Question 1

Evaluate the expression.
-$\frac { 7 ! } { 5 ! 2 ! }$

Accepted Answer

A)  7 
B)  1 
C)  0 ! 
D)  21 
A)  7 
B)  1 
C)  0 ! 
D)  21

Question 2

A sequence of yearly payments of $5000 is invested at an interest rate of 1.5%, compounded annually. What is the total amount of the annuity after 10 years?

Accepted Answer

A)  $54,513.61 
B)  $53,513.61 
C)  $52,513.61 
D)  $53,013.61 
A)  $54,513.61 
B)  $53,513.61 
C)  $52,513.61 
D)  $53,013.61

Question 3

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest
hundredth.
-$$a _ { 5 } = 112 , a _ { 34 } = 605$$

Accepted Answer

A)  $a _ { 1 } = 493 , d = 44$ 
B)  $a _ { 1 } = 493 , d = 17$ 
C)  $\mathrm { a } _ { 1 } = 44 , \mathrm {~d} = 17$ 
D)  $a _ { 1 } = 44 , d = 493$ 
A)  $a _ { 1 } = 493 , d = 44$ 
B)  $a _ { 1 } = 493 , d = 17$ 
C)  $\mathrm { a } _ { 1 } = 44 , \mathrm {~d} = 17$ 
D)  $a _ { 1 } = 44 , d = 493$

Question 4

To graph $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 36 } = 1$ on a graphics calculator, we must consider the union of the graphs of the two functions, $y _ { 1 } = 6 \sqrt { \frac { x ^ { 2 } } { 16 } - 1 }$ and $y _ { 2 } = - 6 \sqrt { \frac { x ^ { 2 } } { 16 } - 1 }$. Using the graph of $y = \frac { x ^ { 2 } } { 16 } - 1$, explain (a) how the solution set of $\frac { x ^ { 2 } } { 16 } - 1 \geq 0$ can be determined graphically and (b) how it relates to the domain of the hyperbola.

Accepted Answer

The graph of @#LAT-DLM& lies above or on

Question 5

Find the sum of the first n terms of the following arithmetic sequence.
-$$\mathrm { a } _ { 1 } = - 5 , \mathrm {~d} = - 6 ; \mathrm { n } = 10$$

Accepted Answer

A)  220 
B)  295 
C)  $- 295$ 
D)  $- 320$ 
A)  220 
B)  295 
C)  $- 295$ 
D)  $- 320$

Question 6

Martin saves $5 on the first day of a 40-day period, $10 on the second day, and so on. For the next 40 days, he increases the amount saved by $10 each day (instead of $5 each day). How much will he have saved after 80
Days?

Accepted Answer

A)  $20,400 
B)  $20,600 
C)  $20,200 
D)  $20,300 
A)  $20,400 
B)  $20,600 
C)  $20,200 
D)  $20,300

Question 7

In how many ways can 8 people line up for play tickets?

Accepted Answer

A)  40,320 
B)  1 
C)  16,777,216 
D)  8 
A)  40,320 
B)  1 
C)  16,777,216 
D)  8

Question 8

Write an equation for the parabola with vertex at the origin.
-Through (8, 8), symmetric with respect to the y-axis

Accepted Answer

A)  $y ^ { 2 } = 8 x$ 
B)  $x = - 8 y ^ { 2 }$ 
C)  $y = 8 x ^ { 2 }$ 
D)  $x ^ { 2 } = 8 y$ 
A)  $y ^ { 2 } = 8 x$ 
B)  $x = - 8 y ^ { 2 }$ 
C)  $y = 8 x ^ { 2 }$ 
D)  $x ^ { 2 } = 8 y$

Question 9

Write an equation for the hyperbola.
-vertices at $( 0,4 ) , ( 0 , - 4 )$; foci at $( 0,10 ) , ( 0 , - 10 )$

Accepted Answer

A)  $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 84 } = 1$ 
B)  $\frac { y ^ { 2 } } { 100 } - \frac { x ^ { 2 } } { 16 } = 1$ 
C)  $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 100 } = 1$ 
D)  $\frac { y ^ { 2 } } { 84 } - \frac { x ^ { 2 } } { 16 } = 1$ 
A)  $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 84 } = 1$ 
B)  $\frac { y ^ { 2 } } { 100 } - \frac { x ^ { 2 } } { 16 } = 1$ 
C)  $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 100 } = 1$ 
D)  $\frac { y ^ { 2 } } { 84 } - \frac { x ^ { 2 } } { 16 } = 1$

Question 10

Find the common ratio r for the given infinite geometric sequence.
-$$\frac { 4 } { 3 } , \frac { 16 } { 3 } , \frac { 64 } { 3 } , \frac { 256 } { 3 } , \frac { 1024 } { 3 } , \ldots$$

Accepted Answer

A)  12 
B)  10 
C)  $\frac { 1 } { 4 }$ 
D)  4 
A)  12 
B)  10 
C)  $\frac { 1 } { 4 }$ 
D)  4

Question 11

The beginning population of a small town was 12,000 people. Due to decline in industrial growth the population has since been decreasing at a rate of 3% every year. What was the population of this town 10 years
Later?

