Question 1

Perform the operation and write the result in standard form. $\left( 2 x ^ { 2 } + 6 \right) - \left( x ^ { 2 } - 5 x + 1 \right)$

Accepted Answer

A)  $x ^ { 2 } - 5 x + 7$ 
B)  $x ^ { 2 } + 5 x + 5$ 
C)  $x ^ { 4 } + 5 x + 5$ 
D)  $x ^ { 4 } - 5 x + 7$ 
E)  $3 x ^ { 4 } - 5 x + 7$ 
A)  $x ^ { 2 } - 5 x + 7$ 
B)  $x ^ { 2 } + 5 x + 5$ 
C)  $x ^ { 4 } + 5 x + 5$ 
D)  $x ^ { 4 } - 5 x + 7$ 
E)  $3 x ^ { 4 } - 5 x + 7$

Question 2

Identify the degree and leading coefficient of the polynomial. 5 - 3x2 - 6x

Accepted Answer

A) degree: 3 leading coefficient: -6 
B) degree: 2 leading coefficient: 3 
C) degree: 3 leading coefficient: 3 
D) degree: 2 leading coefficient: -3 
E) degree: 2 leading coefficient: 5 
A) degree: 3 leading coefficient: -6 
B) degree: 2 leading coefficient: 3 
C) degree: 3 leading coefficient: 3 
D) degree: 2 leading coefficient: -3 
E) degree: 2 leading coefficient: 5

Question 3

Factor the difference of two squares. 1 F1F1F1S1F1F1F10 (s + 8) 2

Accepted Answer

A) (s + 9)(-7 F1F1F1S1F1F1F10s) 
B) (s + 9)(25 F1F1F1S1F1F1F10s) 
C) (25 F1F1F1S1F1F1F10s)2 
D) (-7 F1F1F1S1F1F1F10s)2 
E) (s + 9)2 
A) (s + 9)(-7 F1F1F1S1F1F1F10s) 
B) (s + 9)(25 F1F1F1S1F1F1F10s) 
C) (25 F1F1F1S1F1F1F10s)2 
D) (-7 F1F1F1S1F1F1F10s)2 
E) (s + 9)2

Question 4

Factor out the common factor. 63w5 - 7w4 - 56w3

Accepted Answer

A) 7(9w5 - w4 - 8w3) 
B) 7w3(9w2 - w - 8) 
C) w3(63w 2 - 7w - 56) 
D) 63w3(w 2 - w - 8) 
E) 63(9w5 - w4 - 8w3) 
A) 7(9w5 - w4 - 8w3) 
B) 7w3(9w2 - w - 8) 
C) w3(63w 2 - 7w - 56) 
D) 63w3(w 2 - w - 8) 
E) 63(9w5 - w4 - 8w3)

Question 5

Evaluate the expression. $2 ^ { - 1 } + 3 ^ { - 2 }$

Accepted Answer

A)  $\frac { 2 } { 11 }$ 
B)  $\frac { 11 } { 18 }$ 
C)  $- \frac { 2 } { 11 }$ 
D)  $- \frac { 11 } { 18 }$ 
E) -8 
A)  $\frac { 2 } { 11 }$ 
B)  $\frac { 11 } { 18 }$ 
C)  $- \frac { 2 } { 11 }$ 
D)  $- \frac { 11 } { 18 }$ 
E) -8

Question 6

Evaluate the following polynomial for the indicated value of the variable. $- 7 y ^ { 2 } - 9 y - 2$ , for $y = - 1$

Accepted Answer

A) 0 
B) 2 
C) 14 
D) 16 
E) -18 
A) 0 
B) 2 
C) 14 
D) 16 
E) -18

Question 7

Determine which numbers in the set are rational numbers. $- 1.5252 \ldots , 16 , \frac { 2 } { 3 } \pi , \sqrt { 5 } , \frac { 7 } { 2 } , 4.070070007 \ldots , \sqrt { 81 }$

