } = 16$

Question 2

Find the sum of all the integers from 63 to 83.

Accepted Answer

A)  1387 
B)  1450 
C)  1533 
D)  1470 
A)  1387 
B)  1450 
C)  1533 
D)  1470

Question 3

Graph the circle.
-$y=\sqrt{16-x^{2}}$

Accepted Answer

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

Question 4

Find the sum of the first 5 terms of the geometric sequence  1,-4,16, ...

Accepted Answer

A)   -205 
B)   -341 
C)  341 
D)  205 
A)   -205 
B)   -341 
C)  341 
D)  205

Question 5

A company earned a profit of $5,000,000 in its first year, but its profits decreased by 9% in each of the next 6 years. What is the sum of its yearly profits for its first 7 years? Round your answer to the nearest cent.

Accepted Answer

A)  $26,846,610.04 
B)  $24,007,263.78 
C)  $29,430,415.13 
D)  $46,002,173.38 
A)  $26,846,610.04 
B)  $24,007,263.78 
C)  $29,430,415.13 
D)  $46,002,173.38

Question 6

If $3600 is invested at 8% interest, compounded annually, how long will it take the account to reach $9790.65?

Accepted Answer

A)  11 years 
B)  13 years 
C)  12 years 
D)  14 years 
A)  11 years 
B)  13 years 
C)  12 years 
D)  14 years

Question 7

Determine whether the graph of the equation is a circle or an ellipse.
-$$x ^ { 2 } + y ^ { 2 } - 6 x - 4 y + 4 = 0$$

Accepted Answer

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

Question 8

Write the equation of the circle with the given center and radius.
-center $( 3,0 )$, radius 7

Accepted Answer

A)  $( x - 3 ) ^ { 2 } + y ^ { 2 } = 49$ 
B)  $x ^ { 2 } + ( y + 3 ) ^ { 2 } = 7$ 
C)  $x ^ { 2 } + ( y - 3 ) ^ { 2 } = 7$ 
D)  $( x + 3 ) ^ { 2 } + y ^ { 2 } = 49$ 
A)  $( x - 3 ) ^ { 2 } + y ^ { 2 } = 49$ 
B)  $x ^ { 2 } + ( y + 3 ) ^ { 2 } = 7$ 
C)  $x ^ { 2 } + ( y - 3 ) ^ { 2 } = 7$ 
D)  $( x + 3 ) ^ { 2 } + y ^ { 2 } = 49$

Question 9

Use the given feasible region determined by the constraint inequalities to find the maximum possible value of the
objective function.
-$\mathrm { f } = 7 \mathrm { x } + 6 \mathrm { y }$ subject to the constraints
$$\left\{ \begin{array} { l } 
3 x + 4 y \leq 165 \
x + 2 y \leq 77 \
x \geq 0 , y \geq 0
\end{array} \right.$$

Accepted Answer

A)  385 
B)  405 
C)  275 
D)  231 
A)  385 
B)  405 
C)  275 
D)  231

Question 10

Use the given feasible region determined by the constraint inequalities to find the maximum possible value of the
objective function.
-$f = 5 x + 6 y$ subject to the constraints
$$\left\{ \begin{array} { l } 
x + 2 y \leq 14 \
3 x + 2 y \leq 18 \
- x + 2 y \leq 12 \
x \geq 0 , y \geq 0
\end{array} \right.$$

Accepted Answer

A)  36 
B)  40 
C)  46 
D)  44 
A)  36 
B)  40 
C)  46 
D)  44

Question 11

Use the given feasible region determined by the constraint inequalities to find the maximum possible value of the
objective function.
-$$f = 4 x + 3 y \text { subject to the constraints }$$

Accepted Answer

A)  28 
B)  21 
C)  26 
D)  24 
A)  28 
B)  21 
C)  26 
D)  24

Question 12

Use the given feasible region determined by the constraint inequalities to find the minimum possible value of the
objective function.
-Find the values of $x$ and $y$ that give the minimum possible value of $f = 6 x + 8 y$ subject to the following constraint $\left\{ \begin{array} { l } 2 x + 4 y \geq 12 \ 2 x + y \geq 8 \ x \geq 0 , y \geq 0 \end{array} \right.$

