Question 1

Write in exponential form. Assume all variables are positive real numbers.
-$- 9 \sqrt { 6 m ^{11 }}$

Accepted Answer

A)  $- 9 \cdot 6 ^ { 1 / 2 } \mathrm {~m} ^ { 11 / 2 }$ 
B)  $486 \mathrm {~m} ^ { 2 / 11 }$ 
C)  $( - 9 \cdot 6 ) ^ { 1 / 2 } \mathrm {~m} ^ { 11 / 2 }$ 
D)  $- 486 \mathrm {~m}^{ 11 / 2}$ 
A)  $- 9 \cdot 6 ^ { 1 / 2 } \mathrm {~m} ^ { 11 / 2 }$ 
B)  $486 \mathrm {~m} ^ { 2 / 11 }$ 
C)  $( - 9 \cdot 6 ) ^ { 1 / 2 } \mathrm {~m} ^ { 11 / 2 }$ 
D)  $- 486 \mathrm {~m}^{ 11 / 2}$

Question 2

Factor by any method.
-$15 a ^ { 3 } - 12 a ^ { 2 } b - 10 a b ^ { 2 } + 8 b ^ { 3 }$

Accepted Answer

A)  $\left( 3 a ^ { 2 } + 2 b ^ { 2 } \right) ( 5 a + 4 b )$ 
B)  $\left( 3 a ^ { 2 } - 2 b \right) ( 5 a - 4 b )$ 
C)  $\left( 15 a ^ { 2 } - 2 b ^ { 2 } \right) ( a - 4 b )$ 
D)  $\left( 3 a ^ { 2 } - 2 b ^ { 2 } \right) ( 5 a - 4 b )$ 
A)  $\left( 3 a ^ { 2 } + 2 b ^ { 2 } \right) ( 5 a + 4 b )$ 
B)  $\left( 3 a ^ { 2 } - 2 b \right) ( 5 a - 4 b )$ 
C)  $\left( 15 a ^ { 2 } - 2 b ^ { 2 } \right) ( a - 4 b )$ 
D)  $\left( 3 a ^ { 2 } - 2 b ^ { 2 } \right) ( 5 a - 4 b )$

Question 3

Simplify the expression. Assume all variables represent nonzero real numbers.
-$4 ^ { 8 } \cdot 4 ^ { 6 }$

Accepted Answer

A) $4^ { 48}$ 
B)  $8 ^ { 14 }$ 
C)  $4^ { 14 }$ 
D)  $16 ^ { 48 }$ 
A) $4^ { 48}$ 
B)  $8 ^ { 14 }$ 
C)  $4^ { 14 }$ 
D)  $16 ^ { 48 }$

Question 4

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt [ 3 ] { 125 x ^ { 4 } y ^ { 5 } }$$

Accepted Answer

A)  $3 x ^ { 2 } y ^ { 2 } \sqrt [ 3 ] { x y ^ { 2 } }$ 
B)  $5 x y \sqrt [ 3 ] { x y }$ 
C)  $ 5 x y \sqrt[3]{x y^{2}} $ 
D)  $5 x y ^ { 2 } \sqrt [ 3 ] { x y }$ 
A)  $3 x ^ { 2 } y ^ { 2 } \sqrt [ 3 ] { x y ^ { 2 } }$ 
B)  $5 x y \sqrt [ 3 ] { x y }$ 
C)  $ 5 x y \sqrt[3]{x y^{2}} $ 
D)  $5 x y ^ { 2 } \sqrt [ 3 ] { x y }$

Question 5

Find the product.
-$$( 9 y + x ) ( 9 y - x )$$

Accepted Answer

A)  $81 y ^ { 2 } - 18 x y - x ^ { 2 }$ 
B)  $81 y ^ { 2 } + 18 x y - x ^ { 2 }$ 
C)  $18 y ^ { 2 } - x ^ { 2 }$ 
D)  $81 y ^ { 2 } - x ^ { 2 }$ 
A)  $81 y ^ { 2 } - 18 x y - x ^ { 2 }$ 
B)  $81 y ^ { 2 } + 18 x y - x ^ { 2 }$ 
C)  $18 y ^ { 2 } - x ^ { 2 }$ 
D)  $81 y ^ { 2 } - x ^ { 2 }$

Question 6

Evaluate the expression.
-$$\left[ - \frac { 2 } { 27 } - \left( - \frac { 1 } { 6 } \right) \right] - \left( \frac { 4 } { 3 } - \frac { 1 } { 18 } \right)$$

