Question 1

Find the sum using the formulas for the sums of powers of integers.   $\sum _ { n = 1 } ^ { 2 } n ^ { 4 }$

Accepted Answer

A) 33 
B) 17 
C) 30 
D) 5 
E) 9 
A) 33 
B) 17 
C) 30 
D) 5 
E) 9

Question 2

Find the sum. $\sum _ { k = 1 } ^ { 3 } \frac { 1 } { k ^ { 2 } + 5 }$

Accepted Answer

A)  $\frac { 73 } { 168 }$ 
B)  $\frac { 1 } { 14 }$ 
C)  $\frac { 22 } { 63 }$ 
D) 1 
E)  $\frac { 12 } { 11 }$ 
A)  $\frac { 73 } { 168 }$ 
B)  $\frac { 1 } { 14 }$ 
C)  $\frac { 22 } { 63 }$ 
D) 1 
E)  $\frac { 12 } { 11 }$

Question 3

Evaluate ${ } _ { n } C _ { r }$ using the formula from this section.   ${ } _ { 25 } C _ { 4 }$

Accepted Answer

A) 177,100 
B) 303,600 
C) 480,700 
D) 12,650 
E) 53,130 
A) 177,100 
B) 303,600 
C) 480,700 
D) 12,650 
E) 53,130

Question 4

Evaluate ${ } _ { n } C _ { r }$ using the formula from this section.   ${ } _ { 48 } C _ { 5 }$

Accepted Answer

A) 1,712,304 
B) 377,348,994 
C) 12,271,512 
D) 73,629,072 
E) 205,476,480 
A) 1,712,304 
B) 377,348,994 
C) 12,271,512 
D) 73,629,072 
E) 205,476,480

Question 5

Write the first five terms of the sequence.Determine whether the sequence is arithmetic.If so, find the common difference.(Assume that n begins with 1.) ​
An = 4n - 1
​

Accepted Answer

A) 1, 4, 16, 64, 256Arithmetic sequenced = -4 
B) 256, 64, 16, 4, 1Not an Arithmetic sequence 
C) 1, 4, 16, 64, 256Not an Arithmetic sequence 
D) 256, 64, 16, 4, 1Arithmetic sequenced = 4 
E) 1, 4, 16, 64, 256Arithmetic sequenced = 4 
A) 1, 4, 16, 64, 256Arithmetic sequenced = -4 
B) 256, 64, 16, 4, 1Not an Arithmetic sequence 
C) 1, 4, 16, 64, 256Not an Arithmetic sequence 
D) 256, 64, 16, 4, 1Arithmetic sequenced = 4 
E) 1, 4, 16, 64, 256Arithmetic sequenced = 4

Question 6

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1.)   $\frac { 2 } { 7 } , \frac { 3 } { 15 } , \frac { 4 } { 23 } , \frac { 5 } { 31 } , \frac { 6 } { 39 } , \ldots$

Accepted Answer

A)  $a _ { n } = \frac { n + 1 } { 8 n - 8 }$ 
B)  $a _ { n } = \frac { n - 1 } { 8 n + 1 }$ 
C)  $a _ { n } = \frac { n + 1 } { 8 n + 1 }$ 
D)  $a _ { n } = \frac { n - 1 } { 8 n - 1 }$ 
E)  $a _ { n } = \frac { n + 1 } { 8 n - 1 }$ 
A)  $a _ { n } = \frac { n + 1 } { 8 n - 8 }$ 
B)  $a _ { n } = \frac { n - 1 } { 8 n + 1 }$ 
C)  $a _ { n } = \frac { n + 1 } { 8 n + 1 }$ 
D)  $a _ { n } = \frac { n - 1 } { 8 n - 1 }$ 
E)  $a _ { n } = \frac { n + 1 } { 8 n - 1 }$

Question 7

Use the Binomial Theorem to expand and simplify the expression.   $( x + 5 ) ^ { 6 }$

