Question 1

Find the product.
-$$\left( 2 x + \frac { 1 } { 10 } \right) \left( 10 x - \frac { 1 } { 5 } \right)$$

Accepted Answer

A)  $20 x ^ { 2 } - \frac { 7 } { 5 } x - \frac { 1 } { 50 }$ 
B)  $20 x ^ { 2 } + \frac { 3 } { 5 } x - \frac { 1 } { 50 }$ 
C)  $20 x ^ { 2 } + \frac { 3 } { 5 } x + \frac { 1 } { 50 }$ 
D)  $20 x ^ { 2 } - \frac { 3 } { 5 } x + \frac { 1 } { 50 }$ 
A)  $20 x ^ { 2 } - \frac { 7 } { 5 } x - \frac { 1 } { 50 }$ 
B)  $20 x ^ { 2 } + \frac { 3 } { 5 } x - \frac { 1 } { 50 }$ 
C)  $20 x ^ { 2 } + \frac { 3 } { 5 } x + \frac { 1 } { 50 }$ 
D)  $20 x ^ { 2 } - \frac { 3 } { 5 } x + \frac { 1 } { 50 }$

Question 2

Identify the expression as a polynomial or not a polynomial.
-$0.5 x ^ { 4 } - 9$

Accepted Answer

A)  Polynomial 
B)  Not a polynomial 
A)  Polynomial 
B)  Not a polynomial

Question 3

Divide.
-$$\frac { x ^ { 4 } + 3 x ^ { 2 } + 8 } { x ^ { 2 } + 1 }$$

Accepted Answer

A)  $x ^ { 2 } + 2 x + 6$ 
B)  $x ^ { 2 } + 2$ 
C)  $x ^ { 2 } + 2 x + \frac { 5 } { 2 }$ 
D)  $x ^ { 2 } + 2 + \frac { 6 } { x ^ { 2 } + 1 }$ 
A)  $x ^ { 2 } + 2 x + 6$ 
B)  $x ^ { 2 } + 2$ 
C)  $x ^ { 2 } + 2 x + \frac { 5 } { 2 }$ 
D)  $x ^ { 2 } + 2 + \frac { 6 } { x ^ { 2 } + 1 }$

Question 4

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$6 x ^ { 0 }$

Accepted Answer

A)  6 
B)  0 
C)  x 
D)  1 
A)  6 
B)  0 
C)  x 
D)  1

Question 5

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero
real numbers.
-$\frac { \left( x ^ { - 4 } \right) ^ { 0 } } { 12 x ^ { - 12 } }$

Accepted Answer

A)  $\frac { x ^ { 16 } } { 12 }$ 
B)  0 
C)  $12 x ^ { 12 }$ 
D)  $\frac { x ^ { 12 } } { 12 }$ 
A)  $\frac { x ^ { 16 } } { 12 }$ 
B)  0 
C)  $12 x ^ { 12 }$ 
D)  $\frac { x ^ { 12 } } { 12 }$

Question 6

Write in radical form. Assume all variables represent positive real numbers.
-$m ^ { 4 / 3 }$

Accepted Answer

A)  $( \sqrt [ 4 ] { m } ) ^ { 3 }$ 
B)  $\sqrt [ 4 ] { \mathrm { m } ^ { 3 } }$ 
C)  $( \sqrt [ 3 ] { \mathrm { m } } ) ^ { 4 }$ 
D)  $\frac { 1 } { \sqrt [ 4 ] { m } }$ 
A)  $( \sqrt [ 4 ] { m } ) ^ { 3 }$ 
B)  $\sqrt [ 4 ] { \mathrm { m } ^ { 3 } }$ 
C)  $( \sqrt [ 3 ] { \mathrm { m } } ) ^ { 4 }$ 
D)  $\frac { 1 } { \sqrt [ 4 ] { m } }$

Question 7

Factor by any method.
-$64 k ^ { 2 } - 49 m ^ { 2 }$

Accepted Answer

A)  $( 8 k + 7 m ) ^ { 2 }$ 
B)  $( 8 k - 7 m ) ^ { 2 }$ 
C)  $( 8 k + 7 m ) ( 8 k - 7 m )$ 
D)  $( 64 k + m ) ( k - 49 m )$ 
A)  $( 8 k + 7 m ) ^ { 2 }$ 
B)  $( 8 k - 7 m ) ^ { 2 }$ 
C)  $( 8 k + 7 m ) ( 8 k - 7 m )$ 
D)  $( 64 k + m ) ( k - 49 m )$