Accepted Answer

A)  $- 1.5252 \ldots , 16 , \frac { 7 } { 2 } , 4.070070007 \ldots$ 
B)  $- 1.5252 \ldots , 16 , \frac { 7 } { 2 } , 4.070070007 \ldots , \sqrt { 81 }$ 
C)  $16 , \sqrt { 5 } , \frac { 7 } { 2 } , \sqrt { 81 }$ 
D)  $- 1.5252 \ldots , 16 , \frac { 7 } { 2 } , \sqrt { 81 }$ 
E)  $- 1.5252 \ldots , 16 , \frac { 2 } { 3 } \pi , \frac { 7 } { 2 }$ 
A)  $- 1.5252 \ldots , 16 , \frac { 7 } { 2 } , 4.070070007 \ldots$ 
B)  $- 1.5252 \ldots , 16 , \frac { 7 } { 2 } , 4.070070007 \ldots , \sqrt { 81 }$ 
C)  $16 , \sqrt { 5 } , \frac { 7 } { 2 } , \sqrt { 81 }$ 
D)  $- 1.5252 \ldots , 16 , \frac { 7 } { 2 } , \sqrt { 81 }$ 
E)  $- 1.5252 \ldots , 16 , \frac { 2 } { 3 } \pi , \frac { 7 } { 2 }$

Question 8

Use a calculator to evaluate the expression. Write your answer in scientific notation. (Round values to three decimal places.) $\frac { 8,200,000 + 9,600,000 } { 0.077 }$

Accepted Answer

A) 1.329 F1F1F1S1?F1F1F10 108 
B) 1.329 F1F1F1S1?F1F1F10 109 
C) 2.312 F1F1F1S1?F1F1F10 107 
D) 2.312 F1F1F1S1?F1F1F10 109 
E) 2.312 F1F1F1S1?F1F1F10 108 
A) 1.329 F1F1F1S1?F1F1F10 108 
B) 1.329 F1F1F1S1?F1F1F10 109 
C) 2.312 F1F1F1S1?F1F1F10 107 
D) 2.312 F1F1F1S1?F1F1F10 109 
E) 2.312 F1F1F1S1?F1F1F10 108

Question 9

Perform the operation and write the result in standard form. $- 8 x \left( 8 - 7 x ^ { 4 } \right)$

Accepted Answer

A)  $56 x ^ { 5 } - 64 x$ 
B)  $- 56 x ^ { 5 } - 64 x$ 
C)  $- 64 x + 56 x ^ { 4 }$ 
D)  $- 64 + 56 x ^ { 4 }$ 
E)  $- 64 - 56 x ^ { 4 }$ 
A)  $56 x ^ { 5 } - 64 x$ 
B)  $- 56 x ^ { 5 } - 64 x$ 
C)  $- 64 x + 56 x ^ { 4 }$ 
D)  $- 64 + 56 x ^ { 4 }$ 
E)  $- 64 - 56 x ^ { 4 }$

Question 10

Find the domain of the expression. $\frac { x + 6 } { x + 7 }$

Accepted Answer

A) all real numbers 
B) all real numbers except x = -7 
C) all real numbers except x = -6 
D) all real numbers except x = -6 and x = -7 
E) x = -6 or x = -7 
A) all real numbers 
B) all real numbers except x = -7 
C) all real numbers except x = -6 
D) all real numbers except x = -6 and x = -7 
E) x = -6 or x = -7

Question 11

Multiply. (2x + 2)(-7x + 6)

Accepted Answer

A) -5x + 8 
B) -5x2 + 8 
C) -16x + 12 
D) -5x2 + 3x + 8 
E) -14x2 - 2x + 12 
A) -5x + 8 
B) -5x2 + 8 
C) -16x + 12 
D) -5x2 + 3x + 8 
E) -14x2 - 2x + 12

Question 12

Find the product below. $\left( x ^ { 2 } + 4 x + 2 \right) \left( x ^ { 2 } - 4 x + 2 \right)$

