Question 1

Write the first four terms of the binomial expansion.
-$\left(p^{2}-q^{2}\right)^{16}$

Accepted Answer

A)  $p^{32}+p^{30} q^{2}+p^{28} q^{4}+p^{26} q^{6}$ 
B)  $p^{32}-32 p^{30} q^{2}+240 p^{28} q^{4}-1120 p^{26} q^{6}$ 
C)  $p^{16}-16 p^{15} q+120 p^{14} q^{2}-560 p^{13} q^{3}$ 
D)  $p^{32}-16 p^{30} q^{2}+120 p^{28} q^{4}-560 p^{26} q^{6}$ 
A)  $p^{32}+p^{30} q^{2}+p^{28} q^{4}+p^{26} q^{6}$ 
B)  $p^{32}-32 p^{30} q^{2}+240 p^{28} q^{4}-1120 p^{26} q^{6}$ 
C)  $p^{16}-16 p^{15} q+120 p^{14} q^{2}-560 p^{13} q^{3}$ 
D)  $p^{32}-16 p^{30} q^{2}+120 p^{28} q^{4}-560 p^{26} q^{6}$

Question 2

Find a general term for the geometric sequence.
-$2,6, \ldots$

Accepted Answer

A)  $a_{n}=4^{n-1}+2$ 
B)  $a_{n}=2(3)^{n-1}$ 
C)  $a_{n}=4 n-2$ 
D)  $a_{n}=2-6^{n}$ 
A)  $a_{n}=4^{n-1}+2$ 
B)  $a_{n}=2(3)^{n-1}$ 
C)  $a_{n}=4 n-2$ 
D)  $a_{n}=2-6^{n}$

Question 3

Find the indicated term for the sequence.
-$a_{n}=4(4 n-1)$; $a_{8}$

Accepted Answer

A)  124 
B)  128 
C)  112 
D)  136 
A)  124 
B)  128 
C)  112 
D)  136

Question 4

Find a general term for the geometric sequence.
-$-5,15, \ldots$

Accepted Answer

A)  $a_{n}=20 n-25$ 
B)  $a_{n}=-5(-3)^{n-1}$ 
C)  $a_{n}=-5-15^{n}$ 
D)  $a_{n}=20^{n-1}-5$ 
A)  $a_{n}=20 n-25$ 
B)  $a_{n}=-5(-3)^{n-1}$ 
C)  $a_{n}=-5-15^{n}$ 
D)  $a_{n}=20^{n-1}-5$

Question 5

An investment is worth $\$ 1000$, and its value is increasing by $9 \%$ every year. What will its value be at the end of 9 years? Round your answer to the nearest dollar.

Accepted Answer

A)  $\$ 2367$ 
B)  $\$ 2172$ 
C)  $\$ 1810$ 
D)  \$1993 
A)  $\$ 2367$ 
B)  $\$ 2172$ 
C)  $\$ 1810$ 
D)  \$1993

Question 6

Find the number of terms in the arithmetic sequence.
-$8,-1,-10, \ldots,-109$

Accepted Answer

A)  12 
B)  15 
C)  14 
D)  13 
A)  12 
B)  15 
C)  14 
D)  13

Question 7

A woman borrowed $\$ 30,000$ at $12 \%$ interest compounded annually. If the loan was paid off at the end of 4 years, how much did she pay? Round your answer to the nearest cent.

Accepted Answer

A)  $\$ 17,205.58$ 
B)  $\$ 47,205.58$ 
C)  $\$ 33,600.00$ 
D)  $\$ 44,400.00$ 
A)  $\$ 17,205.58$ 
B)  $\$ 47,205.58$ 
C)  $\$ 33,600.00$ 
D)  $\$ 44,400.00$

Question 8

Find the indicated term for the arithmetic sequence.
-$\mathrm{a}_{11}=24, \mathrm{a}_{16}=34 ; \mathrm{a}_{1}$

Accepted Answer

A)  4 
B)  2 
C)  6 
D)  8 
A)  4 
B)  2 
C)  6 
D)  8

Question 9

Write the first five terms of the arithmetic sequence.
-$\mathrm{a}_{1}=10, \mathrm{~d}=-2$

