Elementary Algebra: Term I

Front 1

Natural Numbers are.

Back 1

{1,2,3,4,...}

Front 2

Whole Numbers are.

Back 2

{0,1,2,3,...}

Front 3

Integer Numbers are.

Back 3

{...,-3,-2,-1,0,1,2,3,...}

Front 4

Rational Numbers are.

Back 4

{Quotient of two integers, denominator not 0}

Front 5

The sum of two positive numbers will be a.

Back 5

Positive Number

Front 6

The sum of two negative numbers will be a.

Back 6

Negative Number

Front 7

The sum of a postive number and a negative number can be either a.

Back 7

Positive or Negative number.

Front 8

The product (or quotient) of two numbers with like signs will be a.

Back 8

Positive number.

Front 9

b^5 = ?

Back 9

b*b*b*b*b

Front 10

1st Order of Operations (1/4)

Back 10

Evaluate expressions within parentheses.

Front 11

2nd Order of Operations (2/4)

Back 11

Evaluate expressions with exponents.

Front 12

3rd Order of Operations (3/4)

Back 12

Perform Multiplications or divisions moving from left to right.

Front 13

4th Order of Operations (4/4)

Back 13

Perform additions or subtractions moving from left to right.

Front 14

Commutative Property:
a+b =
a*b =

Back 14

b+a
b*a

Front 15

Associative Property:
(a+b) + c =
(a*b) * c =

Back 15

a+(b+c)
a*(b*c)

Front 16

Distributive Property:
a(b+c) =

Back 16

a*b+a*c

Front 17

Identity Property:
a+0 =
1*a =

Back 17

0+a = a
a*1 = a

Front 18

Inverse Property:
a + (-a) =
a * 1/a =

Back 18

-a + a = 0
1/a*a = 1

Front 19

Variable

Back 19

a letter or symbol used to represent an unknown number

Front 20

Constant

Back 20

a value that does not change

Front 21

Numerical Expression

Back 21

contains only constants and/or operations

Front 22

Algebraic Expression

Back 22

contains only variables, constants, and/or operations

Front 23

Evaluate an Expression

Back 23

to find its value...substitute given numbers for the variables and then simplify the expression using the order of operations

Front 24

Equation

Back 24

a mathematical statement that two expressions are equal

Front 25

Solution of an Equation

Back 25

a value of the variable that makes the equation true

Front 26

Properties of Equalities

Back 26

you can add, subtract, multiply, or divide the same number to both sides of an equation, and the statement will still be true...used to solve equations

Front 27

Distributive Property

Back 27

for all real numbers, a, b, and c, a(b+c)=ab+ac
Example: 3(2x+1)=6x+3

Front 28

Coefficient

Back 28

a number that is multiplied by a variable...in 3x, 3 is the coefficient (x is the variable)

Front 29

Like Terms

Back 29

terms that have the same variables with the same exponents...to collect like terms, you add or subtract their coefficients (variables and exponents stay the same)

Front 30

Identity

Back 30

an equation that is always true no matter what value is substituted for the variable...the solution is All Real Numbers
If when solving, the variables cancel and the remaining equation is true, then the equation is an identity
If the remaining equation is false, then the equation has no solutions (but has no special name)

Front 31

Formula

Back 31

an equation that states a rule for a relationship among quantities

Front 32

Literal Equation

Back 32

an equation with two or more variables...a formula is a type of literal equation

Front 33

Absolute Value of a Number

Back 33

its distance from zero on a number line

Front 34

Steps for Solving an Absolute Value Equation

Back 34

1. Use inverse operations to isolate the absolute–value expression
2. Rewrite the resulting equation as two cases (one positive answer and the other negative answer) without absolute values
3. Solve the equation in each of the two cases

Front 35

Ratio

Back 35

a comparison of two quantities by division (a fraction a/b or a:b)

Front 36

Proportion

Back 36

a statement that two ratios are equal

Front 37

Rate

Back 37

a ratio with two quantities with different units
Ex: 34 km/ 2 hr

Front 38

Unit Rate

Back 38

a rate with a denominator of 1...you can change any rate to a unit rate
Ex: 16 km/1hr or 16 km/hr