Accepted Answer

A)  $x ^ { 6 } + 30 x ^ { 5 } + 500 x ^ { 4 } + 2500 x ^ { 3 } + 9375 x ^ { 2 } + 15625 x + 625$ 
B)  $x ^ { 6 } + 500 x ^ { 5 } + 375 x ^ { 4 } + 3125 x ^ { 3 } + 9375 x ^ { 2 } + 18750 x + 15625$ 
C)  $x ^ { 6 } + 30 x ^ { 5 } + 375 x ^ { 4 } + 2500 x ^ { 3 } + 9375 x ^ { 2 } + 18750 x + 15625$ 
D)  $x ^ { 6 } + 30 x ^ { 5 } + 375 x ^ { 4 } + 2500 x ^ { 3 } + 9375 x ^ { 2 } - 18750 x + 625$ 
E)  $x ^ { 6 } + 30 x ^ { 5 } + 25 x ^ { 4 } + 3125 x ^ { 3 } + 9375 x ^ { 2 } + 18750 x + 15625$ 
A)  $x ^ { 6 } + 30 x ^ { 5 } + 500 x ^ { 4 } + 2500 x ^ { 3 } + 9375 x ^ { 2 } + 15625 x + 625$ 
B)  $x ^ { 6 } + 500 x ^ { 5 } + 375 x ^ { 4 } + 3125 x ^ { 3 } + 9375 x ^ { 2 } + 18750 x + 15625$ 
C)  $x ^ { 6 } + 30 x ^ { 5 } + 375 x ^ { 4 } + 2500 x ^ { 3 } + 9375 x ^ { 2 } + 18750 x + 15625$ 
D)  $x ^ { 6 } + 30 x ^ { 5 } + 375 x ^ { 4 } + 2500 x ^ { 3 } + 9375 x ^ { 2 } - 18750 x + 625$ 
E)  $x ^ { 6 } + 30 x ^ { 5 } + 25 x ^ { 4 } + 3125 x ^ { 3 } + 9375 x ^ { 2 } + 18750 x + 15625$

Question 8

Use the Binomial Theorem to expand and simplify the expression.   $( 2 x + y ) ^ { 3 }$

Accepted Answer

A)  $8 x ^ { 3 } - 12 x ^ { 2 } y + 6 x y ^ { 2 } + y ^ { 3 }$ 
B)  $8 x ^ { 3 } + 12 x ^ { 2 } y - 6 x y ^ { 2 } + y ^ { 3 }$ 
C)  $x ^ { 3 } + 12 x ^ { 2 } y + 6 x y ^ { 2 } + y ^ { 3 }$ 
D)  $8 x ^ { 3 } + 12 x ^ { 2 } y + 6 x y ^ { 2 } + y ^ { 3 }$ 
E)  $8 x ^ { 3 } + 12 x ^ { 2 } y + 6 x y ^ { 2 } - y ^ { 3 }$ 
A)  $8 x ^ { 3 } - 12 x ^ { 2 } y + 6 x y ^ { 2 } + y ^ { 3 }$ 
B)  $8 x ^ { 3 } + 12 x ^ { 2 } y - 6 x y ^ { 2 } + y ^ { 3 }$ 
C)  $x ^ { 3 } + 12 x ^ { 2 } y + 6 x y ^ { 2 } + y ^ { 3 }$ 
D)  $8 x ^ { 3 } + 12 x ^ { 2 } y + 6 x y ^ { 2 } + y ^ { 3 }$ 
E)  $8 x ^ { 3 } + 12 x ^ { 2 } y + 6 x y ^ { 2 } - y ^ { 3 }$

Question 9

Find the sum of the infinite series. $\sum _ { i = 1 } ^ { \infty } 3 \left( - \frac { 1 } { 4 } \right) ^ { i }$

Accepted Answer

A) undefined 
B) 3 
C)  $- \frac { 3 } { 5 }$ 
D)  $\frac { 6 } { 5 }$ 
E)  $- \frac { 1 } { 1 }$ 
A) undefined 
B) 3 
C)  $- \frac { 3 } { 5 }$ 
D)  $\frac { 6 } { 5 }$ 
E)  $- \frac { 1 } { 1 }$

