Question 1

Give the focus, directrix, and axis for the parabola.
-$$( x + 5 ) ^ { 2 } = - 20 ( y - 4 )$$

Accepted Answer

A)  $( - 5 , - 1 ) , y = 9 , x = - 5$ 
B)  $( - 5 , - 1 ) , y = 9 , x = 5$ 
C)  $( - 5 , - 1 ) , y = 9 , x = 4$ 
D)  $( - 10 , - 1 ) , y = 9 , x = - 5$ 
A)  $( - 5 , - 1 ) , y = 9 , x = - 5$ 
B)  $( - 5 , - 1 ) , y = 9 , x = 5$ 
C)  $( - 5 , - 1 ) , y = 9 , x = 4$ 
D)  $( - 10 , - 1 ) , y = 9 , x = - 5$

Question 2

What are the odds in favor of spinning a D on this spinner?

Accepted Answer

A)  5 to 1 
B)  6 to 1 
C)  1 to 6 
D)  1 to 7 
A)  5 to 1 
B)  6 to 1 
C)  1 to 6 
D)  1 to 7

Question 3

Evaluate the expression.
-$$\left( \begin{array} { c } 
12 \
7
\end{array} \right)$$

Accepted Answer

A)  240 
B)  792 
C)  95,040 
D)  1,995,840 
A)  240 
B)  792 
C)  95,040 
D)  1,995,840

Question 4

Provide an appropriate response.
-Explain in your own words how you can tell from the equation whether the branches of a hyperbola open up
and down or left and right.

Accepted Answer

The branches open left and rig

Question 5

Identify the type of graph.
-$$x ^ { 2 } - 12 x + y = 0$$

Accepted Answer

A)  The graph is a parabola opening downward. 
B)  The graph is a parabola opening upward. 
C)  The graph is an ellipse with center (0, 12). 
D)  The equation has no graph. 
A)  The graph is a parabola opening downward. 
B)  The graph is a parabola opening upward. 
C)  The graph is an ellipse with center (0, 12). 
D)  The equation has no graph.

Question 6

Identify the type of conic section.
-Identify the type of conic section consisting of the set of all points in the plane for which the absolute value of the difference of the distances from the points (0 $( 0,6 ) \text { and } ( 0 , - 6 ) \text { is } 2$

Accepted Answer

A)  Circle 
B)  Parabola 
C)  Hyperbola 
D)  Ellipse 
A)  Circle 
B)  Parabola 
C)  Hyperbola 
D)  Ellipse

Question 7

Write an equation for the parabola with vertex at the origin.
-Through (4, 3), opening to the right

Accepted Answer

A)  $y ^ { 2 } = \frac { 9 } { 4 } x$ 
B)  $y ^ { 2 } = - \frac { 9 } { 4 } x$ 
C)  $x = \frac { 9 } { 4 } y ^ { 2 }$ 
D)  $x ^ { 2 } = \frac { 16 } { 3 } y$ 
A)  $y ^ { 2 } = \frac { 9 } { 4 } x$ 
B)  $y ^ { 2 } = - \frac { 9 } { 4 } x$ 
C)  $x = \frac { 9 } { 4 } y ^ { 2 }$ 
D)  $x ^ { 2 } = \frac { 16 } { 3 } y$

Question 8

Use the formula for SS1U1B1nS1U1B0 to find the sum of the first five terms of the geometric sequence.
-5, 20, 80, 320, . . .

Accepted Answer

A)  1707 
B)  1705 
C)  1701 
D)  1715 
A)  1707 
B)  1705 
C)  1701 
D)  1715

Question 9

Find the sum of all the integers from $- 38 \text { to } 39$

Accepted Answer

A)  39 
B)  38 
C)  77 
D)  0 
A)  39 
B)  38 
C)  77 
D)  0

Question 10

Write an equation for the hyperbola.
-vertices at $( - 9,7 ) , ( - 9 , - 11 ) ;$ asymptotes $y = \pm \frac { 9 } { 6 } ( x + 9 ) - 2$

Accepted Answer

A)  $\frac { ( x + 9 ) ^ { 2 } } { 81 } - \frac { ( y + 2 ) ^ { 2 } } { 81 } = 1$ 
B)  $\frac { ( x - 9 ) ^ { 2 } } { 81 } - \frac { ( y - 2 ) ^ { 2 } } { 81 } = 1$ 
C)  $\frac { ( y + 2 ) ^ { 2 } } { 81 } - \frac { ( x + 9 ) ^ { 2 } } { 36 } = 1$ 
D)  $\frac { ( y - 2 ) ^ { 2 } } { 81 } - \frac { ( x - 9 ) ^ { 2 } } { 36 } = 1$ 
A)  $\frac { ( x + 9 ) ^ { 2 } } { 81 } - \frac { ( y + 2 ) ^ { 2 } } { 81 } = 1$ 
B)  $\frac { ( x - 9 ) ^ { 2 } } { 81 } - \frac { ( y - 2 ) ^ { 2 } } { 81 } = 1$ 
C)  $\frac { ( y + 2 ) ^ { 2 } } { 81 } - \frac { ( x + 9 ) ^ { 2 } } { 36 } = 1$ 
D)  $\frac { ( y - 2 ) ^ { 2 } } { 81 } - \frac { ( x - 9 ) ^ { 2 } } { 36 } = 1$

