Question 1

Evaluate using Pascal's Triangle.   ${ } _ { 12 } C _ { 4 }$

Accepted Answer

A) 496 
B) 495 
C) 497 
D) 494 
E) 493 
A) 496 
B) 495 
C) 497 
D) 494 
E) 493

Question 2

Find a quadratic model for the sequence with the indicated terms.  
A0 = 3, a1 = 3, a4 = 15

Accepted Answer

A) an = n2 - n + 15 
B) an = n2 + n - 3 
C) an = n2 - n - 3 
D) an = n2 + n +  3 
E) an = n2 - n + 3 
A) an = n2 - n + 15 
B) an = n2 + n - 3 
C) an = n2 - n - 3 
D) an = n2 + n +  3 
E) an = n2 - n + 3

Question 3

Find the specified nth term in the expansion of the binomial.   $( x + y ) ^ { 9 } , n = 10$

Accepted Answer

A)  $y ^ { 9 }$ 
B)  $x ^ { 9 } y ^ { 10 }$ 
C)  $x y ^ { 9 }$ 
D)  $x ^ { 9 } y$ 
E)  $y ^ { 10 }$ 
A)  $y ^ { 9 }$ 
B)  $x ^ { 9 } y ^ { 10 }$ 
C)  $x y ^ { 9 }$ 
D)  $x ^ { 9 } y$ 
E)  $y ^ { 10 }$

Question 4

Evaluate ${ } _ { n } P _ { r }$ .   $100 P _ { 5 }$

Accepted Answer

A) 94,109,400 
B) 970,200 
C) 75,287,520 
D) 9,034,502,400 
E) 858,277,728,000 
A) 94,109,400 
B) 970,200 
C) 75,287,520 
D) 9,034,502,400 
E) 858,277,728,000

Question 5

The figure shows the results of a recent survey in which 1040 adults were asked to grade U.S.public schools.Estimate the number of adults who gave U.S.public schools a B. ​   ​

Accepted Answer

A) 265 
B) 260 
C) 255 
D) 250 
E) 270 
A) 265 
B) 260 
C) 255 
D) 250 
E) 270

Question 6

Use the binomial theorem to expand the binomial.
​ $( a + 3 t ) ^ { 3 }$

Accepted Answer

The answer of Use the binomial theorem to expand the...

Question 7

Find a formula for the sum of the first n terms of the sequence.   $9,12,15,18,21 , \ldots$

Accepted Answer

A)  $S _ { n } = \frac { n } { 2 } ( 3 n + 15 )$ 
B)  $S _ { n } = \frac { n } { 2 } ( 3 n + 3 )$ 
C)  $S _ { n } = \frac { n } { 2 } ( - 3 n - 15 )$ 
D)  $S _ { n } = \frac { n } { 2 } ( 3 n - 15 )$ 
E)  $S _ { n } = \frac { n } { 2 } ( - 3 n + 15 )$ 
A)  $S _ { n } = \frac { n } { 2 } ( 3 n + 15 )$ 
B)  $S _ { n } = \frac { n } { 2 } ( 3 n + 3 )$ 
C)  $S _ { n } = \frac { n } { 2 } ( - 3 n - 15 )$ 
D)  $S _ { n } = \frac { n } { 2 } ( 3 n - 15 )$ 
E)  $S _ { n } = \frac { n } { 2 } ( - 3 n + 15 )$

Question 8

How many 3-digit numbers can be formed if the leading digit cannot be zero?

Accepted Answer

A) ​900 
B) 100 
C) 9999 
D) 901 
E) 999 
A) ​900 
B) 100 
C) 9999 
D) 901 
E) 999

Question 9

Find the indicated nth term of the geometric sequence.  
9th term : $13,39,117 , \ldots$

Accepted Answer

A)  $a _ { 9 } = 3,159$ 
B)  $a _ { 9 } = 255,879$ 
C)  $a _ { 9 } = 28,431$ 
D)  $a _ { 9 } = 85,293$ 
E)  $a _ { 9 } = 9,477$ 
A)  $a _ { 9 } = 3,159$ 
B)  $a _ { 9 } = 255,879$ 
C)  $a _ { 9 } = 28,431$ 
D)  $a _ { 9 } = 85,293$ 
E)  $a _ { 9 } = 9,477$

Question 10

Evaluate the expression.   $\left( \begin{array} { l } 
96 \
95
\end{array} \right)$

Accepted Answer

A) 86 
B) 1 
C) 96 
D) 95 
E) -9 
A) 86 
B) 1 
C) 96 
D) 95 
E) -9

Question 11

Determine the sample space for the experiment.  
Two prize winners are selected from six people: A, B, C, D, E, and F.

