Question 1

Identify the type of graph.
$- x ^ { 2 } - 6 x + 5 y ^ { 2 } + 10 y = 25$

Accepted Answer

A)  The graph is a circle with center $\left( \frac { 5 } { 9 } , - \frac { 2 } { 3 } \right)$ 
B)  The graph is a hyperbola opening to the right and left. 
C)  The equation has no graph. 
D)  The graph is an ellipse with center $\left( - \frac { 5 } { 9 } , \frac { 2 } { 3 } \right)$ 
A)  The graph is a circle with center $\left( \frac { 5 } { 9 } , - \frac { 2 } { 3 } \right)$ 
B)  The graph is a hyperbola opening to the right and left. 
C)  The equation has no graph. 
D)  The graph is an ellipse with center $\left( - \frac { 5 } { 9 } , \frac { 2 } { 3 } \right)$

Question 2

The eccentricity of ellipse A is eA= 0.2 and the eccentricity of ellipse B is $\mathrm { eB } ^ { = } = 0.81$ . Which ellipse is flatter?

Accepted Answer

The answer of The eccentricity of ellipse A is eA=...

Question 3

Using only this graph of f(x) $f ( x ) = a ( x - h ) ^ { 2 } + k$ k, what are the signs of h and k?

Accepted Answer

A)  Both are positive. 
B)  h is negative and k is positive. 
C)  h is positive and k is negative. 
D)  Both are negative. 
A)  Both are positive. 
B)  h is negative and k is positive. 
C)  h is positive and k is negative. 
D)  Both are negative.

Question 4

Write an equation for the parabola.
-vertex $( 7 , - 6 )$, focus $( 10 , - 6 )$

Accepted Answer

A)  $( x - 7 ) ^ { 2 } = 12 ( y + 6 )$ 
B)  $x - 7 = 3 ( y + 6 ) ^ { 2 }$ 
C)  $( y + 6 ) ^ { 2 } = 12 ( x - 7 )$ 
D)  $\frac { 3 } { 4 } ( x - 7 ) = ( y + 6 ) ^ { 2 }$ 
A)  $( x - 7 ) ^ { 2 } = 12 ( y + 6 )$ 
B)  $x - 7 = 3 ( y + 6 ) ^ { 2 }$ 
C)  $( y + 6 ) ^ { 2 } = 12 ( x - 7 )$ 
D)  $\frac { 3 } { 4 } ( x - 7 ) = ( y + 6 ) ^ { 2 }$

Question 5

Match the equation of the ellipse with the appropriate description.
-$$49 y ^ { 2 } = 11,025 - 9 x ^ { 2 }$$

Accepted Answer

A)  $x$-intercepts $( 35,0 ) , ( - 35,0 )$; y-intercepts $( 0,15 ) , ( 0 , - 15 )$ 
B)  $x$-intercepts $( 15,0 ) , ( - 15,0 )$; y-intercepts $( 0,35 ) , ( 0 , - 35 )$ 
C)  $x$-intercepts $( 225,0 ) , ( - 225,0 )$; y-intercepts $( 0,1225 ) , ( 0 , - 1225 )$ 
D)  $x$-intercepts $( 1225,0 ) , ( - 1225,0 )$; y-intercepts $( 0,225 ) , ( 0 , - 225 )$ 
A)  $x$-intercepts $( 35,0 ) , ( - 35,0 )$; y-intercepts $( 0,15 ) , ( 0 , - 15 )$ 
B)  $x$-intercepts $( 15,0 ) , ( - 15,0 )$; y-intercepts $( 0,35 ) , ( 0 , - 35 )$ 
C)  $x$-intercepts $( 225,0 ) , ( - 225,0 )$; y-intercepts $( 0,1225 ) , ( 0 , - 1225 )$ 
D)  $x$-intercepts $( 1225,0 ) , ( - 1225,0 )$; y-intercepts $( 0,225 ) , ( 0 , - 225 )$

Question 6

What is the probability that the arrow will land on 5 or 4?

Accepted Answer

A)  $\frac { 4 } { 3 }$ 
B)  $\frac { 2 } { 5 }$ 
C)  5 
D)  $\frac { 3 } { 5 }$ 
A)  $\frac { 4 } { 3 }$ 
B)  $\frac { 2 } { 5 }$ 
C)  5 
D)  $\frac { 3 } { 5 }$

Question 7

If an object is thrown upward with an initial velocity of 10 ft per second, then its height is given by h = -10t2 + 80t. What is its maximum height?

