Question 1

Evaluate the sum.
-$$\sum _ { j = 400 } ^ { 3000 } j$$

Accepted Answer

A)  4,421,700 
B)  6,461,700 
C)  5,781,700 
D)  3,741,700 
A)  4,421,700 
B)  6,461,700 
C)  5,781,700 
D)  3,741,700

Question 2

Find a general term aS1U1B1nS1U1B0 for the geometric sequence.
-$$a _ { 1 } = 2 , r = \frac { 2 } { 9 }$$

Accepted Answer

A)  $a _ { n } = 2 ^ { n - 1 } - \frac { 16 } { 9 }$ 
B)  $a _ { n } = 2 + \frac { 1 } { 9 } ( n - 1 )$ 
C)  $a _ { n } = 2 \cdot \left( \frac { 2 } { 9 } \right) ^ { n - 1 }$ 
D)  $a _ { n } = 2 - \frac { 16 } { 9 } ( n - 1 )$ 
A)  $a _ { n } = 2 ^ { n - 1 } - \frac { 16 } { 9 }$ 
B)  $a _ { n } = 2 + \frac { 1 } { 9 } ( n - 1 )$ 
C)  $a _ { n } = 2 \cdot \left( \frac { 2 } { 9 } \right) ^ { n - 1 }$ 
D)  $a _ { n } = 2 - \frac { 16 } { 9 } ( n - 1 )$

Question 3

Identify the type of graph.
-$$\frac { x ^ { 2 } } { 7 } = 1 + \frac { y ^ { 2 } } { 1 }$$

Accepted Answer

A)  The graph is an ellipse with foci on the y-axis. 
B)  The graph is a hyperbola that opens upward and downward. 
C)  The graph is an ellipse with foci on the x-axis. 
D)  The graph is a hyperbola that opens to the right and left. 
A)  The graph is an ellipse with foci on the y-axis. 
B)  The graph is a hyperbola that opens upward and downward. 
C)  The graph is an ellipse with foci on the x-axis. 
D)  The graph is a hyperbola that opens to the right and left.

Question 4

Graph the conic section.
-$3 x^{2}+4 y^{2}-24 x+48 y+180=0$

Accepted Answer

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

Question 5

List the elements in the sample space of the experiment.
-A lottery uses balls numbered 1 through 35. List the sample space of the event picking one even-numbered ball.

Accepted Answer

A)  {34} 
B)  {2} 
C)  {2, 4, 6, . . ., 34} 
D)  {1, 2, 3, . . ., 35} 
A)  {34} 
B)  {2} 
C)  {2, 4, 6, . . ., 34} 
D)  {1, 2, 3, . . ., 35}

Question 6

In how many ways can 4 people be chosen and arranged in a straight line, if there are 10 people from whom to choose?

Accepted Answer

A)  40 
B)  302,400 
C)  151,200 
D)  5040 
A)  40 
B)  302,400 
C)  151,200 
D)  5040

Question 7

Identify the type of conic section.
-Identify the type of conic section consisting of the set of all points in the plane for which the sum of the distances from the point $$( 3,0 ) \text { and } ( - 3,0 ) \text { is } 21$$

Accepted Answer

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

Question 8

A woman borrowed $30,000 at 2% interest compounded annually. If the loan was paid off in one lump sum at the end of 6 years, how much did she pay?

Accepted Answer

A)  $33,784.87 
B)  $33,600.00 
C)  $30,600.00 
D)  $3784.87 
A)  $33,784.87 
B)  $33,600.00 
C)  $30,600.00 
D)  $3784.87

Question 9

Evaluate the series, if it converges.
-$$\sum _ { i = 1 } ^ { \infty } 9 \left( \frac { 3 } { 2 } \right) ^ { i - 1 }$$

Accepted Answer

A)  Does not converge. 
B)  27 
C)  18 
D)  $- 18$ 
A)  Does not converge. 
B)  27 
C)  18 
D)  $- 18$

Question 10

Evaluate the sum. Round to two decimal places, if necessary.
-$$\sum _ { k = 3 } ^ { 6 } \frac { \left( k ^ { 2 } - 2 \right) } { 2 }$$

Accepted Answer

A)  78 
B)  40 
C)  21 
D)  39 
A)  78 
B)  40 
C)  21 
D)  39

Evaluate the sum. - $\sum _ { j = 400 } ^ { 3000 } j$

Find a general term a_n for the geometric sequence. - $a _ { 1 } = 2 , r = \frac { 2 } { 9 }$

Identify the type of graph. - $\frac { x ^ { 2 } } { 7 } = 1 + \frac { y ^ { 2 } } { 1 }$

Graph the conic section. - $3 x^{2}+4 y^{2}-24 x+48 y+180=0$ $Graph the conic section. - 3 x^{2}+4 y^{2}-24 x+48 y+180=0$

List the elements in the sample space of the experiment. -A lottery uses balls numbered 1 through 35. List the sample space of the event picking one even-numbered ball.

