Question 1

Use mathematical induction to prove that the statement is true for every positive integer n.
-$$0.06 ^ { n } < 1$$

Accepted Answer

Answers will vary. One possible proof fo

Question 2

Decide whether the given sequence is finite or infinite.
-$$a _ { 1 } = 2 ; \text { for } 2 \leq n \leq 20 , a _ { n } = 2 \cdot a _ { n - 1 } + 3$$

Accepted Answer

A)  Finite 
B)  Infinite 
A)  Finite 
B)  Infinite

Question 3

Choose the equation that matches the graph.
-

Accepted Answer

A)  $\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 16 } = 1$ 
B)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 16 } = 1$ 
C)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 36 } = 1$ 
D)  $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 36 } = 1$ 
A)  $\frac { x ^ { 2 } } { 36 } - \frac { y ^ { 2 } } { 16 } = 1$ 
B)  $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 16 } = 1$ 
C)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 36 } = 1$ 
D)  $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 36 } = 1$

Question 4

Use a graphing calculator to evaluate the sum. Round to the nearest thousandth.
-$$\sum _ { i = 2 } ^ { 9 } 4 ( 1.45 ) \mathrm { i }$$

Accepted Answer

A)  233.171 
B)  338.098 
C)  86.627 
D)  346.508 
A)  233.171 
B)  338.098 
C)  86.627 
D)  346.508

Question 5

Write an equation for the parabola.
-vertex $( 3 , - 4 )$, focus $( 3,1 )$

Accepted Answer

A)  $20 ( y + 4 ) = ( x - 3 ) ^ { 2 }$ 
B)  $y + 4 = 20 ( x + 3 ) ^ { 2 }$ 
C)  $20 ( y - 4 ) = ( x + 3 ) ^ { 2 }$ 
D)  $x + 3 = 20 ( y + 4 ) ^ { 2 }$ 
A)  $20 ( y + 4 ) = ( x - 3 ) ^ { 2 }$ 
B)  $y + 4 = 20 ( x + 3 ) ^ { 2 }$ 
C)  $20 ( y - 4 ) = ( x + 3 ) ^ { 2 }$ 
D)  $x + 3 = 20 ( y + 4 ) ^ { 2 }$

Question 6

Write an equation for the parabola.
-vertex $( 5 , - 6 )$, focus $( 5,0 )$

Accepted Answer

A)  $y - 6 = 24 ( x + 5 ) ^ { 2 }$ 
B)  $24 ( y - 6 ) = ( x + 5 ) ^ { 2 }$ 
C)  $( x - 5 ) ^ { 2 } = 24 ( y + 6 )$ 
D)  $( y + 6 ) ^ { 2 } = 24 ( x - 5 )$ 
A)  $y - 6 = 24 ( x + 5 ) ^ { 2 }$ 
B)  $24 ( y - 6 ) = ( x + 5 ) ^ { 2 }$ 
C)  $( x - 5 ) ^ { 2 } = 24 ( y + 6 )$ 
D)  $( y + 6 ) ^ { 2 } = 24 ( x - 5 )$

Question 7

An ordinary die is tossed. What are the odds in favor of the die showing a number less than 3?

Accepted Answer

A)  1 to 3 
B)  1 to 1 
C)  2 to 1 
D)  1 to 2 
A)  1 to 3 
B)  1 to 1 
C)  2 to 1 
D)  1 to 2

Question 8

Find the center, foci, and asymptotes of the hyperbola.
-$\frac { ( y - 1 ) ^ { 2 } } { 16 } - \frac { ( x - 1 ) ^ { 2 } } { 9 } = 1$

