Question 1

An ellipse has eccentricity between 0 and 1.

Accepted Answer

A) True 
 B)False

Question 2

Identify the type of graph.
-$$- 5 x ^ { 2 } + 30 x + 5 y ^ { 2 } - 70 y - 45 = - 245$$

Accepted Answer

A)  The graph is a hyperbola opening upward and downward. 
B)  The equation has no graph. 
C)  The graph is a circle with center (3, 7). 
D)  The graph is the point (3, 7). 
A)  The graph is a hyperbola opening upward and downward. 
B)  The equation has no graph. 
C)  The graph is a circle with center (3, 7). 
D)  The graph is the point (3, 7).

Question 3

Provide an appropriate response.
-Consider the arrangements of the letters in the word ALGEBRA. Is this a combination, a permutation, or neither?

Accepted Answer

A)  Neither 
B)  Combination 
C)  Permutation 
A)  Neither 
B)  Combination 
C)  Permutation

Question 4

Write out the first five terms of the sequence.
-$$a _ { n } = \frac { 2 } { n ^ { 2 } }$$

Accepted Answer

A)  $1 , \frac { 2 } { 4 } , \frac { 3 } { 9 } , \frac { 4 } { 16 } , \frac { 5 } { 25 }$ 
B)  $1 , \frac { 1 } { 2 } , \frac { 1 } { 3 } , \frac { 1 } { 4 } , \frac { 1 } { 5 }$ 
C)  $2 , \frac { 1 } { 2 } , \frac { 2 } { 9 } , \frac { 1 } { 8 } , \frac { 2 } { 25 }$ 
D)  $\frac { 1 } { 4 } , \frac { 2 } { 9 } , \frac { 3 } { 16 } , \frac { 4 } { 25 } , \frac { 5 } { 36 }$ 
A)  $1 , \frac { 2 } { 4 } , \frac { 3 } { 9 } , \frac { 4 } { 16 } , \frac { 5 } { 25 }$ 
B)  $1 , \frac { 1 } { 2 } , \frac { 1 } { 3 } , \frac { 1 } { 4 } , \frac { 1 } { 5 }$ 
C)  $2 , \frac { 1 } { 2 } , \frac { 2 } { 9 } , \frac { 1 } { 8 } , \frac { 2 } { 25 }$ 
D)  $\frac { 1 } { 4 } , \frac { 2 } { 9 } , \frac { 3 } { 16 } , \frac { 4 } { 25 } , \frac { 5 } { 36 }$

Question 5

Find the probability.
-Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice will be greater than 10?

Accepted Answer

A)  $\frac { 1 } { 12 }$ 
B)  $\frac { 5 } { 18 }$ 
C)  3 
D)  $\frac { 1 } { 18 }$ 
A)  $\frac { 1 } { 12 }$ 
B)  $\frac { 5 } { 18 }$ 
C)  3 
D)  $\frac { 1 } { 18 }$

Question 6

Decide whether the given sequence is finite or infinite.
-10, 11, 12, 13

Accepted Answer

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

Question 7

Provide an appropriate response.
-Consider the selection of a nominating committee for a club. Is this a combination, a permutation, or neither?

Accepted Answer

A)  Combination 
B)  Neither 
C)  Permutation 
A)  Combination 
B)  Neither 
C)  Permutation

Question 8

Evaluate the expression.
-$$\frac { 10 ! } { 5 ! 5 ! }$$

Accepted Answer

A)  504 
B)  126 
C)  30,240 
D)  252 
A)  504 
B)  126 
C)  30,240 
D)  252

Question 9

How many different three-digit numbers can be written using digits from the set {5, 6, 7, 8, 9} without any repeating digits?

Accepted Answer

A)  20 
B)  60 
C)  10 
D)  120 
A)  20 
B)  60 
C)  10 
D)  120

Question 10

A man borrowed $2000 at 0.5% interest compounded annually. If he paid off the loan in full at the end of 6 years, how much did he pay?

