Question 1

Draw the graph of the equation.
-$$x ^ { 2 } = - 7 y$$

Accepted Answer

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

Question 2

Write the inequalities that describe the constraints on production.
-The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. The company can produce up to 84 rings each day, using up to 210 total man-hours of labor. It takes 3 man-hours to make one VIP ring and 7 man-hours to make one SST ring. Let x represent the number of VIP rings, and let y represent The number of SST rings.

Accepted Answer

A)  $0 \leq x \leq 84,0 \leq y \leq 84,7 x + 3 y \leq 210$ 
B)  $x + y \leq 84,7 x + 3 y \leq 210 , x \geq 0 , y \geq 0$ 
C)  $0 \leq x \leq 84,0 \leq y \leq 84,3 x + 7 y \leq 210$ 
D)  $x + y \leq 84,3 x + 7 y \leq 210 , x \geq 0 , y \geq 0$ 
A)  $0 \leq x \leq 84,0 \leq y \leq 84,7 x + 3 y \leq 210$ 
B)  $x + y \leq 84,7 x + 3 y \leq 210 , x \geq 0 , y \geq 0$ 
C)  $0 \leq x \leq 84,0 \leq y \leq 84,3 x + 7 y \leq 210$ 
D)  $x + y \leq 84,3 x + 7 y \leq 210 , x \geq 0 , y \geq 0$

Question 3

A town has a population of 10,000 people and is increasing by 10% every year. What will the population be at the end of 4 years?

Accepted Answer

A)  14,641 
B)  14,000 
C)  13,310 
D)  4641 
A)  14,641 
B)  14,000 
C)  13,310 
D)  4641

Question 4

Draw the graph of the equation.
-$$\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 16 } = 1$$

Accepted Answer

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

Question 5

Express the function in terms of x.
-If $f ( u ) = u ^ { 5 }$ and $u = x ^ { 3 } + 8$, then express $5 u ^ { 4 } \cdot 3 x ^ { 2 }$ in terms of $x$ alone.

Accepted Answer

A)  $x ^ { 2 } \left( 15 x ^ { 3 } + 8 \right) ^ { 4 }$ 
B)  $15 \left( x ^ { 5 } + 8 \right) ^ { 4 }$ 
C)  $15 x ^ { 2 } \left( x ^ { 3 } + 8 \right) ^ { 4 }$ 
D)  $\left( 15 x ^ { 5 } + 8 \right) ^ { 4 }$ 
A)  $x ^ { 2 } \left( 15 x ^ { 3 } + 8 \right) ^ { 4 }$ 
B)  $15 \left( x ^ { 5 } + 8 \right) ^ { 4 }$ 
C)  $15 x ^ { 2 } \left( x ^ { 3 } + 8 \right) ^ { 4 }$ 
D)  $\left( 15 x ^ { 5 } + 8 \right) ^ { 4 }$

Question 6

Evaluate the sum.
-$$\sum _ { i = 1 } ^ { 5 } \left( \frac { 1 } { 5 } \right) ^ { i }$$

Accepted Answer

A)  $\frac { 156 } { 625 }$ 
B)  $\frac { 3906 } { 15625 }$ 
C)  $\frac { 781 } { 3125 }$ 
D)  $\frac { 781 } { 625 }$ 
A)  $\frac { 156 } { 625 }$ 
B)  $\frac { 3906 } { 15625 }$ 
C)  $\frac { 781 } { 3125 }$ 
D)  $\frac { 781 } { 625 }$

Question 7

Find the sum of the series, if possible.
-$\sum _ { i = 1 } ^ { \infty } 5 ( 4 ) ^ { i }$

Accepted Answer

A)  3441 
B)  3072 
C)  1886 
D)  Not possible, infinite 
A)  3441 
B)  3072 
C)  1886 
D)  Not possible, infinite

Question 8

Graph the circle.
-$$x ^ { 2 } + y ^ { 2 } - 8 x + 6 y = - 9$$

Accepted Answer

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

Question 9

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: $f ( x ) = 3 x - x ^ { 2 }$; associated equation: $0 = 3 - 2 x$

