Question 1

Identify the equation as a parabola, circle, ellipse, or hyperbola.
-$$3 x = 2 y ^ { 2 } - 33$$

Accepted Answer

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

Question 2

Find the eccentricity $ e $ of the hyperbola.
-$$x ^ { 2 } - y ^ { 2 } = 49$$

Accepted Answer

A)  $\sqrt { 2 }$ 
B)  $\sqrt { 7 }$ 
C)  0 
D)  1 
A)  $\sqrt { 2 }$ 
B)  $\sqrt { 7 }$ 
C)  0 
D)  1

Question 3

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

Accepted Answer

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

Question 4

The x-intercepts of the hyperbola with equation $$\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 25 } = 1 \text { are } ( 8,0 ) \text { and } ( - 8,0 )$$

Accepted Answer

A) True 
 B)False

Question 5

A box contains 4 slips of paper, on each of which is written the number 1, 2, 3, or 4, respectively. A slip is drawn, and the number on it is noted. That slip is put aside, and another slip is drawn and the number on it noted. What is the
Probability that
a) the sum of the two numbers is 5?
b) the first number drawn is a 2 and the second number is not 5?
c) the sum of the two numbers is not 10?

Accepted Answer

A)  a) $\frac { 1 } { 3 }$ b) $\frac { 1 } { 4 } \quad$ c) 1 
B)  a) $\frac { 1 } { 4 } \quad$ b) $\frac { 1 } { 3 } \quad$ c) 1 
C)  a) $\frac { 1 } { 4 }$ b) $\frac { 1 } { 3 }$ c) 0 
D)  a) $\frac { 1 } { 3 }$ b) $\frac { 1 } { 4 } \quad$ c) 0 
A)  a) $\frac { 1 } { 3 }$ b) $\frac { 1 } { 4 } \quad$ c) 1 
B)  a) $\frac { 1 } { 4 } \quad$ b) $\frac { 1 } { 3 } \quad$ c) 1 
C)  a) $\frac { 1 } { 4 }$ b) $\frac { 1 } { 3 }$ c) 0 
D)  a) $\frac { 1 } { 3 }$ b) $\frac { 1 } { 4 } \quad$ c) 0

Question 6

Write out the first five terms of the sequence.
-$$a _ { n } = \frac { n ^ { 2 } - 5 } { n ^ { 2 } + 5 }$$

Accepted Answer

A)  $1,1,1,1,1$ 
B)  $- \frac { 2 } { 3 } , - \frac { 1 } { 9 } , \frac { 2 } { 7 } , \frac { 11 } { 21 } , \frac { 2 } { 3 }$ 
C)  $- \frac { 2 } { 3 } , 1 , \frac { 2 } { 7 } , 1 , \frac { 3 } { 2 }$ 
D)  $1 , - \frac { 1 } { 9 } , 1 , \frac { 11 } { 21 } , 1$ 
A)  $1,1,1,1,1$ 
B)  $- \frac { 2 } { 3 } , - \frac { 1 } { 9 } , \frac { 2 } { 7 } , \frac { 11 } { 21 } , \frac { 2 } { 3 }$ 
C)  $- \frac { 2 } { 3 } , 1 , \frac { 2 } { 7 } , 1 , \frac { 3 } { 2 }$ 
D)  $1 , - \frac { 1 } { 9 } , 1 , \frac { 11 } { 21 } , 1$

Question 7

Match the equation of the parabola with the appropriate description.
-$$y + 8 = 2 ( x - 16 ) ^ { 2 }$$

Accepted Answer

A)  Vertex at $( - 16,8 )$ 
B)  Vertex at $( 16 , - 8 )$ 
C)  Vertex at $( - 16,4 )$ 
D)  Vertex at $( 32,8 )$ 
A)  Vertex at $( - 16,8 )$ 
B)  Vertex at $( 16 , - 8 )$ 
C)  Vertex at $( - 16,4 )$ 
D)  Vertex at $( 32,8 )$

Question 8

Evaluate the expression.
-$$\left( \begin{array} { l } 
10 \
10
\end{array} \right)$$

Accepted Answer

A)  2 
B)  0 
C)  3,628,800 
D)  1 
A)  2 
B)  0 
C)  3,628,800 
D)  1

Question 9

Identify the equation as a parabola, circle, ellipse, or hyperbola.
-$$15 y = 4 ( x + 6 ) ^ { 2 }$$

Accepted Answer

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

Question 10

An ordinary die is tossed. What are the odds in favor of the die showing an odd number?

