Question 1

Write an equation for the hyperbola.
-vertices $( - 7,2 ) , ( - 7,18 ) ; e = \frac { 2 \sqrt { 17 } } { 8 }$

Accepted Answer

A)  $\frac { ( y + 7 ) ^ { 2 } } { 4 } - \frac { ( x - 10 ) ^ { 2 } } { 64 } = 1$ 
B)  $\frac { ( y - 7 ) ^ { 2 } } { 64 } - \frac { ( x - 10 ) ^ { 2 } } { 4 } = 1$ 
C)  $\frac { ( y - 10 ) ^ { 2 } } { 64 } - \frac { ( x + 7 ) ^ { 2 } } { 4 } = 1$ 
D)  $\frac { ( y - 7 ) ^ { 2 } } { 64 } - \frac { ( x + 10 ) ^ { 2 } } { 4 } = 1$ 
A)  $\frac { ( y + 7 ) ^ { 2 } } { 4 } - \frac { ( x - 10 ) ^ { 2 } } { 64 } = 1$ 
B)  $\frac { ( y - 7 ) ^ { 2 } } { 64 } - \frac { ( x - 10 ) ^ { 2 } } { 4 } = 1$ 
C)  $\frac { ( y - 10 ) ^ { 2 } } { 64 } - \frac { ( x + 7 ) ^ { 2 } } { 4 } = 1$ 
D)  $\frac { ( y - 7 ) ^ { 2 } } { 64 } - \frac { ( x + 10 ) ^ { 2 } } { 4 } = 1$

Question 2

Find $a _ { n } \text { and } a _ { 6 }$ for the following arithmetic sequence.
-2, 6, 10, 14, 18, . . .

Accepted Answer

A)  $a _ { n } = 2 n - 4 ; a _ { 6 } = 8$ 
B)  $a _ { n } = 4 n - 2 ; a _ { 6 } = 22$ 
C)  $a _ { n } = n + 4 ; a _ { 6 } = 10$ 
D)  $a _ { n } = 2 ( 4 ) ^ { n - 1 } ; a _ { 6 } = 32,768$ 
A)  $a _ { n } = 2 n - 4 ; a _ { 6 } = 8$ 
B)  $a _ { n } = 4 n - 2 ; a _ { 6 } = 22$ 
C)  $a _ { n } = n + 4 ; a _ { 6 } = 10$ 
D)  $a _ { n } = 2 ( 4 ) ^ { n - 1 } ; a _ { 6 } = 32,768$

Question 3

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest
hundredth.
-$$\mathrm { Sg } = 108 , \mathrm { ag } = 16$$

Accepted Answer

A)  $a _ { 1 } = 8 , d = 1$ 
B)  $a _ { 1 } = - 120 , d = 1$ 
C)  $\mathrm { a } _ { 1 } = 8 , \mathrm {~d} = 3.56$ 
D)  $a _ { 1 } = - 120 , d = 3.56$ 
A)  $a _ { 1 } = 8 , d = 1$ 
B)  $a _ { 1 } = - 120 , d = 1$ 
C)  $\mathrm { a } _ { 1 } = 8 , \mathrm {~d} = 3.56$ 
D)  $a _ { 1 } = - 120 , d = 3.56$

Question 4

Find the eccentricity of the conic section shown in the graph.
-$x = - 21$

Accepted Answer

A)  $e = \frac { \sqrt { 29 } } { 5 }$ 
B)  $e = \frac { 5 } { 2 }$ 
C)  e=1 
D)  $e = \frac { \sqrt { 21 } } { 5 }$ 
A)  $e = \frac { \sqrt { 29 } } { 5 }$ 
B)  $e = \frac { 5 } { 2 }$ 
C)  e=1 
D)  $e = \frac { \sqrt { 21 } } { 5 }$

Question 5

Three noncollinear points determine a triangle. How many triangles can be formed with 8 noncollinear points?

Accepted Answer

A)  56 
B)  6720 
C)  336 
D)  24 
A)  56 
B)  6720 
C)  336 
D)  24

Question 6

The series of sketches below starts with an equilateral triangle having sides of length 1 (one). In the following
steps, equilateral triangles are constructed by joining the midpoints of the sides of the preceding triangle.
Develop a formula for the area of the nth new triangle. Use math induction to prove your answer.

Accepted Answer

The answer of The series of sketches below starts with...