Accepted Answer

A)  120 ft 
B)  80 ft 
C)  240 ft 
D)  160 ft 
A)  120 ft 
B)  80 ft 
C)  240 ft 
D)  160 ft

Question 8

Write an equation for the parabola.
-vertex: $( - 3,4 )$, directrix: $y = 10$

Accepted Answer

A)  $( x + 3 ) ^ { 2 } = - 24 ( y - 4 )$ 
B)  $( x + 3 ) ^ { 2 } = - 24 ( y + 4 )$ 
C)  $( y + 3 ) ^ { 2 } = 8 ( x - 4 )$ 
D)  $( y + 3 ) ^ { 2 } = - 24 ( x - 4 )$ 
A)  $( x + 3 ) ^ { 2 } = - 24 ( y - 4 )$ 
B)  $( x + 3 ) ^ { 2 } = - 24 ( y + 4 )$ 
C)  $( y + 3 ) ^ { 2 } = 8 ( x - 4 )$ 
D)  $( y + 3 ) ^ { 2 } = - 24 ( x - 4 )$

Question 9

Graph the hyperbola.
-$$\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 25 } = 1$$

Accepted Answer

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

Question 10

Write the binomial expansion of the expression.
-$\left( 2 + \frac { y } { 3 } \right) ^ { 5 }$

Accepted Answer

A)  $32 - \frac { 80 } { 3 } y - \frac { 80 } { 9 } y ^ { 2 } - \frac { 40 } { 27 } y ^ { 3 } - \frac { 10 } { 81 } y ^ { 4 } - \frac { 1 } { 243 } y ^ { 5 }$ 
B)  $- 32 + \frac { 80 } { 3 } y - \frac { 80 } { 9 } y ^ { 2 } + \frac { 40 } { 27 } y ^ { 3 } - \frac { 10 } { 81 } y ^ { 4 } + \frac { 1 } { 243 } y ^ { 5 }$ 
C)  $32 - \frac { 10000 } { 3 } y + \frac { 8000 } { 9 } y ^ { 2 } - \frac { 400 } { 27 } y ^ { 3 } + \frac { 10 } { 81 } y ^ { 4 } - \frac { 1 } { 243 } y ^ { 5 }$ 
D)  $32 + \frac { 80 } { 3 } y + \frac { 80 } { 9 } y ^ { 2 } + \frac { 40 } { 27 } y ^ { 3 } + \frac { 10 } { 81 } y ^ { 4 } + \frac { 1 } { 243 } y ^ { 5 }$ 
A)  $32 - \frac { 80 } { 3 } y - \frac { 80 } { 9 } y ^ { 2 } - \frac { 40 } { 27 } y ^ { 3 } - \frac { 10 } { 81 } y ^ { 4 } - \frac { 1 } { 243 } y ^ { 5 }$ 
B)  $- 32 + \frac { 80 } { 3 } y - \frac { 80 } { 9 } y ^ { 2 } + \frac { 40 } { 27 } y ^ { 3 } - \frac { 10 } { 81 } y ^ { 4 } + \frac { 1 } { 243 } y ^ { 5 }$ 
C)  $32 - \frac { 10000 } { 3 } y + \frac { 8000 } { 9 } y ^ { 2 } - \frac { 400 } { 27 } y ^ { 3 } + \frac { 10 } { 81 } y ^ { 4 } - \frac { 1 } { 243 } y ^ { 5 }$ 
D)  $32 + \frac { 80 } { 3 } y + \frac { 80 } { 9 } y ^ { 2 } + \frac { 40 } { 27 } y ^ { 3 } + \frac { 10 } { 81 } y ^ { 4 } + \frac { 1 } { 243 } y ^ { 5 }$

Question 11

Use the formula for SS1U1B1nS1U1B0 to find the sum of the first five terms of the geometric sequence.
-$3 , - 9,27 , - 81 , \ldots$

Accepted Answer

A)  $- 183$ 
B)  183 
C)  363 
D)  $- 363$ 
A)  $- 183$ 
B)  183 
C)  363 
D)  $- 363$

Question 12

Write out the first five terms of the sequence.
-$$a _ { n } = n - 5$$

Accepted Answer

A)  $- 4 , - 3 , - 2 , - 1,0$ 
B)  $- 5 , - 4 , - 3 , - 2 , - 1$ 
C)  $- 20 , - 15 , - 10 , - 5,0$ 
D)  $0,1,2,3,4$ 
A)  $- 4 , - 3 , - 2 , - 1,0$ 
B)  $- 5 , - 4 , - 3 , - 2 , - 1$ 
C)  $- 20 , - 15 , - 10 , - 5,0$ 
D)  $0,1,2,3,4$

Question 13

Graph the ellipse.
-$4(x+1)^{2}+9(y+2)^{2}=36$

Accepted Answer

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

Question 14

The roof of a building is in the shape of the hyperbola $y ^ { 2 } - 6 x ^ { 2 } = 46$, where $x$ and $y$ are in meters. Refer to the figure and determine the height, h, of the outside walls.
$$A = 9 \mathrm {~m}$$