Question 11

Graph the hyperbola.
-$$\frac { ( y + 1 ) ^ { 2 } } { 64 } - \frac { ( x + 2 ) ^ { 2 } } { 9 } = 1$$

Accepted Answer

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

Question 12

If it has been determined that the probability of an earthquake occurring on a certain day in a certain area is 0.05, what are the odds against an earthquake?

Accepted Answer

A)  19 to 1 
B)  1 to 20 
C)  18 to 1 
D)  20 to 1 
A)  19 to 1 
B)  1 to 20 
C)  18 to 1 
D)  20 to 1

Question 13

For a hyperbolic mirror the two foci are 44 cm apart. The distance of the vertex from one focus is 6 cm and from the other focus is 38 cm. Position a coordinate system with the origin at the center of the hyperbola and with the
Foci on the y-axis. Find the equation of the hyperbola.

Accepted Answer

A)  $\frac { y ^ { 2 } } { 256 } - \frac { x ^ { 2 } } { 228 } = 1$ 
B)  $\frac { y ^ { 2 } } { 256 } - \frac { x ^ { 2 } } { 228 } = 5$ 
C)  $\frac { x ^ { 2 } } { 256 } - \frac { y ^ { 2 } } { 228 } = 1$ 
D)  $\frac { x ^ { 2 } } { 256 } - \frac { y ^ { 2 } } { 228 } = 5$ 
A)  $\frac { y ^ { 2 } } { 256 } - \frac { x ^ { 2 } } { 228 } = 1$ 
B)  $\frac { y ^ { 2 } } { 256 } - \frac { x ^ { 2 } } { 228 } = 5$ 
C)  $\frac { x ^ { 2 } } { 256 } - \frac { y ^ { 2 } } { 228 } = 1$ 
D)  $\frac { x ^ { 2 } } { 256 } - \frac { y ^ { 2 } } { 228 } = 5$

Question 14

A parabola has eccentricity greater than 1.

Accepted Answer

A) True 
 B)False

Question 15

Write out the first five terms of the sequence.
-$$a _ { n } = 3 n - 1$$

Accepted Answer

A)  $4,7,10,13,16$ 
B)  $2,3,4,5,6$ 
C)  $2,5,8,11,14$ 
D)  $- 2 , - 5 , - 8 , - 11 , - 14$ 
A)  $4,7,10,13,16$ 
B)  $2,3,4,5,6$ 
C)  $2,5,8,11,14$ 
D)  $- 2 , - 5 , - 8 , - 11 , - 14$

Question 16

Provide an appropriate response.
-If an ellipse has vertices at (-6, 0), (6, 0), (0, 2), and (0, -2), what is its domain? What is its range?

Accepted Answer

A)  Domain: $[ - 6,2 ]$; Range: $[ - 2,6 ]$ 
B)  Domain: $[ - 6,6 ]$; Range: $[ - 2,2 ]$ 
C)  Domain: $[ - 2,2 ]$; Range: $[ - 6,6 ]$ 
D)  Domain: $[ 0,6 ]$; Range: $[ 0,2 ]$ 
A)  Domain: $[ - 6,2 ]$; Range: $[ - 2,6 ]$ 
B)  Domain: $[ - 6,6 ]$; Range: $[ - 2,2 ]$ 
C)  Domain: $[ - 2,2 ]$; Range: $[ - 6,6 ]$ 
D)  Domain: $[ 0,6 ]$; Range: $[ 0,2 ]$

Question 17

A railroad tunnel is shaped like a semi-ellipse. The height of the tunnel at the center is 25 ft and the vertical clearance must be 20 ft at a point 18 ft from the center. Find an equation for the ellipse.