Accepted Answer

A) S = {AB, AC, AD, AE, BC, BD, BE, CD, CE, DE} 
B) S = {AB, AC, AD, AE, AF} 
C) S = {AB, AC, AD, AE, AF, BC, BD, BE, BF, CD, CE, CF, DE, DF, EF} 
D) S = {AB, AC, AD, BC, BD, CD} 
E) S = {AB, CD, EF} 
A) S = {AB, AC, AD, AE, BC, BD, BE, CD, CE, DE} 
B) S = {AB, AC, AD, AE, AF} 
C) S = {AB, AC, AD, AE, AF, BC, BD, BE, BF, CD, CE, CF, DE, DF, EF} 
D) S = {AB, AC, AD, BC, BD, CD} 
E) S = {AB, CD, EF}

Question 12

Find the sum using the formulas for the sums of powers of integers.   $\sum _ { j = 1 } ^ { 11 } \left( 4 - \frac { 1 } { 2 } j + \frac { 1 } { 2 } j ^ { 2 } \right)$

Accepted Answer

A) -264 
B) 264 
C) -506 
D) 759 
E) 506 
A) -264 
B) 264 
C) -506 
D) 759 
E) 506

Question 13

Find the sum of the infinite series.   $\sum _ { i = 1 } ^ { \infty } 2 \left( \frac { 1 } { 10 } \right) ^ { i }$

Accepted Answer

A)  $\frac { 2 } { 9 }$ 
B)  $\frac { 9 k } { 2 }$ 
C)  $\frac { 9 } { 2 }$ 
D)  $- \frac { 2 k } { 9 }$ 
E)  $\frac { 2 k } { 9 }$ 
A)  $\frac { 2 } { 9 }$ 
B)  $\frac { 9 k } { 2 }$ 
C)  $\frac { 9 } { 2 }$ 
D)  $- \frac { 2 k } { 9 }$ 
E)  $\frac { 2 k } { 9 }$

Question 14

Find pk + 1 for the given pk.   $p _ { k } = \frac { 1 } { 4 ( k + 2 ) }$

Accepted Answer

A)  $p _ { k + 1 } = \frac { 1 } { k ( k + 3 ) }$ 
B)  $p _ { k + 1 } = \frac { 4 } { ( k + 1 ) ( k + 2 ) }$ 
C)  $p _ { k + 1 } = \frac { 4 } { k ( k + 3 ) }$ 
D)  $p _ { k + 1 } = \frac { 1 } { ( k + 3 ) ( k + 2 ) }$ 
E)  $p _ { k + 1 } = \frac { 1 } { 4 ( k + 3 ) }$ 
A)  $p _ { k + 1 } = \frac { 1 } { k ( k + 3 ) }$ 
B)  $p _ { k + 1 } = \frac { 4 } { ( k + 1 ) ( k + 2 ) }$ 
C)  $p _ { k + 1 } = \frac { 4 } { k ( k + 3 ) }$ 
D)  $p _ { k + 1 } = \frac { 1 } { ( k + 3 ) ( k + 2 ) }$ 
E)  $p _ { k + 1 } = \frac { 1 } { 4 ( k + 3 ) }$

Question 15

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1.)   $1,7,13,19,25 , \ldots$

Accepted Answer

A)  $a _ { n } = - 6 n - 5$ 
B)  $a _ { n } = 6 n - 5$ 
C)  $a _ { n } = 5 n + 6$ 
D)  $a _ { n } = 5 n - 6$ 
E)  $a _ { n } = 6 n + 5$ 
A)  $a _ { n } = - 6 n - 5$ 
B)  $a _ { n } = 6 n - 5$ 
C)  $a _ { n } = 5 n + 6$ 
D)  $a _ { n } = 5 n - 6$ 
E)  $a _ { n } = 6 n + 5$

Question 16

Use the Binominal Theorem to expand the complex number.Simplify your result.   $( 4 - 6 i ) ^ { 4 }$