Front 39

dimensional analysis

Back 39

a process that uses rates to convert measurements from one unit to another

Front 40

Conversion factor

Back 40

a rate in which two quantities are equal but have different units...used to convert from one set of units to another

Front 41

Proportion

Back 41

a statement that sets two ratios (fractions) equal to each other...The idea of proportions is that a ratio can be written in many ways and still be equal to the same value

Front 42

Cross Products Property

Back 42

used to solve proportions...if a/b=c/d, then ad=bc

Front 43

Scale

Back 43

a ratio between two sets of measurements such as

Hint 43

1 in: 5 miles

Front 44

Scale Drawing

Back 44

uses a scale to represent an object as much smaller or larger than the actual object...a map is an example of a scale drawing

Front 45

Similar Figures

Back 45

figures that have exactly the same shape but not necessarily the same size

Front 46

Corresponding Sides/Angles

Back 46

sides/angles of two figures that are in the same relative position...Two figures are similar IFF the lengths of the corresponding sides are proportional and the corresponding angles have equal measures

Front 47

Indirect Measurement

Back 47

method of measurement that allows you to solve a proportion involving similar triangles to find a length that is not easily measured..Ex: Using shadows

Front 48

Precision

Back 48

level of detail in a measurement...determined by the smallest unit or fraction of a unit that you can reasonably measure

Front 49

Accuracy

Back 49

the closeness of a measured value to the actual or true value

Front 50

Tolerence

Back 50

describes the amount by which a measurement is permitted to vary from a specified value...Usually expressed as a range of values

Front 51

Translate the sentence into an equation: Fifteen more than a number times six is eleven less than a different number times two.

Back 51

15 + 6z = 2y – 11

Front 52

Translate the sentence into an equation: The quotient of a number and 3 is the same as a the same number less seven.

Back 52

b/3 = b – 7

Front 53

Translate the sentence into an equation: The product of a number and 17 is the same as the number squared and then increased by 3.

Back 53

//dp11i9uvzjqmt.cloudfront.net/2/images/upload-flashcards/88/09/41/3880941_m.jpg

Front 54

Translate the equation into a sentence: 12 – 2x = –5

Back 54

Twelve minus two times a number equals the opposite of five.

Front 55

Translate the equation into a sentence: 12 – 3x = 6

Back 55

Twelve reduced by three times a number is six.

Front 56

//dp11i9uvzjqmt.cloudfront.net/2/images/upload-flashcards/88/10/22/3881022_m.jpg

Back 56

A number cubed added to three–fifths is the same as two.

Front 57

Tim's bank contains quarters, dimes, and nickels. He has three more dimes than quarters and 6 fewer nickels than quarters. If he has 63 coins, write and solve an equation to find how many quarters he has.

Back 57

x = number of quarters.
x + 3 = number of dimes
x – 6 = number of nickels
x + (x + 3 ) + (x – 6) = 63
3x – 3 = 63
3x = 66
x = 22

Front 58

Solve the equation: x – 11 = 34

Back 58

x = 45

Front 59

Solve for x: –1/3 + x = 2/3

Back 59

x = 1

Front 60

Solve for x: 5x = 25

Back 60

x = 5

Front 61

Solve for x: –3/4x = 15

Back 61

x = –20

Front 62

Solve for x: x/3 = –5/6

Back 62

x = –15/6 = –5/2

Front 63

An X–Men #1 comic book in mint condition recently sold for $45,000. An Action Comics #63 (Mile HIgh), also in mint condition, sold for $15,000.
1) Define a variable to determine the difference in selling price.
2) Write an equation using the variable from part 1.
3) Solve for how much more the X–Men comic book sold for than the Action Comics book.

Back 63

1) D = difference in price of the comic books.
2) D = $45,000 – $15,000
3) D = $30,000

Front 64

Solve for x: 2x + 18 = 12

Back 64

x = –3

Front 65

//dp11i9uvzjqmt.cloudfront.net/2/images/upload-flashcards/88/12/41/3881241_m.jpg

Back 65

x = 62

Front 66

Show how to use algebra to find three consecutive integers that sum to –36.