Accepted Answer

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

Question 11

Write the binomial expansion of the expression.
-$$( 5 x + 3 ) ^ { 3 }$$

Accepted Answer

A)  $125 x ^ { 3 } + 225 x ^ { 2 } + 225 x + 27$ 
B)  $25 x ^ { 2 } + 30 x + 9$ 
C)  $125 x ^ { 3 } + 225 x ^ { 2 } + 135 x + 27$ 
D)  $25 x ^ { 6 } + 15 x ^ { 3 } + 729$ 
A)  $125 x ^ { 3 } + 225 x ^ { 2 } + 225 x + 27$ 
B)  $25 x ^ { 2 } + 30 x + 9$ 
C)  $125 x ^ { 3 } + 225 x ^ { 2 } + 135 x + 27$ 
D)  $25 x ^ { 6 } + 15 x ^ { 3 } + 729$

Question 12

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest
hundredth.
-$$\mathrm { S } _ { 30 } = - 1575 , \text { a } _ { 30 } = - 96$$

Accepted Answer

A)  $\mathrm { a } _ { 1 } = 2775 , \mathrm {~d} = - 3$ 
B)  $\mathrm { a } _ { 1 } = - 9 , \mathrm {~d} = - 6.4$ 
C)  $a _ { 1 } = - 9 , d = - 3$ 
D)  $\mathrm { a } _ { 1 } = 2775 , \mathrm {~d} = - 6.4$ 
A)  $\mathrm { a } _ { 1 } = 2775 , \mathrm {~d} = - 3$ 
B)  $\mathrm { a } _ { 1 } = - 9 , \mathrm {~d} = - 6.4$ 
C)  $a _ { 1 } = - 9 , d = - 3$ 
D)  $\mathrm { a } _ { 1 } = 2775 , \mathrm {~d} = - 6.4$

Question 13

Evaluate the expression.
-$$\left( \begin{array} { l } 
10 \
10
\end{array} \right)$$

Accepted Answer

A)  1,814,400 
B)  10 
C)  1 
D)  3,628,800 
A)  1,814,400 
B)  10 
C)  1 
D)  3,628,800

Question 14

John does 8 pushups on the first day of a 30-day month, and then increases the number of pushups by 3 pushups a day. How many pushups has he done by the end of the month?

Accepted Answer

A)  1537 
B)  1545 
C)  1635 
D)  1590 
A)  1537 
B)  1545 
C)  1635 
D)  1590

Question 15

Find the future value of the annuity.
-There are payments of $1000 at the end of each year for 14 years at 2% interest compounded annually

Accepted Answer

A)  $15,973.94 
B)  $65,973.94 
C)  $14,680.33 
D)  $6468.03 
A)  $15,973.94 
B)  $65,973.94 
C)  $14,680.33 
D)  $6468.03

Question 16

A die is rolled 10 times. Find the probability of rolling no more than 4 ones.

Accepted Answer

A)  Approximately 0.155 
B)  Approximately 0.054 
C)  Approximately 0.985 
D)  Approximately 0.930 
A)  Approximately 0.155 
B)  Approximately 0.054 
C)  Approximately 0.985 
D)  Approximately 0.930

Question 17

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest
hundredth.
-$$\mathrm { S } _ { 8 } = 40 , \mathrm { a } 8 = 19$$

Accepted Answer

A)  $a _ { 1 } = - 142 , d = 4.75$ 
B)  $a _ { 1 } = - 9 , d = 4$ 
C)  $\mathrm { a } _ { 1 } = - 9 , \mathrm {~d} = 4.75$ 
D)  $a _ { 1 } = - 142 , d = 4$ 
A)  $a _ { 1 } = - 142 , d = 4.75$ 
B)  $a _ { 1 } = - 9 , d = 4$ 
C)  $\mathrm { a } _ { 1 } = - 9 , \mathrm {~d} = 4.75$ 
D)  $a _ { 1 } = - 142 , d = 4$

Question 18

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

Accepted Answer

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

Question 19

The beginning population of a town was 33,200. If the population decreased by 350 people per year, how many people lived in the town 15 years later?

Accepted Answer

A)  27,600 
B)  5250 
C)  27,950 
D)  28,300 
A)  27,600 
B)  5250 
C)  27,950 
D)  28,300

Question 20

A shirt company has 4 designs that can be made with short or long sleeves. There are 7 color patterns available. How many different types of shirts are available from this company?

Accepted Answer

A)  11 
B)  13 
C)  28 
D)  56 
A)  11 
B)  13 
C)  28 
D)  56

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $3 x = 2 y ^ { 2 } - 33$

Find the eccentricity $e$ of the hyperbola. - $x ^ { 2 } - y ^ { 2 } = 49$

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

The x-intercepts of the hyperbola with equation $\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 25 } = 1 \text { are } ( 8,0 ) \text { and } ( - 8,0 )$

Write out the first five terms of the sequence. - $a _ { n } = \frac { n ^ { 2 } - 5 } { n ^ { 2 } + 5 }$

Match the equation of the parabola with the appropriate description. - $y + 8 = 2 ( x - 16 ) ^ { 2 }$

Evaluate the expression. - $\left( \begin{array} { l } 10 \\10\end{array} \right)$

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $15 y = 4 ( x + 6 ) ^ { 2 }$

An ordinary die is tossed. What are the odds in favor of the die showing an odd number?

