Question 1

Write the number in decimal notation. One bushel equals approximately 3.524 F1F1F1S1F1F1F10 101 liters.

Accepted Answer

A) 35.24 
B) 3524 
C) 352.4 
D) -35.24 
E) 3.524 
A) 35.24 
B) 3524 
C) 352.4 
D) -35.24 
E) 3.524

Question 2

Determine which numbers in the set are natural numbers. $- 13,6,11 , \sqrt { 49 } , 0 , - 9 , \sqrt { 65 }$

Accepted Answer

A)  $6,11 , \sqrt { 49 } , 0 , \sqrt { 65 }$ 
B)  $6,11 , \sqrt { 49 }$ 
C)  $6,11,0$ 
D)  $6,11$ 
E)  $- 13,6,11,0 , - 9$ 
A)  $6,11 , \sqrt { 49 } , 0 , \sqrt { 65 }$ 
B)  $6,11 , \sqrt { 49 }$ 
C)  $6,11,0$ 
D)  $6,11$ 
E)  $- 13,6,11,0 , - 9$

Question 3

A wind chill temperature is a measure of how cold it feels outside. The wind chill temperature $W$ (in degrees Fahrenheit) is given by $W = 35.75 + 0.6215 T - 35.75 v ^ { 0.16 } + 0.4275 T v ^ { 0.16 }$ where $T$ is the actual temperature (in degrees Fahrenheit) and $v$ is the wind speed (in miles per hour). Find the wind chill temperature for the given conditions below. Actual temperature: $15 ^ { \circ } F,$ wind speed: $10$ mph

Accepted Answer

A)  $- 16.0 ^ { \circ } \mathrm { F }$ 
B)  $68.8 ^ { \circ } F$ 
C)  $2.7 ^ { \circ } \mathrm { F }$ 
D)  $- 5.6 ^ { \circ } F$ 
E)  $106.0 ^ { \circ } \mathrm { F }$ 
A)  $- 16.0 ^ { \circ } \mathrm { F }$ 
B)  $68.8 ^ { \circ } F$ 
C)  $2.7 ^ { \circ } \mathrm { F }$ 
D)  $- 5.6 ^ { \circ } F$ 
E)  $106.0 ^ { \circ } \mathrm { F }$

Question 4

Simplify the rational expression below. $\frac { 8 x ^ { 3 } - 12 x ^ { 2 } + 18 x } { 8 x ^ { 3 } + 27 }$

Accepted Answer

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

Question 5

Change the following number from scientific notation to decimal notation. $2.61 \times 10 ^ { - 3 }$

Accepted Answer

A) 0.261 
B) 0.00261 
C) 2.61 
D) 26.1 
E) 0.0261 
A) 0.261 
B) 0.00261 
C) 2.61 
D) 26.1 
E) 0.0261

Question 6

The percent of people in a research study that have a particular health risk is 44.5%. The total number of people in the study is 14,677. How many people have the health risk?

Accepted Answer

A) 1614 people 
B) 14,677 people 
C) 21,208 people 
D) 6531 people 
E) 8146 people 
A) 1614 people 
B) 14,677 people 
C) 21,208 people 
D) 6531 people 
E) 8146 people

Question 7

Write each number in the expression below in scientific notation. Perform the operation and write your answer in scientific notation. $\frac { 242,000,000 } { 440 }$

Accepted Answer

A)  $5.5 \times 10 ^ { 8 }$ 
B)  $5.5 \times 10 ^ { 7 }$ 
C)  $55 \times 10 ^ { 4 }$ 
D)  $5.5 \times 10 ^ { 5 }$ 
E)  $5.5 \times 10 ^ { 4 }$ 
A)  $5.5 \times 10 ^ { 8 }$ 
B)  $5.5 \times 10 ^ { 7 }$ 
C)  $55 \times 10 ^ { 4 }$ 
D)  $5.5 \times 10 ^ { 5 }$ 
E)  $5.5 \times 10 ^ { 4 }$

Question 8

Place the correct symbol (, or =) between the pair of real numbers. $- ( - 3 )$ $- 3$

Accepted Answer

A)  $- ( - 3 )  - 3$ 
C)  $- ( - 3 ) = - 3$ 
A)  $- ( - 3 )  - 3$ 
C)  $- ( - 3 ) = - 3$

Question 9

Simplify the following rational expression. $\frac { 7 x - 8 } { x + 11 } - \frac { 11 x + 15 } { x + 11 }$