Back 66

x = 1st number
x + 1 = 2nd number
x + 2 = 3rd number
x + (x + 1)+ (x + 2) = –36
3x + 3 = –36
3x = –39
x = –13

–13, –12, –11

Front 67

The cost of a bag of potatoes is $1.50 less than 1/2 the price of apples. Write and solve an equation to find the cost of potatoes if apples cost $6.99/bag.

Back 67

P = cost of potatoes
P = 1/2($6.99) – 1.50
P = $2.00

Front 68

Solve for x: 3x + 2 = 7x

Back 68

x = 1/2

Front 69

5a + 2 = 6 – 7a

Back 69

a = 1/3

Front 70

Name for when an equation is true for all values of the variable.

Back 70

Identity

Front 71

–2(3x – 2) = 4 – 6x

Back 71

x = infinite solutions

Front 72

2s + 5 = 2(s – 3)

Back 72

no solution

Front 73

8 = 4(r + 4)

Back 73

r = –2

Front 74

//dp11i9uvzjqmt.cloudfront.net/2/images/upload-flashcards/88/12/89/3881289_m.jpg

Back 74

x = 4

Front 75

Solve the equation and graph the solution set.
|x + 3| = 6

Back 75

//dp11i9uvzjqmt.cloudfront.net/2/images/upload-flashcards/91/66/71/3916671_m.jpg

Front 76

On a map the scale is 5 inches = 31 miles. What is the distance represented by 3 1/2 inches on the map.

Back 76

21.7 miles

Front 77

Evaluate the expression: 15 – |g + 9| for g = –5

Back 77

11

Front 78

Evaluate the expression: |3 – h| + 7 for h = 5

Back 78

9

Front 79

//dp11i9uvzjqmt.cloudfront.net/2/images/upload-flashcards/91/66/83/3916683_m.jpg

Back 79

|x – 1| = 3

Front 80

For a company to invest in a product, they must believe they will receive a 12% return on investment (ROI) plus or minus 3%. Write an equation to find the least and the greatest ROI they believe they will receive.

Back 80

|x – 12| = 3; x = 9% or x = 15%

Front 81

//dp11i9uvzjqmt.cloudfront.net/2/images/upload-flashcards/91/68/36/3916836_m.jpg

Back 81

yes, they are equivalent.

Front 82

//dp11i9uvzjqmt.cloudfront.net/2/images/upload-flashcards/91/68/57/3916857_m.jpg

Back 82

No, these are not equivalent.

Front 83

Find the percentage of change from 96 to 25. Round to the hundredths place. Is this an increase or decrease?

Back 83

Decrease by 73.96%

Front 84

//dp11i9uvzjqmt.cloudfront.net/2/images/upload-flashcards/91/69/32/3916932_m.jpg

Back 84

x = 2

Front 85

Mrs. B can run 3 miles in 31 minutes. If she could maintain this pace how long would it take her to run a marathon which is 26.2 miles?
1) Give your answer in minutes
2) Convert your answer to hours

Back 85

1) 270.73 minutes
2) 4.5 hours

Front 86

Find the percent of change from 13 to 17. Round your answer to the hundredths of a percent. Indicate if this is an increase or decrease.

Back 86

Increase by 30.77%

Front 87

Find the total price of an item that costs 12.99 with a 9.5% tax rate.

Back 87

12.99 x (1.095) = $14.23

Front 88

Each bowling game costs $2.50. If Mrs. B bowled 3 games and the tax rate is 7.5% what was the total charge for bowling?

Back 88

3(2.5)(1.075) = $8.07

Front 89

What is the discounted price of an item that cost $65 if the discount is 15%?

Back 89

$65 * .85 = $55.25

Front 90

Solve the equation for g: 7h + f = 2h + g

Back 90

5h + f = g

Front 91

A car's fuel economy (E) is given by the formula E = m/g where m is the number of miles driven and g is the number of gallons of fuel. Solve the formula for m.

Back 91

m = Eg

Front 92

Mrs. B went to Guatemala. The currency there is quetzal. $1 dollar equals 7.8 quetzal. If Mrs. B took $125 on her trip. How many quetzals does that represent?

