Question 1

Factor out the common factor. 30y - 5

Accepted Answer

A) 5(25y) 
B) 5(6y) 
C) 5(6y - 1) 
D) 30(y - 1) 
E) 30(y + 1) 
A) 5(25y) 
B) 5(6y) 
C) 5(6y - 1) 
D) 30(y - 1) 
E) 30(y + 1)

Question 2

Perform the indicated operation below and write the answer in scientific notation. $\frac { \left( 4.9 \times 10 ^ { 18 } \right) \left( 6.8 \times 10 ^ { 11 } \right) } { \left( 3.4 \times 10 ^ { - 12 } \right) }$

Accepted Answer

A)  $9.8 \times 10 ^ { - 5 }$ 
B)  $9.8 \times 10 ^ { 17 }$ 
C)  $9.8 \times 10 ^ { 5 }$ 
D)  $9.8 \times 10 ^ { 19 }$ 
E)  $9.8 \times 10 ^ { 41 }$ 
A)  $9.8 \times 10 ^ { - 5 }$ 
B)  $9.8 \times 10 ^ { 17 }$ 
C)  $9.8 \times 10 ^ { 5 }$ 
D)  $9.8 \times 10 ^ { 19 }$ 
E)  $9.8 \times 10 ^ { 41 }$

Question 3

Write the expression as a single radical. Then simplify your answer. $\sqrt { \sqrt [ 3 ] { 14 t ^ { 7 } p } }$

Accepted Answer

A)  $t \sqrt [ 4 ] { 14 t ^ { 3 } p }$ 
B)  $t \sqrt [ 6 ] { 14 t p }$ 
C)  $t \sqrt [ 5 ] { 14 t ^ { 2 } p }$ 
D)  $t \sqrt [ 3 ] { 14 t ^ { 4 } p }$ 
E)  $\sqrt [ 9 ] { 14 t ^ { 7 } p }$ 
A)  $t \sqrt [ 4 ] { 14 t ^ { 3 } p }$ 
B)  $t \sqrt [ 6 ] { 14 t p }$ 
C)  $t \sqrt [ 5 ] { 14 t ^ { 2 } p }$ 
D)  $t \sqrt [ 3 ] { 14 t ^ { 4 } p }$ 
E)  $\sqrt [ 9 ] { 14 t ^ { 7 } p }$

Question 4

Completely factor the expression. 3n2 F1F1F1S1F1F1F10 12

Accepted Answer

A) (3n - 6)(n + 2) 
B) (3n + 6)(n - 2) 
C) (3n + 6)(n + 2) 
D) 3(n + 2)(n - 2) 
E) 3(n + 4)(n - 4) 
A) (3n - 6)(n + 2) 
B) (3n + 6)(n - 2) 
C) (3n + 6)(n + 2) 
D) 3(n + 2)(n - 2) 
E) 3(n + 4)(n - 4)

Question 5

Factor the sum or difference of cubes. s3 + 8

Accepted Answer

A) (s + 2)(s2 - 2s + 4) 
B) (s - 2)(s2 + 2s + 4) 
C) (s + 2)(s2 + 2s + 4) 
D) (s - 2)3 
E) (s + 2)3 
A) (s + 2)(s2 - 2s + 4) 
B) (s - 2)(s2 + 2s + 4) 
C) (s + 2)(s2 + 2s + 4) 
D) (s - 2)3 
E) (s + 2)3

Question 6

Evaluate the expression. $\frac { 5 ^ { - 4 } } { 5 ^ { - 6 } }$

Accepted Answer

A)  $\frac { 2 } { 3 }$ 
B)  $- \frac { 1 } { 25 }$ 
C)  $\frac { 1 } { 25 }$ 
D) 25 
E) -25 
A)  $\frac { 2 } { 3 }$ 
B)  $- \frac { 1 } { 25 }$ 
C)  $\frac { 1 } { 25 }$ 
D) 25 
E) -25