Accepted Answer

A)  7185 people 
B)  9805 people 
C)  7978 people 
D)  8849 people 
A)  7185 people 
B)  9805 people 
C)  7978 people 
D)  8849 people

Question 12

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

Accepted Answer

A)  18 
B)  16 
C)  12 
D)  20 
A)  18 
B)  16 
C)  12 
D)  20

Question 13

Evaluate the sum. Round to two decimal places, if necessary.
-$$\sum _ { i = 9 } ^ { 12 } ( i + 5 ) ^ { - 1 }$$

Accepted Answer

A)  $- 0.82$ 
B)  $0.26$ 
C)  62 
D)  $0.62$ 
A)  $- 0.82$ 
B)  $0.26$ 
C)  62 
D)  $0.62$

Question 14

In how many ways can a group of 8 students be selected from 9 students?

Accepted Answer

A)  8 
B)  1 
C)  72 
D)  9 
A)  8 
B)  1 
C)  72 
D)  9

Question 15

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

Accepted Answer

A)  Does not converge. 
B)  $- \frac { 400 } { 17 }$ 
C)  $\frac { 280 } { 17 }$ 
D)  $\frac { 7 } { 17 }$ 
A)  Does not converge. 
B)  $- \frac { 400 } { 17 }$ 
C)  $\frac { 280 } { 17 }$ 
D)  $\frac { 7 } { 17 }$

Question 16

How many different three-number "combinations" are possible on a combination lock having 25 numbers on its dial without repeating a number?

Accepted Answer

A)  13,200 
B)  26,400 
C)  6900 
D)  13,800 
A)  13,200 
B)  26,400 
C)  6900 
D)  13,800

Question 17

Write an equation for the ellipse.
-$x$-intercepts $( \pm 2,0 ) ; y$-intercepts $( 0 , \pm 8 )$

Accepted Answer

A)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 4 } = 1$ 
B)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 64 } = 1$ 
C)  $\frac { x ^ { 2 } } { 8 } + \frac { y ^ { 2 } } { 2 } = 1$ 
D)  $\frac { x ^ { 2 } } { 2 } + \frac { y ^ { 2 } } { 8 } = 1$ 
A)  $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 4 } = 1$ 
B)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 64 } = 1$ 
C)  $\frac { x ^ { 2 } } { 8 } + \frac { y ^ { 2 } } { 2 } = 1$ 
D)  $\frac { x ^ { 2 } } { 2 } + \frac { y ^ { 2 } } { 8 } = 1$

Question 18

100 employees of a company are asked how they get to work and whether they work full time or part time. The figure below shows the results. If one of the 100 employees is randomly selected, find the probability that the
Person does not work full time.   1. Public transportation: 6 full time, 7 part time
2. Bicycle: 5 full time, 5 part time
3. Drive alone: 34 full time, 28 part time
4. Car pool: 6 full time, 9 part time

Accepted Answer

A)  0.51 
B)  0.44 
C)  0.28 
D)  0.49 
A)  0.51 
B)  0.44 
C)  0.28 
D)  0.49

Question 19

A lottery game has balls numbered 1 through 21. What is the probability of selecting an even numbered ball or a 11?

Accepted Answer

A)  $\frac { 10 } { 11 }$ 
B)  $\frac { 11 } { 21 }$ 
C)  $\frac { 3 } { 7 }$ 
D)  $\frac { 10 } { 21 }$ 
A)  $\frac { 10 } { 11 }$ 
B)  $\frac { 11 } { 21 }$ 
C)  $\frac { 3 } { 7 }$ 
D)  $\frac { 10 } { 21 }$

Question 20

Evaluate the expression.
-$$\left( \begin{array} { c } 
10 \
5
\end{array} \right)$$

Accepted Answer

A)  30,240 
B)  126 
C)  2 
D)  252 
A)  30,240 
B)  126 
C)  2 
D)  252

Evaluate the expression. - $\frac { 7 ! } { 5 ! 2 ! }$

A sequence of yearly payments of $5000 is invested at an interest rate of 1.5%, compounded annually. What is the total amount of the annuity after 10 years?

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest hundredth. - $a _ { 5 } = 112 , a _ { 34 } = 605$

Find the sum of the first n terms of the following arithmetic sequence. - $\mathrm { a } _ { 1 } = - 5 , \mathrm {~d} = - 6 ; \mathrm { n } = 10$

Martin saves $5 on the first day of a 40-day period, $10 on the second day, and so on. For the next 40 days, he increases the amount saved by $10 each day (instead of $5 each day). How much will he have saved after 80 Days?

In how many ways can 8 people line up for play tickets?