Accepted Answer

A)  $\frac { x ^ { 2 } } { 324 } + \frac { y ^ { 2 } } { 625 } = 1$ 
B)  $\frac { x ^ { 2 } } { 900 } + \frac { y ^ { 2 } } { 625 } = 1$ 
C)  $\frac { x ^ { 2 } } { 900 } + \frac { y ^ { 2 } } { 400 } = 1$ 
D)  $\frac { x ^ { 2 } } { 625 } + \frac { y ^ { 2 } } { 900 } = 1$ 
A)  $\frac { x ^ { 2 } } { 324 } + \frac { y ^ { 2 } } { 625 } = 1$ 
B)  $\frac { x ^ { 2 } } { 900 } + \frac { y ^ { 2 } } { 625 } = 1$ 
C)  $\frac { x ^ { 2 } } { 900 } + \frac { y ^ { 2 } } { 400 } = 1$ 
D)  $\frac { x ^ { 2 } } { 625 } + \frac { y ^ { 2 } } { 900 } = 1$

Question 18

Use a calculator to evaluate the expression.
-$${ } _ { 11 } \mathrm { P } _ { 8 }$$

Accepted Answer

A)  165 
B)  6,652,800 
C)  831,600 
D)  330 
A)  165 
B)  6,652,800 
C)  831,600 
D)  330

Question 19

Evaluate the sum. Round to two decimal places, if necessary.
-$$\sum _ { k = 3 } ^ { 6 } \left( k ^ { 2 } - 3 \right)$$

Accepted Answer

A)  99 
B)  74 
C)  41 
D)  86 
A)  99 
B)  74 
C)  41 
D)  86

Question 20

Use mathematical induction to prove that the statement is true for every positive integer n.
-$$4 + 8 + 12 + \ldots + 4 n = 2 n ( n + 1 )$$

Accepted Answer

Answers will vary. One possible proof fo

Give the focus, directrix, and axis for the parabola. - $( x + 5 ) ^ { 2 } = - 20 ( y - 4 )$

What are the odds in favor of spinning a D on this spinner?

Evaluate the expression. - $\left( \begin{array} { c } 12 \\7\end{array} \right)$

Provide an appropriate response. -Explain in your own words how you can tell from the equation whether the branches of a hyperbola open up and down or left and right.

Identify the type of graph. - $x ^ { 2 } - 12 x + y = 0$

Identify the type of conic section. -Identify the type of conic section consisting of the set of all points in the plane for which the absolute value of the difference of the distances from the points (0 $( 0,6 ) \text { and } ( 0 , - 6 ) \text { is } 2$

Write an equation for the parabola with vertex at the origin. -Through (4, 3), opening to the right

Use the formula for S_n to find the sum of the first five terms of the geometric sequence. -5, 20, 80, 320, . . .

Find the sum of all the integers from $- 38 \text { to } 39$

Write an equation for the hyperbola. -vertices at $( - 9,7 ) , ( - 9 , - 11 ) ;$ asymptotes $y = \pm \frac { 9 } { 6 } ( x + 9 ) - 2$

Graph the hyperbola. - $\frac { ( y + 1 ) ^ { 2 } } { 64 } - \frac { ( x + 2 ) ^ { 2 } } { 9 } = 1$ $Graph the hyperbola. - \frac { ( y + 1 ) ^ { 2 } } { 64 } - \frac { ( x + 2 ) ^ { 2 } } { 9 } = 1$

If it has been determined that the probability of an earthquake occurring on a certain day in a certain area is 0.05, what are the odds against an earthquake?

For a hyperbolic mirror the two foci are 44 cm apart. The distance of the vertex from one focus is 6 cm and from the other focus is 38 cm. Position a coordinate system with the origin at the center of the hyperbola and with the Foci on the y-axis. Find the equation of the hyperbola.

A parabola has eccentricity greater than 1.

Write out the first five terms of the sequence. - $a _ { n } = 3 n - 1$

Provide an appropriate response. -If an ellipse has vertices at (-6, 0), (6, 0), (0, 2), and (0, -2), what is its domain? What is its range?

A railroad tunnel is shaped like a semi-ellipse. The height of the tunnel at the center is 25 ft and the vertical clearance must be 20 ft at a point 18 ft from the center. Find an equation for the ellipse.

Use a calculator to evaluate the expression. - ${ } _ { 11 } \mathrm { P } _ { 8 }$

Evaluate the sum. Round to two decimal places, if necessary. - $\sum _ { k = 3 } ^ { 6 } \left( k ^ { 2 } - 3 \right)$

Use mathematical induction to prove that the statement is true for every positive integer n. - $4 + 8 + 12 + \ldots + 4 n = 2 n ( n + 1 )$

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

Give the focus, directrix, and axis for the parabola. - (x+5)2=−20(y−4)( x + 5 ) ^ { 2 } = - 20 ( y - 4 )(x+5)2=−20(y−4)

What are the odds in favor of spinning a D on this spinner?