Accepted Answer

A)  $2060.76 
B)  $2060.00 
C)  $2010.00 
D)  $60.76 
A)  $2060.76 
B)  $2060.00 
C)  $2010.00 
D)  $60.76

Question 11

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

Accepted Answer

A)  $\mathrm { C } : ( 0,0 ) ; \mathrm { F } : ( 4,0 ) , ( - 4,0 ) ; \mathrm { A } : \mathrm { y } = \frac { 1 } { 4 } \mathrm { x } , \mathrm { y } = - \frac { 1 } { 4 } \mathrm { x }$ 
B)  C: $( 0,0 ) ; \mathrm { F } : ( \sqrt { 17 } , 0 ) , ( - \sqrt { 17 } , 0 ) ; \mathrm { A } : \mathrm { y } = 4 \mathrm { x } , \mathrm { y } = - 4 \mathrm { x }$ 
C)  C: $( 0,0 ) ; \mathrm { F } : ( \sqrt { 17 } , 0 ) , ( - \sqrt { 17 } , 0 ) ; \mathrm { A } : \mathrm { y } = \frac { 1 } { 5 } \mathrm { x } , \mathrm { y } = - \frac { 1 } { 5 } \mathrm { x }$ 
D)  C: $( 4,0 ) ; F : ( \sqrt { 17 } , 0 ) , ( - \sqrt { 17 } , 0 ) ; A : y = \frac { 1 } { 4 } x , y = - \frac { 1 } { 4 } x$ 
A)  $\mathrm { C } : ( 0,0 ) ; \mathrm { F } : ( 4,0 ) , ( - 4,0 ) ; \mathrm { A } : \mathrm { y } = \frac { 1 } { 4 } \mathrm { x } , \mathrm { y } = - \frac { 1 } { 4 } \mathrm { x }$ 
B)  C: $( 0,0 ) ; \mathrm { F } : ( \sqrt { 17 } , 0 ) , ( - \sqrt { 17 } , 0 ) ; \mathrm { A } : \mathrm { y } = 4 \mathrm { x } , \mathrm { y } = - 4 \mathrm { x }$ 
C)  C: $( 0,0 ) ; \mathrm { F } : ( \sqrt { 17 } , 0 ) , ( - \sqrt { 17 } , 0 ) ; \mathrm { A } : \mathrm { y } = \frac { 1 } { 5 } \mathrm { x } , \mathrm { y } = - \frac { 1 } { 5 } \mathrm { x }$ 
D)  C: $( 4,0 ) ; F : ( \sqrt { 17 } , 0 ) , ( - \sqrt { 17 } , 0 ) ; A : y = \frac { 1 } { 4 } x , y = - \frac { 1 } { 4 } x$

Question 12

Find a general term aS1U1B1nS1U1B0 for the geometric sequence.
-$\frac { 1 } { 2 } , 2,8 , \ldots$

Accepted Answer

A)  $a _ { n } = \frac { 1 } { 2 } + \frac { 3 } { 2 } ( n - 1 )$ 
B)  $a _ { n } = \frac { 1 } { 2 } + 4 ( n - 1 )$ 
C)  $a _ { n } = \left( \frac { 1 } { 2 } \right) ^ { n - 1 } + \frac { 3 } { 2 }$ 
D)  $a _ { n } = \frac { 1 } { 2 } ( 4 ) ^ { n - 1 }$ 
A)  $a _ { n } = \frac { 1 } { 2 } + \frac { 3 } { 2 } ( n - 1 )$ 
B)  $a _ { n } = \frac { 1 } { 2 } + 4 ( n - 1 )$ 
C)  $a _ { n } = \left( \frac { 1 } { 2 } \right) ^ { n - 1 } + \frac { 3 } { 2 }$ 
D)  $a _ { n } = \frac { 1 } { 2 } ( 4 ) ^ { n - 1 }$

Question 13

A hyperbola has eccentricity 1.