Question 10

Find the coefficient a of the term in the expansion of the binomial. $\begin{array}{lr}\text { Binominal }&\text { Terms }\
(6x-y)^{10} & a x^{2} y^{8}
\end{array}$

Accepted Answer

A) 1,621 
B) 1,620 
C) 1,619 
D) 1,623 
E) 1,618 
A) 1,621 
B) 1,620 
C) 1,619 
D) 1,623 
E) 1,618

Question 11

Evaluate ${ } _ { n } P _ { r }$ .   ${ } _ { 16 } P _ { 8 }$

Accepted Answer

A) 57,657,600 
B) 524,160 
C) 5,765,760 
D) 518,918,400 
E) 12,870 
A) 57,657,600 
B) 524,160 
C) 5,765,760 
D) 518,918,400 
E) 12,870

Question 12

Find the coefficient a of the term in the expansion of the binomial. $\begin{array}{lr}\text { Binominal }&\text { Terms }\
(2 x-5 y)^{9} &a x^{4} y^{5}
\end{array}$

Accepted Answer

A) -6,300,001 
B) -6,300,002 
C) -6,299,999 
D) -6,300,000 
E) -6,299,997 
A) -6,300,001 
B) -6,300,002 
C) -6,299,999 
D) -6,300,000 
E) -6,299,997

Question 13

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.  
A 1 = 3
An = n - an - 1

Accepted Answer

A) 3, -1, 4, 0, 5, 1
First differences: -9, 9, -9, 9
Second differences: -4, 5, -4, 5, -4
Linear 
B) 0, 3, -1, 4, 0, 5
First differences: -4, 5, -4, 5, -4
Second differences: -9, -9, -9, -9
Quadratic 
C) 3, -1, 4, 0, 5, 1
First differences: -9, -9, -9, -9
Second differences: -4, 5, -4, 5, -4
Neither 
D) 3, -1, 4, -0, 5, -1
First differences: -9, -9, -9, -9
Second differences: -4, 5, -4, 5, -4
Linear 
E) 3, -1, 4, 0, 5, 1
First differences: -4, 5, -4, 5, -4
Second differences: 9, -9, 9, -9
Neither 
A) 3, -1, 4, 0, 5, 1
First differences: -9, 9, -9, 9
Second differences: -4, 5, -4, 5, -4
Linear 
B) 0, 3, -1, 4, 0, 5
First differences: -4, 5, -4, 5, -4
Second differences: -9, -9, -9, -9
Quadratic 
C) 3, -1, 4, 0, 5, 1
First differences: -9, -9, -9, -9
Second differences: -4, 5, -4, 5, -4
Neither 
D) 3, -1, 4, -0, 5, -1
First differences: -9, -9, -9, -9
Second differences: -4, 5, -4, 5, -4
Linear 
E) 3, -1, 4, 0, 5, 1
First differences: -4, 5, -4, 5, -4
Second differences: 9, -9, 9, -9
Neither

Question 14

Find the 3rd term in the binomial expansion.
  $( z + t ) ^ { 4 }$

Accepted Answer

The answer of Find the 3rd term in the binomial...

Question 15

Find the coefficient a of the term in the expansion of the binomial.  $\begin{array}{lr}\text { Binominal }&\text { Terms }\
(x+7)^{12} & a x^{5}
\end{array}$

Accepted Answer

A) -407,653,785 
B) -652,246,056 
C) 760,953,732 
D) 181,179,460 
E) 652,246,056 
A) -407,653,785 
B) -652,246,056 
C) 760,953,732 
D) 181,179,460 
E) 652,246,056

Question 16

Find the indicated nth term of the geometric sequence.  
22th term : $8,32,128 , \ldots$