Question 8

Perform the indicated operation and write your answer with positive integer exponents.
-$$\frac { m ^ { - 1 } - n ^ { - 1 } } { m ^ { - 1 } + n ^ { - 1 } } \cdot \frac { m + n } { m - n }$$

Accepted Answer

A)  $\frac { \mathrm { m } - \mathrm { n } } { \mathrm { m } }$ 
B)  $- 1$ 
C)  1 
D)  $\frac { m n } { m + n }$ 
A)  $\frac { \mathrm { m } - \mathrm { n } } { \mathrm { m } }$ 
B)  $- 1$ 
C)  1 
D)  $\frac { m n } { m + n }$

Question 9

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$\frac { \frac { 5 } { y } } { \frac { 9 } { y + 3 } }$

Accepted Answer

A)  $\frac { y + 3 } { 45 y }$ 
B)  $\frac { 9 y } { 5 ( y + 3 ) }$ 
C)  $45 y ( y + 3 )$ 
D)  $\frac { 5 ( y + 3 ) } { 9 y }$ 
A)  $\frac { y + 3 } { 45 y }$ 
B)  $\frac { 9 y } { 5 ( y + 3 ) }$ 
C)  $45 y ( y + 3 )$ 
D)  $\frac { 5 ( y + 3 ) } { 9 y }$

Question 10

Factor the polynomial by substitution.
-$15 z ^ { 4 } + 2 z ^ { 2 } - 8$

Accepted Answer

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

Question 11

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent
positive real numbers.
-$\left( \frac { x ^ { 2 } } { y ^ { - 4 } } \right) ^ { 1 / 2 }$

Accepted Answer

A)  $x y ^ { 1 / 2 }$ 
B)  $x y$ 
C)  $x y ^ { 2 }$ 
D)  $\frac { x } { y ^ { 2 } }$ 
A)  $x y ^ { 1 / 2 }$ 
B)  $x y$ 
C)  $x y ^ { 2 }$ 
D)  $\frac { x } { y ^ { 2 } }$

Question 12

Find the sum or difference.
-$\left( - 7 - 5 x ^ { 6 } + 8 x ^ { 8 } + 4 x ^ { 7 } \right) + \left( 9 x ^ { 7 } + 7 x ^ { 6 } + 4 + 3 x ^ { 8 } \right)$

Accepted Answer

A)  $26 x ^ { 42 } - 3$ 
B)  $11 x ^ { 16 } + 13 x ^ { 14 } + 2 x ^ { 12 } - 3$ 
C)  $2 x ^ { 8 } + 2 x ^ { 7 } + 12 x ^ { 6 } + 7$ 
D)  $11 x ^ { 8 } + 13 x ^ { 7 } + 2 x ^ { 6 } - 3$ 
A)  $26 x ^ { 42 } - 3$ 
B)  $11 x ^ { 16 } + 13 x ^ { 14 } + 2 x ^ { 12 } - 3$ 
C)  $2 x ^ { 8 } + 2 x ^ { 7 } + 12 x ^ { 6 } + 7$ 
D)  $11 x ^ { 8 } + 13 x ^ { 7 } + 2 x ^ { 6 } - 3$

Question 13

Insert $\in \mathbf { Or } \notin$ in the blank to make the statement is true.
-8 ____$\varnothing$

Accepted Answer

A) $ \in$ 
B)  $\notin$ 
A) $ \in$ 
B)  $\notin$

Question 14

Use set notation, and list all the elements of the set.
-The first six natural numbers.