Accepted Answer

A)  $- \frac { 18 x + 7 } { x + 11 }$ 
B)  $\frac { 18 x + 7 } { x + 11 }$ 
C)  $\frac { 18 x - 23 } { x + 11 }$ 
D)  $- \frac { 4 x - 7 } { x + 11 }$ 
E)  $- \frac { 4 x + 23 } { x + 11 }$ 
A)  $- \frac { 18 x + 7 } { x + 11 }$ 
B)  $\frac { 18 x + 7 } { x + 11 }$ 
C)  $\frac { 18 x - 23 } { x + 11 }$ 
D)  $- \frac { 4 x - 7 } { x + 11 }$ 
E)  $- \frac { 4 x + 23 } { x + 11 }$

Question 10

Factor the trinomial. s2 - 5s - 36

Accepted Answer

A) s(s - 5)- 36 
B) s(s - 41) 
C) (s - 4)(s - 9) 
D) (s + 4)(s - 9) 
E) (s - 4)(s + 9) 
A) s(s - 5)- 36 
B) s(s - 41) 
C) (s - 4)(s - 9) 
D) (s + 4)(s - 9) 
E) (s - 4)(s + 9)

Question 11

Give a verbal description of the subset of real numbers represented by the inequality. 1 F1F1F1S1F1F1F10 x F1F1F1S1F1F1F10 8

Accepted Answer

A) all real numbers less than 1 and greater than 8 
B) all real numbers between 1 and 8 not including 1 or 8 
C) all real numbers between 1 and 8, including 1 but not including 8 
D) all real numbers between 1 and 8, including 8 but not including 1 
E) all real numbers between 1 and 8, including 1 and 8 
A) all real numbers less than 1 and greater than 8 
B) all real numbers between 1 and 8 not including 1 or 8 
C) all real numbers between 1 and 8, including 1 but not including 8 
D) all real numbers between 1 and 8, including 8 but not including 1 
E) all real numbers between 1 and 8, including 1 and 8

Question 12

Perform the subtraction and simplify. $\frac { 2 x } { x - 3 } - \frac { 2 } { 3 - x }$

Accepted Answer

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

Question 13

Use a calculator to approximate the number. (Round your answer to three decimal places.) $\left( \frac { 7 } { 3 } \right) ^ { - 7 / 8 } - \left( - \frac { 12 } { 5 } \right) ^ { 1 / 3 }$

Accepted Answer

A) -0.862 
B) 1.536 
C) -1.536 
D) 1.815 
E) 3.438 
A) -0.862 
B) 1.536 
C) -1.536 
D) 1.815 
E) 3.438

Question 14

Find the product below. $( 2 x + 3 y ) ^ { 3 }$

Accepted Answer

A)  $8 x ^ { 3 } - 36 x ^ { 2 } y - 54 x y ^ { 2 } + 27 y ^ { 3 }$ 
B)  $8 x ^ { 3 } - 54 x ^ { 2 } y + 36 x y ^ { 2 } + 27 y ^ { 3 }$ 
C)  $8 x ^ { 3 } + 12 x ^ { 2 } y - 18 x y ^ { 2 } - 27 y ^ { 3 }$ 
D)  $8 x ^ { 3 } + 36 x ^ { 2 } y + 54 x y ^ { 2 } + 27 y ^ { 3 }$ 
E)  $8 x ^ { 3 } + 12 x ^ { 2 } y + 18 x y ^ { 2 } + 27 y ^ { 3 }$ 
A)  $8 x ^ { 3 } - 36 x ^ { 2 } y - 54 x y ^ { 2 } + 27 y ^ { 3 }$ 
B)  $8 x ^ { 3 } - 54 x ^ { 2 } y + 36 x y ^ { 2 } + 27 y ^ { 3 }$ 
C)  $8 x ^ { 3 } + 12 x ^ { 2 } y - 18 x y ^ { 2 } - 27 y ^ { 3 }$ 
D)  $8 x ^ { 3 } + 36 x ^ { 2 } y + 54 x y ^ { 2 } + 27 y ^ { 3 }$ 
E)  $8 x ^ { 3 } + 12 x ^ { 2 } y + 18 x y ^ { 2 } + 27 y ^ { 3 }$

Question 15

Write the rational expression in simplest form. $\frac { 3 y - 9 y ^ { 2 } } { 12 y - 4 }$