Question 7

Write the rational expression in simplest form. $\frac { s ^ { 2 } - 1 } { s ^ { 2 } - 3 s + 2 }$

Accepted Answer

A)  $\frac { s - 1 } { s + 2 } , \quad s \neq 1$ 
B)  $\frac { s - 1 } { s - 2 } , \quad s \neq 1$ 
C)  $\frac { s - 1 } { s - 2 } , \quad s \neq - 1$ 
D)  $\frac { s + 1 } { s - 2 } , \quad s \neq - 1$ 
E)  $\frac { s + 1 } { s - 2 } , \quad s \neq 1$ 
A)  $\frac { s - 1 } { s + 2 } , \quad s \neq 1$ 
B)  $\frac { s - 1 } { s - 2 } , \quad s \neq 1$ 
C)  $\frac { s - 1 } { s - 2 } , \quad s \neq - 1$ 
D)  $\frac { s + 1 } { s - 2 } , \quad s \neq - 1$ 
E)  $\frac { s + 1 } { s - 2 } , \quad s \neq 1$

Question 8

Evaluate the expression without using a calculator. $- \left( \frac { 1 } { 125 } \right) ^ { - 2 / 3 }$

Accepted Answer

A)  $\frac { 1 } { 25 }$ 
B)  $- \frac { 2 } { 375 }$ 
C)  $\frac { 2 } { 375 }$ 
D) 25 
E) -25 
A)  $\frac { 1 } { 25 }$ 
B)  $- \frac { 2 } { 375 }$ 
C)  $\frac { 2 } { 375 }$ 
D) 25 
E) -25

Question 9

Use inequality notation to describe the set. n is positive

Accepted Answer

A) n F1F1F1S1F1F1F10 F1F1F1S1F1F1F10 
B) n F1F1F1S1F1F1F10 F1F1F1S1F1F1F10 
C) n F1F1F1S1F1F1F10 0 
D) n F1F1F1S1F1F1F10 0 
E) n F1F1F1S1F1F1F10 0 
A) n F1F1F1S1F1F1F10 F1F1F1S1F1F1F10 
B) n F1F1F1S1F1F1F10 F1F1F1S1F1F1F10 
C) n F1F1F1S1F1F1F10 0 
D) n F1F1F1S1F1F1F10 0 
E) n F1F1F1S1F1F1F10 0

Question 10

Simplify the expression below. $- 5 \sqrt { 8 } + 2 \sqrt { 32 }$

Accepted Answer

A)  $8 \sqrt { 2 } - 10 \sqrt { 3 }$ 
B)  $- 10 \sqrt { 2 } + 8 \sqrt { 3 }$ 
C)  $12 \sqrt { 2 }$ 
D)  $- 2 \sqrt { 2 }$ 
E)  $10 \sqrt { 2 } + 8 \sqrt { 3 }$ 
A)  $8 \sqrt { 2 } - 10 \sqrt { 3 }$ 
B)  $- 10 \sqrt { 2 } + 8 \sqrt { 3 }$ 
C)  $12 \sqrt { 2 }$ 
D)  $- 2 \sqrt { 2 }$ 
E)  $10 \sqrt { 2 } + 8 \sqrt { 3 }$

Question 11

The average yearly cost of tuition, fees, and room and board at private four-year colleges in the United States was $20,805 for the academic year 1998/1999 and $24,817 for the academic year 2002/2003. Find the average yearly rate of inflation over this five-year period. Round to the nearest hundredth of a percent.