Accepted Answer

A) True 
 B)False

Question 14

Evaluate the series, if it converges.
-$$\sum _ { i = 1 } ^ { \infty } 40 \left( - \frac { 7 } { 10 } \right) ^ { i - 1 }$$

Accepted Answer

A)  $\frac { 400 } { 17 }$ 
B)  Does not converge. 
C)  $\frac { 10 } { 17 }$ 
D)  $- \frac { 280 } { 17 }$ 
A)  $\frac { 400 } { 17 }$ 
B)  Does not converge. 
C)  $\frac { 10 } { 17 }$ 
D)  $- \frac { 280 } { 17 }$

Question 15

Match the equation of the ellipse with the appropriate description.
-$\frac { 64 x ^ { 2 } } { 25 } + 4 y ^ { 2 } = 6400$

Accepted Answer

A)  x-intercepts $( 40,0 ) , ( - 40,0 ) ;$ y-intercepts $( 0,50 ) , ( 0 , - 50 )$ 
B)  $x$-intercepts $( 16,0 ) , ( - 16,0 ) ; y$-intercepts $( 0,80 ) , ( 0 , - 80 )$ 
C)  $x$-intercepts $( 2500,0 ) , ( - 2500,0 )$; $y$-intercepts $( 0,89 ) , ( 0 , - 89 )$ 
D)  $x$-intercepts $( 50,0 ) , ( - 50,0 )$; y-intercepts $( 0,40 ) , ( 0 , - 40 )$ 
A)  x-intercepts $( 40,0 ) , ( - 40,0 ) ;$ y-intercepts $( 0,50 ) , ( 0 , - 50 )$ 
B)  $x$-intercepts $( 16,0 ) , ( - 16,0 ) ; y$-intercepts $( 0,80 ) , ( 0 , - 80 )$ 
C)  $x$-intercepts $( 2500,0 ) , ( - 2500,0 )$; $y$-intercepts $( 0,89 ) , ( 0 , - 89 )$ 
D)  $x$-intercepts $( 50,0 ) , ( - 50,0 )$; y-intercepts $( 0,40 ) , ( 0 , - 40 )$

Question 16

Give the focus, directrix, and axis for the parabola.
-$$\mathrm { y } ^ { 2 } = 4 \mathrm { x }$$

Accepted Answer

A)  $( 1,0 ) , x = - 1 , x$-axis 
B)  $( 1,0 ) , x = - 1 , y$-axis 
C)  $( 0,1 ) , y = - 1 , y$-axis 
D)  $( 1,1 ) , x = 1 , x$-axis 
A)  $( 1,0 ) , x = - 1 , x$-axis 
B)  $( 1,0 ) , x = - 1 , y$-axis 
C)  $( 0,1 ) , y = - 1 , y$-axis 
D)  $( 1,1 ) , x = 1 , x$-axis

Question 17

Find a general term aS1U1B1nS1U1B0 for the geometric sequence.
-$$a _ { 1 } = \frac { 1 } { 7 } , r = 6$$

Accepted Answer

A)  $a _ { n } = \frac { 1 } { 7 } \cdot 6 ^ { n - 1 }$ 
B)  $a _ { n } = \frac { 1 } { 7 } - \frac { 5 } { 42 } ( n - 1 )$ 
C)  $a _ { n } = \left( \frac { 1 } { 7 } \right) ^ { n - 1 } - \frac { 5 } { 42 }$ 
D)  $a _ { n } = \frac { 1 } { 7 } + \frac { 1 } { 6 } ( n - 1 )$ 
A)  $a _ { n } = \frac { 1 } { 7 } \cdot 6 ^ { n - 1 }$ 
B)  $a _ { n } = \frac { 1 } { 7 } - \frac { 5 } { 42 } ( n - 1 )$ 
C)  $a _ { n } = \left( \frac { 1 } { 7 } \right) ^ { n - 1 } - \frac { 5 } { 42 }$ 
D)  $a _ { n } = \frac { 1 } { 7 } + \frac { 1 } { 6 } ( n - 1 )$