Accepted Answer

A)  $a _ { 22 } = 35,184,372,088,832$ 
B)  $a _ { 22 } = 549,755,813,888$ 
C)  $a _ { 22 } = 2,199,023,255,552$ 
D)  $a _ { 22 } = 8,796,093,022,208$ 
E)  $a _ { 22 } = 140,737,488,355,328$ 
A)  $a _ { 22 } = 35,184,372,088,832$ 
B)  $a _ { 22 } = 549,755,813,888$ 
C)  $a _ { 22 } = 2,199,023,255,552$ 
D)  $a _ { 22 } = 8,796,093,022,208$ 
E)  $a _ { 22 } = 140,737,488,355,328$

Question 17

Find the sum of the infinite geometric sequence.   $\sum _ { n = 1 } ^ { \infty } 8 - \left( \frac { 1 } { 6 } \right) ^ { n - 1 }$

Accepted Answer

A)  s = $\frac { 5 } { 34 }$ 
B)  s = $\frac { 34 } { 5 }$ 
C)  s = $\frac { 42 } { 5 }$ 
D)  s = $\frac { 46 } { 5 }$ 
E)  s = $\frac { 1 } { 5 }$ 
A)  s = $\frac { 5 } { 34 }$ 
B)  s = $\frac { 34 } { 5 }$ 
C)  s = $\frac { 42 } { 5 }$ 
D)  s = $\frac { 46 } { 5 }$ 
E)  s = $\frac { 1 } { 5 }$

Question 18

Use the Binomial Theorem to expand and simplify the expression. $( 4 x + 5 y ) ^ { 4 }$

Accepted Answer

A)  $256 x ^ { 4 } + 1280 x ^ { 3 } y + 2400 x ^ { 2 } y ^ { 2 } + 2000 x y ^ { 3 } + 625 y ^ { 4 }$ 
B)  $256 x ^ { 4 } + 1280 x ^ { 3 } y + 2400 x ^ { 2 } y ^ { 2 } + 2000 x y ^ { 3 } - y ^ { 4 }$ 
C)  $256 x ^ { 4 } + 320 x ^ { 3 } y + 2400 x ^ { 2 } y ^ { 2 } + 2000 x y ^ { 3 } + 625 y ^ { 4 }$ 
D)  $256 x ^ { 4 } + 500 x ^ { 3 } y + 2400 x ^ { 2 } y ^ { 2 } + 2000 x y ^ { 3 } - 625 y ^ { 4 }$ 
E)  $x ^ { 4 } + 1280 x ^ { 3 } y + 2400 x ^ { 2 } y ^ { 2 } + 2000 x y ^ { 3 } + y ^ { 4 }$ 
A)  $256 x ^ { 4 } + 1280 x ^ { 3 } y + 2400 x ^ { 2 } y ^ { 2 } + 2000 x y ^ { 3 } + 625 y ^ { 4 }$ 
B)  $256 x ^ { 4 } + 1280 x ^ { 3 } y + 2400 x ^ { 2 } y ^ { 2 } + 2000 x y ^ { 3 } - y ^ { 4 }$ 
C)  $256 x ^ { 4 } + 320 x ^ { 3 } y + 2400 x ^ { 2 } y ^ { 2 } + 2000 x y ^ { 3 } + 625 y ^ { 4 }$ 
D)  $256 x ^ { 4 } + 500 x ^ { 3 } y + 2400 x ^ { 2 } y ^ { 2 } + 2000 x y ^ { 3 } - 625 y ^ { 4 }$ 
E)  $x ^ { 4 } + 1280 x ^ { 3 } y + 2400 x ^ { 2 } y ^ { 2 } + 2000 x y ^ { 3 } + y ^ { 4 }$

Question 19

Eight sprinters have qualified for the finals in the 100-meter dash at the NCAA national track meet.In how many ways can the sprinters come in first, second, and third? (Assume there are no ties.) ​