Accepted Answer

A)  $\frac { 28 } { 27 }$ 
B)  $\frac { 37 } { 27 }$ 
C)  $- \frac { 41 } { 27 }$ 
D)  $- \frac { 32 } { 27 }$ 
A)  $\frac { 28 } { 27 }$ 
B)  $\frac { 37 } { 27 }$ 
C)  $- \frac { 41 } { 27 }$ 
D)  $- \frac { 32 } { 27 }$

Question 7

Evaluate the expression for x = -2, y = 3, and a = -4.
-$$\frac { - ( x + 1 ) ^ { 2 } - 4 y } { 6 - a }$$

Accepted Answer

A)  $- \frac { 11 } { 10 }$ 
B)  $\frac { 11 } { 10 }$ 
C)  $- \frac { 13 } { 10 }$ 
D)  $\frac { 13 } { 10 }$ 
A)  $- \frac { 11 } { 10 }$ 
B)  $\frac { 11 } { 10 }$ 
C)  $- \frac { 13 } { 10 }$ 
D)  $\frac { 13 } { 10 }$

Question 8

Find the product. Assume variables represent positive real numbers.
-$$\mathrm { y } ^ { 2 / 17 } \left( \mathrm { y } ^ { 5 / 17 } - 2 \mathrm { y } 4 / 17 \right)$$

Accepted Answer

A)  $y ^ { - 3 / 17 } - 2 y ^ { - 2 / 17 }$ 
B)  $y ^ { 7 / 17 } - 2 y ^ { 6 / 17 }$ 
C)  $\mathrm { y } ^ { 10 / 289 } - 2 \mathrm { y } 8 / 289$ 
D)  $y ^ { 2 / 5 } - 2 y ^ { 2 / 4 }$ 
A)  $y ^ { - 3 / 17 } - 2 y ^ { - 2 / 17 }$ 
B)  $y ^ { 7 / 17 } - 2 y ^ { 6 / 17 }$ 
C)  $\mathrm { y } ^ { 10 / 289 } - 2 \mathrm { y } 8 / 289$ 
D)  $y ^ { 2 / 5 } - 2 y ^ { 2 / 4 }$

Question 9

Use these sets to find the following. Identify any disjoint sets.
-Let $\mathrm { U } = \{ 8,9,10,11,12,13,14,15,16,17,18 \} , \mathrm { M } = \{ 8,10,12,14 \} , \mathrm { N } = \{ 9,11,13,15,17 \}$, $Q = \{ 8,10,12,14,16,18 \}$, and $R = \{ 8,9,10,11 \}$.
$( \mathrm { U } \cup \varnothing ) \cap \mathrm { R } ^ { \prime }$

Accepted Answer

A)  $\mathrm { R }$, or $\{ 8,9,10,11 \}$ 
B)  $U$, or $\{ 8,9,10,11,12,13,14,15,16,17,18 \}$ 
C)  $\{ 12,13,14,15,16,17,18 \}$ 
D)  $\varnothing$; $R ^ { \prime }$ and $( \mathrm { U } \cup \varnothing )$ are disjoint sets. 
A)  $\mathrm { R }$, or $\{ 8,9,10,11 \}$ 
B)  $U$, or $\{ 8,9,10,11,12,13,14,15,16,17,18 \}$ 
C)  $\{ 12,13,14,15,16,17,18 \}$ 
D)  $\varnothing$; $R ^ { \prime }$ and $( \mathrm { U } \cup \varnothing )$ are disjoint sets.

Question 10

Identify the polynomial as a monomial, binomial, trinomial, or none of these.
-$15 s ^ { 9 } + 2 s - 6$

Accepted Answer

A)  Trinomial 
B)  Binomial 
C)  Monomial 
D)  None of these 
A)  Trinomial 
B)  Binomial 
C)  Monomial 
D)  None of these

Question 11

Factor by grouping.
-$10 x ^ { 2 } - 12 x + 15 x - 18$

Accepted Answer

A)  $( 10 x - 3 ) ( x + 6 )$ 
B)  $( 2 x + 3 ) ( 5 x - 6 )$ 
C)  $( 2 x - 3 ) ( 5 x + 6 )$ 
D)  $( 10 x + 3 ) ( x - 6 )$ 
A)  $( 10 x - 3 ) ( x + 6 )$ 
B)  $( 2 x + 3 ) ( 5 x - 6 )$ 
C)  $( 2 x - 3 ) ( 5 x + 6 )$ 
D)  $( 10 x + 3 ) ( x - 6 )$