Accepted Answer

A)  $\frac { 3 y } { 4 } , \quad y \neq 0$ 
B)  $\frac { 3 y } { 4 } , \quad y \neq \frac { 1 } { 3 }$ 
C)  $- \frac { 3 y } { 4 } , \quad y \neq \frac { 1 } { 3 }$ 
D)  $- \frac { 3 y } { 4 } , \quad y \neq \frac { 1 } { 3 } , y \neq 0$ 
E)  $- \frac { 3 y } { 4 } , \quad y \neq 0$ 
A)  $\frac { 3 y } { 4 } , \quad y \neq 0$ 
B)  $\frac { 3 y } { 4 } , \quad y \neq \frac { 1 } { 3 }$ 
C)  $- \frac { 3 y } { 4 } , \quad y \neq \frac { 1 } { 3 }$ 
D)  $- \frac { 3 y } { 4 } , \quad y \neq \frac { 1 } { 3 } , y \neq 0$ 
E)  $- \frac { 3 y } { 4 } , \quad y \neq 0$

Question 16

Simplify the following complex fraction. $\frac { \frac { 1 } { x + 7 } - \frac { 8 } { x - 9 } } { \frac { x } { x - 9 } + \frac { 5 } { x + 7 } }$

Accepted Answer

A)  $\frac { - 7 x - 65 } { x ^ { 2 } + 12 x - 45 }$ 
B)  $\frac { - 7 } { x + 5 }$ 
C)  $\frac { x - 17 } { x ^ { 2 } + 7 x + 5 }$ 
D)  $\frac { - 7 x + 47 } { x ^ { 2 } + 12 }$ 
E)  $\frac { x - 2 } { x ^ { 2 } - 2 x - 63 }$ 
A)  $\frac { - 7 x - 65 } { x ^ { 2 } + 12 x - 45 }$ 
B)  $\frac { - 7 } { x + 5 }$ 
C)  $\frac { x - 17 } { x ^ { 2 } + 7 x + 5 }$ 
D)  $\frac { - 7 x + 47 } { x ^ { 2 } + 12 }$ 
E)  $\frac { x - 2 } { x ^ { 2 } - 2 x - 63 }$

Question 17

Plot the two real numbers on the real number line. Then place the appropriate inequality symbol () between them. 2, -3

Accepted Answer

A) 2  -3 
A) 2  -3

Question 18

Simplify the following rational expression. $\frac { 1 } { x ^ { 2 } - 7 x - 120 } + \frac { 1 } { x ^ { 2 } - 225 } + \frac { 1 } { x ^ { 2 } - 64 }$

Accepted Answer

A)  $\frac { 3 x ^ { 2 } + 7 x - 409 } { ( x - 15 ) ( x + 8 ) }$ 
B)  $\frac { 3 x ^ { 2 } + 7 x - 409 } { ( x - 15 ) ( x + 15 ) ( x + 8 ) ( x - 8 ) }$ 
C)  $\frac { 3 x ^ { 2 } + 7 x } { ( x + 15 ) ( x + 8 ) ( x - 8 ) }$ 
D)  $\frac { 3 } { ( x - 15 ) ( x + 15 ) ( x + 8 ) ( x - 8 ) }$ 
E)  $\frac { 7 x - 409 } { ( x - 15 ) ( x + 15 ) ( x + 8 ) ( x - 8 ) }$ 
A)  $\frac { 3 x ^ { 2 } + 7 x - 409 } { ( x - 15 ) ( x + 8 ) }$ 
B)  $\frac { 3 x ^ { 2 } + 7 x - 409 } { ( x - 15 ) ( x + 15 ) ( x + 8 ) ( x - 8 ) }$ 
C)  $\frac { 3 x ^ { 2 } + 7 x } { ( x + 15 ) ( x + 8 ) ( x - 8 ) }$ 
D)  $\frac { 3 } { ( x - 15 ) ( x + 15 ) ( x + 8 ) ( x - 8 ) }$ 
E)  $\frac { 7 x - 409 } { ( x - 15 ) ( x + 15 ) ( x + 8 ) ( x - 8 ) }$

Question 19

Factor the perfect square trinomial. $p ^ { 2 } + \frac { 12 } { 5 } p + \frac { 36 } { 25 }$

Accepted Answer

A)  $\left( p + \frac { 12 } { 5 } \right) ^ { 2 }$ 
B)  $\left( p + \frac { 6 } { 5 } \right) ^ { 2 }$ 
C)  $\left( p - \frac { 6 } { 5 } \right) ^ { 2 }$ 
D)  $\left( p - \frac { 12 } { 5 } \right) ^ { 2 }$ 
E)  $\left( p + \frac { 6 } { 5 } \right) \left( p - \frac { 6 } { 5 } \right)$ 
A)  $\left( p + \frac { 12 } { 5 } \right) ^ { 2 }$ 
B)  $\left( p + \frac { 6 } { 5 } \right) ^ { 2 }$ 
C)  $\left( p - \frac { 6 } { 5 } \right) ^ { 2 }$ 
D)  $\left( p - \frac { 12 } { 5 } \right) ^ { 2 }$ 
E)  $\left( p + \frac { 6 } { 5 } \right) \left( p - \frac { 6 } { 5 } \right)$

