Question 1

Write an equation for the parabola with vertex at the origin.
-Through $( 3 , - 6 )$, opening downward

Accepted Answer

A)  $x ^ { 2 } = - \frac { 3 } { 2 } y$ 
B)  $x ^ { 2 } = - \frac { 2 } { 3 }$ 
C)  $y = \frac { 2 } { 3 } x ^ { 2 }$ 
D)  $x = - \frac { 2 } { 3 } y ^ { 2 }$ 
A)  $x ^ { 2 } = - \frac { 3 } { 2 } y$ 
B)  $x ^ { 2 } = - \frac { 2 } { 3 }$ 
C)  $y = \frac { 2 } { 3 } x ^ { 2 }$ 
D)  $x = - \frac { 2 } { 3 } y ^ { 2 }$

Question 2

List the elements in the sample space of the experiment.
-A box contains 3 blue cards numbered 1 through 3, and 4 green cards numbered 1 through 4. List the sample space of picking a blue card followed by a green card.

Accepted Answer

A)  {12} 
B)  {7} 
C)  {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (4, 1), (4, 2), (4, 3)} 
D)  {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (3, 4)} 
A)  {12} 
B)  {7} 
C)  {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (4, 1), (4, 2), (4, 3)} 
D)  {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (3, 4)}

Question 3

Find the sum of the first 656 positive even integers.

Accepted Answer

A)  430,336 
B)  429,680 
C)  430,992 
D)  431,649 
A)  430,336 
B)  429,680 
C)  430,992 
D)  431,649

Question 4

Explain the differences between an ellipse and a hyperbola. Both definitions emphasize distance, but how is
distance used differently in these two definitions?

Accepted Answer

Answers will vary. One possibility: An e

Question 5

Evaluate the sum.
-$$\sum _ { i = 4 } ^ { 12 } ( i + 7 )$$

Accepted Answer

A)  135 
B)  123 
C)  131 
D)  119 
A)  135 
B)  123 
C)  131 
D)  119

Question 6

Find the sum of the first 284 positive odd integers.

Accepted Answer

A)  80,089 
B)  80,656 
C)  80,940 
D)  81,225 
A)  80,089 
B)  80,656 
C)  80,940 
D)  81,225

Question 7

Identify the type of graph.
-$$\frac { ( x - 8 ) ^ { 2 } } { 5 } + \frac { ( y - 4 ) ^ { 2 } } { 9 } = 0$$

Accepted Answer

A)  The graph is the point $( 8,4 )$. 
B)  The graph is an ellipse with center at $( - 8 , - 4 )$. 
C)  The graph is a hyperbola opening right and left. 
D)  The graph is an ellipse with center at $( 8,4 )$. 
A)  The graph is the point $( 8,4 )$. 
B)  The graph is an ellipse with center at $( - 8 , - 4 )$. 
C)  The graph is a hyperbola opening right and left. 
D)  The graph is an ellipse with center at $( 8,4 )$.

Question 8

Suppose there are 6 roads connecting town A to town B and 4 roads connecting town B to town C. In how many ways can a person travel from A to C via B?

Accepted Answer

A)  24 
B)  36 
C)  10 
D)  16 
A)  24 
B)  36 
C)  10 
D)  16

Question 9

Write the series using summation notation.
-$$1 ^ { 10 } + 2 ^ { 10 } + 3 ^ { 10 } + 4 ^ { 10 } + \ldots$$

Accepted Answer

A)  $\sum _ { \mathrm { k } = 1 } ^ { 4 } \mathrm { k } ^ { 10 }$ 
B)  $\sum _ { k = 1 } ^ { \infty } k ^ { 9 }$ 
C)  $\sum _ { k = 0 } ^ { \infty } 10 ^ { k }$ 
D)  $\sum _ { k = 1 } ^ { \infty } \mathrm { k } ^ { 10 }$ 
A)  $\sum _ { \mathrm { k } = 1 } ^ { 4 } \mathrm { k } ^ { 10 }$ 
B)  $\sum _ { k = 1 } ^ { \infty } k ^ { 9 }$ 
C)  $\sum _ { k = 0 } ^ { \infty } 10 ^ { k }$ 
D)  $\sum _ { k = 1 } ^ { \infty } \mathrm { k } ^ { 10 }$

Question 10

Graph the hyperbola.
-$4 y^{2}-25 x^{2}=100$

Accepted Answer

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

Question 11

Determine the two equations necessary to graph the ellipse with a graphing calculator.
-$$\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 64 } = 1$$

