Question 1

Identify the degree of each term and the degree of the polynomial.
-$2 x - 2 x ^ { 2 } + 3 - 4 x ^ { 3 }$

Accepted Answer

A)  $1 , - 2,0 , - 3 ; 1$ 
B)  $2 , - 2,3 , - 4 ; 2$ 
C)  $3,2,1,0 ; 3$ 
D)  $1,2,0,3 ; 3$ 
A)  $1 , - 2,0 , - 3 ; 1$ 
B)  $2 , - 2,3 , - 4 ; 2$ 
C)  $3,2,1,0 ; 3$ 
D)  $1,2,0,3 ; 3$

Question 2

Solve the problem.
-The weight $\mathrm { W }$ (in ounces) of a fish caught in a certain lake is given by $\mathrm { W } = 0.001 \mathrm { x } ^ { 3 } + 0.03 \mathrm { x } ^ { 2 } + 1.2$, where $\mathrm { x }$ is the length in inches. Use the graph below to find the approximate value of $0.001 x ^ { 3 } + 0.03 x ^ { 2 } + 1.2$ for $x = 14$.

Accepted Answer

A) 13 ounces 
B) 11 ounces 
C) 9 ounces 
D) 7 ounces 
A) 13 ounces 
B) 11 ounces 
C) 9 ounces 
D) 7 ounces

Question 3

Convert to decimal notation.
-$7.942 \times 10 ^ { - 5 }$

Accepted Answer

A)  $0.0007942$ 
B)  $- 794,200$ 
C)  $0.000007942$ 
D)  $0.00007942$ 
A)  $0.0007942$ 
B)  $- 794,200$ 
C)  $0.000007942$ 
D)  $0.00007942$

Question 4

Simplify.
-$\left( \frac { 5 } { 2 y } \right) ^ { 2 }$

Accepted Answer

A)  $\frac { 25 } { 4 y ^ { 2 } }$ 
B)  $\frac { 25 y ^ { 2 } } { 4 }$ 
C)  $\frac { 25 } { 2 y ^ { 2 } }$ 
D)  $\frac { 25 } { 4 y }$ 
A)  $\frac { 25 } { 4 y ^ { 2 } }$ 
B)  $\frac { 25 y ^ { 2 } } { 4 }$ 
C)  $\frac { 25 } { 2 y ^ { 2 } }$ 
D)  $\frac { 25 } { 4 y }$

Question 5

Convert to decimal notation.
-$1.0892 \times 10 ^ { - 7 }$

Accepted Answer

A)  $0.000000010892$ 
B)  $0.00000010892$ 
C)  $- 108,920,000$ 
D)  $0.0000010892$ 
A)  $0.000000010892$ 
B)  $0.00000010892$ 
C)  $- 108,920,000$ 
D)  $0.0000010892$

Question 6

Solve the problem.
-During the first seconds, the height $h$ in feet of a baseball after $t$ seconds is given by $h = - 16 t ^ { 2 } + 119 t + 3.1$. Use the graph below to estimate the height of the ball after 4 seconds.

Accepted Answer

A) 323 feet 
B) 223 feet 
C) 479 feet 
D) 179 feet 
A) 323 feet 
B) 223 feet 
C) 479 feet 
D) 179 feet

Question 7

Solve the problem. Express the answer in scientific notation to two decimals unless requested otherwise.
-A computer can do one calculation in $1.4 \times 10 ^ { - 7 }$ seconds. How long would it take the computer to do a trillion (1012) calculations?

Accepted Answer

A)  $1.4 \times 10 ^ { 12 } \mathrm { sec }$ 
B)  $1.4 \times 10 ^ { 6 } \mathrm { sec }$ 
C)  $1.4 \times 10 ^ { 5 } \mathrm { sec }$ 
D)  $1.4 \times 10 ^ { - 7 } \mathrm { sec }$ 
A)  $1.4 \times 10 ^ { 12 } \mathrm { sec }$ 
B)  $1.4 \times 10 ^ { 6 } \mathrm { sec }$ 
C)  $1.4 \times 10 ^ { 5 } \mathrm { sec }$ 
D)  $1.4 \times 10 ^ { - 7 } \mathrm { sec }$

Question 8

Solve the problem. Express the answer in scientific notation to two decimals unless requested otherwise.
-The national debt of a country is $28,400,000,000 and the population is 3,550,000. What is the debt per person? Write answer without exponents.