Question 12

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt [ 4 ] { \frac { 81 } { y } }$

Accepted Answer

A)  $\frac { 3 \sqrt [ 4 ] { y } } { y }$ 
B)  $\frac { 3 \sqrt [ 4 ] { y ^ { 3 } } } { y }$ 
C)  $\frac { 3 \sqrt [ 4 ] { y ^ { 2 } } } { y }$ 
D)  $\frac { 3 \sqrt [ 4 ] { y ^ { 3 } } } { y ^ { 2 } }$ 
A)  $\frac { 3 \sqrt [ 4 ] { y } } { y }$ 
B)  $\frac { 3 \sqrt [ 4 ] { y ^ { 3 } } } { y }$ 
C)  $\frac { 3 \sqrt [ 4 ] { y ^ { 2 } } } { y }$ 
D)  $\frac { 3 \sqrt [ 4 ] { y ^ { 3 } } } { y ^ { 2 } }$

Question 13

Divide.
-$$\frac { x ^ { 2 } + 14 x + 49 } { x + 7 }$$

Accepted Answer

A)  $x ^ { 2 } + 7$ 
B)  $x - 42$ 
C)  $x ^ { 3 } - 42$ 
D)  $x + 7$ 
A)  $x ^ { 2 } + 7$ 
B)  $x - 42$ 
C)  $x ^ { 3 } - 42$ 
D)  $x + 7$

Question 14

Factor the trinomial, if possible.
-$15 x ^ { 2 } + 19 x + 6$

Accepted Answer

A)  $( 15 x + 2 ) ( x + 3 )$ 
B)  $( 3 x + 2 ) ( 5 x + 3 )$ 
C)  $( 3 x - 2 ) ( 5 x - 3 )$ 
D)  $( 15 x + 1 ) ( x + 6 )$ 
A)  $( 15 x + 2 ) ( x + 3 )$ 
B)  $( 3 x + 2 ) ( 5 x + 3 )$ 
C)  $( 3 x - 2 ) ( 5 x - 3 )$ 
D)  $( 15 x + 1 ) ( x + 6 )$

Question 15

Factor the trinomial, if possible.
-$$x ^ { 2 } + 6 x y - 160 y ^ { 2 }$$

Accepted Answer

A)  $( x - 16 y ) ( x + y )$ 
B)  $( x - 16 y ) ( x + 10 y )$ 
C)  prime 
D)  $( x + 16 y ) ( x - 10 y )$ 
A)  $( x - 16 y ) ( x + y )$ 
B)  $( x - 16 y ) ( x + 10 y )$ 
C)  prime 
D)  $( x + 16 y ) ( x - 10 y )$

Question 16

Find the product.
-$$( 3 m - 10 w ) ( 3 m + 10 w )$$

Accepted Answer

A)  $9 m ^ { 2 } + 60 m w - 100 w ^ { 2 }$ 
B)  $9 m ^ { 2 } - 60 m w - 100 w ^ { 2 }$ 
C)  $9 m ^ { 2 } - 100 w ^ { 2 }$ 
D)  $3 m ^ { 2 } - 10 w ^ { 2 }$ 
A)  $9 m ^ { 2 } + 60 m w - 100 w ^ { 2 }$ 
B)  $9 m ^ { 2 } - 60 m w - 100 w ^ { 2 }$ 
C)  $9 m ^ { 2 } - 100 w ^ { 2 }$ 
D)  $3 m ^ { 2 } - 10 w ^ { 2 }$

Question 17

Find the product.
-$11 a x ^ { 7 } \left( 10 a x ^ { 7 } - 2 x ^ { 2 } - 5 \right)$

Accepted Answer

A)  $- 110 a ^ { 2 } x ^ { 49 } + 22 a x ^ { 14 } + 55 a x ^ { 7 }$ 
B)  $- 110 a ^ { 2 } x ^ { 14 } + 22 a x ^ { 9 } + 55 a x ^ { 7 }$ 
C)  $110 a ^ { 2 } x ^ { 14 } - 22 a x ^ { 9 } - 55 a x ^ { 7 }$ 
D)  $110 a x ^ { 49 } - 22 a x ^ { 14 } - 55 a x ^ { 7 }$ 
A)  $- 110 a ^ { 2 } x ^ { 49 } + 22 a x ^ { 14 } + 55 a x ^ { 7 }$ 
B)  $- 110 a ^ { 2 } x ^ { 14 } + 22 a x ^ { 9 } + 55 a x ^ { 7 }$ 
C)  $110 a ^ { 2 } x ^ { 14 } - 22 a x ^ { 9 } - 55 a x ^ { 7 }$ 
D)  $110 a x ^ { 49 } - 22 a x ^ { 14 } - 55 a x ^ { 7 }$