Accepted Answer

A)  $x = \sqrt { \frac { 192 - x ^ { 2 } } { 8 } }$ and $x = - \sqrt { \frac { 192 - y ^ { 2 } } { 8 } }$ 
B)  $x = \frac { 3 \sqrt { 9 - y ^ { 2 } } } { 64 }$ and $x = - \frac { 3 \sqrt { 9 - y ^ { 2 } } } { 64 }$ 
C)  $y = \frac { 8 \sqrt { 9 - x ^ { 2 } } } { 3 }$ and $y = - \frac { 8 \sqrt { 9 - x ^ { 2 } } } { 3 }$ 
D)  $y = \frac { 8 \sqrt { 9 - x ^ { 2 } } } { 9 }$ and $y = - \frac { 8 \sqrt { 9 + x ^ { 2 } } } { 9 }$ 
A)  $x = \sqrt { \frac { 192 - x ^ { 2 } } { 8 } }$ and $x = - \sqrt { \frac { 192 - y ^ { 2 } } { 8 } }$ 
B)  $x = \frac { 3 \sqrt { 9 - y ^ { 2 } } } { 64 }$ and $x = - \frac { 3 \sqrt { 9 - y ^ { 2 } } } { 64 }$ 
C)  $y = \frac { 8 \sqrt { 9 - x ^ { 2 } } } { 3 }$ and $y = - \frac { 8 \sqrt { 9 - x ^ { 2 } } } { 3 }$ 
D)  $y = \frac { 8 \sqrt { 9 - x ^ { 2 } } } { 9 }$ and $y = - \frac { 8 \sqrt { 9 + x ^ { 2 } } } { 9 }$

Question 12

Use the summation properties to evaluate the series. The following rules may be needed: $$\sum _ { i = 1 } ^ { n } i = \frac { n ( n + 1 ) } { 2 } ; \quad \sum _ { i = 1 } ^ { n } i ^ { 2 } = \frac { n ( n + 1 ) ( 2 n + 1 ) } { 6 } ; \quad \sum _ { i = 1 } ^ { n } i ^ { 3 } = \frac { n ^ { 2 } ( n + 1 ) ^ { 2 } } { 4 }$$
-$$\sum _ { i = 1 } ^ { 3 } \left( i ^ { 2 } + i - 7 \right)$$

Accepted Answer

A)  29 
B)  15 
C)  13 
D)  $- 1$ 
A)  29 
B)  15 
C)  13 
D)  $- 1$

Question 13

Write the binomial expansion of the expression.
-$$( 3 x + 1 ) ^ { 4 }$$

Accepted Answer

A)  $\left( 9 x ^ { 2 } + 3 x + 1 \right) ^ { 4 }$ 
B)  $81 x ^ { 4 } + 108 x ^ { 3 } + 54 x ^ { 2 } + 12 x + 1$ 
C)  $81 x ^ { 4 } + 108 x ^ { 3 } + 54 x ^ { 2 } + 12 x + 2$ 
D)  $81 x ^ { 3 } + 108 x ^ { 2 } + 54 x + 12$ 
A)  $\left( 9 x ^ { 2 } + 3 x + 1 \right) ^ { 4 }$ 
B)  $81 x ^ { 4 } + 108 x ^ { 3 } + 54 x ^ { 2 } + 12 x + 1$ 
C)  $81 x ^ { 4 } + 108 x ^ { 3 } + 54 x ^ { 2 } + 12 x + 2$ 
D)  $81 x ^ { 3 } + 108 x ^ { 2 } + 54 x + 12$

Question 14

Write an equation for the parabola with vertex at the origin.
-Focus $\left( - \frac { 1 } { 6 } , 0 \right)$

Accepted Answer

A)  $x ^ { 2 } = - 24 y$ 
B)  $y ^ { 2 } = - \frac { 2 } { 3 } x$ 
C)  $y ^ { 2 } = - 24 x$ 
D)  $x ^ { 2 } = - \frac { 2 } { 3 } y$ 
A)  $x ^ { 2 } = - 24 y$ 
B)  $y ^ { 2 } = - \frac { 2 } { 3 } x$ 
C)  $y ^ { 2 } = - 24 x$ 
D)  $x ^ { 2 } = - \frac { 2 } { 3 } y$

Question 15

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or
diverges.
-$$a _ { n } = \frac { n - 58 } { 2 n }$$

Accepted Answer

A)  Converges 
B)  Diverges 
A)  Converges 
B)  Diverges

Question 16

The roof of a building is in the shape of the hyperbola $5 y ^ { 2 } - x ^ { 2 } = 47$, where $x$ and $y$ are in meters. Refer to the figure and determine the height, $h$, of the outside walls.
$$A = 3 m$$

Accepted Answer

A)  7.5 m 
B)  3.3 m 
C)  11.2 m 
D)  56 m 
A)  7.5 m 
B)  3.3 m 
C)  11.2 m 
D)  56 m

Question 17

Graph the ellipse.
-$$\frac { ( x + 4 ) ^ { 2 } } { 25 } + \frac { ( y + 3 ) ^ { 2 } } { 36 } = 1$$