Question 18

Evaluate the series, if it converges.
-$$10 + 4 + \frac { 8 } { 5 } + \frac { 16 } { 25 } + \ldots$$

Accepted Answer

A)  $\frac { 5 } { 3 }$ 
B)  $\frac { 50 } { 3 }$ 
C)  Does not converge 
D)  $\frac { 20 } { 3 }$ 
A)  $\frac { 5 } { 3 }$ 
B)  $\frac { 50 } { 3 }$ 
C)  Does not converge 
D)  $\frac { 20 } { 3 }$

Question 19

Provide an appropriate response.
-Convert the decimal .2949494. . . to a fraction by writing it as the infinite series $$\frac { 2 } { 10 } + \frac { 94 } { 10 \cdot 100 } + \frac { 94 } { 10 \cdot 100 ^ { 2 } } + \frac { 94 } { 10 \cdot 100 ^ { 3 } } + \ldots$$

Accepted Answer

A)  0.29494949 
B)  0.29170829 
C)  0.29229229 
D)  0.292 
A)  0.29494949 
B)  0.29170829 
C)  0.29229229 
D)  0.292

Question 20

Graph the parabola.
-$$x = \frac { 2 } { 3 } ( y + 5 ) ^ { 2 } - 2$$

Accepted Answer

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

An ellipse has eccentricity between 0 and 1.

Identify the type of graph. - $- 5 x ^ { 2 } + 30 x + 5 y ^ { 2 } - 70 y - 45 = - 245$

Provide an appropriate response. -Consider the arrangements of the letters in the word ALGEBRA. Is this a combination, a permutation, or neither?

Write out the first five terms of the sequence. - $a _ { n } = \frac { 2 } { n ^ { 2 } }$

Find the probability. -Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice will be greater than 10?

Decide whether the given sequence is finite or infinite. -10, 11, 12, 13

Provide an appropriate response. -Consider the selection of a nominating committee for a club. Is this a combination, a permutation, or neither?

Evaluate the expression. - $\frac { 10 ! } { 5 ! 5 ! }$

How many different three-digit numbers can be written using digits from the set {5, 6, 7, 8, 9} without any repeating digits?

A man borrowed $2000 at 0.5% interest compounded annually. If he paid off the loan in full at the end of 6 years, how much did he pay?

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

Find a general term a_n for the geometric sequence. - $\frac { 1 } { 2 } , 2,8 , \ldots$

A hyperbola has eccentricity 1.

Evaluate the series, if it converges. - $\sum _ { i = 1 } ^ { \infty } 40 \left( - \frac { 7 } { 10 } \right) ^ { i - 1 }$

Match the equation of the ellipse with the appropriate description. - $\frac { 64 x ^ { 2 } } { 25 } + 4 y ^ { 2 } = 6400$

Give the focus, directrix, and axis for the parabola. - $\mathrm { y } ^ { 2 } = 4 \mathrm { x }$

Find a general term a_n for the geometric sequence. - $a _ { 1 } = \frac { 1 } { 7 } , r = 6$

Evaluate the series, if it converges. - $10 + 4 + \frac { 8 } { 5 } + \frac { 16 } { 25 } + \ldots$

Provide an appropriate response. -Convert the decimal .2949494. . . to a fraction by writing it as the infinite series $\frac { 2 } { 10 } + \frac { 94 } { 10 \cdot 100 } + \frac { 94 } { 10 \cdot 100 ^ { 2 } } + \frac { 94 } { 10 \cdot 100 ^ { 3 } } + \ldots$

Graph the parabola. - $x = \frac { 2 } { 3 } ( y + 5 ) ^ { 2 } - 2$ $Graph the parabola. - x = \frac { 2 } { 3 } ( y + 5 ) ^ { 2 } - 2$

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

An ellipse has eccentricity between 0 and 1.