Accepted Answer

A)  $\left( \frac { 3 } { 2 } , - \frac { 9 } { 4 } \right)$ 
B)  $\left( - \frac { 3 } { 2 } , - \frac { 9 } { 4 } \right)$ 
C)  $\left( \frac { 3 } { 2 } , \frac { 9 } { 4 } \right)$ 
D)  $\left( - \frac { 3 } { 2 } , \frac { 9 } { 4 } \right)$ 
A)  $\left( \frac { 3 } { 2 } , - \frac { 9 } { 4 } \right)$ 
B)  $\left( - \frac { 3 } { 2 } , - \frac { 9 } { 4 } \right)$ 
C)  $\left( \frac { 3 } { 2 } , \frac { 9 } { 4 } \right)$ 
D)  $\left( - \frac { 3 } { 2 } , \frac { 9 } { 4 } \right)$

Question 10

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 $f ( x ) = x ^ { 2 } + x$ at $( 5,30 )$ is 11 , write the equation of this tangent line.

Accepted Answer

A)  $y = - 11 x + 85$ 
B)  $y = 11 x - 25$ 
C)  $y = 11 x + 25$ 
D)  $y = - 11 x - 85$ 
A)  $y = - 11 x + 85$ 
B)  $y = 11 x - 25$ 
C)  $y = 11 x + 25$ 
D)  $y = - 11 x - 85$

Question 11

Evaluate the derivative.
-$$f ^ { \prime } ( 2 ) \text { if } f ^ { \prime } ( x ) = 4 x ^ { 3 } - 2 x ^ { 2 } + 2 x - 12$$

Accepted Answer

A)  16 
B)  42 
C)  32 
D)  56 
A)  16 
B)  42 
C)  32 
D)  56

Question 12

Graph the inequality.
-$x+y<-5$

Accepted Answer

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

Question 13

Assuming two parents, four grandparents, etc., what is the total number of ancestors a person has going back 8 generations?

Accepted Answer

A)  128 
B)  256 
C)  254 
D)  510 
A)  128 
B)  256 
C)  254 
D)  510

Question 14

Graph the solution region for the system of inequalities and identify the corners of the region.
-$$\left\{ \begin{array} { l } 
3 y + x \geq - 6 \
y + 2 x \leq 8 \
y \leq 0 , x \geq 0
\end{array} \right.$$

Accepted Answer

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

Question 15

Draw the graph of the equation.
-$4 x^{2}+36 y^{2}=144$

Accepted Answer

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

Question 16

Graph.
-$\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 16 } = 1$

Accepted Answer

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

Question 17

An elliptical riding path is to be built on a rectangular piece of property that measures 10 mi by 6 mi. Find an equation for the ellipse if the path is to touch the center of the property line on all 4 sides

Accepted Answer

A)  $\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 9 } = 1$ 
B)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 25 } = 1$ 
C)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 100 } = 1$ 
D)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 6 } = 1$ 
A)  $\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 9 } = 1$ 
B)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 25 } = 1$ 
C)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 100 } = 1$ 
D)  $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 6 } = 1$

Question 18

Graph the region that satisfies the constraints.
-A rectangular enclosure must have an area of at least 6300 square yards. If 320 yards of fencing is to be used, and the width cannot exceed the length, within what limits must the width of the enclosure lie?

Accepted Answer

A)  $0 \leq w \leq 70$ 
B)  $70 \leq w \leq 90$ 
C)  $80 \leq w \leq 90$ 
D)  $70 \leq w \leq 80$ 
A)  $0 \leq w \leq 70$ 
B)  $70 \leq w \leq 90$ 
C)  $80 \leq w \leq 90$ 
D)  $70 \leq w \leq 80$

Question 19

An important calculation in calculus is the evaluation of the expression $$\frac { f ( x + h ) - f ( x ) } { h } , \text { where } h \neq 0 \text {. Find } \frac { f ( x + h ) - f ( x ) } { h }$$
-$$f ( x ) = 9 x + 6$$

Accepted Answer

A)  6 
B)  9 
C)  $- 6 + 2 h$ 
D)  $- 9$ 
A)  6 
B)  9 
C)  $- 6 + 2 h$ 
D)  $- 9$

Question 20

Find the next three terms of the arithmetic sequence.
-Find term 25 of the arithmetic sequence with first term 5 and common difference $- \frac { 3 } { 4 }$.