Accepted Answer

A)  $\{ 0,1,2,3,4,5,6 \}$ 
B)  $\{ 1,2,3,4,5,6 \}$ 
C)  $\{ 0,1,2,3,4,5 \}$ 
D)  $\{ 0,2,4,6,8,10 \}$ 
A)  $\{ 0,1,2,3,4,5,6 \}$ 
B)  $\{ 1,2,3,4,5,6 \}$ 
C)  $\{ 0,1,2,3,4,5 \}$ 
D)  $\{ 0,2,4,6,8,10 \}$

Question 15

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0.
-$x y < 0$

Accepted Answer

A)  $x$ and $y$ have the same sign. 
B)  $x$ and $y$ have different signs. 
C)  $x$ and $y$ must be negative. 
D)  $x$ and $y$ must be positive. 
A)  $x$ and $y$ have the same sign. 
B)  $x$ and $y$ have different signs. 
C)  $x$ and $y$ must be negative. 
D)  $x$ and $y$ must be positive.

Question 16

Decide whether the statement is true or false. If false, correct the statement so it is true.
-$$| - 4 \cdot 11 | = | - 4 | \cdot | 11 |$$

Accepted Answer

A)  True 
B)  False; $| - 4 \cdot 11 | = - | 4 | \cdot | 11 |$ 
A)  True 
B)  False; $| - 4 \cdot 11 | = - | 4 | \cdot | 11 |$

Question 17

Simplify the expression. Assume all variables represent positive real numbers.
-$$- \sqrt { \frac { 81 } { 8 } }$$

Accepted Answer

A)  $- 9 \sqrt { 2 }$ 
B)  $- \frac { 9 \sqrt { 2 } } { 4 }$ 
C)  $- 8$ 
D)  $- \frac { 9 \sqrt { 2 } } { 2 }$ 
A)  $- 9 \sqrt { 2 }$ 
B)  $- \frac { 9 \sqrt { 2 } } { 4 }$ 
C)  $- 8$ 
D)  $- \frac { 9 \sqrt { 2 } } { 2 }$

Question 18

Solve the problem.
-The NSC (Not So Consistent) Corporation has just completed its first year of business. The following chart shows its monthly profit (or loss).

The loss was greatest in

Accepted Answer

A)  February 
B)  June 
C)  December 
D)  January 
A)  February 
B)  June 
C)  December 
D)  January

Question 19

Find the domain of the expression.
-$$\frac { x ^ { 2 } - 25 } { x ^ { 2 } - 6 x + 5 }$$

Accepted Answer

A)  $\{ x \mid x \neq - 5$ and $x \neq + 5 \}$ 
B)  $\{ x \mid x \neq 5$ and $x \neq 1 \}$ 
C)  $\{ x \mid x \neq 0 \}$ 
D)  $\{ x \mid x \neq - 5$ and $x \neq - 1 \}$ 
A)  $\{ x \mid x \neq - 5$ and $x \neq + 5 \}$ 
B)  $\{ x \mid x \neq 5$ and $x \neq 1 \}$ 
C)  $\{ x \mid x \neq 0 \}$ 
D)  $\{ x \mid x \neq - 5$ and $x \neq - 1 \}$

Question 20

Find the distance between two points given their coordinates.
-Find the distance between points $\mathrm { P }$ and $\mathrm { Q }$ on a number line, with coordinates $- 7$ and 4 , respectively.

Accepted Answer

A)  $d ( P , Q ) = - 11$ 
B)  $\mathrm { d } ( P , Q ) = - 3$ 
C)  $d ( P , Q ) = 11$ 
D)  $d ( P , Q ) = 3$ 
A)  $d ( P , Q ) = - 11$ 
B)  $\mathrm { d } ( P , Q ) = - 3$ 
C)  $d ( P , Q ) = 11$ 
D)  $d ( P , Q ) = 3$

Find the product. - $\left( 2 x + \frac { 1 } { 10 } \right) \left( 10 x - \frac { 1 } { 5 } \right)$

Identify the expression as a polynomial or not a polynomial. - $0.5 x ^ { 4 } - 9$

Divide. - $\frac { x ^ { 4 } + 3 x ^ { 2 } + 8 } { x ^ { 2 } + 1 }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $6 x ^ { 0 }$

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { \left( x ^ { - 4 } \right) ^ { 0 } } { 12 x ^ { - 12 } }$

Write in radical form. Assume all variables represent positive real numbers. - $m ^ { 4 / 3 }$

