Question 1

Determine which of the points $( - 5,0 )$ , $( 2,23 )$ , and $( - \sqrt { 2 } , \sqrt { 23 } )$ are on the graph of the equation $x ^ { 2 } + y ^ { 2 } = 25$ .

Accepted Answer

A)  $( 2,23 )$ ,
$( - \sqrt { 2 } , \sqrt { 23 } )$ 
B)  $( - 5,0 )$ ,
$( - \sqrt { 2 } , \sqrt { 23 } )$ 
C)  $( - 5,0 )$ ,
$( 2,23 )$ ,
$( - \sqrt { 2 } , \sqrt { 23 } )$ 
D)  $( - 5,0 )$ ,
$( 2,23 )$ 
E)  None 
A)  $( 2,23 )$ ,
$( - \sqrt { 2 } , \sqrt { 23 } )$ 
B)  $( - 5,0 )$ ,
$( - \sqrt { 2 } , \sqrt { 23 } )$ 
C)  $( - 5,0 )$ ,
$( 2,23 )$ ,
$( - \sqrt { 2 } , \sqrt { 23 } )$ 
D)  $( - 5,0 )$ ,
$( 2,23 )$ 
E)  None

Question 2

Express the repeating decimal $2 . \overline { 45 }$ as a fraction.

Accepted Answer

The answer of Express the repeating decimal \(2 . \overline...

Question 3

Determine an appropriate viewing rectangle for the equation $y = x ^ { 5 } - 3 x ^ { 4 } + x ^ { 3 }$ and use it to draw the graph.

Accepted Answer

The answer of Determine an appropriate viewing rectangle for the...

Question 4

Factor out the common factor. $- 14 x ^ { 4 } y ^ { 2 } + 7 x y ^ { 3 } - 21 x ^ { 4 }$

Accepted Answer

The answer of Factor out the common factor. \(- 14...

Question 5

Perform the indicated operations. $\frac { \frac { 2 } { 5 } + \frac { 1 } { 2 } } { \frac { 1 } { 10 } + \frac { 3 } { 5 } }$

Accepted Answer

The answer of Perform the indicated operations. \(\frac { \frac...

Question 6

Solve the equation. $3 x ^ { 2 } - 6 x - 2 = 0$

Accepted Answer

A)  $x = - 6$ ,
$x = - 4$ 
B)  $x = 4$ ,
$x = - 6$ 
C)  $x = 1 \pm \frac { \sqrt { 13 } } { 3 }$ 
D)  $x = 1 \pm \frac { \sqrt { 3 } } { 3}$ 
E)  $x = - 1 \pm \frac { 3 \sqrt { 3 } } { 3 }$ 
A)  $x = - 6$ ,
$x = - 4$ 
B)  $x = 4$ ,
$x = - 6$ 
C)  $x = 1 \pm \frac { \sqrt { 13 } } { 3 }$ 
D)  $x = 1 \pm \frac { \sqrt { 3 } } { 3}$ 
E)  $x = - 1 \pm \frac { 3 \sqrt { 3 } } { 3 }$

Question 7

Solve the equation. $\frac { x } { 4 x ^ { 2 } + x } + \frac { 2 } { x - 1 } = \frac { 3 } { 4 x + 1 }$

Accepted Answer

A)  $- 1$ 
B)  $- \frac { 3 } { 2 }$ 
C)  $1$ 
D)  $- \frac { 2 } { 3 }$ 
E)  $\frac { 2 } { 3 }$ 
A)  $- 1$ 
B)  $- \frac { 3 } { 2 }$ 
C)  $1$ 
D)  $- \frac { 2 } { 3 }$ 
E)  $\frac { 2 } { 3 }$

Question 8

Factor the expression. $x ^ { 2 } ( x - 5 ) ^ { 3 } + x ^ { 3 } ( x - 5 ) ^ { 2 }$