Accepted Answer

A)  $-10,-8,-6,-4,-2$ 
B)  $10,8,6,4,2$ 
C)  $14,11,8,5$, 2 
D)  $0,10,8,6,4$ 
A)  $-10,-8,-6,-4,-2$ 
B)  $10,8,6,4,2$ 
C)  $14,11,8,5$, 2 
D)  $0,10,8,6,4$

Question 10

Find the number of terms in the arithmetic sequence.
-$3, \frac{5}{2}, 2, \ldots,-4$

Accepted Answer

A)  13 
B)  16 
C)  15 
D)  14 
A)  13 
B)  16 
C)  15 
D)  14

Question 11

Find the sum, if it exists, of the terms of the infinite geometric sequence.
-$\mathrm{a}_{1}=1, \mathrm{r}=\frac{1}{4}$

Accepted Answer

A)  $\frac{4}{7}$ 
B)  $\frac{4}{3}$ 
C)  $\frac{3}{4}$ 
D)  Does not exist 
A)  $\frac{4}{7}$ 
B)  $\frac{4}{3}$ 
C)  $\frac{3}{4}$ 
D)  Does not exist

Question 12

Explain how to use the binomial theorem to expand $(4 a-3 b)^{n}$.

Accepted Answer

Expand the binomial

Question 13

Write the formula for the general term $a_{n}$ of an arithmetic sequence with first term $a_{1}$ and common difference $\mathrm{d}$.

Accepted Answer

The answer of Write the formula for the general term...

Question 14

Which of these is not an arithmetic sequence?

Accepted Answer

A)  3, 6, 12, 24 
B)  1, 3, 5, 7 
C)  -5, 2, 9, 16 
D)  $\frac{1}{3}, \frac{2}{3}, 1, \frac{4}{3}$ 
A)  3, 6, 12, 24 
B)  1, 3, 5, 7 
C)  -5, 2, 9, 16 
D)  $\frac{1}{3}, \frac{2}{3}, 1, \frac{4}{3}$

Question 15

Write out the first five terms of the sequence.
-$\mathrm{a}_{\mathrm{n}}=4^{\mathrm{n}}$

Accepted Answer

A)  $1,16,81,256,625$ 
B)  $1,4,16,64,256$ 
C)  $16,64,256,1024,4096$ 
D)  $4,16,64,256,1024$ 
A)  $1,16,81,256,625$ 
B)  $1,4,16,64,256$ 
C)  $16,64,256,1024,4096$ 
D)  $4,16,64,256,1024$

Question 16

For what value or values of $n$ does $(x+y)^{n}=x^{n}+y^{n}$, for all $x$ and $y$ ?

Accepted Answer

The answer of For what value or values of $n$...

Question 17

Write the fifth term of $\left(5 x-\frac{y}{4}\right)^{10}$.

Accepted Answer

A)  $\frac{1171875}{128} x^{6} y^{4}$ 
B)  $\frac{1640625}{64} x^{6} y^{4}$ 
C)  $\frac{4921875}{4} x^{6} y^{4}$ 
D)  $\frac{1640625}{128} x^{6} y^{4}$ 
A)  $\frac{1171875}{128} x^{6} y^{4}$ 
B)  $\frac{1640625}{64} x^{6} y^{4}$ 
C)  $\frac{4921875}{4} x^{6} y^{4}$ 
D)  $\frac{1640625}{128} x^{6} y^{4}$

Question 18

If the sequence is arithmetic, find the common difference. If the sequence is not arithmetic, say so.
-$4,8,16,32,64, \ldots$

Accepted Answer

A)  $\frac{1}{2}$ 
B)  8 
C)  2 
D)  Not arithmetic 
A)  $\frac{1}{2}$ 
B)  8 
C)  2 
D)  Not arithmetic

Question 19

A ball is dropped from a height of 43 feet. On each bounce, it bounces to $77 \%$ of its previous height. How high does it get after the 5th bounce? (Round to the nearest hundredth, if necessary.)

