Deck 12: Preliminary Concepts

Question 1

Use absolute value notation to describe the statement below. z is more than 4 units from 9 but less than 16 units from 9.

A)
B)
C)
D)
E)

Answer 1

Question 2

Graph the following set.

A)
B)Æ
C)
D)
E)

Answer 2

Question 3

Simplify the variable expression below.

A)
B)
C)
D)
E)

Answer 3

Question 4

Graph the following set.

A)
B)
C)
D)
E)Æ

Question 5

Write in interval notation.

A)
B)
C)
D)
E)

Question 6

Write the interval in set notation.

A)
B)
C)
D)
E)

Question 7

Given that , , and determine the following:

A)
B)
C)Æ
D)
E)

Question 8

Graph the following set.

A)
B)
C)
D)
E)

Question 9

List the four smallest elements in the following set.

A)-11, -6, -3, -2
B)-18, -11, -6, -3
C)-1, 2, 7, 14
D)-2, -1, 0, 1
E)-2, -1, 2, 7

Question 10

Perform the following operation, given A is any set.

A)
B)
C)
D)
E)

Question 11

Use absolute value notation to describe the distance between a and -4.

A)
B)
C)
D)
E)

Question 12

Simplify: -5(2 w - 2 x )- 2( w - 5 x )

A)3 w + 20 x
B)-12 w + 20 x
C)-4 w - 14 x
D)-5 w - 7 x
E)-21 w + 49 x

Question 13

Evaluate when and .

A)-101
B)400
C)-2
D)4
E)-200

Question 14

Determine if the following real number is both composite and rational, both prime and rational, only rational or only irrational.

A)rational
B)irrational
C)composite and rational
D)prime and rational

Question 15

The volume of a rectangular box is given by Volume=lwh where l is the length, w is the width, and h is the height of the box. Find the volume of a garage that has length of 22 feet, a width of 18 feet, and a height of 14 feet.

A)4312 ft³
B)7128 ft³
C)10,648 ft³
D)5544 ft³
E)8712 ft³

Question 16

Evaluate when and .

A)-160
B)-16,000
C)-4,096,000
D)12,800
E)-4000

Question 17

Write the following expression without absolute value symbols.

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

Question 18

The minimum number of calories necessary, per day, for a female to maintain basic life processes such as blood circulation, body temperature and breathing can be approximated by the formula , where w is the person s weight in pounds, h is their height in inches and a is their age in years. Approximate the calories needed to sustain life for a 33 year old female weighing 124 pounds and 4 feet 11 inches tall. Round to nearest whole number.

A)808 calories
B)1227 calories
C)1829 calories
D)1367 calories
E)1689 calories

Question 19

Write each expression without absolute value symbols.

A)9
B)
C)
D)
E)

Question 20

Determine the property of real numbers or the property of equality that is used below.

A)Symmetric Property of Equality
B)Identity Property of Equality
C)Reflexive Property of Equality
D)Substitution Property of Equality
E)Transitive Property of Equality

Question 21

The number of committees consisting of exactly 3 people that can be formed from a group of n people is given by the polynomial . Find the number of committees consisting of exactly 3 people that can be formed from a group of 45 people. Round to the nearest whole number.

A)14,528
B)16,215
C)14,175
D)16,208
E)14,190

Question 22

The distance that a car travels from the time a driver decides to apply the brakes to the time the car comes to a complete stop is called the braking distance. For a certain automobile traveling v mph, the braking distance d (in feet)is given by . Find the braking distance of a car that is traveling 35 mph. Round to nearest whole number.

A)122 ft
B)64 ft
C)258 ft
D)66 ft
E)99 ft

Question 23

The height, in feet, of a ball t seconds after it is thrown upward is given by . Find the height of the ball 4 seconds after it has been released.

A)18 feet
B)36 feet
C)228 feet
D)12 feet
E)174 feet

Question 24

Write the following number in scientific notation. 226,000

A)
B)
C)
D)
E)

Question 25

Write the following exponential expression in simplest form.

A)
B)
C)
D)
E)

Question 26

Which of the following expressions is a binomial of degree 8?
I:
II:
III:
IV:
V:

A)III
B)V
C)II
D)IV
E)I

Question 27

Evaluate the expression below.

A)
B)
C)1024
D)
E)16

Question 28

Perform the indicated operation below and write the answer in scientific notation.

A)
B)
C)
D)
E)

Question 29

Simplify the following expression by rationalizing the denominator. Write the result in simplest form.