Accepted Answer

A)  $x = 0 , y = 3$ 
B)  $x = 0 , y = 0$ 
C)  $x = \frac { 10 } { 3 } , y = \frac { 4 } { 3 }$ 
D)  $x = 6 , y = 0$ 
A)  $x = 0 , y = 3$ 
B)  $x = 0 , y = 0$ 
C)  $x = \frac { 10 } { 3 } , y = \frac { 4 } { 3 }$ 
D)  $x = 6 , y = 0$

Question 13

Simplify the expression representing the derivative of a function.
-$$f ^ { \prime } ( x ) = \left( 4 x ^ { 4 } - 3 x ^ { 3 } + 6 x - 5 \right) ( 6 x ) + ( x - 3 ) \left( 6 x ^ { 2 } - 6 \right)$$

Accepted Answer

A)  $24 x ^ { 5 } - 18 x ^ { 4 } + 6 x ^ { 3 } - 36 x ^ { 2 } - 36 x + 18$ 
B)  $24 x ^ { 5 } - 18 x ^ { 4 } + 6 x ^ { 3 } + 18 x ^ { 2 } - 36 x + 18$ 
C)  $24 x ^ { 5 } - 18 x ^ { 4 } - 6 x ^ { 3 } + 18 x ^ { 2 } - 36 x - 18$ 
D)  $24 x ^ { 5 } - 18 x ^ { 4 } - 18 x ^ { 2 } - 30 x + 18$ 
A)  $24 x ^ { 5 } - 18 x ^ { 4 } + 6 x ^ { 3 } - 36 x ^ { 2 } - 36 x + 18$ 
B)  $24 x ^ { 5 } - 18 x ^ { 4 } + 6 x ^ { 3 } + 18 x ^ { 2 } - 36 x + 18$ 
C)  $24 x ^ { 5 } - 18 x ^ { 4 } - 6 x ^ { 3 } + 18 x ^ { 2 } - 36 x - 18$ 
D)  $24 x ^ { 5 } - 18 x ^ { 4 } - 18 x ^ { 2 } - 30 x + 18$

Question 14

Calculus can be used to find the slope of the line tangent to a curve. The slope of the tangent to the curve $y = f ( x ) \text { at } x = a$ is f'(a). Use f'(x) to find the slope of the tangent to $y = f ( x )$ at the given value of x.
-The derivative of a function can be used to find the slope of the line tangent to its graph. If the slope of the line tangent to the graph of $f ( x ) = - x ^ { 3 } + 7$ at $( 3 , - 20 )$ is $- 27$, write the equation of this tangent line.

Accepted Answer

A)  $y = - 27 x + 47$ 
B)  $\mathrm { y } = - 27 \mathrm { x } - 61$ 
C)  $\mathrm { y } = - 27 \mathrm { x } - 47$ 
D)  $y = - 27 x + 61$ 
A)  $y = - 27 x + 47$ 
B)  $\mathrm { y } = - 27 \mathrm { x } - 61$ 
C)  $\mathrm { y } = - 27 \mathrm { x } - 47$ 
D)  $y = - 27 x + 61$

Question 15

Evaluate the expression.
-$\left( \begin{array} { l } 
10 \
10
\end{array} \right)$

Accepted Answer

A)  0 
B)  2 
C)  1 
D)  3,628,800 
A)  0 
B)  2 
C)  1 
D)  3,628,800

Question 16

The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to 24 rings each day using up to 60 total man-hours of labor. It takes 3 man-hours to make one VIP ring and 2
Man-hours to make one SST ring. How many of each type of ring should be made daily to maximize the
Company's profit, if the profit on a VIP ring is $50 and on an SST ring is $10?

Accepted Answer

A)  20 VIP and 4 SST 
B)  24 VIP and 0 SST 
C)  20 VIP and 0 SST 
D)  24 VIP and 4 SST 
A)  20 VIP and 4 SST 
B)  24 VIP and 0 SST 
C)  20 VIP and 0 SST 
D)  24 VIP and 4 SST

Question 17

Write the expression without negative exponents.
-$$y = - 5 x ^ { - 3 } - x ^ { - 2 } + 2 x ^ { - 1 } + 2 x ^ { 2 } + 4 x$$