Accepted Answer

A)   $- 256 + 1536 i + 3456 + 3456 i ^ { 3 } - 1296$ 
B)   $256 + 1536 i - 3456 + 3456 i ^ { 3 } + 1296$ 
C)   $- 256 - 1536 i + 3456 - 3456 i ^ { 3 } - 1296$ 
D)   $256 - 1536 i - 3456 - 3456 i ^ { 3 } + 1296$ 
E)   $1296 - 3456 i - 3456 - 1536 i ^ { 3 } + 256$ 
A)   $- 256 + 1536 i + 3456 + 3456 i ^ { 3 } - 1296$ 
B)   $256 + 1536 i - 3456 + 3456 i ^ { 3 } + 1296$ 
C)   $- 256 - 1536 i + 3456 - 3456 i ^ { 3 } - 1296$ 
D)   $256 - 1536 i - 3456 - 3456 i ^ { 3 } + 1296$ 
E)   $1296 - 3456 i - 3456 - 1536 i ^ { 3 } + 256$

Question 17

Find the first five terms of the geometric sequence.   $a _ { 1 } = 4 , r = 2 x$

Accepted Answer

A)  $4,2 x , 2 x ^ { 2 } , 2 x ^ { 3 } , 2 x ^ { 4 }$ 
B)  $4,8 x , 16 x ^ { 2 } , 32 x ^ { 3 } , 64 x ^ { 4 }$ 
C)  $4,2 x ^ { 2 } , 2 x ^ { 3 } , 2 x ^ { 4 } , 2 x ^ { 5 }$ 
D)  $4,8 x ^ { 2 } , 16 x ^ { 3 } , 32 x ^ { 4 } , 64 x ^ { 5 }$ 
E)  $4 , x ^ { 2 } , x ^ { 3 } , x ^ { 4 } , x ^ { 5 }$ 
A)  $4,2 x , 2 x ^ { 2 } , 2 x ^ { 3 } , 2 x ^ { 4 }$ 
B)  $4,8 x , 16 x ^ { 2 } , 32 x ^ { 3 } , 64 x ^ { 4 }$ 
C)  $4,2 x ^ { 2 } , 2 x ^ { 3 } , 2 x ^ { 4 } , 2 x ^ { 5 }$ 
D)  $4,8 x ^ { 2 } , 16 x ^ { 3 } , 32 x ^ { 4 } , 64 x ^ { 5 }$ 
E)  $4 , x ^ { 2 } , x ^ { 3 } , x ^ { 4 } , x ^ { 5 }$

Question 18

Find the specified nth term in the expansion of the binomial.   $( x + y ) ^ { 10 } , n = 6$

Accepted Answer

A) 251 $x ^ { 5 } y ^ { 5 }$ 
B) 254 $x ^ { 5 } y ^ { 5 }$ 
C) 253 $x ^ { 5 } y ^ { 5 }$ 
D) 252 $x ^ { 5 } y ^ { 5 }$ 
E) 250 $x ^ { 5 } y ^ { 5 }$ 
A) 251 $x ^ { 5 } y ^ { 5 }$ 
B) 254 $x ^ { 5 } y ^ { 5 }$ 
C) 253 $x ^ { 5 } y ^ { 5 }$ 
D) 252 $x ^ { 5 } y ^ { 5 }$ 
E) 250 $x ^ { 5 } y ^ { 5 }$

Question 19

Find the sum of the infinite series. $\sum _ { i = 1 } ^ { \infty } 2 \left( - \frac { 1 } { 4 } \right) ^ { i }$

Accepted Answer

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

Question 20

Write the first six terms of the sequence beginning with the given term.Then calculate the first and second differences of the sequence.State whether the sequence has a linear model, a quadratic model, or neither.  
A0 = 1
An = an - 1 + n