Accepted Answer

A)  C: $( 1,1 ) ; \mathrm { F } : ( - 2,1 ) , ( 4,1 ) ; \mathrm { A } : \mathrm { y } = \frac { 16 } { 9 } \mathrm { x } - \frac { 7 } { 9 } , \mathrm { y } = - \frac { 16 } { 9 } \mathrm { x } - \frac { 7 } { 9 }$ 
B)  C: $( 1,1 ) ; F : ( 1 , - 4 ) , ( 1,6 ) ; A : y = \frac { 4 } { 3 } x + \frac { 1 } { 3 } , y = - \frac { 4 } { 3 } x - \frac { 7 } { 3 }$ 
C)  $\mathrm { C } : ( 1,1 ) ; \mathrm { F } : ( 1 , - 2 ) , ( 1,4 ) ; \mathrm { A } : \mathrm { y } = \frac { 16 } { 9 } \mathrm { x } + \frac { 1 } { 9 } , \mathrm { y } = - \frac { 16 } { 9 } \mathrm { x } - \frac { 7 } { 9 }$ 
D)  C: $( 1,1 ) ; F : ( 1,6 ) , ( 1 , - 4 ) ; \mathrm { A } : \mathrm { y } = \frac { 4 } { 3 } \mathrm { x } - \frac { 1 } { 3 } , \mathrm { y } = - \frac { 4 } { 3 } \mathrm { x } + \frac { 7 } { 3 }$ 
A)  C: $( 1,1 ) ; \mathrm { F } : ( - 2,1 ) , ( 4,1 ) ; \mathrm { A } : \mathrm { y } = \frac { 16 } { 9 } \mathrm { x } - \frac { 7 } { 9 } , \mathrm { y } = - \frac { 16 } { 9 } \mathrm { x } - \frac { 7 } { 9 }$ 
B)  C: $( 1,1 ) ; F : ( 1 , - 4 ) , ( 1,6 ) ; A : y = \frac { 4 } { 3 } x + \frac { 1 } { 3 } , y = - \frac { 4 } { 3 } x - \frac { 7 } { 3 }$ 
C)  $\mathrm { C } : ( 1,1 ) ; \mathrm { F } : ( 1 , - 2 ) , ( 1,4 ) ; \mathrm { A } : \mathrm { y } = \frac { 16 } { 9 } \mathrm { x } + \frac { 1 } { 9 } , \mathrm { y } = - \frac { 16 } { 9 } \mathrm { x } - \frac { 7 } { 9 }$ 
D)  C: $( 1,1 ) ; F : ( 1,6 ) , ( 1 , - 4 ) ; \mathrm { A } : \mathrm { y } = \frac { 4 } { 3 } \mathrm { x } - \frac { 1 } { 3 } , \mathrm { y } = - \frac { 4 } { 3 } \mathrm { x } + \frac { 7 } { 3 }$

Question 9

Match the equation of the ellipse with the appropriate description.
-$$4 x ^ { 2 } + 25 y ^ { 2 } = 2500$$

Accepted Answer

A)  $x$-intercepts $( 25,0 ) , ( - 25,0 ) ; y$-intercepts $( 0,10 ) , ( 0 , - 10 )$ 
B)  $x$-intercepts $( 100,0 ) , ( - 100,0 )$; $y$-intercepts $( 0,625 ) , ( 0 , - 625 )$ 
C)  x-intercepts $( 625,0 ) , ( - 625,0 ) ; y$-intercepts $( 0,100 ) , ( 0 , - 100 )$ 
D)  $x$-intercepts $( 10,0 ) , ( - 10,0 )$; y-intercepts $( 0,25 ) , ( 0 , - 25 )$ 
A)  $x$-intercepts $( 25,0 ) , ( - 25,0 ) ; y$-intercepts $( 0,10 ) , ( 0 , - 10 )$ 
B)  $x$-intercepts $( 100,0 ) , ( - 100,0 )$; $y$-intercepts $( 0,625 ) , ( 0 , - 625 )$ 
C)  x-intercepts $( 625,0 ) , ( - 625,0 ) ; y$-intercepts $( 0,100 ) , ( 0 , - 100 )$ 
D)  $x$-intercepts $( 10,0 ) , ( - 10,0 )$; y-intercepts $( 0,25 ) , ( 0 , - 25 )$

Question 10

Use the summation properties to evaluate the series. The following rules may be needed: $$\sum _ { i = 1 } ^ { n } i = \frac { n ( n + 1 ) } { 2 } ; \quad \sum _ { i = 1 } ^ { n } i ^ { 2 } = \frac { n ( n + 1 ) ( 2 n + 1 ) } { 6 } ; \quad \sum _ { i = 1 } ^ { n } i ^ { 3 } = \frac { n ^ { 2 } ( n + 1 ) ^ { 2 } } { 4 }$$
-$$\sum _ { i = 1 } ^ { 5 } ( - 3 i - 4 )$$