Back 92

975 quetzals

Front 93

Mrs. B returned from her trip to Guatemala with 120 quetzals. The exchange rate is $1 dollar = 7.8 quetzals. How much does this amount represent in dollars?

Back 93

$15.38

Front 94

How many cm are in 2 feet?
1 inch = 2.54 cm
12 inch = 1 foot

Back 94

//dp11i9uvzjqmt.cloudfront.net/2/images/upload-flashcards/91/72/50/3917250_m.jpg

Front 95

Grades are often computed using a weighted average. Suppose that homework counts 10%, quizzes 20%, and tests 70%.

If Pat has a homework grade of 92, a quiz grade of 68, and a test grade of 81, what is his final grade?

Back 95

Pat's overall grade = (0.10)(92) + (0.20)(68) + (0.70)(81)

Front 96

Bob had three carries of 8 yards each and five carries of 6 yards each in a recent football game. What was has rushing average (average yards per carry)?

Back 96

(3 x 8 + 5 x 6)/8 = 6.75 yards per carry

Front 97

A boat travels 16 miles due north in 2 hours and 24 miles due west in 2 hours. What is the average speed of the boat?

Back 97

16/2 + 24/2 = 20 miles per hour

Front 98

A cyclist begins traveling 18 miles per hour. At the same time and at the same starting point, an inline skater follows the cyclist's path and begins traveling 6 miles per hour. After how much time will they be 24 miles apart?

Back 98

24 = 18t – 6t where t = time
24 = 12t
2 hours = t

Front 99

What is a mixed number?

Back 99

A mixed number is the sum of a whole number and a fraction.

Front 100

Why is it impossible to draw a mathematical line?

Back 100

It is impossible to draw a mathematical line because it is a straight line that has no width and no ends.

Front 101

How do we show a location on a mathematical line?

Back 101

To show the location of a mathematical line, we draw a pencil line and put arrowheads on both ends to emphasize that the mathematical line goes on and on in both directions.

Front 102

What is a line segment?

Back 102

A line segment is a part of a line. It contains the endpoints and all points between the endpoints.

Front 103

How do we show the location of a line segment?

Back 103

To show the location of a line segment, we use a pencil line with no arrowheads. We name a segment by naming the endpoints of the segment.

Front 104

Tell me about intersecting lines.

Back 104

If two lines cross, we say that the lines intersect.

Front 105

Tell me about the Point of Intersection.

Back 105

The point of intersection is the place where the lines cross.

Front 106

Tell me about parallel lines.

Back 106

Parallel lines are two lines in the same plane that do not intersect.

Front 107

Tell me about perpendicular lines.

Back 107

If two lines make square corners at the point of intersection, we say that the lines are perpendicular.

Front 108

Tell me about right angles.

Back 108

Right angles are the angles made by perpendicular lines.

Front 109

Tell me about a straight angle.

Back 109

A straight angle is formed by two right angles.

Front 110

Tell me about an acute angle.

Back 110

An acute angle is an angle that is smaller than a right angle.

Front 111

Tell me about an obtuse angle.

Back 111

An obtuse angle is an angle greater than a right angle, but less than a straight angle.

Front 112

How many degrees does a right angle measure?

Back 112

A right angle measures 90 degrees.

Front 113

How many degrees does a straight angle measure?

Back 113

A straight angle measures 180 degrees.

Front 114

How many degrees does a circle measure?

Back 114

A circle measure 360 degrees.

Front 115

Tell me about a polygon.

Back 115

A polygon is a simple, closed, flat geometric figure whose sides are line segments.

Front 116

Tell me about the attributes of a polygon.

Back 116

1. Each segment of a polygon is called a side.
2. Each endpoint of a side is called a vertex of the polygon. The plural of vertex is vertices.
3. For a polygon, the number of sides is always equal to the number of vertices.

Front 117

Tell me about a concave polygon.

Back 117

A concave polygon is a polygon that has an indentation. (a cave)

Front 118

Tell me about a convex polygon.

Back 118

A convex polygon does not have an indentation.

Front 119

Tell me about an equilateral polygon.

Back 119

An equilateral polygon is a polygon whose sides all have equal length.

Front 120

Tell me about an equiangular polygon.