A)
B)
C)
D)
E)

Question 30

Find the indicated product and express the result in simplest form.

A)
B)
C)
D)
E)

Question 31

The fuel efficiency (in miles per gallon of gas)of a car is given by the expression where v is the speed of the car in miles per hour. Find the fuel efficiency when miles per hour. Round your answer to the nearest tenth.

A)48.8 miles per gallon
B)35.5 miles per gallon
C)39.9 miles per gallon
D)31.1 miles per gallon
E)44.4 miles per gallon

Question 32

Perform the indicated operation(s)below and simplify.

A)
B)
C)
D)
E)

Question 33

Write the exponential expression below in simplest form.

A)
B)
C)
D)
E)

Question 34

Use the FOIL method to find the indicated product below.

A)
B)
C)
D)
E)

Question 35

Evaluate the following polynomial for the indicated value of the variable. , for .

A)-3
B)5
C)-15
D)-7
E)-1

Question 36

On an expressway, the recommended safe distance between cars in feet is given by where v is the speed of the car in miles per hour. Find the safe distance when miles per hour. Round your answer to the nearest tenth.

A)156.3 feet
B)130.3 feet
C)65.1 feet
D)143.3 feet
E)104.2 feet

Question 37

Perform the indicated operation below and simplify if possible by combining like terms. Write the result in standard form.

A)
B)
C)
D)
E)

Question 38

Write the exponential expression below in simplest form.

A)
B)
C)
D)
E)

Question 39

Change the following number from scientific notation to decimal notation.

A)29
B)0.29
C)0.0029
D)2.9
E)0.029

Question 40

Simplify the following radical expression.

A)
B)
C)
D)
E)

Question 41

Last month, Jacob traveled from Miami to New Orleans by train and made two stops along the way. The average speed for the three legs of his trip is defined as , and respectively. The average speed for the entire trip is given by . a. Simplify the complex fraction. b. Find the average speed for the entire trip when . Round to nearest mph.

A)a. ; b. 94 mph
B)a. ; b. 95 mph
C)a. ; b. 95 mph
D)a. ; b. 92 mph
E)a. ; b. 92 mph

Question 42

Write the expression below as a complex number in standard form.

A)-5
B)5 i
C)5
D)1- 5 i
E)-5 i

Question 43

Simplify the following rational expression.

A)
B)
C)
D)
E)

Question 44

Simplify and write the following complex number in standard form.

A)0
B)25- i
C)26
D)-10 i
E)10

Question 45

Factor the trinomial below over the integers.

A)
B)
C)
D)
E)

Question 46

Simplify the following complex fraction.

A)
B)
C)
D)
E)

Question 47

Find the rational expression in simplest form that represents the sum of the reciprocals of the consecutive integers and .

A)
B)
C)
D)
E)

Question 48

Simplify the following algebraic fraction. Write the answer with positive exponents.

A)
B)
C)
D)
E)

Question 49

Simplify the following rational expression.

A)
B)
C)
D)
E)

Question 50

Simplify the following rational expression.

A)
B)
C)
D)
E)

Question 51

Simplify and write the complex number in standard form.

A)16
B)-16
C)-24
D)24
E)-36

Question 52

Simplify the rational expression below.

A)
B)
C)
D)
E)

Question 53

Use the general factoring strategy to completely factor the following polynomial. It the polynomial does not factor, then state that it is nonfactorable over the integers.

A)
B)Nonfactorable over the integers.
C)
D)
E)

Question 54

Simplify and write the following complex number in standard form.

A)
B)
C)
D)
E)

Question 55

Simplify and write the following complex number in standard form.

A)
B)
C)
D)
E)

Question 56

Simplify and write the following complex number in standard form.

A)
B)
C)
D)
E)

Question 57

Factor the trinomial below over the integers.

A)
B)
C)
D)
E)

Question 58

Use the general factoring strategy to completely factor the following polynomial. It the polynomial does not factor, then state that it is nonfactorable over the integers.

A)
B)
C)Nonfactorable over the integers.
D)
E)

Question 59

Write the complex number in standard form.

A)
B)
C)
D)
E)

Question 60

Simplify the following complex fraction.

A)
B)
C)
D)
E)

Question 61

Evaluate the power of i .

A)
B)
C)0
D)
E)

Question 62

Write the following expression as a complex number in standard form.

A) + i
B) i
C)5+ 6 i
D) i
E) i

Question 63

Evaluate for the values , , and . Write your answer as a complex number in standard form.

A)
B)
C)
D)
E)