Accepted Answer

A)  $- 33$ 
B)  $- 85$ 
C)  $- 45$ 
D)  $- 65$ 
A)  $- 33$ 
B)  $- 85$ 
C)  $- 45$ 
D)  $- 65$

Question 11

Find the first six terms of the sequence.
-$$a _ { 1 } = - 3 , a _ { n } = 4 \cdot a _ { n - 1 }$$

Accepted Answer

A)  $- 3 , - 12 , - 48 , - 192 , - 768 , - 3072$ 
B)  $0,4 , - 12 , - 8 , - 4,0$ 
C)  $- 3 , - 12 , - 8 , - 4,0,4$ 
D)  $- 12 , - 48 , - 192 , - 768 , - 3072 , - 12,288$ 
A)  $- 3 , - 12 , - 48 , - 192 , - 768 , - 3072$ 
B)  $0,4 , - 12 , - 8 , - 4,0$ 
C)  $- 3 , - 12 , - 8 , - 4,0,4$ 
D)  $- 12 , - 48 , - 192 , - 768 , - 3072 , - 12,288$

Question 12

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator.
-$$\mathrm { x } = 2 \mathrm { y } ^ { 2 } - 7 \mathrm { y } + 3$$

Accepted Answer

A)  $y = \frac { 7 - \sqrt { 8 x - - 25 } } { 2 }$ and $y = - \frac { 7 + \sqrt { 8 x - - 25 } } { 2 }$ 
B)  $y = \frac { 7 - \sqrt { 8 x - - 25 } } { 4 }$ and $y = \frac { 7 + \sqrt { 8 x - - 25 } } { 4 }$ 
C)  $y = \sqrt { \frac { x - 3 } { - 7 } }$ and $y = - \sqrt { \frac { x - 3 } { - 7 } }$ 
D)  $y = \frac { \sqrt { x - 3 } } { - 7 }$ and $y = - \frac { \sqrt { x - 3 } } { - 7 }$ 
A)  $y = \frac { 7 - \sqrt { 8 x - - 25 } } { 2 }$ and $y = - \frac { 7 + \sqrt { 8 x - - 25 } } { 2 }$ 
B)  $y = \frac { 7 - \sqrt { 8 x - - 25 } } { 4 }$ and $y = \frac { 7 + \sqrt { 8 x - - 25 } } { 4 }$ 
C)  $y = \sqrt { \frac { x - 3 } { - 7 } }$ and $y = - \sqrt { \frac { x - 3 } { - 7 } }$ 
D)  $y = \frac { \sqrt { x - 3 } } { - 7 }$ and $y = - \frac { \sqrt { x - 3 } } { - 7 }$

Question 13

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

Accepted Answer

A)  623 
B)  $- 3108$ 
C)  $- 259$ 
D)  $- 1036$ 
A)  623 
B)  $- 3108$ 
C)  $- 259$ 
D)  $- 1036$

Question 14

Provide an appropriate response.
-Explain why the vertex of a parabola must lie on its axis.

Accepted Answer

Explanations will vary. One possibility:

Question 15

Graph the parabola.
-$$x = y ^ { 2 } - 4$$

Accepted Answer

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

Question 16

Identify the equation as a parabola, circle, ellipse, or hyperbola.
-$$( x - 7 ) ^ { 2 } = 9 - y ^ { 2 }$$

Accepted Answer

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

Question 17

Graph the parabola.
-$x=y^{2}-3 y+2$

Accepted Answer

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

Question 18

Write an equation for the hyperbola.
-center at $( 6 , - 8 ) ;$ focus at $( 6 - \sqrt { 58 } , - 8 ) ; e = \frac { \sqrt { 58 } } { 7 }$