Accepted Answer

A) 486 
B) 386 
C) 436 
D) 336 
E) 536 
A) 486 
B) 386 
C) 436 
D) 336 
E) 536

Question 20

Find the coefficient a of the term in the expansion of the binomial. $\begin{array}{lr}\text { Binominal }&\text { Terms }\
(x-7 y)^{10}& a x^{8} y^{2}
\end{array}$

Accepted Answer

A) 2,208 
B) 2,204 
C) 2,206 
D) 2,205 
E) 2,203 
A) 2,208 
B) 2,204 
C) 2,206 
D) 2,205 
E) 2,203

Find the sum using the formulas for the sums of powers of integers. $\sum _ { n = 1 } ^ { 2 } n ^ { 4 }$

Find the sum. $\sum _ { k = 1 } ^ { 3 } \frac { 1 } { k ^ { 2 } + 5 }$

Evaluate ${ } _ { n } C _ { r }$ using the formula from this section. ${ } _ { 25 } C _ { 4 }$

Evaluate ${ } _ { n } C _ { r }$ using the formula from this section. ${ } _ { 48 } C _ { 5 }$

Write the first five terms of the sequence.Determine whether the sequence is arithmetic.If so, find the common difference.(Assume that n begins with 1.) A_n = 4n - ¹

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1.) $\frac { 2 } { 7 } , \frac { 3 } { 15 } , \frac { 4 } { 23 } , \frac { 5 } { 31 } , \frac { 6 } { 39 } , \ldots$

Use the Binomial Theorem to expand and simplify the expression. $( x + 5 ) ^ { 6 }$

Use the Binomial Theorem to expand and simplify the expression. $( 2 x + y ) ^ { 3 }$

Find the sum of the infinite series. $\sum _ { i = 1 } ^ { \infty } 3 \left( - \frac { 1 } { 4 } \right) ^ { i }$

Find the coefficient a of the term in the expansion of the binomial. Binominal Terms (6x-y a

Evaluate ${ } _ { n } P _ { r }$ . ${ } _ { 16 } P _ { 8 }$

Find the coefficient a of the term in the expansion of the binomial. Binominal Terms (2x-5y a

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. A ₁ = 3 A_n = n - an_{- 1}

Find the 3rd term in the binomial expansion. $( z + t ) ^ { 4 }$

Find the coefficient a of the term in the expansion of the binomial. Binominal Terms (x+7 a

Find the indicated nth term of the geometric sequence. 22th term : $8,32,128 , \ldots$

Find the sum of the infinite geometric sequence. $\sum _ { n = 1 } ^ { \infty } 8 - \left( \frac { 1 } { 6 } \right) ^ { n - 1 }$

Use the Binomial Theorem to expand and simplify the expression. $( 4 x + 5 y ) ^ { 4 }$

Eight sprinters have qualified for the finals in the 100-meter dash at the NCAA national track meet.In how many ways can the sprinters come in first, second, and third? (Assume there are no ties.)

Find the coefficient a of the term in the expansion of the binomial. Binominal Terms (x-7y a

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

Find the sum using the formulas for the sums of powers of integers. ∑n=12n4\sum _ { n = 1 } ^ { 2 } n ^ { 4 }∑n=12​n4

Find the sum. ∑k=131k2+5\sum _ { k = 1 } ^ { 3 } \frac { 1 } { k ^ { 2 } + 5 }∑k=13​k2+51​

Evaluate nCr{ } _ { n } C _ { r }n​Cr​ using the formula from this section. 25C4{ } _ { 25 } C _ { 4 }25​C4​

Evaluate nCr{ } _ { n } C _ { r }n​Cr​ using the formula from this section. 48C5{ } _ { 48 } C _ { 5 }48​C5​

Write the first five terms of the sequence.Determine whether the sequence is arithmetic.If so, find the common difference.(Assume that n begins with 1.) ​ An = 4n - 1 ​

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1.) 27,315,423,531,639,…\frac { 2 } { 7 } , \frac { 3 } { 15 } , \frac { 4 } { 23 } , \frac { 5 } { 31 } , \frac { 6 } { 39 } , \ldots72​,153​,234​,315​,396​,…