Back 120

An equiangular polygon is a polygon whose angles all have equal measure.

Front 121

Tell me about a regular polygon.

Back 121

A regular polygon is a polygon in which all sides have the same length and all angles have the same measure.

Front 122

What is the sum of the measures of the three angles in any triangle?

Back 122

The sum of the measures of the three angles in any triangle is 180 degrees.

Front 123

Tell me about a right triangle.

Back 123

A right triangle is a triangle that has a right angle.

Front 124

Tell me about an acute triangle.

Back 124

An acute triangle is a triangle in which all the angles are less than 90 degrees. (all angles are acute)

Front 125

Tell me about an obtuse triangle.

Back 125

An obtuse triangle is a triangle which contains an obtuse angle. (greater than 90 degrees)

Front 126

Tell me about an equiangular triangle.

Back 126

An equiangular triangle is a triangle in which the measures of all the angles are equal. (Each angle in an equiangular triangle must have a measure of 60 degrees.)

Front 127

Tell me about an isosceles triangle.

Back 127

An isosceles triangle is a triangle that has at least two sides of equal length.

Front 128

Tell me about an equilateral triangle.

Back 128

An equilateral triangle is a triangle in which the lengths of all sides are equal.

Front 129

Tell me about a scalene triangle.

Back 129

A scalene triangle is a triangle that has no sides of equal length.

Front 130

What are five types of quadrilaterals?

Back 130

Five types of quadrilaterals are:
1.Parallelogram
2.Trapezoid
3. Rectangle
4. Rhombus
5. Square

Front 131

Tell me about a parallelogram.

Back 131

A parallelogram is a quadrilateral that has two pairs of parallel sides.

Front 132

Tell me about a trapezoid.

Back 132

A trapezoid is a quadrilateral that has exactly two parallel sides.

Front 133

Tell me about a rectangle.

Back 133

A rectangle is a parallelogram with four right angles.

Front 134

Tell me about a rhombus.

Back 134

A rhombus is an equilateral parallelogram.

Front 135

Tell me about a square.

Back 135

A square is a rhombus with four right angles.

Front 136

Tell me about perimeter.

Back 136

Perimeter is the distance around the outside of a closed, planar geometric figure.

Front 137

Tell me about the radius of a circle.

Back 137

The radius of a circle is the distance from the center of the circle to any given point on a circle.

Front 138

Tell me about the diameter of a circle.

Back 138

In reference to a circle, the length of a chord of a circle that passes through the center of the circle. The diameter of a circle is twice the length of the radius.

Front 139

Tell me about the circumference of a circle.

Back 139

The circumference of a circle is the distance around a circle. (the perimeter)

Front 140

What is an irrational number?

Back 140

An irrational number is a number that cannot be written as a quotient of integers.

Front 141

What is pi?

Back 141

Pi is the ratio of the circumference of a circle to the diameter of that circle. Pi ~ 3.14.

Front 142

What is a number?

Back 142

A number is an idea.

Front 143

What is a numeral?

Back 143

A numeral is a single symbol or a collection of symbols that we use to express the idea of a particular number.

Front 144

What is the value of a numeral?

Back 144

The value of a numeral is the number represented by the numeral, and we see that the words 'value' and 'number' have the same meaning.

Front 145

Tell me about the decimal system.

Back 145

The decimal system is the system of numeration that we use to designate numbers. The decimal system uses 10 symbols that we call digits.

Front 146

What are natural numbers (or counting numbers)?

Back 146

Natural numbers (or counting numbers) are the numbers that we use to count objects or things.

Front 147

What is a positive real number?

Back 147

A positive real number is any number that can be used to describe a physical distance greater than zero.

Front 148

Tell me about the number zero.

Back 148

The number zero is not a positive number. It is a real number.

Front 149

What is a real number?

Back 149

A real number isthe set of numbers that includes all members of the set of rational numbers and all members of the set of irrational numbers.

Front 150

Tell me about negative numbers.

Back 150

Negative numbers are real numbers. Every positive number has a negative counterpart, and we call these numbers negative real numbers. We must always use a minus sign when we designate a negative number.

Front 151

What is a number line?