Question 18

List all the elements of set B that belong to the indicated set.
-$$\mathrm { B } = \left\{ 4 , \sqrt { 8 } , - 21,0 , \frac { 0 } { 6 } , \sqrt { 9 } \right\}$$
Integers

Accepted Answer

A)  $4,0 , \sqrt { 9 }$ 
B)  $4 , - 21,0$ 
C)  $4 , - 21,0 , \frac { 0 } { 6 } , \sqrt { 9 }$ 
D)  4,0 
A)  $4,0 , \sqrt { 9 }$ 
B)  $4 , - 21,0$ 
C)  $4 , - 21,0 , \frac { 0 } { 6 } , \sqrt { 9 }$ 
D)  4,0

Question 19

Find the product.
-$$\left( 3 y ^ { 2 } - 5 y - 4 \right) \left( y ^ { 2 } + 3 y - 4 \right)$$

Accepted Answer

A)  $3 y ^ { 4 } + 9 y ^ { 3 } - 27 y ^ { 2 } + 8 y + 16$ 
B)  $3 y ^ { 4 } + 4 y ^ { 3 } - 27 y ^ { 2 } + 8 y + 16$ 
C)  $3 y ^ { 4 } + 9 y ^ { 3 } - 31 y ^ { 2 } + 8 y + 16$ 
D)  $3 y ^ { 4 } + 4 y ^ { 3 } - 31 y ^ { 2 } + 8 y + 16$ 
A)  $3 y ^ { 4 } + 9 y ^ { 3 } - 27 y ^ { 2 } + 8 y + 16$ 
B)  $3 y ^ { 4 } + 4 y ^ { 3 } - 27 y ^ { 2 } + 8 y + 16$ 
C)  $3 y ^ { 4 } + 9 y ^ { 3 } - 31 y ^ { 2 } + 8 y + 16$ 
D)  $3 y ^ { 4 } + 4 y ^ { 3 } - 31 y ^ { 2 } + 8 y + 16$

Question 20

Find the product.
-$$( a - 7 ) ( a + 7 )$$

Accepted Answer

A)  $a ^ { 2 } - 14 a - 49$ 
B)  $a ^ { 2 } + 14 a - 49$ 
C)  $a ^ { 2 } - 14$ 
D)  $a ^ { 2 } - 49$ 
A)  $a ^ { 2 } - 14 a - 49$ 
B)  $a ^ { 2 } + 14 a - 49$ 
C)  $a ^ { 2 } - 14$ 
D)  $a ^ { 2 } - 49$

Write in exponential form. Assume all variables are positive real numbers. - $- 9 \sqrt { 6 m ^{11 }}$

Factor by any method. - $15 a ^ { 3 } - 12 a ^ { 2 } b - 10 a b ^ { 2 } + 8 b ^ { 3 }$

Simplify the expression. Assume all variables represent nonzero real numbers. - $4 ^ { 8 } \cdot 4 ^ { 6 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { 125 x ^ { 4 } y ^ { 5 } }$

Find the product. - $( 9 y + x ) ( 9 y - x )$

Evaluate the expression. - $\left[ - \frac { 2 } { 27 } - \left( - \frac { 1 } { 6 } \right) \right] - \left( \frac { 4 } { 3 } - \frac { 1 } { 18 } \right)$

Evaluate the expression for x = -2, y = 3, and a = -4. - $\frac { - ( x + 1 ) ^ { 2 } - 4 y } { 6 - a }$

Find the product. Assume variables represent positive real numbers. - $\mathrm { y } ^ { 2 / 17 } \left( \mathrm { y } ^ { 5 / 17 } - 2 \mathrm { y } 4 / 17 \right)$

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - $15 s ^ { 9 } + 2 s - 6$

Factor by grouping. - $10 x ^ { 2 } - 12 x + 15 x - 18$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 4 ] { \frac { 81 } { y } }$