Accepted Answer

A)  532 m 
B)  9.3 m 
C)  87 m 
D)  23.1 m 
A)  532 m 
B)  9.3 m 
C)  87 m 
D)  23.1 m

Question 15

Evaluate the expression.
-P(11, 3)

Accepted Answer

A)  495 
B)  80,640 
C)  990 
D)  6,652,800 
A)  495 
B)  80,640 
C)  990 
D)  6,652,800

Question 16

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

Accepted Answer

A)  $\frac { 63 } { 2 }$ 
B)  171 
C)  $\frac { 63 } { 4 }$ 
D)  63 
A)  $\frac { 63 } { 2 }$ 
B)  171 
C)  $\frac { 63 } { 4 }$ 
D)  63

Question 17

Find a formula for the nth term of the arithmetic sequence shown in the graph.
-

Accepted Answer

A)  $a _ { n } = n + 1$ 
B)  $a _ { n } = n + 2$ 
C)  $a _ { n } = n - 1$ 
D)  $a _ { n } = n - 2$ 
A)  $a _ { n } = n + 1$ 
B)  $a _ { n } = n + 2$ 
C)  $a _ { n } = n - 1$ 
D)  $a _ { n } = n - 2$

Question 18

How many 10-digit telephone numbers (area code + number) are possible if the first digit cannot be zero, the first three digits cannot be 800 or 900, and the number must end in 0000?

Accepted Answer

A)  654,642 
B)  898,000 
C)  900,000 
D)  899,000 
A)  654,642 
B)  898,000 
C)  900,000 
D)  899,000

Question 19

It can be shown that $( 1 + x ) ^ { n } = 1 + n x + \frac { n ( n - 1 ) } { 2 ! } x ^ { 2 } + \frac { n ( n - 1 ) ( n - 2 ) } { 3 ! } x ^ { 3 } \ldots$ is true for any real number $n$ (not just positive integer values) and any real number $x$, where $| x | < 1$. Use this series to approximate the given number to the nearest thousandth.
-$$( 1.03 ) ^ { - 5 }$$

Accepted Answer

A)  0.863 
B)  1.159 
C)  1.154 
D)  0.867 
A)  0.863 
B)  1.159 
C)  1.154 
D)  0.867

Question 20

Give the focus, directrix, and axis for the parabola.
-$$( x + 3 ) ^ { 2 } = 8 y$$

Accepted Answer

A)  $( - 3,2 ) , y = - 2 , x = - 3$ 
B)  $( - 3,0 ) , y = 2 , x = - 3$ 
C)  $( - 3 , - 2 ) , y = - 2 , x = - 3$ 
D)  $( 3,2 ) , y = 2 , x = 3$ 
A)  $( - 3,2 ) , y = - 2 , x = - 3$ 
B)  $( - 3,0 ) , y = 2 , x = - 3$ 
C)  $( - 3 , - 2 ) , y = - 2 , x = - 3$ 
D)  $( 3,2 ) , y = 2 , x = 3$

Identify the type of graph. $- x ^ { 2 } - 6 x + 5 y ^ { 2 } + 10 y = 25$

The eccentricity of ellipse A is eA= 0.2 and the eccentricity of ellipse B is $\mathrm { eB } ^ { = } = 0.81$ . Which ellipse is flatter?

$Using only this graph of f(x) f ( x ) = a ( x - h ) ^ { 2 } + k k, what are the signs of h and k?$ Using only this graph of f(x) $f ( x ) = a ( x - h ) ^ { 2 } + k$ k, what are the signs of h and k?

Write an equation for the parabola. -vertex $( 7 , - 6 )$ , focus $( 10 , - 6 )$

Match the equation of the ellipse with the appropriate description. - $49 y ^ { 2 } = 11,025 - 9 x ^ { 2 }$

What is the probability that the arrow will land on 5 or 4?

If an object is thrown upward with an initial velocity of 10 ft per second, then its height is given by h = -10t2 + 80t. What is its maximum height?

Write an equation for the parabola. -vertex: $( - 3,4 )$ , directrix: $y = 10$

Graph the hyperbola. - $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 25 } = 1$ $Graph the hyperbola. - \frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 25 } = 1$

Write the binomial expansion of the expression. - $\left( 2 + \frac { y } { 3 } \right) ^ { 5 }$

Use the formula for S_n to find the sum of the first five terms of the geometric sequence. - $3 , - 9,27 , - 81 , \ldots$

Write out the first five terms of the sequence. - $a _ { n } = n - 5$

Graph the ellipse. - $4(x+1)^{2}+9(y+2)^{2}=36$ $Graph the ellipse. - 4(x+1)^{2}+9(y+2)^{2}=36$

Evaluate the expression. -P(11, 3)

Find a formula for the nth term of the arithmetic sequence shown in the graph. -

How many 10-digit telephone numbers (area code + number) are possible if the first digit cannot be zero, the first three digits cannot be 800 or 900, and the number must end in 0000?