Accepted Answer

A)  23 
B)  $\frac { 95 } { 4 }$ 
C)  $- \frac { 55 } { 4 }$ 
D)  $- 13$ 
A)  23 
B)  $\frac { 95 } { 4 }$ 
C)  $- \frac { 55 } { 4 }$ 
D)  $- 13$

Draw the graph of the equation. - $x ^ { 2 } = - 7 y$ $Draw the graph of the equation. - x ^ { 2 } = - 7 y$

A town has a population of 10,000 people and is increasing by 10% every year. What will the population be at the end of 4 years?

Draw the graph of the equation. - $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 16 } = 1$ $Draw the graph of the equation. - \frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 16 } = 1$

Express the function in terms of x. -If $f ( u ) = u ^ { 5 }$ and $u = x ^ { 3 } + 8$ , then express $5 u ^ { 4 } \cdot 3 x ^ { 2 }$ in terms of $x$ alone.

Evaluate the sum. - $\sum _ { i = 1 } ^ { 5 } \left( \frac { 1 } { 5 } \right) ^ { i }$

Find the sum of the series, if possible. - $\sum _ { i = 1 } ^ { \infty } 5 ( 4 ) ^ { i }$

Graph the circle. - $x ^ { 2 } + y ^ { 2 } - 8 x + 6 y = - 9$ $Graph the circle. - x ^ { 2 } + y ^ { 2 } - 8 x + 6 y = - 9$

Evaluate the derivative. - $f ^ { \prime } ( 2 ) \text { if } f ^ { \prime } ( x ) = 4 x ^ { 3 } - 2 x ^ { 2 } + 2 x - 12$

Graph the inequality. - $x+y<-5$

Assuming two parents, four grandparents, etc., what is the total number of ancestors a person has going back 8 generations?

Draw the graph of the equation. - $4 x^{2}+36 y^{2}=144$ $Draw the graph of the equation. - 4 x^{2}+36 y^{2}=144$

Graph. - $\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 16 } = 1$ $Graph. - \frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 16 } = 1$

An elliptical riding path is to be built on a rectangular piece of property that measures 10 mi by 6 mi. Find an equation for the ellipse if the path is to touch the center of the property line on all 4 sides

Graph the region that satisfies the constraints. -A rectangular enclosure must have an area of at least 6300 square yards. If 320 yards of fencing is to be used, and the width cannot exceed the length, within what limits must the width of the enclosure lie?

An important calculation in calculus is the evaluation of the expression $\frac { f ( x + h ) - f ( x ) } { h } , \text { where } h \neq 0 \text {. Find } \frac { f ( x + h ) - f ( x ) } { h }$ - $f ( x ) = 9 x + 6$

Find the next three terms of the arithmetic sequence. -Find term 25 of the arithmetic sequence with first term 5 and common difference $- \frac { 3 } { 4 }$ .

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

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Exam 8: Special Topics in Algebra

Draw the graph of the equation. - x2=−7yx ^ { 2 } = - 7 yx2=−7y

A town has a population of 10,000 people and is increasing by 10% every year. What will the population be at the end of 4 years?

Draw the graph of the equation. - x249+y216=1\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 16 } = 149x2​+16y2​=1

Express the function in terms of x. -If f(u)=u5f ( u ) = u ^ { 5 }f(u)=u5 and u=x3+8u = x ^ { 3 } + 8u=x3+8 , then express 5u4⋅3x25 u ^ { 4 } \cdot 3 x ^ { 2 }5u4⋅3x2 in terms of xxx alone.