Write the binomial expansion of the expression. - $( 5 x + 3 ) ^ { 3 }$

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest hundredth. - $\mathrm { S } _ { 30 } = - 1575 , \text { a } _ { 30 } = - 96$

Evaluate the expression. - $\left( \begin{array} { l } 10 \\10\end{array} \right)$

John does 8 pushups on the first day of a 30-day month, and then increases the number of pushups by 3 pushups a day. How many pushups has he done by the end of the month?

Find the future value of the annuity. -There are payments of $1000 at the end of each year for 14 years at 2% interest compounded annually

A die is rolled 10 times. Find the probability of rolling no more than 4 ones.

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest hundredth. - $\mathrm { S } _ { 8 } = 40 , \mathrm { a } 8 = 19$

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

The beginning population of a town was 33,200. If the population decreased by 350 people per year, how many people lived in the town 15 years later?

A shirt company has 4 designs that can be made with short or long sleeves. There are 7 color patterns available. How many different types of shirts are available from this company?

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

Identify the equation as a parabola, circle, ellipse, or hyperbola. - 3x=2y2−333 x = 2 y ^ { 2 } - 333x=2y2−33

Find the eccentricity e e e of the hyperbola. - x2−y2=49x ^ { 2 } - y ^ { 2 } = 49x2−y2=49

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

The x-intercepts of the hyperbola with equation x264−y225=1 are (8,0) and (−8,0)\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 25 } = 1 \text { are } ( 8,0 ) \text { and } ( - 8,0 )64x2​−25y2​=1 are (8,0) and (−8,0)

Write out the first five terms of the sequence. - an=n2−5n2+5a _ { n } = \frac { n ^ { 2 } - 5 } { n ^ { 2 } + 5 }an​=n2+5n2−5​

Match the equation of the parabola with the appropriate description. - y+8=2(x−16)2y + 8 = 2 ( x - 16 ) ^ { 2 }y+8=2(x−16)2

Evaluate the expression. - (1010)\left( \begin{array} { l } 10 \\10\end{array} \right)(1010​)

Identify the equation as a parabola, circle, ellipse, or hyperbola. - 15y=4(x+6)215 y = 4 ( x + 6 ) ^ { 2 }15y=4(x+6)2

An ordinary die is tossed. What are the odds in favor of the die showing an odd number?

Write the binomial expansion of the expression. - (5x+3)3( 5 x + 3 ) ^ { 3 }(5x+3)3

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest hundredth. - S30=−1575, a 30=−96\mathrm { S } _ { 30 } = - 1575 , \text { a } _ { 30 } = - 96S30​=−1575, a 30​=−96

Evaluate the expression. - (1010)\left( \begin{array} { l } 10 \\10\end{array} \right)(1010​)

John does 8 pushups on the first day of a 30-day month, and then increases the number of pushups by 3 pushups a day. How many pushups has he done by the end of the month?

Find the future value of the annuity. -There are payments of $1000 at the end of each year for 14 years at 2% interest compounded annually

A die is rolled 10 times. Find the probability of rolling no more than 4 ones.

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest hundredth. - S8=40,a8=19\mathrm { S } _ { 8 } = 40 , \mathrm { a } 8 = 19S8​=40,a8=19

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

The beginning population of a town was 33,200. If the population decreased by 350 people per year, how many people lived in the town 15 years later?

A shirt company has 4 designs that can be made with short or long sleeves. There are 7 color patterns available. How many different types of shirts are available from this company?

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 equation as a parabola, circle, ellipse, or hyperbola. - $3 x = 2 y ^ { 2 } - 33$

Find the eccentricity $e$ of the hyperbola. - $x ^ { 2 } - y ^ { 2 } = 49$

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

The x-intercepts of the hyperbola with equation $\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 25 } = 1 \text { are } ( 8,0 ) \text { and } ( - 8,0 )$

Write out the first five terms of the sequence. - $a _ { n } = \frac { n ^ { 2 } - 5 } { n ^ { 2 } + 5 }$

Match the equation of the parabola with the appropriate description. - $y + 8 = 2 ( x - 16 ) ^ { 2 }$

Evaluate the expression. - $\left( \begin{array} { l } 10 \\10\end{array} \right)$

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $15 y = 4 ( x + 6 ) ^ { 2 }$

Write the binomial expansion of the expression. - $( 5 x + 3 ) ^ { 3 }$

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest hundredth. - $\mathrm { S } _ { 30 } = - 1575 , \text { a } _ { 30 } = - 96$

Evaluate the expression. - $\left( \begin{array} { l } 10 \\10\end{array} \right)$

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest hundredth. - $\mathrm { S } _ { 8 } = 40 , \mathrm { a } 8 = 19$