Accepted Answer

A) $100,820,000 
B) $8000 
C) $80,000 
D) $800 
A) $100,820,000 
B) $8000 
C) $80,000 
D) $800

Question 9

Simplify.
-$$\left( \mathrm { x } ^ { - 2 } \right) ^ { - 5 }$$

Accepted Answer

A)  $- 5 x ^ { - 2 }$ 
B)  $x ^ { - 3 }$ 
C)  $\frac { 1 } { { } _ { x } 10 }$ 
D)  $x ^ { 10 }$ 
A)  $- 5 x ^ { - 2 }$ 
B)  $x ^ { - 3 }$ 
C)  $\frac { 1 } { { } _ { x } 10 }$ 
D)  $x ^ { 10 }$

Question 10

Multiply and simplify.
-$y ^ { - 9 } \cdot y ^ { - 2 }$

Accepted Answer

A)  $\frac { 1 } { y ^ { 11 } }$ 
B)  $\frac { 1 } { y ^ { 7 } }$ 
C)  $\frac { 1 } { y ^ { - 11 } }$ 
D)  $\mathrm { y } ^ { 11 }$ 
A)  $\frac { 1 } { y ^ { 11 } }$ 
B)  $\frac { 1 } { y ^ { 7 } }$ 
C)  $\frac { 1 } { y ^ { - 11 } }$ 
D)  $\mathrm { y } ^ { 11 }$

Question 11

Identify the polynomial as a monomial, binomial, trinomial, or none of these. Give its degree.
-$$5 z + 6$$

Accepted Answer

A)  Binomial, degree 2 
B)  Binomial, degree 1 
C)  Monomial, degree $- 5$ 
D)  Binomial, degree 0 
A)  Binomial, degree 2 
B)  Binomial, degree 1 
C)  Monomial, degree $- 5$ 
D)  Binomial, degree 0

Question 12

Write the number in scientific notation.
-89,000,000

Accepted Answer

A) 8.9 × 107 
B) 8.9 × 10-7 
C) 8.9 × 108 
D) 8.9 × 10-8 
A) 8.9 × 107 
B) 8.9 × 10-7 
C) 8.9 × 108 
D) 8.9 × 10-8

Question 13

What is the meaning of the expression?
-$5 ^ { 2 }$

Accepted Answer

A) 5 ·5 
B) 2 ·5 
C) 3 
D) 7 
A) 5 ·5 
B) 2 ·5 
C) 3 
D) 7

Question 14

Identify the polynomial as a monomial, binomial, trinomial, or none of these. Give its degree.
-$$11 s ^ { 4 } - 3 s - 6$$

Accepted Answer

A)  Trinomial, degree 6 
B)  Trinomial, degree 5 
C)  Trinomial, degree 4 
D)  Binomial, degree 5 
A)  Trinomial, degree 6 
B)  Trinomial, degree 5 
C)  Trinomial, degree 4 
D)  Binomial, degree 5

Question 15

Express using positive exponents. Then simplify.
-$- 2 ^- 3$

Accepted Answer

A)  $- 8$ 
B)  8 
C)  $\frac { 1 } { 6 }$ 
D)  $- \frac { 1 } { 8 }$ 
A)  $- 8$ 
B)  8 
C)  $\frac { 1 } { 6 }$ 
D)  $- \frac { 1 } { 8 }$

Question 16

Solve the problem. Express the answer in scientific notation to two decimals unless requested otherwise.
-A light-year is the distance that light travels in one year. Find the number of miles in a light-year if light travels $1.86 \times 10 ^ { 5 } \mathrm { miles } / \mathrm { second }$.

Accepted Answer

A)  $5.87 \times 1012$ miles 
B)  $5.87 \times 10 ^ { 7 }$ miles 
C)  $5.87 \times 10 ^ { 14 }$ miles 
D)  $5.87 \times 10 ^ { 5 }$ miles 
A)  $5.87 \times 1012$ miles 
B)  $5.87 \times 10 ^ { 7 }$ miles 
C)  $5.87 \times 10 ^ { 14 }$ miles 
D)  $5.87 \times 10 ^ { 5 }$ miles

Question 17

Multiply and simplify.
-$3 ^ { - 3 } \cdot 3 ^ { 6 }$

Accepted Answer

A)  1 
B)  $3 ^ { 6 }$ 
C)  $3 ^ { 9 }$ 
D)  $3 ^ { 3 }$ 
A)  1 
B)  $3 ^ { 6 }$ 
C)  $3 ^ { 9 }$ 
D)  $3 ^ { 3 }$

Question 18

Evaluate.
-$x ^ { 2 } - 2$ when $x = - 10$

Accepted Answer

A)  $- 12$ 
B)  $x ^ { 2 } - 10$ 
C)  96 
D)  98 
A)  $- 12$ 
B)  $x ^ { 2 } - 10$ 
C)  96 
D)  98

Question 19

If the number in the statement is written in scientific notation, write it without exponents. If it is written without exponents, write it in scientific notation.
-It has been estimated that the average American watches 58,240 hours of television in a lifetime.