Evaluate the sum. - ∑i=15(15)i\sum _ { i = 1 } ^ { 5 } \left( \frac { 1 } { 5 } \right) ^ { i }∑i=15​(51​)i

Find the sum of the series, if possible. - ∑i=1∞5(4)i\sum _ { i = 1 } ^ { \infty } 5 ( 4 ) ^ { i }∑i=1∞​5(4)i

Graph the circle. - x2+y2−8x+6y=−9x ^ { 2 } + y ^ { 2 } - 8 x + 6 y = - 9x2+y2−8x+6y=−9

Evaluate the derivative. - f′(2) if f′(x)=4x3−2x2+2x−12f ^ { \prime } ( 2 ) \text { if } f ^ { \prime } ( x ) = 4 x ^ { 3 } - 2 x ^ { 2 } + 2 x - 12f′(2) if f′(x)=4x3−2x2+2x−12

Graph the inequality. - x+y<−5x+y<-5x+y<−5

Assuming two parents, four grandparents, etc., what is the total number of ancestors a person has going back 8 generations?

Graph the solution region for the system of inequalities and identify the corners of the region. - {3y+x≥−6y+2x≤8y≤0,x≥0\left\{ \begin{array} { l } 3 y + x \geq - 6 \\y + 2 x \leq 8 \\y \leq 0 , x \geq 0\end{array} \right.⎩⎨⎧​3y+x≥−6y+2x≤8y≤0,x≥0​

Draw the graph of the equation. - 4x2+36y2=1444 x^{2}+36 y^{2}=1444x2+36y2=144

Graph. - x249−y216=1\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 16 } = 149x2​−16y2​=1

An elliptical riding path is to be built on a rectangular piece of property that measures 10 mi by 6 mi. Find an equation for the ellipse if the path is to touch the center of the property line on all 4 sides

Graph the region that satisfies the constraints. -A rectangular enclosure must have an area of at least 6300 square yards. If 320 yards of fencing is to be used, and the width cannot exceed the length, within what limits must the width of the enclosure lie?

Find the next three terms of the arithmetic sequence. -Find term 25 of the arithmetic sequence with first term 5 and common difference −34- \frac { 3 } { 4 }−43​ .

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

Draw the graph of the equation. - $x ^ { 2 } = - 7 y$ $Draw the graph of the equation. - x ^ { 2 } = - 7 y$

Draw the graph of the equation. - $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 16 } = 1$ $Draw the graph of the equation. - \frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 16 } = 1$

Express the function in terms of x. -If $f ( u ) = u ^ { 5 }$ and $u = x ^ { 3 } + 8$ , then express $5 u ^ { 4 } \cdot 3 x ^ { 2 }$ in terms of $x$ alone.

Evaluate the sum. - $\sum _ { i = 1 } ^ { 5 } \left( \frac { 1 } { 5 } \right) ^ { i }$

Find the sum of the series, if possible. - $\sum _ { i = 1 } ^ { \infty } 5 ( 4 ) ^ { i }$

Graph the circle. - $x ^ { 2 } + y ^ { 2 } - 8 x + 6 y = - 9$ $Graph the circle. - x ^ { 2 } + y ^ { 2 } - 8 x + 6 y = - 9$

Evaluate the derivative. - $f ^ { \prime } ( 2 ) \text { if } f ^ { \prime } ( x ) = 4 x ^ { 3 } - 2 x ^ { 2 } + 2 x - 12$

Graph the inequality. - $x+y<-5$

Draw the graph of the equation. - $4 x^{2}+36 y^{2}=144$ $Draw the graph of the equation. - 4 x^{2}+36 y^{2}=144$

Graph. - $\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 16 } = 1$ $Graph. - \frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 16 } = 1$

Find the next three terms of the arithmetic sequence. -Find term 25 of the arithmetic sequence with first term 5 and common difference $- \frac { 3 } { 4 }$ .