Accepted Answer

A)  11.64 feet 
B)  136.35 feet 
C)  186.96 feet 
D)  15.12 feet 
A)  11.64 feet 
B)  136.35 feet 
C)  186.96 feet 
D)  15.12 feet

Question 20

${ }_{9} \mathrm{C}_{6}$

Accepted Answer

A)  84 
B)  504 
C)  60,480 
D)  181,440 
A)  84 
B)  504 
C)  60,480 
D)  181,440

Write the first four terms of the binomial expansion. - $\left(p^{2}-q^{2}\right)^{16}$

Find a general term for the geometric sequence. - $2,6, \ldots$

Find the indicated term for the sequence. - $a_{n}=4(4 n-1)$ ; $a_{8}$

Find a general term for the geometric sequence. - $-5,15, \ldots$

An investment is worth $\$ 1000$ , and its value is increasing by $9 \%$ every year. What will its value be at the end of 9 years? Round your answer to the nearest dollar.

Find the number of terms in the arithmetic sequence. - $8,-1,-10, \ldots,-109$

A woman borrowed $\$ 30,000$ at $12 \%$ interest compounded annually. If the loan was paid off at the end of 4 years, how much did she pay? Round your answer to the nearest cent.

Find the indicated term for the arithmetic sequence. - $\mathrm{a}_{11}=24, \mathrm{a}_{16}=34 ; \mathrm{a}_{1}$

Write the first five terms of the arithmetic sequence. - $\mathrm{a}_{1}=10, \mathrm{~d}=-2$

Find the number of terms in the arithmetic sequence. - $3, \frac{5}{2}, 2, \ldots,-4$

Find the sum, if it exists, of the terms of the infinite geometric sequence. - $\mathrm{a}_{1}=1, \mathrm{r}=\frac{1}{4}$

Explain how to use the binomial theorem to expand $(4 a-3 b)^{n}$ .

Write the formula for the general term $a_{n}$ of an arithmetic sequence with first term $a_{1}$ and common difference $\mathrm{d}$ .

Which of these is not an arithmetic sequence?

Write out the first five terms of the sequence. - $\mathrm{a}_{\mathrm{n}}=4^{\mathrm{n}}$

For what value or values of $n$ does $(x+y)^{n}=x^{n}+y^{n}$ , for all $x$ and $y$ ?

Write the fifth term of $\left(5 x-\frac{y}{4}\right)^{10}$ .

If the sequence is arithmetic, find the common difference. If the sequence is not arithmetic, say so. - $4,8,16,32,64, \ldots$

A ball is dropped from a height of 43 feet. On each bounce, it bounces to $77 \%$ of its previous height. How high does it get after the 5th bounce? (Round to the nearest hundredth, if necessary.)

${ }_{9} \mathrm{C}_{6}$

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Appendices

Filters

Exam 12: Further Topics in Algebra

Write the first four terms of the binomial expansion. - (p2−q2)16\left(p^{2}-q^{2}\right)^{16}(p2−q2)16

Find a general term for the geometric sequence. - 2,6,…2,6, \ldots2,6,…

Find the indicated term for the sequence. - an=4(4n−1)a_{n}=4(4 n-1)an​=4(4n−1) ; a8a_{8}a8​

Find a general term for the geometric sequence. - −5,15,…-5,15, \ldots−5,15,…

An investment is worth $1000\$ 1000$1000 , and its value is increasing by 9%9 \%9% every year. What will its value be at the end of 9 years? Round your answer to the nearest dollar.

Find the number of terms in the arithmetic sequence. - 8,−1,−10,…,−1098,-1,-10, \ldots,-1098,−1,−10,…,−109

A woman borrowed $30,000\$ 30,000$30,000 at 12%12 \%12% interest compounded annually. If the loan was paid off at the end of 4 years, how much did she pay? Round your answer to the nearest cent.