Accepted Answer

A)  $x ( 2 x + 5 ) ( x - 5 ) ^ { 2 }$ 
B)  $x ^ { 2 } ( 2 x + 5 ) ( x - 5 ) ^ { 2 }$ 
C)  $x ( 2 x - 5 ) ^ { 2 } ( x - 5 ) ^ { 2 }$ 
D)  $x ^ { 2 } ( 5 x - 5 ) ( 2 x - 5 )$ 
E)  $x ^ { 2 } ( 2 x - 5 ) ( x - 5 ) ^ { 2 }$ 
A)  $x ( 2 x + 5 ) ( x - 5 ) ^ { 2 }$ 
B)  $x ^ { 2 } ( 2 x + 5 ) ( x - 5 ) ^ { 2 }$ 
C)  $x ( 2 x - 5 ) ^ { 2 } ( x - 5 ) ^ { 2 }$ 
D)  $x ^ { 2 } ( 5 x - 5 ) ( 2 x - 5 )$ 
E)  $x ^ { 2 } ( 2 x - 5 ) ( x - 5 ) ^ { 2 }$

Question 9

Solve the equation by completing the square. $5 x ^ { 2 } - x = 0$

Accepted Answer

The answer of Solve the equation by completing the square....

Question 10

Solve the equation for the indicated variable. $A = 2 y ^ { 2 } + 4 y h ; \text { for } y$

Accepted Answer

The answer of Solve the equation for the indicated variable....

Question 11

Rationalize the numerator of the expression. $\sqrt { x ^ { 2 } + 5 x + 6 } - \sqrt { x }$

Accepted Answer

The answer of Rationalize the numerator of the expression. \(\sqrt...

Question 12

Determine an appropriate viewing rectangle for the equation $y = x ^ { 2 } + \frac { 2 } { x }$ .

Accepted Answer

The answer of Determine an appropriate viewing rectangle for the...

Question 13

Simplify the expression and eliminate any negative exponents(s).
Assume that all letters denote positive numbers. $\sqrt [ 3 ] { 11 \sqrt { 11 } }$

Accepted Answer

The answer of Simplify the expression and eliminate any negative...

Question 14

Which of the numbers $\frac { 10 } { 0.001 }$ and $\frac { 10 } { 0.01 }$ is smaller?

Accepted Answer

@#LAT-DLM& is smalle

Question 15

Solve the inequality $\left| t + \frac { 1 } { 2 } \right| \geq 2$ .

Accepted Answer

A) 
 $t \in ( - \infty , - 2 ] \cup [ 3 , \infty )$ 
B) 
 $t \in \left( - \infty , - \frac { 1 } { 2 } \right] \cup \left[ \frac { 3 } { 2 } , \infty \right)$ 
C) 
 $t \in \left( - \infty , - \frac { 3} { 2 } \right] \cup \left[ \frac { 3 } { 2 } , \infty \right)$ 
D) 
   
E) 
 $t \in \left( - \infty , - \frac { 5 } { 2 } \right] \cup \left[ \frac { 3 } { 2 } , \infty \right)$ 
A) 
 $t \in ( - \infty , - 2 ] \cup [ 3 , \infty )$ 
B) 
 $t \in \left( - \infty , - \frac { 1 } { 2 } \right] \cup \left[ \frac { 3 } { 2 } , \infty \right)$ 
C) 
 $t \in \left( - \infty , - \frac { 3} { 2 } \right] \cup \left[ \frac { 3 } { 2 } , \infty \right)$ 
D) 
   
E) 
 $t \in \left( - \infty , - \frac { 5 } { 2 } \right] \cup \left[ \frac { 3 } { 2 } , \infty \right)$

Question 16

Solve the equation. $\frac { x } { \frac { x } { 2 } + \frac { 2 ( x + 3 ) } { 5 } } = 2$

Accepted Answer

A)  $- 4$ 
B)  $- 3$ 
C)  $3$ 
D)  $12$ 
E)  $4$ 
A)  $- 4$ 
B)  $- 3$ 
C)  $3$ 
D)  $12$ 
E)  $4$

Question 17

Simplify the compound fractional expression. $\frac { x ^ { - 1 } + y ^ { - 1 } } { x ^ { - 2 } + y ^ { - 1 } }$

Accepted Answer

The answer of Simplify the compound fractional expression. \(\frac {...

Question 18

Determine whether the given values of the variables are solutions of the equation. $\frac { a x - b x } { b x - a } = \frac { b x + a } { - a - b }$ 
(a)
 $x = 1$ 
(b)
 $x = - a / b$

Accepted Answer

a) LHS @#LAT-DLM& , RHS @#LAT-DLM& LHS.