Accepted Answer

A) 3.47% 
B) 3.77% 
C) 3.59% 
D) 3.68% 
E) 4.03% 
A) 3.47% 
B) 3.77% 
C) 3.59% 
D) 3.68% 
E) 4.03%

Question 12

Find the domain of the expression. x2 + 7x - 18

Accepted Answer

A) all real numbers 
B) all real numbers except x = -9 and x = 2 
C) all real numbers except x = 0 
D) x = -9 or x = 2 
E) x > 0 
A) all real numbers 
B) all real numbers except x = -9 and x = 2 
C) all real numbers except x = 0 
D) x = -9 or x = 2 
E) x > 0

Question 13

Factor the difference of two squares. 9y2 F1F1F1S1F1F1F10 25

Accepted Answer

A) (9y + 5)(9y F1F1F1S1F1F1F10 5) 
B) (9y + 25)(9y F1F1F1S1F1F1F10 25) 
C) (3y F1F1F1S1F1F1F10 5)2 
D) (3y F1F1F1S1F1F1F10 5)2 
E) (3y + 5)(3y F1F1F1S1F1F1F10 5) 
A) (9y + 5)(9y F1F1F1S1F1F1F10 5) 
B) (9y + 25)(9y F1F1F1S1F1F1F10 25) 
C) (3y F1F1F1S1F1F1F10 5)2 
D) (3y F1F1F1S1F1F1F10 5)2 
E) (3y + 5)(3y F1F1F1S1F1F1F10 5)

Question 14

Rewrite the expression below with positive exponents and simplify. $\left( \frac { x ^ { - 2 } y ^ { 4 } } { 2 } \right) ^ { - 3 }$

Accepted Answer

A)  $\frac { x ^ { 6 } y ^ { 12 } } { 8 }$ 
B)  $\frac { 8 y ^ { 12 } } { x ^ { 6 } }$ 
C)  $\frac { 8 x ^ { 6 } } { y ^ { 12 } }$ 
D)  $\frac { x ^ { 6 } } { 8 y ^ { 12 } }$ 
E)  $\frac { y ^ { 12 } } { 8 x ^ { 6 } }$ 
A)  $\frac { x ^ { 6 } y ^ { 12 } } { 8 }$ 
B)  $\frac { 8 y ^ { 12 } } { x ^ { 6 } }$ 
C)  $\frac { 8 x ^ { 6 } } { y ^ { 12 } }$ 
D)  $\frac { x ^ { 6 } } { 8 y ^ { 12 } }$ 
E)  $\frac { y ^ { 12 } } { 8 x ^ { 6 } }$

Question 15

Identify the terms of the algebraic expression below. $6 x ^ { 2 } - 6 x + 5$

Accepted Answer

A)  $6,$ $- 6,$ and $5$ 
B)  $6 x ^ { 2 }$ and $- 6 x$ 
C)  $6 x ^ { 2 }$ and $5$ 
D)  $- 6 x$ and $5$ 
E)  $6 x ^ { 2 },$ $- 6 x,$ and $5$ 
A)  $6,$ $- 6,$ and $5$ 
B)  $6 x ^ { 2 }$ and $- 6 x$ 
C)  $6 x ^ { 2 }$ and $5$ 
D)  $- 6 x$ and $5$ 
E)  $6 x ^ { 2 },$ $- 6 x,$ and $5$

Question 16

Write the rational expression in simplest form. $\frac { 36 s ^ { 5 } } { 63 s ^ { 6 } }$

Accepted Answer

A)  $\frac { 4 s ^ { 5 } } { 7 s ^ { 6 } } , s \neq 0$ . 
B)  $\frac { 12 s } { 21 } , \quad s \neq 0$ 
C)  $\frac { 12 } { 21 s } , \quad s \neq 0$. 
D)  $\frac { 4 } { 7 s } , \quad s \neq 0$ . 
E)  $\frac { 12 } { 21 s } , \quad s \neq 0$ . 
A)  $\frac { 4 s ^ { 5 } } { 7 s ^ { 6 } } , s \neq 0$ . 
B)  $\frac { 12 s } { 21 } , \quad s \neq 0$ 
C)  $\frac { 12 } { 21 s } , \quad s \neq 0$. 
D)  $\frac { 4 } { 7 s } , \quad s \neq 0$ . 
E)  $\frac { 12 } { 21 s } , \quad s \neq 0$ .