Question 7

It can be shown that a hyperbola with center at the origin, foci at $\mathrm { F } ^ { \prime } ( - \mathrm { c } , 0 )$ and $\mathrm { F } ( \mathrm { c } , 0 )$, and equation $d \left( P , F ^ { \prime } \right) - d ( P , F ) = 2 a$ has equation $\frac { x ^ { 2 } } { a ^ { 2 } } - \frac { y ^ { 2 } } { b ^ { 2 } } = 1$. Use this result to find an equation of a hyperbola with center at the origin, foci at $( - 8,0 )$ and $( 8,0 )$, and absolute value of the distances from any point of the hyperbola to the two foci equal to 8 .

Accepted Answer

A)  $\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 8 } = 1$ 
B)  $x ^ { 2 } - y ^ { 2 } = 8$ 
C)  $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 48 } = 1$ 
D)  $\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 80 } = 1$ 
A)  $\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 8 } = 1$ 
B)  $x ^ { 2 } - y ^ { 2 } = 8$ 
C)  $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 48 } = 1$ 
D)  $\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 80 } = 1$

Question 8

Find the sum of the geometric series.
-$$\sum _ { i = 1 } ^ { 5 } 4 ( 3 ) ^ { i }$$

Accepted Answer

A)  1452 
B)  2460 
C)  480 
D)  93 
A)  1452 
B)  2460 
C)  480 
D)  93

Question 9

Evaluate the sum using the given information.
-$$\begin{array} { l } 
x _ { 1 } = - 5 , x _ { 2 } = 4 , x _ { 3 } = 5 , x _ { 4 } = 3 \text {, and } \Delta x = 0.1 ; f ( x ) = x ^ { 2 } \
\sum _ { i = 1 } ^ { 4 } f \left( x _ { i } \right) \Delta x
\end{array}$$

Accepted Answer

A)  30 
B)  $5.7$ 
C)  $1.1685$ 
D)  $7.5$ 
A)  30 
B)  $5.7$ 
C)  $1.1685$ 
D)  $7.5$

Question 10

Graph the ellipse.
-$$\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 36 } = 1$$

Accepted Answer

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

Question 11

There are some fundamental differences between graphing a hyperbola centered at the origin and graphing an
ellipse centered at the origin. What are these differences?

Accepted Answer

Answers will vary. One possibility: To g

Question 12

Evaluate the sum. Round to two decimal places, if necessary.
-$$\sum _ { \mathrm { k } = 2 } ^ { 5 } ( - 1 ) ^ { \mathrm { k } + 1 } ( \mathrm { k } + 8 ) ^ { 2 }$$

Accepted Answer

A)  $- 534$ 
B)  534 
C)  351,788 
D)  46 
A)  $- 534$ 
B)  534 
C)  351,788 
D)  46

Question 13

Find the sum of the first n terms of the following arithmetic sequence.
-$$a _ { 1 } = 5 , d = 5 ; \quad n = 4$$

Accepted Answer

A)  50 
B)  20 
C)  15 
D)  25 
A)  50 
B)  20 
C)  15 
D)  25

Question 14

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

Accepted Answer

A)  $- 48$ 
B)  $- 36$ 
C)  20 
D)  $- 60$ 
A)  $- 48$ 
B)  $- 36$ 
C)  20 
D)  $- 60$

Question 15

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest
hundredth.
-$$a _ { 5 } = 15 , a _ { 21 } = 95$$

Accepted Answer

A)  $a _ { 1 } = 80 , d = 5$ 
B)  $\mathrm { a } _ { 1 } = 80 , \mathrm {~d} = - 5$ 
C)  $a _ { 1 } = - 5 , d = 5$ 
D)  $a _ { 1 } = - 5 , d = 80$ 
A)  $a _ { 1 } = 80 , d = 5$ 
B)  $\mathrm { a } _ { 1 } = 80 , \mathrm {~d} = - 5$ 
C)  $a _ { 1 } = - 5 , d = 5$ 
D)  $a _ { 1 } = - 5 , d = 80$

Question 16

Evaluate the series, if it converges.
-$$\sum _ { i = 1 } ^ { \infty } 30 \left( \frac { 1 } { 3 } \right) ^ { i - 1 }$$

Accepted Answer

A)  $\frac { 3 } { 2 }$ 
B)  15 
C)  45 
D)  Does not converge. 
A)  $\frac { 3 } { 2 }$ 
B)  15 
C)  45 
D)  Does not converge.