Accepted Answer

A) 0, 1, 2, -4, 7, -11
First differences: 1, 1, 2, 3, 4
Second differences: -1, 1, -1, 1
Neither 
B) 1, -2, 4, -7, 11, -16
First differences: -1, 1, -1, 1
Second differences: 1, 2, 3, 4, 5
Neither 
C) 0, 1, 2, 4, 7, 11
First differences: 1, 1, 2, 3, 4
Second differences: -1, 1, -1, 1
Linear 
D) 0, 1, 2, 4, 7, 11
First differences: 1, 1, 2, 3, 4
Second differences: -1, 1, -1, 1
Quadratic 
E) 1, 2, 4, 7, 11, 16
First differences: 1, 2, 3, 4, 5
Second differences: 1, 1, 1, 1
Quadratic 
A) 0, 1, 2, -4, 7, -11
First differences: 1, 1, 2, 3, 4
Second differences: -1, 1, -1, 1
Neither 
B) 1, -2, 4, -7, 11, -16
First differences: -1, 1, -1, 1
Second differences: 1, 2, 3, 4, 5
Neither 
C) 0, 1, 2, 4, 7, 11
First differences: 1, 1, 2, 3, 4
Second differences: -1, 1, -1, 1
Linear 
D) 0, 1, 2, 4, 7, 11
First differences: 1, 1, 2, 3, 4
Second differences: -1, 1, -1, 1
Quadratic 
E) 1, 2, 4, 7, 11, 16
First differences: 1, 2, 3, 4, 5
Second differences: 1, 1, 1, 1
Quadratic

Evaluate using Pascal's Triangle. ${ } _ { 12 } C _ { 4 }$

Find a quadratic model for the sequence with the indicated terms. A₀ = 3, a₁ = 3, a₄ = 15

Find the specified nth term in the expansion of the binomial. $( x + y ) ^ { 9 } , n = 10$

Evaluate ${ } _ { n } P _ { r }$ . $100 P _ { 5 }$

The figure shows the results of a recent survey in which 1040 adults were asked to grade U.S.public schools.Estimate the number of adults who gave U.S.public schools a B.

Use the binomial theorem to expand the binomial. $( a + 3 t ) ^ { 3 }$

Find a formula for the sum of the first n terms of the sequence. $9,12,15,18,21 , \ldots$

How many 3-digit numbers can be formed if the leading digit cannot be zero?

Find the indicated nth term of the geometric sequence. 9th term : $13,39,117 , \ldots$

Evaluate the expression. $\left( \begin{array} { l } 96 \\95\end{array} \right)$

Determine the sample space for the experiment. Two prize winners are selected from six people: A, B, C, D, E, and F.

Find the sum using the formulas for the sums of powers of integers. $\sum _ { j = 1 } ^ { 11 } \left( 4 - \frac { 1 } { 2 } j + \frac { 1 } { 2 } j ^ { 2 } \right)$

Find the sum of the infinite series. $\sum _ { i = 1 } ^ { \infty } 2 \left( \frac { 1 } { 10 } \right) ^ { i }$

Find pk_{+ 1} for the given pk. $p _ { k } = \frac { 1 } { 4 ( k + 2 ) }$

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1.) $1,7,13,19,25 , \ldots$

Use the Binominal Theorem to expand the complex number.Simplify your result. $( 4 - 6 i ) ^ { 4 }$

Find the first five terms of the geometric sequence. $a _ { 1 } = 4 , r = 2 x$

Find the specified nth term in the expansion of the binomial. $( x + y ) ^ { 10 } , n = 6$

Find the sum of the infinite series. $\sum _ { i = 1 } ^ { \infty } 2 \left( - \frac { 1 } { 4 } \right) ^ { i }$

Write the first six terms of the sequence beginning with the given term.Then calculate the first and second differences of the sequence.State whether the sequence has a linear model, a quadratic model, or neither. A₀ = 1 A_n = an_{- 1} + n

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Exam 9: Sequences Series and Probability

Evaluate using Pascal's Triangle. 12C4{ } _ { 12 } C _ { 4 }12​C4​

Find a quadratic model for the sequence with the indicated terms. A0 = 3, a1 = 3, a4 = 15

Find the specified nth term in the expansion of the binomial. (x+y)9,n=10( x + y ) ^ { 9 } , n = 10(x+y)9,n=10

Evaluate nPr{ } _ { n } P _ { r }n​Pr​ . 100P5100 P _ { 5 }100P5​

The figure shows the results of a recent survey in which 1040 adults were asked to grade U.S.public schools.Estimate the number of adults who gave U.S.public schools a B. ​ ​

Use the binomial theorem to expand the binomial. ​ (a+3t)3( a + 3 t ) ^ { 3 }(a+3t)3

Find a formula for the sum of the first n terms of the sequence. 9,12,15,18,21,…9,12,15,18,21 , \ldots9,12,15,18,21,…

How many 3-digit numbers can be formed if the leading digit cannot be zero?