Question 17

Evaluate the expression. $\left( 3 ^ { - 2 } \right) ^ { 3 }$

Accepted Answer

A) 3 
B) -18 
C) -729 
D)  $- \frac { 1 } { 729 }$ 
E)  $\frac { 1 } { 729 }$ 
A) 3 
B) -18 
C) -729 
D)  $- \frac { 1 } { 729 }$ 
E)  $\frac { 1 } { 729 }$

Question 18

Rewrite the expression below by rationalizing the denominator. Simplify your answer. $\frac { 4 } { \sqrt { 7 } + \sqrt { 6 } }$

Accepted Answer

A)  $4 ( \sqrt { 7 } + \sqrt { 6 } )$ 
B)  $4 ( \sqrt { 7 } - \sqrt { 6 } )$ 
C)  $4 ( \sqrt { 6 } - \sqrt { 7 } )$ 
D)  $\frac { 16 } { 13 }$ 
E)  $\frac { 4 } { 13 }$ 
A)  $4 ( \sqrt { 7 } + \sqrt { 6 } )$ 
B)  $4 ( \sqrt { 7 } - \sqrt { 6 } )$ 
C)  $4 ( \sqrt { 6 } - \sqrt { 7 } )$ 
D)  $\frac { 16 } { 13 }$ 
E)  $\frac { 4 } { 13 }$

Question 19

Plot the two real numbers on the real number line. Then place the appropriate inequality symbol () between them. $- \frac { 7 } { 10 } , \frac { 1 } { 17 }$

Accepted Answer

A)  $- \frac { 7 } { 10 }  \frac { 1 } { 17 }$ 
A)  $- \frac { 7 } { 10 }  \frac { 1 } { 17 }$

Factor out the common factor. 30y - 5

Perform the indicated operation below and write the answer in scientific notation. $\frac { \left( 4.9 \times 10 ^ { 18 } \right) \left( 6.8 \times 10 ^ { 11 } \right) } { \left( 3.4 \times 10 ^ { - 12 } \right) }$

Write the expression as a single radical. Then simplify your answer. $\sqrt { \sqrt [ 3 ] { 14 t ^ { 7 } p } }$

Completely factor the expression. 3n2  12

Factor the sum or difference of cubes. s3 + 8

Evaluate the expression. $\frac { 5 ^ { - 4 } } { 5 ^ { - 6 } }$

Write the rational expression in simplest form. $\frac { s ^ { 2 } - 1 } { s ^ { 2 } - 3 s + 2 }$

Evaluate the expression without using a calculator. $- \left( \frac { 1 } { 125 } \right) ^ { - 2 / 3 }$

Use inequality notation to describe the set. n is positive

Simplify the expression below. $- 5 \sqrt { 8 } + 2 \sqrt { 32 }$

Find the domain of the expression. x2 + 7x - 18

Factor the difference of two squares. 9y2  25

Rewrite the expression below with positive exponents and simplify. $\left( \frac { x ^ { - 2 } y ^ { 4 } } { 2 } \right) ^ { - 3 }$

Identify the terms of the algebraic expression below. $6 x ^ { 2 } - 6 x + 5$

Write the rational expression in simplest form. $\frac { 36 s ^ { 5 } } { 63 s ^ { 6 } }$

Evaluate the expression. $\left( 3 ^ { - 2 } \right) ^ { 3 }$

Rewrite the expression below by rationalizing the denominator. Simplify your answer. $\frac { 4 } { \sqrt { 7 } + \sqrt { 6 } }$

Plot the two real numbers on the real number line. Then place the appropriate inequality symbol (< or >) between them. $- \frac { 7 } { 10 } , \frac { 1 } { 17 }$

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Applications of the Derivative

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Exam 1: Fundamental Concepts of Algebra