Accepted Answer

A)  $y = - \frac { 5 } { x ^ { 3 } } - \frac { 1 } { x ^ { 2 } } + \frac { 2 } { x } + 2 x ^ { 2 } + 4 x$ 
B)  $y = - 5 x ^ { 1 / 3 } - x ^ { 1 / 2 } + 2 x ^ { 2 } + 6 x$ 
C)  $y = - \frac { 5 } { x ^ { 3 } } + \frac { 1 } { x ^ { 2 } } + \frac { 6 } { x }$ 
D)  $y = - \frac { 5 } { x ^ { 3 } } - \frac { 1 } { x ^ { 2 } } + \frac { 2 } { x } + \frac { 2 } { x ^ { 2 } } + \frac { 4 } { x }$ 
A)  $y = - \frac { 5 } { x ^ { 3 } } - \frac { 1 } { x ^ { 2 } } + \frac { 2 } { x } + 2 x ^ { 2 } + 4 x$ 
B)  $y = - 5 x ^ { 1 / 3 } - x ^ { 1 / 2 } + 2 x ^ { 2 } + 6 x$ 
C)  $y = - \frac { 5 } { x ^ { 3 } } + \frac { 1 } { x ^ { 2 } } + \frac { 6 } { x }$ 
D)  $y = - \frac { 5 } { x ^ { 3 } } - \frac { 1 } { x ^ { 2 } } + \frac { 2 } { x } + \frac { 2 } { x ^ { 2 } } + \frac { 4 } { x }$

Question 18

Evaluate the expression.
-${ } _ { 11 } \mathrm { C } _ { 7 }$

Accepted Answer

A)  330 
B)  7920 
C)  $1,663,200$ 
D)  $\frac { 11 } { 28 }$ 
A)  330 
B)  7920 
C)  $1,663,200$ 
D)  $\frac { 11 } { 28 }$

Question 19

Write the binomial expansion of the expression.
-$$( 3 x + 5 ) ^ { 3 }$$

Accepted Answer

A)  $27 x ^ { 3 } + 135 x ^ { 2 } + 135 x + 125$ 
B)  $27 x ^ { 3 } + 135 x ^ { 2 } + 225 x + 125$ 
C)  $9 x ^ { 6 } + 15 x ^ { 3 } + 15,625$ 
D)  $9 x ^ { 2 } + 30 x + 25$ 
A)  $27 x ^ { 3 } + 135 x ^ { 2 } + 135 x + 125$ 
B)  $27 x ^ { 3 } + 135 x ^ { 2 } + 225 x + 125$ 
C)  $9 x ^ { 6 } + 15 x ^ { 3 } + 15,625$ 
D)  $9 x ^ { 2 } + 30 x + 25$

Question 20

Match the solution of the system of inequalities with the graph.
-$$\left\{ \begin{array} { l } 
2 x + y \geq 4 \
x + 2 y \geq 5 \
x \geq 0 \
y \geq 0
\end{array} \right.$$

Accepted Answer

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

Write the equation for the shape described. -The circle with endpoints of a diameter at $( - 1,4 )$ and $( - 1 , - 4 )$

Find the sum of all the integers from 63 to 83.

Graph the circle. - $y=\sqrt{16-x^{2}}$ $Graph the circle. - y=\sqrt{16-x^{2}}$

Find the sum of the first 5 terms of the geometric sequence 1,-4,16, ...

A company earned a profit of $5,000,000 in its first year, but its profits decreased by 9% in each of the next 6 years. What is the sum of its yearly profits for its first 7 years? Round your answer to the nearest cent.

If $3600 is invested at 8% interest, compounded annually, how long will it take the account to reach $9790.65?

Determine whether the graph of the equation is a circle or an ellipse. - $x ^ { 2 } + y ^ { 2 } - 6 x - 4 y + 4 = 0$

Write the equation of the circle with the given center and radius. -center $( 3,0 )$ , radius 7

Simplify the expression representing the derivative of a function. - $f ^ { \prime } ( x ) = \left( 4 x ^ { 4 } - 3 x ^ { 3 } + 6 x - 5 \right) ( 6 x ) + ( x - 3 ) \left( 6 x ^ { 2 } - 6 \right)$

Evaluate the expression. - $\left( \begin{array} { l } 10 \\10\end{array} \right)$

Write the expression without negative exponents. - $y = - 5 x ^ { - 3 } - x ^ { - 2 } + 2 x ^ { - 1 } + 2 x ^ { 2 } + 4 x$

Evaluate the expression. - ${ } _ { 11 } \mathrm { C } _ { 7 }$

Write the binomial expansion of the expression. - $( 3 x + 5 ) ^ { 3 }$

Match the solution of the system of inequalities with the graph. - $\left\{ \begin{array} { l } 2 x + y \geq 4 \\x + 2 y \geq 5 \\x \geq 0 \\y \geq 0\end{array} \right.$

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

Write the equation for the shape described. -The circle with endpoints of a diameter at (−1,4)( - 1,4 )(−1,4) and (−1,−4)( - 1 , - 4 )(−1,−4)

Find the sum of all the integers from 63 to 83.