Accepted Answer

A)  $5.824 \times 10 ^ { 4 }$ hours 
B)  $5.824 \times 10 ^ { 3 }$ hours 
C)  $58.24 \times 10 ^ { 3 }$ hours 
D)  $5.824 \times 10 ^ { 5 }$ hours 
A)  $5.824 \times 10 ^ { 4 }$ hours 
B)  $5.824 \times 10 ^ { 3 }$ hours 
C)  $58.24 \times 10 ^ { 3 }$ hours 
D)  $5.824 \times 10 ^ { 5 }$ hours

Question 20

Divide and simplify.
-$\frac { ( 3 p ) ^ { 10 } } { ( 3 p ) ^ { 6 } }$

Accepted Answer

A)  $81 p ^ { 4 }$ 
B)  $\frac { 1 } { 81 p ^ { 4 } }$ 
C)  $\frac { 81 } { \mathrm { p } ^ { 4 } }$ 
D)  $\frac { p ^ { 4 } } { 81 }$ 
A)  $81 p ^ { 4 }$ 
B)  $\frac { 1 } { 81 p ^ { 4 } }$ 
C)  $\frac { 81 } { \mathrm { p } ^ { 4 } }$ 
D)  $\frac { p ^ { 4 } } { 81 }$

Identify the degree of each term and the degree of the polynomial. - $2 x - 2 x ^ { 2 } + 3 - 4 x ^ { 3 }$

Convert to decimal notation. - $7.942 \times 10 ^ { - 5 }$

Simplify. - $\left( \frac { 5 } { 2 y } \right) ^ { 2 }$

Convert to decimal notation. - $1.0892 \times 10 ^ { - 7 }$

Solve the problem. Express the answer in scientific notation to two decimals unless requested otherwise. -A computer can do one calculation in $1.4 \times 10 ^ { - 7 }$ seconds. How long would it take the computer to do a trillion (1012) calculations?

Solve the problem. Express the answer in scientific notation to two decimals unless requested otherwise. -The national debt of a country is $28,400,000,000 and the population is 3,550,000. What is the debt per person? Write answer without exponents.

Simplify. - $\left( \mathrm { x } ^ { - 2 } \right) ^ { - 5 }$

Multiply and simplify. - $y ^ { - 9 } \cdot y ^ { - 2 }$

Identify the polynomial as a monomial, binomial, trinomial, or none of these. Give its degree. - $5 z + 6$

Write the number in scientific notation. -89,000,000

What is the meaning of the expression? - $5 ^ { 2 }$

Identify the polynomial as a monomial, binomial, trinomial, or none of these. Give its degree. - $11 s ^ { 4 } - 3 s - 6$

Express using positive exponents. Then simplify. - $- 2 ^- 3$

Solve the problem. Express the answer in scientific notation to two decimals unless requested otherwise. -A light-year is the distance that light travels in one year. Find the number of miles in a light-year if light travels $1.86 \times 10 ^ { 5 } \mathrm { miles } / \mathrm { second }$ .

Multiply and simplify. - $3 ^ { - 3 } \cdot 3 ^ { 6 }$

Evaluate. - $x ^ { 2 } - 2$ when $x = - 10$

If the number in the statement is written in scientific notation, write it without exponents. If it is written without exponents, write it in scientific notation. -It has been estimated that the average American watches 58,240 hours of television in a lifetime.

Divide and simplify. - $\frac { ( 3 p ) ^ { 10 } } { ( 3 p ) ^ { 6 } }$

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Factoring

Rational Expressions and Equations

Graphs, Functions, and Applications

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Radical Expressions, Equations, and Functions

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Exam 4: Polynomials: Operations

Identify the degree of each term and the degree of the polynomial. - 2x−2x2+3−4x32 x - 2 x ^ { 2 } + 3 - 4 x ^ { 3 }2x−2x2+3−4x3

Convert to decimal notation. - 7.942×10−57.942 \times 10 ^ { - 5 }7.942×10−5

Simplify. - (52y)2\left( \frac { 5 } { 2 y } \right) ^ { 2 }(2y5​)2

Convert to decimal notation. - 1.0892×10−71.0892 \times 10 ^ { - 7 }1.0892×10−7

Solve the problem. -During the first seconds, the height hhh in feet of a baseball after ttt seconds is given by h=−16t2+119t+3.1h = - 16 t ^ { 2 } + 119 t + 3.1h=−16t2+119t+3.1 . Use the graph below to estimate the height of the ball after 4 seconds.

Solve the problem. Express the answer in scientific notation to two decimals unless requested otherwise. -A computer can do one calculation in 1.4×10−71.4 \times 10 ^ { - 7 }1.4×10−7 seconds. How long would it take the computer to do a trillion (1012) calculations?