Question 17

The hyperbola with equation $$\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 36 } = 1$$ 1 opens left and right.

Accepted Answer

A) True 
 B)False

Question 18

Use a calculator to evaluate the expression.
-$${ } _ { 19 } \mathrm { C } _ { 8 }$$

Accepted Answer

A)  75,582 
B)  151,164 
C)  3.047 × 109 
D)  380,933,280 
A)  75,582 
B)  151,164 
C)  3.047 × 109 
D)  380,933,280

Question 19

A railroad bridge is built over a V-shaped canyon. If the supports are 8 feet long at each end, the center support is 560 feet long, and the supports increase in length by 4 feet with each support (from 8 feet to 560 feet),
What is the total length of all the supports?

Accepted Answer

A)  78,384 ft 
B)  78,392 ft 
C)  78,396 ft 
D)  78,388 ft 
A)  78,384 ft 
B)  78,392 ft 
C)  78,396 ft 
D)  78,388 ft

Question 20

Find the nth term of the geometric sequence.
-$\frac { 1 } { 2 } , \frac { 1 } { 4 } , \frac { 1 } { 8 } , \ldots ; \mathrm { n } = 11$

Accepted Answer

A)  $\frac { 1 } { 4096 }$ 
B)  $\frac { 1 } { 44 }$ 
C)  $\frac { 1 } { 1024 }$ 
D)  $\frac { 1 } { 2048 }$ 
A)  $\frac { 1 } { 4096 }$ 
B)  $\frac { 1 } { 44 }$ 
C)  $\frac { 1 } { 1024 }$ 
D)  $\frac { 1 } { 2048 }$

Write an equation for the hyperbola. -vertices $( - 7,2 ) , ( - 7,18 ) ; e = \frac { 2 \sqrt { 17 } } { 8 }$

Find $a _ { n } \text { and } a _ { 6 }$ for the following arithmetic sequence. -2, 6, 10, 14, 18, . . .

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest hundredth. - $\mathrm { Sg } = 108 , \mathrm { ag } = 16$

Find the eccentricity of the conic section shown in the graph. - $x = - 21$

Three noncollinear points determine a triangle. How many triangles can be formed with 8 noncollinear points?

Find the sum of the geometric series. - $\sum _ { i = 1 } ^ { 5 } 4 ( 3 ) ^ { i }$

Evaluate the sum using the given information. - =-5,=4,=5,=3 , and \Deltax=0.1;f(x)= f \Deltax

Graph the ellipse. - $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 36 } = 1$ $Graph the ellipse. - \frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 36 } = 1$

There are some fundamental differences between graphing a hyperbola centered at the origin and graphing an ellipse centered at the origin. What are these differences?

Evaluate the sum. Round to two decimal places, if necessary. - $\sum _ { \mathrm { k } = 2 } ^ { 5 } ( - 1 ) ^ { \mathrm { k } + 1 } ( \mathrm { k } + 8 ) ^ { 2 }$

Find the sum of the first n terms of the following arithmetic sequence. - $a _ { 1 } = 5 , d = 5 ; \quad n = 4$

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest hundredth. - $a _ { 5 } = 15 , a _ { 21 } = 95$

Evaluate the series, if it converges. - $\sum _ { i = 1 } ^ { \infty } 30 \left( \frac { 1 } { 3 } \right) ^ { i - 1 }$

The hyperbola with equation $\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 36 } = 1$ 1 opens left and right.

Use a calculator to evaluate the expression. - ${ } _ { 19 } \mathrm { C } _ { 8 }$

A railroad bridge is built over a V-shaped canyon. If the supports are 8 feet long at each end, the center support is 560 feet long, and the supports increase in length by 4 feet with each support (from 8 feet to 560 feet), What is the total length of all the supports?

Find the nth term of the geometric sequence. - $\frac { 1 } { 2 } , \frac { 1 } { 4 } , \frac { 1 } { 8 } , \ldots ; \mathrm { n } = 11$

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

Write an equation for the hyperbola. -vertices (−7,2),(−7,18);e=2178( - 7,2 ) , ( - 7,18 ) ; e = \frac { 2 \sqrt { 17 } } { 8 }(−7,2),(−7,18);e=8217​​

Find an and a6a _ { n } \text { and } a _ { 6 }an​ and a6​ for the following arithmetic sequence. -2, 6, 10, 14, 18, . . .