Write an equation for the parabola with vertex at the origin. -Through (8, 8), symmetric with respect to the y-axis

Write an equation for the hyperbola. -vertices at $( 0,4 ) , ( 0 , - 4 )$ ; foci at $( 0,10 ) , ( 0 , - 10 )$

Find the common ratio r for the given infinite geometric sequence. - $\frac { 4 } { 3 } , \frac { 16 } { 3 } , \frac { 64 } { 3 } , \frac { 256 } { 3 } , \frac { 1024 } { 3 } , \ldots$

The beginning population of a small town was 12,000 people. Due to decline in industrial growth the population has since been decreasing at a rate of 3% every year. What was the population of this town 10 years Later?

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

Evaluate the sum. Round to two decimal places, if necessary. - $\sum _ { i = 9 } ^ { 12 } ( i + 5 ) ^ { - 1 }$

In how many ways can a group of 8 students be selected from 9 students?

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

How many different three-number "combinations" are possible on a combination lock having 25 numbers on its dial without repeating a number?

Write an equation for the ellipse. - $x$ -intercepts $( \pm 2,0 ) ; y$ -intercepts $( 0 , \pm 8 )$

A lottery game has balls numbered 1 through 21. What is the probability of selecting an even numbered ball or a 11?

Evaluate the expression. - $\left( \begin{array} { c } 10 \\5\end{array} \right)$

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

Evaluate the expression. - 7!5!2!\frac { 7 ! } { 5 ! 2 ! }5!2!7!​

A sequence of yearly payments of $5000 is invested at an interest rate of 1.5%, compounded annually. What is the total amount of the annuity after 10 years?

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest hundredth. - a5=112,a34=605a _ { 5 } = 112 , a _ { 34 } = 605a5​=112,a34​=605

Find the sum of the first n terms of the following arithmetic sequence. - a1=−5, d=−6;n=10\mathrm { a } _ { 1 } = - 5 , \mathrm {~d} = - 6 ; \mathrm { n } = 10a1​=−5, d=−6;n=10

Martin saves $5 on the first day of a 40-day period, $10 on the second day, and so on. For the next 40 days, he increases the amount saved by $10 each day (instead of $5 each day). How much will he have saved after 80 Days?

In how many ways can 8 people line up for play tickets?

Write an equation for the parabola with vertex at the origin. -Through (8, 8), symmetric with respect to the y-axis

Write an equation for the hyperbola. -vertices at (0,4),(0,−4)( 0,4 ) , ( 0 , - 4 )(0,4),(0,−4) ; foci at (0,10),(0,−10)( 0,10 ) , ( 0 , - 10 )(0,10),(0,−10)

Find the common ratio r for the given infinite geometric sequence. - 43,163,643,2563,10243,…\frac { 4 } { 3 } , \frac { 16 } { 3 } , \frac { 64 } { 3 } , \frac { 256 } { 3 } , \frac { 1024 } { 3 } , \ldots34​,316​,364​,3256​,31024​,…

The beginning population of a small town was 12,000 people. Due to decline in industrial growth the population has since been decreasing at a rate of 3% every year. What was the population of this town 10 years Later?

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

Evaluate the sum. Round to two decimal places, if necessary. - ∑i=912(i+5)−1\sum _ { i = 9 } ^ { 12 } ( i + 5 ) ^ { - 1 }∑i=912​(i+5)−1

In how many ways can a group of 8 students be selected from 9 students?

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

How many different three-number "combinations" are possible on a combination lock having 25 numbers on its dial without repeating a number?

Write an equation for the ellipse. - xxx -intercepts (±2,0);y( \pm 2,0 ) ; y(±2,0);y -intercepts (0,±8)( 0 , \pm 8 )(0,±8)

A lottery game has balls numbered 1 through 21. What is the probability of selecting an even numbered ball or a 11?

Evaluate the expression. - (105)\left( \begin{array} { c } 10 \\5\end{array} \right)(105​)

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

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Evaluate the expression. - $\frac { 7 ! } { 5 ! 2 ! }$

Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest hundredth. - $a _ { 5 } = 112 , a _ { 34 } = 605$

Find the sum of the first n terms of the following arithmetic sequence. - $\mathrm { a } _ { 1 } = - 5 , \mathrm {~d} = - 6 ; \mathrm { n } = 10$

Write an equation for the hyperbola. -vertices at $( 0,4 ) , ( 0 , - 4 )$ ; foci at $( 0,10 ) , ( 0 , - 10 )$

Find the common ratio r for the given infinite geometric sequence. - $\frac { 4 } { 3 } , \frac { 16 } { 3 } , \frac { 64 } { 3 } , \frac { 256 } { 3 } , \frac { 1024 } { 3 } , \ldots$

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

Evaluate the sum. Round to two decimal places, if necessary. - $\sum _ { i = 9 } ^ { 12 } ( i + 5 ) ^ { - 1 }$

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

Write an equation for the ellipse. - $x$ -intercepts $( \pm 2,0 ) ; y$ -intercepts $( 0 , \pm 8 )$

Evaluate the expression. - $\left( \begin{array} { c } 10 \\5\end{array} \right)$