Question 20

Use inequality notation to describe the set. m is at least -8 but less than 15

Accepted Answer

A) 15 F1F1F1S1F1F1F10 m F1F1F1S1F1F1F10 -8 
B) 15 F1F1F1S1F1F1F10 m F1F1F1S1F1F1F10 -8 
C) -8 F1F1F1S1F1F1F10 m F1F1F1S1F1F1F10 15 
D) -8 F1F1F1S1F1F1F10 m F1F1F1S1F1F1F10 15 
E) -8 F1F1F1S1F1F1F10 m F1F1F1S1F1F1F10 15 
A) 15 F1F1F1S1F1F1F10 m F1F1F1S1F1F1F10 -8 
B) 15 F1F1F1S1F1F1F10 m F1F1F1S1F1F1F10 -8 
C) -8 F1F1F1S1F1F1F10 m F1F1F1S1F1F1F10 15 
D) -8 F1F1F1S1F1F1F10 m F1F1F1S1F1F1F10 15 
E) -8 F1F1F1S1F1F1F10 m F1F1F1S1F1F1F10 15

Write the number in decimal notation. One bushel equals approximately 3.524  101 liters.

Determine which numbers in the set are natural numbers. $- 13,6,11 , \sqrt { 49 } , 0 , - 9 , \sqrt { 65 }$

Simplify the rational expression below. $\frac { 8 x ^ { 3 } - 12 x ^ { 2 } + 18 x } { 8 x ^ { 3 } + 27 }$

Change the following number from scientific notation to decimal notation. $2.61 \times 10 ^ { - 3 }$

The percent of people in a research study that have a particular health risk is 44.5%. The total number of people in the study is 14,677. How many people have the health risk?

Write each number in the expression below in scientific notation. Perform the operation and write your answer in scientific notation. $\frac { 242,000,000 } { 440 }$

Place the correct symbol (<, >, or =) between the pair of real numbers. $- ( - 3 )$ $- 3$

Simplify the following rational expression. $\frac { 7 x - 8 } { x + 11 } - \frac { 11 x + 15 } { x + 11 }$

Factor the trinomial. s2 - 5s - 36

Give a verbal description of the subset of real numbers represented by the inequality. 1  x  8

Perform the subtraction and simplify. $\frac { 2 x } { x - 3 } - \frac { 2 } { 3 - x }$

Use a calculator to approximate the number. (Round your answer to three decimal places.) $\left( \frac { 7 } { 3 } \right) ^ { - 7 / 8 } - \left( - \frac { 12 } { 5 } \right) ^ { 1 / 3 }$

Find the product below. $( 2 x + 3 y ) ^ { 3 }$

Write the rational expression in simplest form. $\frac { 3 y - 9 y ^ { 2 } } { 12 y - 4 }$

Simplify the following complex fraction. $\frac { \frac { 1 } { x + 7 } - \frac { 8 } { x - 9 } } { \frac { x } { x - 9 } + \frac { 5 } { x + 7 } }$

Plot the two real numbers on the real number line. Then place the appropriate inequality symbol (< or >) between them. 2, -3

Simplify the following rational expression. $\frac { 1 } { x ^ { 2 } - 7 x - 120 } + \frac { 1 } { x ^ { 2 } - 225 } + \frac { 1 } { x ^ { 2 } - 64 }$

Factor the perfect square trinomial. $p ^ { 2 } + \frac { 12 } { 5 } p + \frac { 36 } { 25 }$

Use inequality notation to describe the set. m is at least -8 but less than 15

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants

Limits and Derivatives

Applications of the Derivative

Further Applications of the Derivative

Derivatives of Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions Web

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Exam 1: Fundamental Concepts of Algebra

Write the number in decimal notation. One bushel equals approximately 3.524  101 liters.

Determine which numbers in the set are natural numbers. −13,6,11,49,0,−9,65- 13,6,11 , \sqrt { 49 } , 0 , - 9 , \sqrt { 65 }−13,6,11,49​,0,−9,65​

Simplify the rational expression below. 8x3−12x2+18x8x3+27\frac { 8 x ^ { 3 } - 12 x ^ { 2 } + 18 x } { 8 x ^ { 3 } + 27 }8x3+278x3−12x2+18x​

Change the following number from scientific notation to decimal notation. 2.61×10−32.61 \times 10 ^ { - 3 }2.61×10−3

The percent of people in a research study that have a particular health risk is 44.5%. The total number of people in the study is 14,677. How many people have the health risk?