Accepted Answer

A)  $x ^ { 4 } - 12 x ^ { 2 } + 4$ 
B)  $x ^ { 4 } + 4 x ^ { 2 } + 16$ 
C)  $x ^ { 4 } + 12 x ^ { 2 } + 4$ 
D)  $x ^ { 4 } - 4 x ^ { 2 } + 16$ 
E)  $x ^ { 4 } + 12 x ^ { 2 } - 4$ 
A)  $x ^ { 4 } - 12 x ^ { 2 } + 4$ 
B)  $x ^ { 4 } + 4 x ^ { 2 } + 16$ 
C)  $x ^ { 4 } + 12 x ^ { 2 } + 4$ 
D)  $x ^ { 4 } - 4 x ^ { 2 } + 16$ 
E)  $x ^ { 4 } + 12 x ^ { 2 } - 4$

Question 13

Factor the perfect square trinomial. 49p2 - 126p + 81

Accepted Answer

A) (7p + 9)(7p - 9) 
B) (49p + 9)(p - 9) 
C) (-7p - 9)2 
D) (7p - 9)2 
E) (7p + 9)2 
A) (7p + 9)(7p - 9) 
B) (49p + 9)(p - 9) 
C) (-7p - 9)2 
D) (7p - 9)2 
E) (7p + 9)2

Question 14

Approximate the numbers and place the correct symbol () between them.

Accepted Answer

A) $2 \frac { 1 } { 2 } - 4$ C) $2 \frac { 1 } { 2 } > 4$ D) $1 \frac { 1 } { 2 } > - 4$ E) $2 \frac { 1 } { 2 } < 4$ A) $2 \frac { 1 } { 2 } - 4$ C) $2 \frac { 1 } { 2 } > 4$ D) $1 \frac { 1 } { 2 } > - 4$ E) $2 \frac { 1 } { 2 } < 4$

Question 15

Identify the rules of algebra illustrated from left to right by the following statement. (n + 6) - 6 = n + (6 - 6) = n + 0 = n

Accepted Answer

A) commutative property of addition; additive inverse property; additive identity property 
B) associative property of addition; additive inverse property; additive identity property 
C) commutative property of addition; additive identity property; additive inverse property 
D) associative property of addition; additive identity property; additive inverse property 
E) distributive property; additive identity property; additive inverse property 
A) commutative property of addition; additive inverse property; additive identity property 
B) associative property of addition; additive inverse property; additive identity property 
C) commutative property of addition; additive identity property; additive inverse property 
D) associative property of addition; additive identity property; additive inverse property 
E) distributive property; additive identity property; additive inverse property

Question 16

Simplify the expression below. $3 ^ { n } \cdot 3 ^ { 2 n }$

Accepted Answer

A)  $3 ^ { 2 n ^ { 2 } }$ 
B)  $9 ^ { 3 n }$ 
C)  $27 ^ { n }$ 
D)  $6 ^ { 3 n }$ 
E)  $9 ^ { n ^ { 2 } }$ 
A)  $3 ^ { 2 n ^ { 2 } }$ 
B)  $9 ^ { 3 n }$ 
C)  $27 ^ { n }$ 
D)  $6 ^ { 3 n }$ 
E)  $9 ^ { n ^ { 2 } }$

Question 17

Factor by grouping. p3 - p2 - 9p + 9

Accepted Answer

A) p2 - 9(p - 1) 
B) (p2 - 9)2(p - 1) 
C) (p2 - 9)(p - 1) 
D) (p2 + 9)(p + 1) 
E) (p2 - 9)(p - 1)2 
A) p2 - 9(p - 1) 
B) (p2 - 9)2(p - 1) 
C) (p2 - 9)(p - 1) 
D) (p2 + 9)(p + 1) 
E) (p2 - 9)(p - 1)2

Question 18

In 1967, the movie Imitation of Christ was released and its running time was 480 minutes long. Assuming that this film's speed was 24 frames per second, approximate the total number of frames in the film. Express the answer in scientific notation rounding to two places after the decimal..