Factor out the common factor. 30y - 5

Perform the indicated operation below and write the answer in scientific notation. (4.9×1018)(6.8×1011)(3.4×10−12)\frac { \left( 4.9 \times 10 ^ { 18 } \right) \left( 6.8 \times 10 ^ { 11 } \right) } { \left( 3.4 \times 10 ^ { - 12 } \right) }(3.4×10−12)(4.9×1018)(6.8×1011)​

Write the expression as a single radical. Then simplify your answer. 14t7p3\sqrt { \sqrt [ 3 ] { 14 t ^ { 7 } p } }314t7p​​

Completely factor the expression. 3n2  12

Factor the sum or difference of cubes. s3 + 8

Evaluate the expression. 5−45−6\frac { 5 ^ { - 4 } } { 5 ^ { - 6 } }5−65−4​

Write the rational expression in simplest form. s2−1s2−3s+2\frac { s ^ { 2 } - 1 } { s ^ { 2 } - 3 s + 2 }s2−3s+2s2−1​

Evaluate the expression without using a calculator. −(1125)−2/3- \left( \frac { 1 } { 125 } \right) ^ { - 2 / 3 }−(1251​)−2/3

Use inequality notation to describe the set. n is positive

Simplify the expression below. −58+232- 5 \sqrt { 8 } + 2 \sqrt { 32 }−58​+232​

Find the domain of the expression. x2 + 7x - 18

Factor the difference of two squares. 9y2  25

Rewrite the expression below with positive exponents and simplify. (x−2y42)−3\left( \frac { x ^ { - 2 } y ^ { 4 } } { 2 } \right) ^ { - 3 }(2x−2y4​)−3

Identify the terms of the algebraic expression below. 6x2−6x+56 x ^ { 2 } - 6 x + 56x2−6x+5

Write the rational expression in simplest form. 36s563s6\frac { 36 s ^ { 5 } } { 63 s ^ { 6 } }63s636s5​

Evaluate the expression. (3−2)3\left( 3 ^ { - 2 } \right) ^ { 3 }(3−2)3

Rewrite the expression below by rationalizing the denominator. Simplify your answer. 47+6\frac { 4 } { \sqrt { 7 } + \sqrt { 6 } }7​+6​4​

Plot the two real numbers on the real number line. Then place the appropriate inequality symbol (< or >) between them. −710,117- \frac { 7 } { 10 } , \frac { 1 } { 17 }−107​,171​

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

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Perform the indicated operation below and write the answer in scientific notation. $\frac { \left( 4.9 \times 10 ^ { 18 } \right) \left( 6.8 \times 10 ^ { 11 } \right) } { \left( 3.4 \times 10 ^ { - 12 } \right) }$

Write the expression as a single radical. Then simplify your answer. $\sqrt { \sqrt [ 3 ] { 14 t ^ { 7 } p } }$

Evaluate the expression. $\frac { 5 ^ { - 4 } } { 5 ^ { - 6 } }$

Write the rational expression in simplest form. $\frac { s ^ { 2 } - 1 } { s ^ { 2 } - 3 s + 2 }$

Evaluate the expression without using a calculator. $- \left( \frac { 1 } { 125 } \right) ^ { - 2 / 3 }$

Simplify the expression below. $- 5 \sqrt { 8 } + 2 \sqrt { 32 }$

Rewrite the expression below with positive exponents and simplify. $\left( \frac { x ^ { - 2 } y ^ { 4 } } { 2 } \right) ^ { - 3 }$

Identify the terms of the algebraic expression below. $6 x ^ { 2 } - 6 x + 5$

Write the rational expression in simplest form. $\frac { 36 s ^ { 5 } } { 63 s ^ { 6 } }$

Evaluate the expression. $\left( 3 ^ { - 2 } \right) ^ { 3 }$

Rewrite the expression below by rationalizing the denominator. Simplify your answer. $\frac { 4 } { \sqrt { 7 } + \sqrt { 6 } }$

Plot the two real numbers on the real number line. Then place the appropriate inequality symbol (< or >) between them. $- \frac { 7 } { 10 } , \frac { 1 } { 17 }$