Question 19

Perform the indicated operations and simplify. $\left( - 2 x ^ { 3 } + 6 x ^ { 2 } - 4 x + 8 \right) + \left( 3 x ^ { 3 } + x - 4 \right)$

Accepted Answer

A)  $2 x ^ { 3 } + 6 x ^ { 2 } + 3 x + 5$ 
B)  $2 x ^ { 3 } + 6 x ^ { 2 } + 3 x + 12$ 
C)  $2 x ^ { 3 } + 6 x ^ { 2 } + 3 x - 1$ 
D)  $x ^ { 3 } + 6 x ^ { 2 } + 3 x - 4$ 
E)  $x ^ { 3 } + 6 x ^ { 2 } - 3 x + 4$ 
A)  $2 x ^ { 3 } + 6 x ^ { 2 } + 3 x + 5$ 
B)  $2 x ^ { 3 } + 6 x ^ { 2 } + 3 x + 12$ 
C)  $2 x ^ { 3 } + 6 x ^ { 2 } + 3 x - 1$ 
D)  $x ^ { 3 } + 6 x ^ { 2 } + 3 x - 4$ 
E)  $x ^ { 3 } + 6 x ^ { 2 } - 3 x + 4$

Question 20

Perform the indicated operation(s) and simplify. $\frac { 1 } { 4 } + 5 \left( \frac { 1 } { 4 } \cdot \frac { 1 } { 5 } \right) - \frac { 3 } { 4 }$

Accepted Answer

A)  $- \frac { 3 } { 4 }$ 
B)  $\frac { 3 } { 4 }$ 
C)  $\frac { 1 } { 25 }$ 
D)  $- \frac { 1 } { 4 }$ 
E)  $\frac { 1 } { 4 }$ 
A)  $- \frac { 3 } { 4 }$ 
B)  $\frac { 3 } { 4 }$ 
C)  $\frac { 1 } { 25 }$ 
D)  $- \frac { 1 } { 4 }$ 
E)  $\frac { 1 } { 4 }$

Determine which of the points $( - 5,0 )$ , $( 2,23 )$ , and $( - \sqrt { 2 } , \sqrt { 23 } )$ are on the graph of the equation $x ^ { 2 } + y ^ { 2 } = 25$ .

Express the repeating decimal $2 . \overline { 45 }$ as a fraction.

Determine an appropriate viewing rectangle for the equation $y = x ^ { 5 } - 3 x ^ { 4 } + x ^ { 3 }$ and use it to draw the graph.

Factor out the common factor. $- 14 x ^ { 4 } y ^ { 2 } + 7 x y ^ { 3 } - 21 x ^ { 4 }$

Perform the indicated operations. $\frac { \frac { 2 } { 5 } + \frac { 1 } { 2 } } { \frac { 1 } { 10 } + \frac { 3 } { 5 } }$

Solve the equation. $3 x ^ { 2 } - 6 x - 2 = 0$

Solve the equation. $\frac { x } { 4 x ^ { 2 } + x } + \frac { 2 } { x - 1 } = \frac { 3 } { 4 x + 1 }$

Factor the expression. $x ^ { 2 } ( x - 5 ) ^ { 3 } + x ^ { 3 } ( x - 5 ) ^ { 2 }$

Solve the equation by completing the square. $5 x ^ { 2 } - x = 0$

Solve the equation for the indicated variable. $A = 2 y ^ { 2 } + 4 y h ; \text { for } y$

Rationalize the numerator of the expression. $\sqrt { x ^ { 2 } + 5 x + 6 } - \sqrt { x }$

Determine an appropriate viewing rectangle for the equation $y = x ^ { 2 } + \frac { 2 } { x }$ .

Simplify the expression and eliminate any negative exponents(s). Assume that all letters denote positive numbers. $\sqrt [ 3 ] { 11 \sqrt { 11 } }$

Which of the numbers $\frac { 10 } { 0.001 }$ and $\frac { 10 } { 0.01 }$ is smaller?

Solve the inequality $\left| t + \frac { 1 } { 2 } \right| \geq 2$ .