Accepted Answer

A) 1.15 $\times 10 ^ { 6 }$ 
B) 3.22 $\times 10 ^ { 6 }$ 
C) 6.91 $\times 10 ^ { 5 }$ 
D) 2.88 $\times 10 ^ { 4 }$ 
E) 1.92 $\times 10 ^ { 5 }$ 
A) 1.15 $\times 10 ^ { 6 }$ 
B) 3.22 $\times 10 ^ { 6 }$ 
C) 6.91 $\times 10 ^ { 5 }$ 
D) 2.88 $\times 10 ^ { 4 }$ 
E) 1.92 $\times 10 ^ { 5 }$

Question 19

Use absolute value notation to describe the situation. w is more than two units from -7.

Accepted Answer

A)  $| w + 7 |$ F1F1F1S1?F1F1F10 2 
B)  $| w + 7 |$ F1F1F1S1?F1F1F10 2 
C)  $| w + 7 |$ F1F1F1S1?F1F1F10 2 
D)  $| w - 7 |$ F1F1F1S1?F1F1F10 2 
E)  $| w - 7 |$ F1F1F1S1?F1F1F10 2 
A)  $| w + 7 |$ F1F1F1S1?F1F1F10 2 
B)  $| w + 7 |$ F1F1F1S1?F1F1F10 2 
C)  $| w + 7 |$ F1F1F1S1?F1F1F10 2 
D)  $| w - 7 |$ F1F1F1S1?F1F1F10 2 
E)  $| w - 7 |$ F1F1F1S1?F1F1F10 2

Question 20

Completely factor the expression. 3x3 + 81

Accepted Answer

A) 3(x + 3)2(x - 3) 
B) 3(x + 3)(x - 3)2 
C) 3(x - 3)(x2 + 3x + 9) 
D) 3(x + 3)(x2 + 3x + 9) 
E) 3(x + 3)(x2 - 3x + 9) 
A) 3(x + 3)2(x - 3) 
B) 3(x + 3)(x - 3)2 
C) 3(x - 3)(x2 + 3x + 9) 
D) 3(x + 3)(x2 + 3x + 9) 
E) 3(x + 3)(x2 - 3x + 9)

Perform the operation and write the result in standard form. $\left( 2 x ^ { 2 } + 6 \right) - \left( x ^ { 2 } - 5 x + 1 \right)$

Identify the degree and leading coefficient of the polynomial. 5 - 3x2 - 6x

Factor the difference of two squares. 1  (s + 8) 2

Factor out the common factor. 63w5 - 7w4 - 56w3

Evaluate the expression. $2 ^ { - 1 } + 3 ^ { - 2 }$

Evaluate the following polynomial for the indicated value of the variable. $- 7 y ^ { 2 } - 9 y - 2$ , for $y = - 1$

Determine which numbers in the set are rational numbers. $- 1.5252 \ldots , 16 , \frac { 2 } { 3 } \pi , \sqrt { 5 } , \frac { 7 } { 2 } , 4.070070007 \ldots , \sqrt { 81 }$

Use a calculator to evaluate the expression. Write your answer in scientific notation. (Round values to three decimal places.) $\frac { 8,200,000 + 9,600,000 } { 0.077 }$

Perform the operation and write the result in standard form. $- 8 x \left( 8 - 7 x ^ { 4 } \right)$

Find the domain of the expression. $\frac { x + 6 } { x + 7 }$

Multiply. (2x + 2)(-7x + 6)

Find the product below. $\left( x ^ { 2 } + 4 x + 2 \right) \left( x ^ { 2 } - 4 x + 2 \right)$

Factor the perfect square trinomial. 49p2 - 126p + 81

Approximate the numbers and place the correct symbol (< or >) between them.

Identify the rules of algebra illustrated from left to right by the following statement. (n + 6) - 6 = n + (6 - 6) = n + 0 = n

Simplify the expression below. $3 ^ { n } \cdot 3 ^ { 2 n }$

Factor by grouping. p3 - p2 - 9p + 9

In 1967, the movie Imitation of Christ was released and its running time was 480 minutes long. Assuming that this film's speed was 24 frames per second, approximate the total number of frames in the film. Express the answer in scientific notation rounding to two places after the decimal..

Use absolute value notation to describe the situation. w is more than two units from -7.