Accepted Answer

A)  $\frac { ( x + 6 ) ^ { 2 } } { 49 } - \frac { ( y - 8 ) ^ { 2 } } { 9 } = 1$ 
B)  $\frac { ( x + 6 ) ^ { 2 } } { 9 } - \frac { ( y - 8 ) ^ { 2 } } { 49 } = 1$ 
C)  $\frac { ( x - 6 ) ^ { 2 } } { 9 } - \frac { ( y + 8 ) ^ { 2 } } { 49 } = 1$ 
D)  $\frac { ( x - 6 ) ^ { 2 } } { 49 } - \frac { ( y + 8 ) ^ { 2 } } { 9 } = 1$ 
A)  $\frac { ( x + 6 ) ^ { 2 } } { 49 } - \frac { ( y - 8 ) ^ { 2 } } { 9 } = 1$ 
B)  $\frac { ( x + 6 ) ^ { 2 } } { 9 } - \frac { ( y - 8 ) ^ { 2 } } { 49 } = 1$ 
C)  $\frac { ( x - 6 ) ^ { 2 } } { 9 } - \frac { ( y + 8 ) ^ { 2 } } { 49 } = 1$ 
D)  $\frac { ( x - 6 ) ^ { 2 } } { 49 } - \frac { ( y + 8 ) ^ { 2 } } { 9 } = 1$

Question 19

Evaluate the series, if it converges.
-$$4 + 5 + \frac { 25 } { 4 } + \frac { 125 } { 16 } + \ldots$$

Accepted Answer

A)  $- 20$ 
B)  Does not converge 
C)  20 
D)  16 
A)  $- 20$ 
B)  Does not converge 
C)  20 
D)  16

Question 20

What are the odds in favor of spinning an A on this spinner?

Accepted Answer

A)  4 to 2 
B)  2 to 6 
C)  6 to 2 
D)  3 to 5 
A)  4 to 2 
B)  2 to 6 
C)  6 to 2 
D)  3 to 5

Use mathematical induction to prove that the statement is true for every positive integer n. - $0.06 ^ { n } < 1$

Decide whether the given sequence is finite or infinite. - $a _ { 1 } = 2 ; \text { for } 2 \leq n \leq 20 , a _ { n } = 2 \cdot a _ { n - 1 } + 3$

Choose the equation that matches the graph. -

Use a graphing calculator to evaluate the sum. Round to the nearest thousandth. - $\sum _ { i = 2 } ^ { 9 } 4 ( 1.45 ) \mathrm { i }$

Write an equation for the parabola. -vertex $( 3 , - 4 )$ , focus $( 3,1 )$

Write an equation for the parabola. -vertex $( 5 , - 6 )$ , focus $( 5,0 )$

An ordinary die is tossed. What are the odds in favor of the die showing a number less than 3?

Find the center, foci, and asymptotes of the hyperbola. - $\frac { ( y - 1 ) ^ { 2 } } { 16 } - \frac { ( x - 1 ) ^ { 2 } } { 9 } = 1$

Match the equation of the ellipse with the appropriate description. - $4 x ^ { 2 } + 25 y ^ { 2 } = 2500$

Find the first six terms of the sequence. - $a _ { 1 } = - 3 , a _ { n } = 4 \cdot a _ { n - 1 }$

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator. - $\mathrm { x } = 2 \mathrm { y } ^ { 2 } - 7 \mathrm { y } + 3$

Provide an appropriate response. -Explain why the vertex of a parabola must lie on its axis.

Graph the parabola. - $x = y ^ { 2 } - 4$ $Graph the parabola. - x = y ^ { 2 } - 4$

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $( x - 7 ) ^ { 2 } = 9 - y ^ { 2 }$

Graph the parabola. - $x=y^{2}-3 y+2$ $Graph the parabola. - x=y^{2}-3 y+2$

Write an equation for the hyperbola. -center at $( 6 , - 8 ) ;$ focus at $( 6 - \sqrt { 58 } , - 8 ) ; e = \frac { \sqrt { 58 } } { 7 }$

Evaluate the series, if it converges. - $4 + 5 + \frac { 25 } { 4 } + \frac { 125 } { 16 } + \ldots$

What are the odds in favor of spinning an A on this spinner?

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

Use mathematical induction to prove that the statement is true for every positive integer n. - 0.06n<10.06 ^ { n } < 10.06n<1

Decide whether the given sequence is finite or infinite. - a1=2; for 2≤n≤20,an=2⋅an−1+3a _ { 1 } = 2 ; \text { for } 2 \leq n \leq 20 , a _ { n } = 2 \cdot a _ { n - 1 } + 3a1​=2; for 2≤n≤20,an​=2⋅an−1​+3

Choose the equation that matches the graph. -

Use a graphing calculator to evaluate the sum. Round to the nearest thousandth. - ∑i=294(1.45)i\sum _ { i = 2 } ^ { 9 } 4 ( 1.45 ) \mathrm { i }∑i=29​4(1.45)i

Write an equation for the parabola. -vertex (3,−4)( 3 , - 4 )(3,−4) , focus (3,1)( 3,1 )(3,1)

Write an equation for the parabola. -vertex (5,−6)( 5 , - 6 )(5,−6) , focus (5,0)( 5,0 )(5,0)

An ordinary die is tossed. What are the odds in favor of the die showing a number less than 3?