Write each number in the expression below in scientific notation. Perform the operation and write your answer in scientific notation. 242,000,000440\frac { 242,000,000 } { 440 }440242,000,000​

Place the correct symbol (<, >, or =) between the pair of real numbers. −(−3)- ( - 3 )−(−3) −3- 3−3

Simplify the following rational expression. 7x−8x+11−11x+15x+11\frac { 7 x - 8 } { x + 11 } - \frac { 11 x + 15 } { x + 11 }x+117x−8​−x+1111x+15​

Factor the trinomial. s2 - 5s - 36

Give a verbal description of the subset of real numbers represented by the inequality. 1  x  8

Perform the subtraction and simplify. 2xx−3−23−x\frac { 2 x } { x - 3 } - \frac { 2 } { 3 - x }x−32x​−3−x2​

Use a calculator to approximate the number. (Round your answer to three decimal places.) (73)−7/8−(−125)1/3\left( \frac { 7 } { 3 } \right) ^ { - 7 / 8 } - \left( - \frac { 12 } { 5 } \right) ^ { 1 / 3 }(37​)−7/8−(−512​)1/3

Find the product below. (2x+3y)3( 2 x + 3 y ) ^ { 3 }(2x+3y)3

Write the rational expression in simplest form. 3y−9y212y−4\frac { 3 y - 9 y ^ { 2 } } { 12 y - 4 }12y−43y−9y2​

Simplify the following complex fraction. 1x+7−8x−9xx−9+5x+7\frac { \frac { 1 } { x + 7 } - \frac { 8 } { x - 9 } } { \frac { x } { x - 9 } + \frac { 5 } { x + 7 } }x−9x​+x+75​x+71​−x−98​​

Plot the two real numbers on the real number line. Then place the appropriate inequality symbol (< or >) between them. 2, -3

Simplify the following rational expression. 1x2−7x−120+1x2−225+1x2−64\frac { 1 } { x ^ { 2 } - 7 x - 120 } + \frac { 1 } { x ^ { 2 } - 225 } + \frac { 1 } { x ^ { 2 } - 64 }x2−7x−1201​+x2−2251​+x2−641​

Factor the perfect square trinomial. p2+125p+3625p ^ { 2 } + \frac { 12 } { 5 } p + \frac { 36 } { 25 }p2+512​p+2536​

Use inequality notation to describe the set. m is at least -8 but less than 15

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants

Limits and Derivatives

Applications of the Derivative

Further Applications of the Derivative

Derivatives of Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions Web

Series and Taylor Polynomials Web

Probability Web

Filters

Determine which numbers in the set are natural numbers. $- 13,6,11 , \sqrt { 49 } , 0 , - 9 , \sqrt { 65 }$

Simplify the rational expression below. $\frac { 8 x ^ { 3 } - 12 x ^ { 2 } + 18 x } { 8 x ^ { 3 } + 27 }$

Change the following number from scientific notation to decimal notation. $2.61 \times 10 ^ { - 3 }$

Write each number in the expression below in scientific notation. Perform the operation and write your answer in scientific notation. $\frac { 242,000,000 } { 440 }$

Place the correct symbol (<, >, or =) between the pair of real numbers. $- ( - 3 )$ $- 3$

Simplify the following rational expression. $\frac { 7 x - 8 } { x + 11 } - \frac { 11 x + 15 } { x + 11 }$

Perform the subtraction and simplify. $\frac { 2 x } { x - 3 } - \frac { 2 } { 3 - x }$

Use a calculator to approximate the number. (Round your answer to three decimal places.) $\left( \frac { 7 } { 3 } \right) ^ { - 7 / 8 } - \left( - \frac { 12 } { 5 } \right) ^ { 1 / 3 }$

Find the product below. $( 2 x + 3 y ) ^ { 3 }$

Write the rational expression in simplest form. $\frac { 3 y - 9 y ^ { 2 } } { 12 y - 4 }$

Simplify the following complex fraction. $\frac { \frac { 1 } { x + 7 } - \frac { 8 } { x - 9 } } { \frac { x } { x - 9 } + \frac { 5 } { x + 7 } }$

Simplify the following rational expression. $\frac { 1 } { x ^ { 2 } - 7 x - 120 } + \frac { 1 } { x ^ { 2 } - 225 } + \frac { 1 } { x ^ { 2 } - 64 }$

Factor the perfect square trinomial. $p ^ { 2 } + \frac { 12 } { 5 } p + \frac { 36 } { 25 }$