Factor by any method. - $64 k ^ { 2 } - 49 m ^ { 2 }$

Perform the indicated operation and write your answer with positive integer exponents. - $\frac { m ^ { - 1 } - n ^ { - 1 } } { m ^ { - 1 } + n ^ { - 1 } } \cdot \frac { m + n } { m - n }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\frac { \frac { 5 } { y } } { \frac { 9 } { y + 3 } }$

Factor the polynomial by substitution. - $15 z ^ { 4 } + 2 z ^ { 2 } - 8$

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - $\left( \frac { x ^ { 2 } } { y ^ { - 4 } } \right) ^ { 1 / 2 }$

Find the sum or difference. - $\left( - 7 - 5 x ^ { 6 } + 8 x ^ { 8 } + 4 x ^ { 7 } \right) + \left( 9 x ^ { 7 } + 7 x ^ { 6 } + 4 + 3 x ^ { 8 } \right)$

Insert $\in \mathbf { Or } \notin$ in the blank to make the statement is true. -8 ____ $\varnothing$

Use set notation, and list all the elements of the set. -The first six natural numbers.

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. - $x y < 0$

Decide whether the statement is true or false. If false, correct the statement so it is true. - $| - 4 \cdot 11 | = | - 4 | \cdot | 11 |$

Simplify the expression. Assume all variables represent positive real numbers. - $- \sqrt { \frac { 81 } { 8 } }$

Solve the problem. -The NSC (Not So Consistent) Corporation has just completed its first year of business. The following chart shows its monthly profit (or loss). The loss was greatest in

Find the domain of the expression. - $\frac { x ^ { 2 } - 25 } { x ^ { 2 } - 6 x + 5 }$

Find the distance between two points given their coordinates. -Find the distance between points $\mathrm { P }$ and $\mathrm { Q }$ on a number line, with coordinates $- 7$ and 4 , respectively.

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

Find the product. - (2x+110)(10x−15)\left( 2 x + \frac { 1 } { 10 } \right) \left( 10 x - \frac { 1 } { 5 } \right)(2x+101​)(10x−51​)

Identify the expression as a polynomial or not a polynomial. - 0.5x4−90.5 x ^ { 4 } - 90.5x4−9

Divide. - x4+3x2+8x2+1\frac { x ^ { 4 } + 3 x ^ { 2 } + 8 } { x ^ { 2 } + 1 }x2+1x4+3x2+8​

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - 6x06 x ^ { 0 }6x0

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - (x−4)012x−12\frac { \left( x ^ { - 4 } \right) ^ { 0 } } { 12 x ^ { - 12 } }12x−12(x−4)0​

Write in radical form. Assume all variables represent positive real numbers. - m4/3m ^ { 4 / 3 }m4/3

Factor by any method. - 64k2−49m264 k ^ { 2 } - 49 m ^ { 2 }64k2−49m2

Perform the indicated operation and write your answer with positive integer exponents. - m−1−n−1m−1+n−1⋅m+nm−n\frac { m ^ { - 1 } - n ^ { - 1 } } { m ^ { - 1 } + n ^ { - 1 } } \cdot \frac { m + n } { m - n }m−1+n−1m−1−n−1​⋅m−nm+n​

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - 5y9y+3\frac { \frac { 5 } { y } } { \frac { 9 } { y + 3 } }y+39​y5​​

Factor the polynomial by substitution. - 15z4+2z2−815 z ^ { 4 } + 2 z ^ { 2 } - 815z4+2z2−8

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - (x2y−4)1/2\left( \frac { x ^ { 2 } } { y ^ { - 4 } } \right) ^ { 1 / 2 }(y−4x2​)1/2

Find the sum or difference. - (−7−5x6+8x8+4x7)+(9x7+7x6+4+3x8)\left( - 7 - 5 x ^ { 6 } + 8 x ^ { 8 } + 4 x ^ { 7 } \right) + \left( 9 x ^ { 7 } + 7 x ^ { 6 } + 4 + 3 x ^ { 8 } \right)(−7−5x6+8x8+4x7)+(9x7+7x6+4+3x8)

Insert ∈Or∉\in \mathbf { Or } \notin∈Or∈/ in the blank to make the statement is true. -8 ____ ∅\varnothing∅