Find the center, foci, and asymptotes of the hyperbola. - (y−1)216−(x−1)29=1\frac { ( y - 1 ) ^ { 2 } } { 16 } - \frac { ( x - 1 ) ^ { 2 } } { 9 } = 116(y−1)2​−9(x−1)2​=1

Match the equation of the ellipse with the appropriate description. - 4x2+25y2=25004 x ^ { 2 } + 25 y ^ { 2 } = 25004x2+25y2=2500

Find the first six terms of the sequence. - a1=−3,an=4⋅an−1a _ { 1 } = - 3 , a _ { n } = 4 \cdot a _ { n - 1 }a1​=−3,an​=4⋅an−1​

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator. - x=2y2−7y+3\mathrm { x } = 2 \mathrm { y } ^ { 2 } - 7 \mathrm { y } + 3x=2y2−7y+3

Provide an appropriate response. -Explain why the vertex of a parabola must lie on its axis.

Graph the parabola. - x=y2−4x = y ^ { 2 } - 4x=y2−4

Identify the equation as a parabola, circle, ellipse, or hyperbola. - (x−7)2=9−y2( x - 7 ) ^ { 2 } = 9 - y ^ { 2 }(x−7)2=9−y2

Graph the parabola. - x=y2−3y+2x=y^{2}-3 y+2x=y2−3y+2

Write an equation for the hyperbola. -center at (6,−8);( 6 , - 8 ) ;(6,−8); focus at (6−58,−8);e=587( 6 - \sqrt { 58 } , - 8 ) ; e = \frac { \sqrt { 58 } } { 7 }(6−58​,−8);e=758​​

Evaluate the series, if it converges. - 4+5+254+12516+…4 + 5 + \frac { 25 } { 4 } + \frac { 125 } { 16 } + \ldots4+5+425​+16125​+…

What are the odds in favor of spinning an A on this spinner?

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Filters

Use mathematical induction to prove that the statement is true for every positive integer n. - $0.06 ^ { n } < 1$

Decide whether the given sequence is finite or infinite. - $a _ { 1 } = 2 ; \text { for } 2 \leq n \leq 20 , a _ { n } = 2 \cdot a _ { n - 1 } + 3$

Use a graphing calculator to evaluate the sum. Round to the nearest thousandth. - $\sum _ { i = 2 } ^ { 9 } 4 ( 1.45 ) \mathrm { i }$

Write an equation for the parabola. -vertex $( 3 , - 4 )$ , focus $( 3,1 )$

Write an equation for the parabola. -vertex $( 5 , - 6 )$ , focus $( 5,0 )$

Find the center, foci, and asymptotes of the hyperbola. - $\frac { ( y - 1 ) ^ { 2 } } { 16 } - \frac { ( x - 1 ) ^ { 2 } } { 9 } = 1$

Match the equation of the ellipse with the appropriate description. - $4 x ^ { 2 } + 25 y ^ { 2 } = 2500$

Find the first six terms of the sequence. - $a _ { 1 } = - 3 , a _ { n } = 4 \cdot a _ { n - 1 }$

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator. - $\mathrm { x } = 2 \mathrm { y } ^ { 2 } - 7 \mathrm { y } + 3$

Graph the parabola. - $x = y ^ { 2 } - 4$ $Graph the parabola. - x = y ^ { 2 } - 4$

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $( x - 7 ) ^ { 2 } = 9 - y ^ { 2 }$

Graph the parabola. - $x=y^{2}-3 y+2$ $Graph the parabola. - x=y^{2}-3 y+2$

Write an equation for the hyperbola. -center at $( 6 , - 8 ) ;$ focus at $( 6 - \sqrt { 58 } , - 8 ) ; e = \frac { \sqrt { 58 } } { 7 }$

Evaluate the series, if it converges. - $4 + 5 + \frac { 25 } { 4 } + \frac { 125 } { 16 } + \ldots$