Identify the type of graph. - −5x2+30x+5y2−70y−45=−245- 5 x ^ { 2 } + 30 x + 5 y ^ { 2 } - 70 y - 45 = - 245−5x2+30x+5y2−70y−45=−245

Provide an appropriate response. -Consider the arrangements of the letters in the word ALGEBRA. Is this a combination, a permutation, or neither?

Write out the first five terms of the sequence. - an=2n2a _ { n } = \frac { 2 } { n ^ { 2 } }an​=n22​

Find the probability. -Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice will be greater than 10?

Decide whether the given sequence is finite or infinite. -10, 11, 12, 13

Provide an appropriate response. -Consider the selection of a nominating committee for a club. Is this a combination, a permutation, or neither?

Evaluate the expression. - 10!5!5!\frac { 10 ! } { 5 ! 5 ! }5!5!10!​

How many different three-digit numbers can be written using digits from the set {5, 6, 7, 8, 9} without any repeating digits?

A man borrowed $2000 at 0.5% interest compounded annually. If he paid off the loan in full at the end of 6 years, how much did he pay?

Find the center, foci, and asymptotes of the hyperbola. - x2−y216=1x ^ { 2 } - \frac { y ^ { 2 } } { 16 } = 1x2−16y2​=1

Find a general term an for the geometric sequence. - 12,2,8,…\frac { 1 } { 2 } , 2,8 , \ldots21​,2,8,…

A hyperbola has eccentricity 1.

Evaluate the series, if it converges. - ∑i=1∞40(−710)i−1\sum _ { i = 1 } ^ { \infty } 40 \left( - \frac { 7 } { 10 } \right) ^ { i - 1 }∑i=1∞​40(−107​)i−1

Match the equation of the ellipse with the appropriate description. - 64x225+4y2=6400\frac { 64 x ^ { 2 } } { 25 } + 4 y ^ { 2 } = 64002564x2​+4y2=6400

Give the focus, directrix, and axis for the parabola. - y2=4x\mathrm { y } ^ { 2 } = 4 \mathrm { x }y2=4x

Find a general term an for the geometric sequence. - a1=17,r=6a _ { 1 } = \frac { 1 } { 7 } , r = 6a1​=71​,r=6

Evaluate the series, if it converges. - 10+4+85+1625+…10 + 4 + \frac { 8 } { 5 } + \frac { 16 } { 25 } + \ldots10+4+58​+2516​+…

Graph the parabola. - x=23(y+5)2−2x = \frac { 2 } { 3 } ( y + 5 ) ^ { 2 } - 2x=32​(y+5)2−2

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Filters

Identify the type of graph. - $- 5 x ^ { 2 } + 30 x + 5 y ^ { 2 } - 70 y - 45 = - 245$

Write out the first five terms of the sequence. - $a _ { n } = \frac { 2 } { n ^ { 2 } }$

Evaluate the expression. - $\frac { 10 ! } { 5 ! 5 ! }$

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

Find a general term a_n for the geometric sequence. - $\frac { 1 } { 2 } , 2,8 , \ldots$

Evaluate the series, if it converges. - $\sum _ { i = 1 } ^ { \infty } 40 \left( - \frac { 7 } { 10 } \right) ^ { i - 1 }$

Match the equation of the ellipse with the appropriate description. - $\frac { 64 x ^ { 2 } } { 25 } + 4 y ^ { 2 } = 6400$

Give the focus, directrix, and axis for the parabola. - $\mathrm { y } ^ { 2 } = 4 \mathrm { x }$

Find a general term a_n for the geometric sequence. - $a _ { 1 } = \frac { 1 } { 7 } , r = 6$

Evaluate the series, if it converges. - $10 + 4 + \frac { 8 } { 5 } + \frac { 16 } { 25 } + \ldots$

Graph the parabola. - $x = \frac { 2 } { 3 } ( y + 5 ) ^ { 2 } - 2$ $Graph the parabola. - x = \frac { 2 } { 3 } ( y + 5 ) ^ { 2 } - 2$