Find the indicated nth term of the geometric sequence. 9th term : 13,39,117,…13,39,117 , \ldots13,39,117,…

Evaluate the expression. (9695)\left( \begin{array} { l } 96 \\95\end{array} \right)(9695​)

Determine the sample space for the experiment. Two prize winners are selected from six people: A, B, C, D, E, and F.

Find the sum using the formulas for the sums of powers of integers. ∑j=111(4−12j+12j2)\sum _ { j = 1 } ^ { 11 } \left( 4 - \frac { 1 } { 2 } j + \frac { 1 } { 2 } j ^ { 2 } \right)∑j=111​(4−21​j+21​j2)

Find the sum of the infinite series. ∑i=1∞2(110)i\sum _ { i = 1 } ^ { \infty } 2 \left( \frac { 1 } { 10 } \right) ^ { i }∑i=1∞​2(101​)i

Find pk + 1 for the given pk. pk=14(k+2)p _ { k } = \frac { 1 } { 4 ( k + 2 ) }pk​=4(k+2)1​

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1.) 1,7,13,19,25,…1,7,13,19,25 , \ldots1,7,13,19,25,…

Use the Binominal Theorem to expand the complex number.Simplify your result. (4−6i)4( 4 - 6 i ) ^ { 4 }(4−6i)4

Find the first five terms of the geometric sequence. a1=4,r=2xa _ { 1 } = 4 , r = 2 xa1​=4,r=2x

Find the specified nth term in the expansion of the binomial. (x+y)10,n=6( x + y ) ^ { 10 } , n = 6(x+y)10,n=6

Find the sum of the infinite series. ∑i=1∞2(−14)i\sum _ { i = 1 } ^ { \infty } 2 \left( - \frac { 1 } { 4 } \right) ^ { i }∑i=1∞​2(−41​)i

Write the first six terms of the sequence beginning with the given term.Then calculate the first and second differences of the sequence.State whether the sequence has a linear model, a quadratic model, or neither. A0 = 1 An = an - 1 + n

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Evaluate using Pascal's Triangle. ${ } _ { 12 } C _ { 4 }$

Find a quadratic model for the sequence with the indicated terms. A₀ = 3, a₁ = 3, a₄ = 15

Find the specified nth term in the expansion of the binomial. $( x + y ) ^ { 9 } , n = 10$

Evaluate ${ } _ { n } P _ { r }$ . $100 P _ { 5 }$

The figure shows the results of a recent survey in which 1040 adults were asked to grade U.S.public schools.Estimate the number of adults who gave U.S.public schools a B.

Use the binomial theorem to expand the binomial. $( a + 3 t ) ^ { 3 }$

Find a formula for the sum of the first n terms of the sequence. $9,12,15,18,21 , \ldots$

Find the indicated nth term of the geometric sequence. 9th term : $13,39,117 , \ldots$

Evaluate the expression. $\left( \begin{array} { l } 96 \\95\end{array} \right)$

Find the sum using the formulas for the sums of powers of integers. $\sum _ { j = 1 } ^ { 11 } \left( 4 - \frac { 1 } { 2 } j + \frac { 1 } { 2 } j ^ { 2 } \right)$

Find the sum of the infinite series. $\sum _ { i = 1 } ^ { \infty } 2 \left( \frac { 1 } { 10 } \right) ^ { i }$

Find pk_{+ 1} for the given pk. $p _ { k } = \frac { 1 } { 4 ( k + 2 ) }$

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1.) $1,7,13,19,25 , \ldots$

Use the Binominal Theorem to expand the complex number.Simplify your result. $( 4 - 6 i ) ^ { 4 }$

Find the first five terms of the geometric sequence. $a _ { 1 } = 4 , r = 2 x$

Find the specified nth term in the expansion of the binomial. $( x + y ) ^ { 10 } , n = 6$

Find the sum of the infinite series. $\sum _ { i = 1 } ^ { \infty } 2 \left( - \frac { 1 } { 4 } \right) ^ { i }$

Write the first six terms of the sequence beginning with the given term.Then calculate the first and second differences of the sequence.State whether the sequence has a linear model, a quadratic model, or neither. A₀ = 1 A_n = an_{- 1} + n