Divide. - $\frac { x ^ { 2 } + 14 x + 49 } { x + 7 }$

Factor the trinomial, if possible. - $15 x ^ { 2 } + 19 x + 6$

Factor the trinomial, if possible. - $x ^ { 2 } + 6 x y - 160 y ^ { 2 }$

Find the product. - $( 3 m - 10 w ) ( 3 m + 10 w )$

Find the product. - $11 a x ^ { 7 } \left( 10 a x ^ { 7 } - 2 x ^ { 2 } - 5 \right)$

List all the elements of set B that belong to the indicated set. - $\mathrm { B } = \left\{ 4 , \sqrt { 8 } , - 21,0 , \frac { 0 } { 6 } , \sqrt { 9 } \right\}$ Integers

Find the product. - $\left( 3 y ^ { 2 } - 5 y - 4 \right) \left( y ^ { 2 } + 3 y - 4 \right)$

Find the product. - $( a - 7 ) ( a + 7 )$

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Exam 12: Review of Basic Concepts

Write in exponential form. Assume all variables are positive real numbers. - −96m11- 9 \sqrt { 6 m ^{11 }}−96m11​

Factor by any method. - 15a3−12a2b−10ab2+8b315 a ^ { 3 } - 12 a ^ { 2 } b - 10 a b ^ { 2 } + 8 b ^ { 3 }15a3−12a2b−10ab2+8b3

Simplify the expression. Assume all variables represent nonzero real numbers. - 48⋅464 ^ { 8 } \cdot 4 ^ { 6 }48⋅46

Simplify the expression. Assume all variables represent positive real numbers. - 125x4y53\sqrt [ 3 ] { 125 x ^ { 4 } y ^ { 5 } }3125x4y5​

Find the product. - (9y+x)(9y−x)( 9 y + x ) ( 9 y - x )(9y+x)(9y−x)

Evaluate the expression. - [−227−(−16)]−(43−118)\left[ - \frac { 2 } { 27 } - \left( - \frac { 1 } { 6 } \right) \right] - \left( \frac { 4 } { 3 } - \frac { 1 } { 18 } \right)[−272​−(−61​)]−(34​−181​)

Evaluate the expression for x = -2, y = 3, and a = -4. - −(x+1)2−4y6−a\frac { - ( x + 1 ) ^ { 2 } - 4 y } { 6 - a }6−a−(x+1)2−4y​

Find the product. Assume variables represent positive real numbers. - y2/17(y5/17−2y4/17)\mathrm { y } ^ { 2 / 17 } \left( \mathrm { y } ^ { 5 / 17 } - 2 \mathrm { y } 4 / 17 \right)y2/17(y5/17−2y4/17)

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - 15s9+2s−615 s ^ { 9 } + 2 s - 615s9+2s−6

Factor by grouping. - 10x2−12x+15x−1810 x ^ { 2 } - 12 x + 15 x - 1810x2−12x+15x−18

Simplify the expression. Assume all variables represent positive real numbers. - 81y4\sqrt [ 4 ] { \frac { 81 } { y } }4y81​​

Divide. - x2+14x+49x+7\frac { x ^ { 2 } + 14 x + 49 } { x + 7 }x+7x2+14x+49​

Factor the trinomial, if possible. - 15x2+19x+615 x ^ { 2 } + 19 x + 615x2+19x+6

Factor the trinomial, if possible. - x2+6xy−160y2x ^ { 2 } + 6 x y - 160 y ^ { 2 }x2+6xy−160y2

Find the product. - (3m−10w)(3m+10w)( 3 m - 10 w ) ( 3 m + 10 w )(3m−10w)(3m+10w)

Find the product. - 11ax7(10ax7−2x2−5)11 a x ^ { 7 } \left( 10 a x ^ { 7 } - 2 x ^ { 2 } - 5 \right)11ax7(10ax7−2x2−5)

List all the elements of set B that belong to the indicated set. - B={4,8,−21,0,06,9}\mathrm { B } = \left\{ 4 , \sqrt { 8 } , - 21,0 , \frac { 0 } { 6 } , \sqrt { 9 } \right\}B={4,8​,−21,0,60​,9​} Integers

Find the product. - (3y2−5y−4)(y2+3y−4)\left( 3 y ^ { 2 } - 5 y - 4 \right) \left( y ^ { 2 } + 3 y - 4 \right)(3y2−5y−4)(y2+3y−4)

Find the product. - (a−7)(a+7)( a - 7 ) ( a + 7 )(a−7)(a+7)