Evaluate the expression. - (127)\left( \begin{array} { c } 12 \\7\end{array} \right)(127​)

Provide an appropriate response. -Explain in your own words how you can tell from the equation whether the branches of a hyperbola open up and down or left and right.

Identify the type of graph. - x2−12x+y=0x ^ { 2 } - 12 x + y = 0x2−12x+y=0

Identify the type of conic section. -Identify the type of conic section consisting of the set of all points in the plane for which the absolute value of the difference of the distances from the points (0 (0,6) and (0,−6) is 2( 0,6 ) \text { and } ( 0 , - 6 ) \text { is } 2(0,6) and (0,−6) is 2

Write an equation for the parabola with vertex at the origin. -Through (4, 3), opening to the right

Use the formula for Sn to find the sum of the first five terms of the geometric sequence. -5, 20, 80, 320, . . .

Find the sum of all the integers from −38 to 39- 38 \text { to } 39−38 to 39

Write an equation for the hyperbola. -vertices at (−9,7),(−9,−11);( - 9,7 ) , ( - 9 , - 11 ) ;(−9,7),(−9,−11); asymptotes y=±96(x+9)−2y = \pm \frac { 9 } { 6 } ( x + 9 ) - 2y=±69​(x+9)−2

Graph the hyperbola. - (y+1)264−(x+2)29=1\frac { ( y + 1 ) ^ { 2 } } { 64 } - \frac { ( x + 2 ) ^ { 2 } } { 9 } = 164(y+1)2​−9(x+2)2​=1

If it has been determined that the probability of an earthquake occurring on a certain day in a certain area is 0.05, what are the odds against an earthquake?

For a hyperbolic mirror the two foci are 44 cm apart. The distance of the vertex from one focus is 6 cm and from the other focus is 38 cm. Position a coordinate system with the origin at the center of the hyperbola and with the Foci on the y-axis. Find the equation of the hyperbola.

A parabola has eccentricity greater than 1.

Write out the first five terms of the sequence. - an=3n−1a _ { n } = 3 n - 1an​=3n−1

Provide an appropriate response. -If an ellipse has vertices at (-6, 0), (6, 0), (0, 2), and (0, -2), what is its domain? What is its range?

A railroad tunnel is shaped like a semi-ellipse. The height of the tunnel at the center is 25 ft and the vertical clearance must be 20 ft at a point 18 ft from the center. Find an equation for the ellipse.

Use a calculator to evaluate the expression. - 11P8{ } _ { 11 } \mathrm { P } _ { 8 }11​P8​

Evaluate the sum. Round to two decimal places, if necessary. - ∑k=36(k2−3)\sum _ { k = 3 } ^ { 6 } \left( k ^ { 2 } - 3 \right)∑k=36​(k2−3)

Use mathematical induction to prove that the statement is true for every positive integer n. - 4+8+12+…+4n=2n(n+1)4 + 8 + 12 + \ldots + 4 n = 2 n ( n + 1 )4+8+12+…+4n=2n(n+1)

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Filters

Give the focus, directrix, and axis for the parabola. - $( x + 5 ) ^ { 2 } = - 20 ( y - 4 )$

Evaluate the expression. - $\left( \begin{array} { c } 12 \\7\end{array} \right)$

Identify the type of graph. - $x ^ { 2 } - 12 x + y = 0$

Identify the type of conic section. -Identify the type of conic section consisting of the set of all points in the plane for which the absolute value of the difference of the distances from the points (0 $( 0,6 ) \text { and } ( 0 , - 6 ) \text { is } 2$

Use the formula for S_n to find the sum of the first five terms of the geometric sequence. -5, 20, 80, 320, . . .

Find the sum of all the integers from $- 38 \text { to } 39$

Write an equation for the hyperbola. -vertices at $( - 9,7 ) , ( - 9 , - 11 ) ;$ asymptotes $y = \pm \frac { 9 } { 6 } ( x + 9 ) - 2$

Graph the hyperbola. - $\frac { ( y + 1 ) ^ { 2 } } { 64 } - \frac { ( x + 2 ) ^ { 2 } } { 9 } = 1$ $Graph the hyperbola. - \frac { ( y + 1 ) ^ { 2 } } { 64 } - \frac { ( x + 2 ) ^ { 2 } } { 9 } = 1$

Write out the first five terms of the sequence. - $a _ { n } = 3 n - 1$

Use a calculator to evaluate the expression. - ${ } _ { 11 } \mathrm { P } _ { 8 }$

Evaluate the sum. Round to two decimal places, if necessary. - $\sum _ { k = 3 } ^ { 6 } \left( k ^ { 2 } - 3 \right)$

Use mathematical induction to prove that the statement is true for every positive integer n. - $4 + 8 + 12 + \ldots + 4 n = 2 n ( n + 1 )$