Graph the circle. - y=16−x2y=\sqrt{16-x^{2}}y=16−x2​

Find the sum of the first 5 terms of the geometric sequence 1,-4,16, ...

A company earned a profit of $5,000,000 in its first year, but its profits decreased by 9% in each of the next 6 years. What is the sum of its yearly profits for its first 7 years? Round your answer to the nearest cent.

If $3600 is invested at 8% interest, compounded annually, how long will it take the account to reach $9790.65?

Determine whether the graph of the equation is a circle or an ellipse. - x2+y2−6x−4y+4=0x ^ { 2 } + y ^ { 2 } - 6 x - 4 y + 4 = 0x2+y2−6x−4y+4=0

Write the equation of the circle with the given center and radius. -center (3,0)( 3,0 )(3,0) , radius 7

Use the given feasible region determined by the constraint inequalities to find the maximum possible value of the objective function. - f=4x+3y subject to the constraints f = 4 x + 3 y \text { subject to the constraints }f=4x+3y subject to the constraints

Simplify the expression representing the derivative of a function. - f′(x)=(4x4−3x3+6x−5)(6x)+(x−3)(6x2−6)f ^ { \prime } ( x ) = \left( 4 x ^ { 4 } - 3 x ^ { 3 } + 6 x - 5 \right) ( 6 x ) + ( x - 3 ) \left( 6 x ^ { 2 } - 6 \right)f′(x)=(4x4−3x3+6x−5)(6x)+(x−3)(6x2−6)

Evaluate the expression. - (1010)\left( \begin{array} { l } 10 \\10\end{array} \right)(1010​)

Write the expression without negative exponents. - y=−5x−3−x−2+2x−1+2x2+4xy = - 5 x ^ { - 3 } - x ^ { - 2 } + 2 x ^ { - 1 } + 2 x ^ { 2 } + 4 xy=−5x−3−x−2+2x−1+2x2+4x

Evaluate the expression. - 11C7{ } _ { 11 } \mathrm { C } _ { 7 }11​C7​

Write the binomial expansion of the expression. - (3x+5)3( 3 x + 5 ) ^ { 3 }(3x+5)3

Match the solution of the system of inequalities with the graph. - {2x+y≥4x+2y≥5x≥0y≥0\left\{ \begin{array} { l } 2 x + y \geq 4 \\x + 2 y \geq 5 \\x \geq 0 \\y \geq 0\end{array} \right.⎩⎨⎧​2x+y≥4x+2y≥5x≥0y≥0​

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

Write the equation for the shape described. -The circle with endpoints of a diameter at $( - 1,4 )$ and $( - 1 , - 4 )$

Graph the circle. - $y=\sqrt{16-x^{2}}$ $Graph the circle. - y=\sqrt{16-x^{2}}$

Determine whether the graph of the equation is a circle or an ellipse. - $x ^ { 2 } + y ^ { 2 } - 6 x - 4 y + 4 = 0$

Write the equation of the circle with the given center and radius. -center $( 3,0 )$ , radius 7

Simplify the expression representing the derivative of a function. - $f ^ { \prime } ( x ) = \left( 4 x ^ { 4 } - 3 x ^ { 3 } + 6 x - 5 \right) ( 6 x ) + ( x - 3 ) \left( 6 x ^ { 2 } - 6 \right)$

Evaluate the expression. - $\left( \begin{array} { l } 10 \\10\end{array} \right)$

Write the expression without negative exponents. - $y = - 5 x ^ { - 3 } - x ^ { - 2 } + 2 x ^ { - 1 } + 2 x ^ { 2 } + 4 x$

Evaluate the expression. - ${ } _ { 11 } \mathrm { C } _ { 7 }$

Write the binomial expansion of the expression. - $( 3 x + 5 ) ^ { 3 }$

Match the solution of the system of inequalities with the graph. - $\left\{ \begin{array} { l } 2 x + y \geq 4 \\x + 2 y \geq 5 \\x \geq 0 \\y \geq 0\end{array} \right.$