Use the Binomial Theorem to expand and simplify the expression. (x+5)6( x + 5 ) ^ { 6 }(x+5)6

Use the Binomial Theorem to expand and simplify the expression. (2x+y)3( 2 x + y ) ^ { 3 }(2x+y)3

Find the sum of the infinite series. ∑i=1∞3(−14)i\sum _ { i = 1 } ^ { \infty } 3 \left( - \frac { 1 } { 4 } \right) ^ { i }∑i=1∞​3(−41​)i

Find the coefficient a of the term in the expansion of the binomial. Binominal Terms (6x-y a

Evaluate nPr{ } _ { n } P _ { r }n​Pr​ . 16P8{ } _ { 16 } P _ { 8 }16​P8​

Find the coefficient a of the term in the expansion of the binomial. Binominal Terms (2x-5y a

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. A 1 = 3 An = n - an - 1

Find the 3rd term in the binomial expansion. (z+t)4( z + t ) ^ { 4 }(z+t)4

Find the coefficient a of the term in the expansion of the binomial. Binominal Terms (x+7 a

Find the indicated nth term of the geometric sequence. 22th term : 8,32,128,…8,32,128 , \ldots8,32,128,…

Find the sum of the infinite geometric sequence. ∑n=1∞8−(16)n−1\sum _ { n = 1 } ^ { \infty } 8 - \left( \frac { 1 } { 6 } \right) ^ { n - 1 }∑n=1∞​8−(61​)n−1

Use the Binomial Theorem to expand and simplify the expression. (4x+5y)4( 4 x + 5 y ) ^ { 4 }(4x+5y)4

Eight sprinters have qualified for the finals in the 100-meter dash at the NCAA national track meet.In how many ways can the sprinters come in first, second, and third? (Assume there are no ties.) ​

Find the coefficient a of the term in the expansion of the binomial. Binominal Terms (x-7y a

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

Find the sum using the formulas for the sums of powers of integers. $\sum _ { n = 1 } ^ { 2 } n ^ { 4 }$

Find the sum. $\sum _ { k = 1 } ^ { 3 } \frac { 1 } { k ^ { 2 } + 5 }$

Evaluate ${ } _ { n } C _ { r }$ using the formula from this section. ${ } _ { 25 } C _ { 4 }$

Evaluate ${ } _ { n } C _ { r }$ using the formula from this section. ${ } _ { 48 } C _ { 5 }$

Write the first five terms of the sequence.Determine whether the sequence is arithmetic.If so, find the common difference.(Assume that n begins with 1.) A_n = 4n - ¹

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1.) $\frac { 2 } { 7 } , \frac { 3 } { 15 } , \frac { 4 } { 23 } , \frac { 5 } { 31 } , \frac { 6 } { 39 } , \ldots$

Use the Binomial Theorem to expand and simplify the expression. $( x + 5 ) ^ { 6 }$

Use the Binomial Theorem to expand and simplify the expression. $( 2 x + y ) ^ { 3 }$

Find the sum of the infinite series. $\sum _ { i = 1 } ^ { \infty } 3 \left( - \frac { 1 } { 4 } \right) ^ { i }$

Evaluate ${ } _ { n } P _ { r }$ . ${ } _ { 16 } P _ { 8 }$

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. A ₁ = 3 A_n = n - an_{- 1}

Find the 3rd term in the binomial expansion. $( z + t ) ^ { 4 }$

Find the indicated nth term of the geometric sequence. 22th term : $8,32,128 , \ldots$

Find the sum of the infinite geometric sequence. $\sum _ { n = 1 } ^ { \infty } 8 - \left( \frac { 1 } { 6 } \right) ^ { n - 1 }$

Use the Binomial Theorem to expand and simplify the expression. $( 4 x + 5 y ) ^ { 4 }$

Eight sprinters have qualified for the finals in the 100-meter dash at the NCAA national track meet.In how many ways can the sprinters come in first, second, and third? (Assume there are no ties.)