Give the focus, directrix, and axis for the parabola. - $( x + 3 ) ^ { 2 } = 8 y$

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 type of graph. −x2−6x+5y2+10y=25- x ^ { 2 } - 6 x + 5 y ^ { 2 } + 10 y = 25−x2−6x+5y2+10y=25

The eccentricity of ellipse A is eA= 0.2 and the eccentricity of ellipse B is eB==0.81\mathrm { eB } ^ { = } = 0.81eB==0.81 . Which ellipse is flatter?

Using only this graph of f(x) f(x)=a(x−h)2+kf ( x ) = a ( x - h ) ^ { 2 } + kf(x)=a(x−h)2+k k, what are the signs of h and k?

Write an equation for the parabola. -vertex (7,−6)( 7 , - 6 )(7,−6) , focus (10,−6)( 10 , - 6 )(10,−6)

Match the equation of the ellipse with the appropriate description. - 49y2=11,025−9x249 y ^ { 2 } = 11,025 - 9 x ^ { 2 }49y2=11,025−9x2

What is the probability that the arrow will land on 5 or 4?

If an object is thrown upward with an initial velocity of 10 ft per second, then its height is given by h = -10t2 + 80t. What is its maximum height?

Write an equation for the parabola. -vertex: (−3,4)( - 3,4 )(−3,4) , directrix: y=10y = 10y=10

Graph the hyperbola. - x216−y225=1\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 25 } = 116x2​−25y2​=1

Write the binomial expansion of the expression. - (2+y3)5\left( 2 + \frac { y } { 3 } \right) ^ { 5 }(2+3y​)5

Use the formula for Sn to find the sum of the first five terms of the geometric sequence. - 3,−9,27,−81,…3 , - 9,27 , - 81 , \ldots3,−9,27,−81,…

Write out the first five terms of the sequence. - an=n−5a _ { n } = n - 5an​=n−5

Graph the ellipse. - 4(x+1)2+9(y+2)2=364(x+1)^{2}+9(y+2)^{2}=364(x+1)2+9(y+2)2=36

The roof of a building is in the shape of the hyperbola y2−6x2=46y ^ { 2 } - 6 x ^ { 2 } = 46y2−6x2=46 , where xxx and yyy are in meters. Refer to the figure and determine the height, h, of the outside walls. A=9 mA = 9 \mathrm {~m}A=9 m

Evaluate the expression. -P(11, 3)

Find a formula for the nth term of the arithmetic sequence shown in the graph. -

How many 10-digit telephone numbers (area code + number) are possible if the first digit cannot be zero, the first three digits cannot be 800 or 900, and the number must end in 0000?

Give the focus, directrix, and axis for the parabola. - (x+3)2=8y( x + 3 ) ^ { 2 } = 8 y(x+3)2=8y

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. $- x ^ { 2 } - 6 x + 5 y ^ { 2 } + 10 y = 25$

The eccentricity of ellipse A is eA= 0.2 and the eccentricity of ellipse B is $\mathrm { eB } ^ { = } = 0.81$ . Which ellipse is flatter?

$Using only this graph of f(x) f ( x ) = a ( x - h ) ^ { 2 } + k k, what are the signs of h and k?$ Using only this graph of f(x) $f ( x ) = a ( x - h ) ^ { 2 } + k$ k, what are the signs of h and k?

Write an equation for the parabola. -vertex $( 7 , - 6 )$ , focus $( 10 , - 6 )$

Match the equation of the ellipse with the appropriate description. - $49 y ^ { 2 } = 11,025 - 9 x ^ { 2 }$

Write an equation for the parabola. -vertex: $( - 3,4 )$ , directrix: $y = 10$

Graph the hyperbola. - $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 25 } = 1$ $Graph the hyperbola. - \frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 25 } = 1$

Write the binomial expansion of the expression. - $\left( 2 + \frac { y } { 3 } \right) ^ { 5 }$

Use the formula for S_n to find the sum of the first five terms of the geometric sequence. - $3 , - 9,27 , - 81 , \ldots$

Write out the first five terms of the sequence. - $a _ { n } = n - 5$

Graph the ellipse. - $4(x+1)^{2}+9(y+2)^{2}=36$ $Graph the ellipse. - 4(x+1)^{2}+9(y+2)^{2}=36$

Give the focus, directrix, and axis for the parabola. - $( x + 3 ) ^ { 2 } = 8 y$