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest hundredth. - Sg=108,ag=16\mathrm { Sg } = 108 , \mathrm { ag } = 16Sg=108,ag=16

Find the eccentricity of the conic section shown in the graph. - x=−21x = - 21x=−21

Three noncollinear points determine a triangle. How many triangles can be formed with 8 noncollinear points?

Find the sum of the geometric series. - ∑i=154(3)i\sum _ { i = 1 } ^ { 5 } 4 ( 3 ) ^ { i }∑i=15​4(3)i

Evaluate the sum using the given information. - =-5,=4,=5,=3 , and \Deltax=0.1;f(x)= f \Deltax

Graph the ellipse. - x264+y236=1\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 36 } = 164x2​+36y2​=1

There are some fundamental differences between graphing a hyperbola centered at the origin and graphing an ellipse centered at the origin. What are these differences?

Evaluate the sum. Round to two decimal places, if necessary. - ∑k=25(−1)k+1(k+8)2\sum _ { \mathrm { k } = 2 } ^ { 5 } ( - 1 ) ^ { \mathrm { k } + 1 } ( \mathrm { k } + 8 ) ^ { 2 }∑k=25​(−1)k+1(k+8)2

Find the sum of the first n terms of the following arithmetic sequence. - a1=5,d=5;n=4a _ { 1 } = 5 , d = 5 ; \quad n = 4a1​=5,d=5;n=4

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest hundredth. - a5=15,a21=95a _ { 5 } = 15 , a _ { 21 } = 95a5​=15,a21​=95

Evaluate the series, if it converges. - ∑i=1∞30(13)i−1\sum _ { i = 1 } ^ { \infty } 30 \left( \frac { 1 } { 3 } \right) ^ { i - 1 }∑i=1∞​30(31​)i−1

The hyperbola with equation x249−y236=1\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 36 } = 149x2​−36y2​=1 1 opens left and right.

Use a calculator to evaluate the expression. - 19C8{ } _ { 19 } \mathrm { C } _ { 8 }19​C8​

A railroad bridge is built over a V-shaped canyon. If the supports are 8 feet long at each end, the center support is 560 feet long, and the supports increase in length by 4 feet with each support (from 8 feet to 560 feet), What is the total length of all the supports?

Find the nth term of the geometric sequence. - 12,14,18,…;n=11\frac { 1 } { 2 } , \frac { 1 } { 4 } , \frac { 1 } { 8 } , \ldots ; \mathrm { n } = 1121​,41​,81​,…;n=11

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 hyperbola. -vertices $( - 7,2 ) , ( - 7,18 ) ; e = \frac { 2 \sqrt { 17 } } { 8 }$

Find $a _ { n } \text { and } a _ { 6 }$ for the following arithmetic sequence. -2, 6, 10, 14, 18, . . .

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest hundredth. - $\mathrm { Sg } = 108 , \mathrm { ag } = 16$

Find the eccentricity of the conic section shown in the graph. - $x = - 21$

Find the sum of the geometric series. - $\sum _ { i = 1 } ^ { 5 } 4 ( 3 ) ^ { i }$

Graph the ellipse. - $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 36 } = 1$ $Graph the ellipse. - \frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 36 } = 1$

Evaluate the sum. Round to two decimal places, if necessary. - $\sum _ { \mathrm { k } = 2 } ^ { 5 } ( - 1 ) ^ { \mathrm { k } + 1 } ( \mathrm { k } + 8 ) ^ { 2 }$

Find the sum of the first n terms of the following arithmetic sequence. - $a _ { 1 } = 5 , d = 5 ; \quad n = 4$

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest hundredth. - $a _ { 5 } = 15 , a _ { 21 } = 95$

Evaluate the series, if it converges. - $\sum _ { i = 1 } ^ { \infty } 30 \left( \frac { 1 } { 3 } \right) ^ { i - 1 }$

The hyperbola with equation $\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 36 } = 1$ 1 opens left and right.

Use a calculator to evaluate the expression. - ${ } _ { 19 } \mathrm { C } _ { 8 }$

Find the nth term of the geometric sequence. - $\frac { 1 } { 2 } , \frac { 1 } { 4 } , \frac { 1 } { 8 } , \ldots ; \mathrm { n } = 11$