Accepted Answer

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

Question 18

Write an equation for the parabola.
-vertex $( - 3 , - 9 )$, focus $( - 3 , - 11 )$

Accepted Answer

A)  $( x - 3 ) ^ { 2 } = - 44 ( y - 9 )$ 
B)  $8 ( y - 9 ) = ( x - 3 ) ^ { 2 }$ 
C)  $( x + 3 ) ^ { 2 } = - 8 ( y + 9 )$ 
D)  $8 ( y - 3 ) = ( x - 9 ) ^ { 2 }$ 
A)  $( x - 3 ) ^ { 2 } = - 44 ( y - 9 )$ 
B)  $8 ( y - 9 ) = ( x - 3 ) ^ { 2 }$ 
C)  $( x + 3 ) ^ { 2 } = - 8 ( y + 9 )$ 
D)  $8 ( y - 3 ) = ( x - 9 ) ^ { 2 }$

Question 19

Evaluate the sum.
-$$\sum _ { i = 1 } ^ { 3000 } i$$

Accepted Answer

A)  4,501,500 
B)  4,498,500 
C)  4,503,000.5 
D)  4,504,501 
A)  4,501,500 
B)  4,498,500 
C)  4,503,000.5 
D)  4,504,501

Question 20

Find the first term and the common ratio for the geometric sequence. Round approximations to the nearest hundredth.
-$$a _ { 2 } = - 128 , a _ { 4 } = - 8$$

Accepted Answer

A)  $a _ { 1 } = - 32 , r = 4$ 
B)  $\mathrm { a } _ { 1 } = - 2048 , \mathrm { r } = 0.25$ 
C)  $\mathrm { a } _ { 1 } = - 512 , \mathrm { r } = 0.25$ 
D)  $\mathrm { a } _ { 1 } = - 8 , \mathrm { r } = 4$ 
A)  $a _ { 1 } = - 32 , r = 4$ 
B)  $\mathrm { a } _ { 1 } = - 2048 , \mathrm { r } = 0.25$ 
C)  $\mathrm { a } _ { 1 } = - 512 , \mathrm { r } = 0.25$ 
D)  $\mathrm { a } _ { 1 } = - 8 , \mathrm { r } = 4$

Write an equation for the parabola with vertex at the origin. -Through $( 3 , - 6 )$ , opening downward

List the elements in the sample space of the experiment. -A box contains 3 blue cards numbered 1 through 3, and 4 green cards numbered 1 through 4. List the sample space of picking a blue card followed by a green card.

Find the sum of the first 656 positive even integers.

Explain the differences between an ellipse and a hyperbola. Both definitions emphasize distance, but how is distance used differently in these two definitions?

Evaluate the sum. - $\sum _ { i = 4 } ^ { 12 } ( i + 7 )$

Find the sum of the first 284 positive odd integers.

Identify the type of graph. - $\frac { ( x - 8 ) ^ { 2 } } { 5 } + \frac { ( y - 4 ) ^ { 2 } } { 9 } = 0$

Suppose there are 6 roads connecting town A to town B and 4 roads connecting town B to town C. In how many ways can a person travel from A to C via B?

Write the series using summation notation. - $1 ^ { 10 } + 2 ^ { 10 } + 3 ^ { 10 } + 4 ^ { 10 } + \ldots$

Graph the hyperbola. - $4 y^{2}-25 x^{2}=100$ $Graph the hyperbola. - 4 y^{2}-25 x^{2}=100$

Determine the two equations necessary to graph the ellipse with a graphing calculator. - $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 64 } = 1$

Write the binomial expansion of the expression. - $( 3 x + 1 ) ^ { 4 }$

Write an equation for the parabola with vertex at the origin. -Focus $\left( - \frac { 1 } { 6 } , 0 \right)$

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or diverges. - $a _ { n } = \frac { n - 58 } { 2 n }$

Graph the ellipse. - $\frac { ( x + 4 ) ^ { 2 } } { 25 } + \frac { ( y + 3 ) ^ { 2 } } { 36 } = 1$ $Graph the ellipse. - \frac { ( x + 4 ) ^ { 2 } } { 25 } + \frac { ( y + 3 ) ^ { 2 } } { 36 } = 1$

Write an equation for the parabola. -vertex $( - 3 , - 9 )$ , focus $( - 3 , - 11 )$

Evaluate the sum. - $\sum _ { i = 1 } ^ { 3000 } i$

Find the first term and the common ratio for the geometric sequence. Round approximations to the nearest hundredth. - $a _ { 2 } = - 128 , a _ { 4 } = - 8$

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Filters

Exam 7: Arithmetic Sequence: Common Difference and First n Terms

Write an equation for the parabola with vertex at the origin. -Through (3,−6)( 3 , - 6 )(3,−6) , opening downward

List the elements in the sample space of the experiment. -A box contains 3 blue cards numbered 1 through 3, and 4 green cards numbered 1 through 4. List the sample space of picking a blue card followed by a green card.