Find the indicated term for the arithmetic sequence. - a11=24,a16=34;a1\mathrm{a}_{11}=24, \mathrm{a}_{16}=34 ; \mathrm{a}_{1}a11​=24,a16​=34;a1​

Write the first five terms of the arithmetic sequence. - a1=10, d=−2\mathrm{a}_{1}=10, \mathrm{~d}=-2a1​=10, d=−2

Find the number of terms in the arithmetic sequence. - 3,52,2,…,−43, \frac{5}{2}, 2, \ldots,-43,25​,2,…,−4

Find the sum, if it exists, of the terms of the infinite geometric sequence. - a1=1,r=14\mathrm{a}_{1}=1, \mathrm{r}=\frac{1}{4}a1​=1,r=41​

Explain how to use the binomial theorem to expand (4a−3b)n(4 a-3 b)^{n}(4a−3b)n .

Write the formula for the general term ana_{n}an​ of an arithmetic sequence with first term a1a_{1}a1​ and common difference d\mathrm{d}d .

Which of these is not an arithmetic sequence?

Write out the first five terms of the sequence. - an=4n\mathrm{a}_{\mathrm{n}}=4^{\mathrm{n}}an​=4n

For what value or values of nnn does (x+y)n=xn+yn(x+y)^{n}=x^{n}+y^{n}(x+y)n=xn+yn , for all xxx and yyy ?

Write the fifth term of (5x−y4)10\left(5 x-\frac{y}{4}\right)^{10}(5x−4y​)10 .

If the sequence is arithmetic, find the common difference. If the sequence is not arithmetic, say so. - 4,8,16,32,64,…4,8,16,32,64, \ldots4,8,16,32,64,…

A ball is dropped from a height of 43 feet. On each bounce, it bounces to 77%77 \%77% of its previous height. How high does it get after the 5th bounce? (Round to the nearest hundredth, if necessary.)

9C6{ }_{9} \mathrm{C}_{6}9​C6​

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Appendices

Filters

Write the first four terms of the binomial expansion. - $\left(p^{2}-q^{2}\right)^{16}$

Find a general term for the geometric sequence. - $2,6, \ldots$

Find the indicated term for the sequence. - $a_{n}=4(4 n-1)$ ; $a_{8}$

Find a general term for the geometric sequence. - $-5,15, \ldots$

An investment is worth $\$ 1000$ , and its value is increasing by $9 \%$ every year. What will its value be at the end of 9 years? Round your answer to the nearest dollar.

Find the number of terms in the arithmetic sequence. - $8,-1,-10, \ldots,-109$

A woman borrowed $\$ 30,000$ at $12 \%$ interest compounded annually. If the loan was paid off at the end of 4 years, how much did she pay? Round your answer to the nearest cent.

Find the indicated term for the arithmetic sequence. - $\mathrm{a}_{11}=24, \mathrm{a}_{16}=34 ; \mathrm{a}_{1}$

Write the first five terms of the arithmetic sequence. - $\mathrm{a}_{1}=10, \mathrm{~d}=-2$

Find the number of terms in the arithmetic sequence. - $3, \frac{5}{2}, 2, \ldots,-4$

Find the sum, if it exists, of the terms of the infinite geometric sequence. - $\mathrm{a}_{1}=1, \mathrm{r}=\frac{1}{4}$

Explain how to use the binomial theorem to expand $(4 a-3 b)^{n}$ .

Write the formula for the general term $a_{n}$ of an arithmetic sequence with first term $a_{1}$ and common difference $\mathrm{d}$ .

Write out the first five terms of the sequence. - $\mathrm{a}_{\mathrm{n}}=4^{\mathrm{n}}$

For what value or values of $n$ does $(x+y)^{n}=x^{n}+y^{n}$ , for all $x$ and $y$ ?

Write the fifth term of $\left(5 x-\frac{y}{4}\right)^{10}$ .

If the sequence is arithmetic, find the common difference. If the sequence is not arithmetic, say so. - $4,8,16,32,64, \ldots$

A ball is dropped from a height of 43 feet. On each bounce, it bounces to $77 \%$ of its previous height. How high does it get after the 5th bounce? (Round to the nearest hundredth, if necessary.)

${ }_{9} \mathrm{C}_{6}$