Back 151

A number line is a line divided into units of equal length with one point chosen as the origin, or zero point. The numbers to the right of zero are the positive real numbers, and the numbers to the left of zero are the negative real numbers.

Front 152

Tell me about graphing a number.

Back 152

We graph a number when we place a dot on the number line to indicate the location of a number. The number is said to be the coordinate of the pint that we hae graphed.

Front 153

Why do we use a number line?

Back 153

We use the number line to tell if one number is greater than another number by saying that a number is greater than another number if its graph lies to the right of the graph of the other number.

Front 154

How are fractions multiplied?

Back 154

Fractions are multiplied by mutiplying the numerators to get the new numerator, and by multiplying the denominators to get the new denominator.

Front 155

How do we divide fractions?

Back 155

We divide fractions by inverting the divisor and then multiplying.

Front 156

How do we multiply or divide mixed numbers?

Back 156

We change mixed numbers to improper fractions and then multiply or divide as indicated.

Front 157

What are the four basic operations of algebra?

Back 157

The four basic operations of algebra are:
1. addition
2. subraction
3. multiplication
4. division

Front 158

In an addition problem, what are the addends? What is the sum?

Back 158

The addends are the numbers to be added. The sum is the result of the addition problem.

Front 159

In a subtraction problem, what is the minuend, the subtrahend and the difference?

Back 159

We call the first number the minuend; the second number, the subtrahend; and the result, the difference.

Front 160

Tell me about multiplication.

Back 160

If two numbers are to be multiplied to achieve a result, each of the numbers is called a factor and the result is called a product.

Front 161

What is the product of a particular real number and the number 1?

Back 161

The product of a particular real number and the number 1 is the particular number itself.

Front 162

What is the product of any real number and the number zero?

Back 162

The product of any real number and the number zero is the number zero.

Front 163

Explain the terms dividend, divisor and quotient.

Back 163

The dividend is the number or quantity divided by another number. The divisor is a number or quantity that divides another number or quantity. The quotient is the result of dividing one number or quantity by another number or quantity.

Front 164

What is the numerator?

Back 164

The numerator is the number or quantity above the fraction bar in a fraction; i.e. the dividend of the fraction.

Front 165

What is the denominator?

Back 165

The denominator is the number or quantity under the fraction bar in a fraction; i.e. the divisor in a fraction.

Front 166

Tell me about a unit multiplier.

Back 166

A unit multiplier is a fraction that has units and has a value of 1. Unit multipliers are used to change the unit of a number.

Front 167

Prime number

Back 167

An integer greater than one whose only positive factors are 1 and itself.

Front 168

Composite number

Back 168

A noneprime positive integer greater than 1.

Front 169

Greatest common factor

Back 169

GCF

Front 170

Least common multiple

Back 170

LCM

Front 171

Rational number

Back 171

It is a number that an be expressed as a ratio of 2 integers when the denominator is not equall to 0.

Front 172

Reciprocals
(multiplicative inverses)

Back 172

2 numbers whose product are 1

Front 173

Square root

Back 173

It is one of a numbers 2 equal factors.

Front 174

Cube root

Back 174

It is one of a numbers 3 equal factors.

Front 175

nth root.

Back 175

it is one of a numbers n Equal factors

Front 176

Set

Back 176

A collection of objects.

Front 177

Union of sets

Back 177

It is the set of elements that appear in any of the sets.

Front 178

Intersection of sets

Back 178

It is the set of elements common to all of the sets.

Front 179

Subset

Back 179

One set is a subset of another set if every element of the 1st is contained in the 2nd. A C B

Front 180

Natural numbers

Back 180

The set of counting numbers, beginning with 1 and going infinately.

Front 181

Real numbers

Back 181

The union of sets of rational and irrational numbers.

Front 182

rational number

Back 182

The set of numbers expressed in the form of a fraction, a over b, where a and b are integers and b is not equal to 0.

Front 183

natural numbers

Back 183

The set [1,2,3,...] counting numbers

Front 184

whole numbers

Back 184

The set [0,1,2,3,...]

Front 185

intergers

Back 185

The set [...–2,–1,0,1,2,...]

Front 186

graph

Back 186

To draw, or plot, the points named by certain numbers or ordered pairs on a number line or coordinate plane.