Find the sum of the first 656 positive even integers.

Explain the differences between an ellipse and a hyperbola. Both definitions emphasize distance, but how is distance used differently in these two definitions?

Evaluate the sum. - ∑i=412(i+7)\sum _ { i = 4 } ^ { 12 } ( i + 7 )∑i=412​(i+7)

Find the sum of the first 284 positive odd integers.

Identify the type of graph. - (x−8)25+(y−4)29=0\frac { ( x - 8 ) ^ { 2 } } { 5 } + \frac { ( y - 4 ) ^ { 2 } } { 9 } = 05(x−8)2​+9(y−4)2​=0

Suppose there are 6 roads connecting town A to town B and 4 roads connecting town B to town C. In how many ways can a person travel from A to C via B?

Write the series using summation notation. - 110+210+310+410+…1 ^ { 10 } + 2 ^ { 10 } + 3 ^ { 10 } + 4 ^ { 10 } + \ldots110+210+310+410+…

Graph the hyperbola. - 4y2−25x2=1004 y^{2}-25 x^{2}=1004y2−25x2=100

Determine the two equations necessary to graph the ellipse with a graphing calculator. - x29+y264=1\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 64 } = 19x2​+64y2​=1

Write the binomial expansion of the expression. - (3x+1)4( 3 x + 1 ) ^ { 4 }(3x+1)4

Write an equation for the parabola with vertex at the origin. -Focus (−16,0)\left( - \frac { 1 } { 6 } , 0 \right)(−61​,0)

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or diverges. - an=n−582na _ { n } = \frac { n - 58 } { 2 n }an​=2nn−58​

The roof of a building is in the shape of the hyperbola 5y2−x2=475 y ^ { 2 } - x ^ { 2 } = 475y2−x2=47 , where xxx and yyy are in meters. Refer to the figure and determine the height, hhh , of the outside walls. A=3mA = 3 mA=3m

Graph the ellipse. - (x+4)225+(y+3)236=1\frac { ( x + 4 ) ^ { 2 } } { 25 } + \frac { ( y + 3 ) ^ { 2 } } { 36 } = 125(x+4)2​+36(y+3)2​=1

Write an equation for the parabola. -vertex (−3,−9)( - 3 , - 9 )(−3,−9) , focus (−3,−11)( - 3 , - 11 )(−3,−11)

Evaluate the sum. - ∑i=13000i\sum _ { i = 1 } ^ { 3000 } i∑i=13000​i

Find the first term and the common ratio for the geometric sequence. Round approximations to the nearest hundredth. - a2=−128,a4=−8a _ { 2 } = - 128 , a _ { 4 } = - 8a2​=−128,a4​=−8

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Filters

Write an equation for the parabola with vertex at the origin. -Through $( 3 , - 6 )$ , opening downward

Evaluate the sum. - $\sum _ { i = 4 } ^ { 12 } ( i + 7 )$

Identify the type of graph. - $\frac { ( x - 8 ) ^ { 2 } } { 5 } + \frac { ( y - 4 ) ^ { 2 } } { 9 } = 0$

Write the series using summation notation. - $1 ^ { 10 } + 2 ^ { 10 } + 3 ^ { 10 } + 4 ^ { 10 } + \ldots$

Graph the hyperbola. - $4 y^{2}-25 x^{2}=100$ $Graph the hyperbola. - 4 y^{2}-25 x^{2}=100$

Determine the two equations necessary to graph the ellipse with a graphing calculator. - $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 64 } = 1$

Write the binomial expansion of the expression. - $( 3 x + 1 ) ^ { 4 }$

Write an equation for the parabola with vertex at the origin. -Focus $\left( - \frac { 1 } { 6 } , 0 \right)$

Graph the function corresponding to the sequence defined. Use the graph to decide whether the sequence converges or diverges. - $a _ { n } = \frac { n - 58 } { 2 n }$

Graph the ellipse. - $\frac { ( x + 4 ) ^ { 2 } } { 25 } + \frac { ( y + 3 ) ^ { 2 } } { 36 } = 1$ $Graph the ellipse. - \frac { ( x + 4 ) ^ { 2 } } { 25 } + \frac { ( y + 3 ) ^ { 2 } } { 36 } = 1$

Write an equation for the parabola. -vertex $( - 3 , - 9 )$ , focus $( - 3 , - 11 )$

Evaluate the sum. - $\sum _ { i = 1 } ^ { 3000 } i$

Find the first term and the common ratio for the geometric sequence. Round approximations to the nearest hundredth. - $a _ { 2 } = - 128 , a _ { 4 } = - 8$