Solve the equation. $\frac { x } { \frac { x } { 2 } + \frac { 2 ( x + 3 ) } { 5 } } = 2$

Simplify the compound fractional expression. $\frac { x ^ { - 1 } + y ^ { - 1 } } { x ^ { - 2 } + y ^ { - 1 } }$

Determine whether the given values of the variables are solutions of the equation. $\frac { a x - b x } { b x - a } = \frac { b x + a } { - a - b }$ (a) $x = 1$ (b) $x = - a / b$

Perform the indicated operations and simplify. $\left( - 2 x ^ { 3 } + 6 x ^ { 2 } - 4 x + 8 \right) + \left( 3 x ^ { 3 } + x - 4 \right)$

Perform the indicated operation(s) and simplify. $\frac { 1 } { 4 } + 5 \left( \frac { 1 } { 4 } \cdot \frac { 1 } { 5 } \right) - \frac { 3 } { 4 }$

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions: Unit Circle Approach

Trigonometric Functions: Right Triangle Approach

Analytic Trigonometry

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Conic Sections

Sequences and Series

Limits: a Preview of Calculus

Filters

Exam 1: Fundamentals

Determine which of the points (−5,0)( - 5,0 )(−5,0) , (2,23)( 2,23 )(2,23) , and (−2,23)( - \sqrt { 2 } , \sqrt { 23 } )(−2​,23​) are on the graph of the equation x2+y2=25x ^ { 2 } + y ^ { 2 } = 25x2+y2=25 .

Express the repeating decimal 2.45‾2 . \overline { 45 }2.45 as a fraction.

Determine an appropriate viewing rectangle for the equation y=x5−3x4+x3y = x ^ { 5 } - 3 x ^ { 4 } + x ^ { 3 }y=x5−3x4+x3 and use it to draw the graph.

Factor out the common factor. −14x4y2+7xy3−21x4- 14 x ^ { 4 } y ^ { 2 } + 7 x y ^ { 3 } - 21 x ^ { 4 }−14x4y2+7xy3−21x4

Perform the indicated operations. 25+12110+35\frac { \frac { 2 } { 5 } + \frac { 1 } { 2 } } { \frac { 1 } { 10 } + \frac { 3 } { 5 } }101​+53​52​+21​​

Solve the equation. 3x2−6x−2=03 x ^ { 2 } - 6 x - 2 = 03x2−6x−2=0

Solve the equation. x4x2+x+2x−1=34x+1\frac { x } { 4 x ^ { 2 } + x } + \frac { 2 } { x - 1 } = \frac { 3 } { 4 x + 1 }4x2+xx​+x−12​=4x+13​

Factor the expression. x2(x−5)3+x3(x−5)2x ^ { 2 } ( x - 5 ) ^ { 3 } + x ^ { 3 } ( x - 5 ) ^ { 2 }x2(x−5)3+x3(x−5)2

Solve the equation by completing the square. 5x2−x=05 x ^ { 2 } - x = 05x2−x=0

Solve the equation for the indicated variable. A=2y2+4yh; for yA = 2 y ^ { 2 } + 4 y h ; \text { for } yA=2y2+4yh; for y

Rationalize the numerator of the expression. x2+5x+6−x\sqrt { x ^ { 2 } + 5 x + 6 } - \sqrt { x }x2+5x+6​−x​

Determine an appropriate viewing rectangle for the equation y=x2+2xy = x ^ { 2 } + \frac { 2 } { x }y=x2+x2​ .

Simplify the expression and eliminate any negative exponents(s). Assume that all letters denote positive numbers. 11113\sqrt [ 3 ] { 11 \sqrt { 11 } }31111​​

Which of the numbers 100.001\frac { 10 } { 0.001 }0.00110​ and 100.01\frac { 10 } { 0.01 }0.0110​ is smaller?

Solve the inequality ∣t+12∣≥2\left| t + \frac { 1 } { 2 } \right| \geq 2​t+21​​≥2 .