Completely factor the expression. 3x3 + 81

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Polynomial and Rational Functions

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Limits and Derivatives

Applications of the Derivative

Further Applications of the Derivative

Derivatives of Exponential and Logarithmic Functions

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Exam 1: Fundamental Concepts of Algebra

Perform the operation and write the result in standard form. (2x2+6)−(x2−5x+1)\left( 2 x ^ { 2 } + 6 \right) - \left( x ^ { 2 } - 5 x + 1 \right)(2x2+6)−(x2−5x+1)

Identify the degree and leading coefficient of the polynomial. 5 - 3x2 - 6x

Factor the difference of two squares. 1  (s + 8) 2

Factor out the common factor. 63w5 - 7w4 - 56w3

Evaluate the expression. 2−1+3−22 ^ { - 1 } + 3 ^ { - 2 }2−1+3−2

Evaluate the following polynomial for the indicated value of the variable. −7y2−9y−2- 7 y ^ { 2 } - 9 y - 2−7y2−9y−2 , for y=−1y = - 1y=−1

Determine which numbers in the set are rational numbers. −1.5252…,16,23π,5,72,4.070070007…,81- 1.5252 \ldots , 16 , \frac { 2 } { 3 } \pi , \sqrt { 5 } , \frac { 7 } { 2 } , 4.070070007 \ldots , \sqrt { 81 }−1.5252…,16,32​π,5​,27​,4.070070007…,81​

Use a calculator to evaluate the expression. Write your answer in scientific notation. (Round values to three decimal places.) 8,200,000+9,600,0000.077\frac { 8,200,000 + 9,600,000 } { 0.077 }0.0778,200,000+9,600,000​

Perform the operation and write the result in standard form. −8x(8−7x4)- 8 x \left( 8 - 7 x ^ { 4 } \right)−8x(8−7x4)

Find the domain of the expression. x+6x+7\frac { x + 6 } { x + 7 }x+7x+6​

Multiply. (2x + 2)(-7x + 6)

Find the product below. (x2+4x+2)(x2−4x+2)\left( x ^ { 2 } + 4 x + 2 \right) \left( x ^ { 2 } - 4 x + 2 \right)(x2+4x+2)(x2−4x+2)

Factor the perfect square trinomial. 49p2 - 126p + 81

Approximate the numbers and place the correct symbol (< or >) between them.

Identify the rules of algebra illustrated from left to right by the following statement. (n + 6) - 6 = n + (6 - 6) = n + 0 = n

Simplify the expression below. 3n⋅32n3 ^ { n } \cdot 3 ^ { 2 n }3n⋅32n

Factor by grouping. p3 - p2 - 9p + 9

In 1967, the movie Imitation of Christ was released and its running time was 480 minutes long. Assuming that this film's speed was 24 frames per second, approximate the total number of frames in the film. Express the answer in scientific notation rounding to two places after the decimal..

Use absolute value notation to describe the situation. w is more than two units from -7.

Completely factor the expression. 3x3 + 81

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

Perform the operation and write the result in standard form. $\left( 2 x ^ { 2 } + 6 \right) - \left( x ^ { 2 } - 5 x + 1 \right)$

Evaluate the expression. $2 ^ { - 1 } + 3 ^ { - 2 }$

Evaluate the following polynomial for the indicated value of the variable. $- 7 y ^ { 2 } - 9 y - 2$ , for $y = - 1$

Determine which numbers in the set are rational numbers. $- 1.5252 \ldots , 16 , \frac { 2 } { 3 } \pi , \sqrt { 5 } , \frac { 7 } { 2 } , 4.070070007 \ldots , \sqrt { 81 }$

Use a calculator to evaluate the expression. Write your answer in scientific notation. (Round values to three decimal places.) $\frac { 8,200,000 + 9,600,000 } { 0.077 }$

Perform the operation and write the result in standard form. $- 8 x \left( 8 - 7 x ^ { 4 } \right)$

Find the domain of the expression. $\frac { x + 6 } { x + 7 }$

Find the product below. $\left( x ^ { 2 } + 4 x + 2 \right) \left( x ^ { 2 } - 4 x + 2 \right)$

Simplify the expression below. $3 ^ { n } \cdot 3 ^ { 2 n }$