In how many ways can 4 people be chosen and arranged in a straight line, if there are 10 people from whom to choose?

Identify the type of conic section. -Identify the type of conic section consisting of the set of all points in the plane for which the sum of the distances from the point $( 3,0 ) \text { and } ( - 3,0 ) \text { is } 21$

A woman borrowed $30,000 at 2% interest compounded annually. If the loan was paid off in one lump sum at the end of 6 years, how much did she pay?

Evaluate the series, if it converges. - $\sum _ { i = 1 } ^ { \infty } 9 \left( \frac { 3 } { 2 } \right) ^ { i - 1 }$

Evaluate the sum. Round to two decimal places, if necessary. - $\sum _ { k = 3 } ^ { 6 } \frac { \left( k ^ { 2 } - 2 \right) } { 2 }$

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

Evaluate the sum. - ∑j=4003000j\sum _ { j = 400 } ^ { 3000 } j∑j=4003000​j

Find a general term an for the geometric sequence. - a1=2,r=29a _ { 1 } = 2 , r = \frac { 2 } { 9 }a1​=2,r=92​

Identify the type of graph. - x27=1+y21\frac { x ^ { 2 } } { 7 } = 1 + \frac { y ^ { 2 } } { 1 }7x2​=1+1y2​

Graph the conic section. - 3x2+4y2−24x+48y+180=03 x^{2}+4 y^{2}-24 x+48 y+180=03x2+4y2−24x+48y+180=0

List the elements in the sample space of the experiment. -A lottery uses balls numbered 1 through 35. List the sample space of the event picking one even-numbered ball.

In how many ways can 4 people be chosen and arranged in a straight line, if there are 10 people from whom to choose?

Identify the type of conic section. -Identify the type of conic section consisting of the set of all points in the plane for which the sum of the distances from the point (3,0) and (−3,0) is 21( 3,0 ) \text { and } ( - 3,0 ) \text { is } 21(3,0) and (−3,0) is 21

A woman borrowed $30,000 at 2% interest compounded annually. If the loan was paid off in one lump sum at the end of 6 years, how much did she pay?

Evaluate the series, if it converges. - ∑i=1∞9(32)i−1\sum _ { i = 1 } ^ { \infty } 9 \left( \frac { 3 } { 2 } \right) ^ { i - 1 }∑i=1∞​9(23​)i−1

Evaluate the sum. Round to two decimal places, if necessary. - ∑k=36(k2−2)2\sum _ { k = 3 } ^ { 6 } \frac { \left( k ^ { 2 } - 2 \right) } { 2 }∑k=36​2(k2−2)​

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Filters

Evaluate the sum. - $\sum _ { j = 400 } ^ { 3000 } j$

Find a general term a_n for the geometric sequence. - $a _ { 1 } = 2 , r = \frac { 2 } { 9 }$

Identify the type of graph. - $\frac { x ^ { 2 } } { 7 } = 1 + \frac { y ^ { 2 } } { 1 }$

Graph the conic section. - $3 x^{2}+4 y^{2}-24 x+48 y+180=0$ $Graph the conic section. - 3 x^{2}+4 y^{2}-24 x+48 y+180=0$

Identify the type of conic section. -Identify the type of conic section consisting of the set of all points in the plane for which the sum of the distances from the point $( 3,0 ) \text { and } ( - 3,0 ) \text { is } 21$

Evaluate the series, if it converges. - $\sum _ { i = 1 } ^ { \infty } 9 \left( \frac { 3 } { 2 } \right) ^ { i - 1 }$

Evaluate the sum. Round to two decimal places, if necessary. - $\sum _ { k = 3 } ^ { 6 } \frac { \left( k ^ { 2 } - 2 \right) } { 2 }$