Solve the equation. xx2+2(x+3)5=2\frac { x } { \frac { x } { 2 } + \frac { 2 ( x + 3 ) } { 5 } } = 22x​+52(x+3)​x​=2

Simplify the compound fractional expression. x−1+y−1x−2+y−1\frac { x ^ { - 1 } + y ^ { - 1 } } { x ^ { - 2 } + y ^ { - 1 } }x−2+y−1x−1+y−1​

Determine whether the given values of the variables are solutions of the equation. ax−bxbx−a=bx+a−a−b\frac { a x - b x } { b x - a } = \frac { b x + a } { - a - b }bx−aax−bx​=−a−bbx+a​ (a) x=1x = 1x=1 (b) x=−a/bx = - a / bx=−a/b

Perform the indicated operations and simplify. (−2x3+6x2−4x+8)+(3x3+x−4)\left( - 2 x ^ { 3 } + 6 x ^ { 2 } - 4 x + 8 \right) + \left( 3 x ^ { 3 } + x - 4 \right)(−2x3+6x2−4x+8)+(3x3+x−4)

Perform the indicated operation(s) and simplify. 14+5(14⋅15)−34\frac { 1 } { 4 } + 5 \left( \frac { 1 } { 4 } \cdot \frac { 1 } { 5 } \right) - \frac { 3 } { 4 }41​+5(41​⋅51​)−43​

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions: Unit Circle Approach

Trigonometric Functions: Right Triangle Approach

Analytic Trigonometry

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Conic Sections

Sequences and Series

Limits: a Preview of Calculus

Filters

Determine which of the points $( - 5,0 )$ , $( 2,23 )$ , and $( - \sqrt { 2 } , \sqrt { 23 } )$ are on the graph of the equation $x ^ { 2 } + y ^ { 2 } = 25$ .

Express the repeating decimal $2 . \overline { 45 }$ as a fraction.

Determine an appropriate viewing rectangle for the equation $y = x ^ { 5 } - 3 x ^ { 4 } + x ^ { 3 }$ and use it to draw the graph.

Factor out the common factor. $- 14 x ^ { 4 } y ^ { 2 } + 7 x y ^ { 3 } - 21 x ^ { 4 }$

Perform the indicated operations. $\frac { \frac { 2 } { 5 } + \frac { 1 } { 2 } } { \frac { 1 } { 10 } + \frac { 3 } { 5 } }$

Solve the equation. $3 x ^ { 2 } - 6 x - 2 = 0$

Solve the equation. $\frac { x } { 4 x ^ { 2 } + x } + \frac { 2 } { x - 1 } = \frac { 3 } { 4 x + 1 }$

Factor the expression. $x ^ { 2 } ( x - 5 ) ^ { 3 } + x ^ { 3 } ( x - 5 ) ^ { 2 }$

Solve the equation by completing the square. $5 x ^ { 2 } - x = 0$

Solve the equation for the indicated variable. $A = 2 y ^ { 2 } + 4 y h ; \text { for } y$

Rationalize the numerator of the expression. $\sqrt { x ^ { 2 } + 5 x + 6 } - \sqrt { x }$

Determine an appropriate viewing rectangle for the equation $y = x ^ { 2 } + \frac { 2 } { x }$ .

Simplify the expression and eliminate any negative exponents(s). Assume that all letters denote positive numbers. $\sqrt [ 3 ] { 11 \sqrt { 11 } }$

Which of the numbers $\frac { 10 } { 0.001 }$ and $\frac { 10 } { 0.01 }$ is smaller?

Solve the inequality $\left| t + \frac { 1 } { 2 } \right| \geq 2$ .

Solve the equation. $\frac { x } { \frac { x } { 2 } + \frac { 2 ( x + 3 ) } { 5 } } = 2$

Simplify the compound fractional expression. $\frac { x ^ { - 1 } + y ^ { - 1 } } { x ^ { - 2 } + y ^ { - 1 } }$

Determine whether the given values of the variables are solutions of the equation. $\frac { a x - b x } { b x - a } = \frac { b x + a } { - a - b }$ (a) $x = 1$ (b) $x = - a / b$

Perform the indicated operations and simplify. $\left( - 2 x ^ { 3 } + 6 x ^ { 2 } - 4 x + 8 \right) + \left( 3 x ^ { 3 } + x - 4 \right)$

Perform the indicated operation(s) and simplify. $\frac { 1 } { 4 } + 5 \left( \frac { 1 } { 4 } \cdot \frac { 1 } { 5 } \right) - \frac { 3 } { 4 }$