Front 187

coordinate

Back 187

th number that corresponds to a point on a number line.

Front 188

àbsolute value

Back 188

The absolute value of a number n is the distance from zero on a number line and is represented by |n|.

Front 189

positive numbers
negative numbers

Back 189

+ are to the R of 0
– values less than 0, listed to the left of 0

Front 190

opposites

Back 190

Every positive rational number and its negative pair.

Front 191

additive inverses

Back 191

A number and its opposite are additive inverses of each other. The sum of a number and its additive inverse is 0.

Front 192

division of integers

Back 192

The quotient of two numbers having the same sign is positive, having different signs is negative.

Front 193

line plot

Back 193

A number line labled with a scale to include all the data with an X placed above a data point each time it occurs.

Front 194

measures of central tendency

Back 194

Numbers or pieces of data that can represent the whole set of data. The three basic measures of central tendency are: Mean, Median and Mode.

Front 195

mean

Back 195

The sum of the numbers in a set of data divided by the number of items.

Front 196

mode

Back 196

The middle number or numbers that appear most often in a set of data.If no item appears the most often, the set has no mode.

Front 197

median

Back 197

The middle number of a set of data when the data are arranged in numerical order. If there are an even number of data, the median is the mean of the two middle numbers.

Front 198

line plot

Back 198

A number line labled with a scale to include all the data with an X placed above a data point each time it occurs.

Front 199

frequency

Back 199

How often a piece of data occurs.

Front 200

stem–and–leaf plot

Back 200

A system used to seperate data into two numbers that are used to form a stem–and–leaf.

Front 201

back–to–back–stem–and–leaf plot

Back 201

Used to compare two related sets of data.

Front 202

probability

Back 202

The ratio of the number of favorable outcomes for an event to the number of possible outcomes of the event. P(a) = Number of favorable outcomes / total number of possible outcomes

Front 203

simple event

Back 203

A single event.

Front 204

sample space

Back 204

The list of all possible outcomes.

Front 205

equally likely

Back 205

Outcomes for which the probillity of each occuring is equal.

Front 206

odds

Back 206

The ratio that compares the number of ways an event can occur (successes) to the number of ways the event cannot occur (failures)

Front 207

square root

Back 207

One of two equal factors of a number.

Front 208

perfect square

Back 208

A number whose square root is a rational number.

Front 209

principal square root

Back 209

The nonnegative square root of a number.

Front 210

irrational numbers

Back 210

Numbers that cannot be expressed as terminating or repeating decimals.

Front 211

real numbers

Back 211

The set of rational numbers and the set of irrational numbers together.

Front 212

completeness property

Back 212

Each point on the number line corresponds to exactly one real number.

Front 213

rational approximation

Back 213

A rational number that is close to, but not equal to, the value of an irrational number.

Front 214

multiplicative property of –1

Back 214

The product of any number and –1 is its additive inverse.

Front 215

dividing integers

Back 215

The quotient of two numbers having the same sign is positive, having different signs is negative.

Front 216

multiplying integers

Back 216

Product of two numbers with same sign is positive, different signs is negative.
*even number of negative integers, product is positive, odd number of negative integers, product is negative.

Front 217

radical sign, The radical sign is used to indicate a nonnegative square root.

Back 217

.

Hint 217

//fce-study.netdna-ssl.com/images/upload-flashcards/front/8/3/10638265_m.jpg

Front 218

Consecutive Integers

Back 218

Integers in counting order

Front 219

defining a variable

Back 219

Choosing a variable to represent on of the unspecified numbers in a problem and using it to write expressions for the other unspecified numbers in the problem.

Front 220

dimensional analysis

Back 220

The process of carrying units throughout a computation.

Front 221

equivalent equations

Back 221

Equations that have the same solutions.

Front 222

extremes

Back 222

In the rations a/b =c/d, a and d are the extremes.

Front 223

formula

Back 223

An equation that states a rule in the relationship between certain quantities.

Front 224

four–step problem solving

Back 224

1. Explore the problem
2. Plan the solution
3. Solve the problem
4. Check the solution

Front 225

identity

Back 225

Equations that are true for all values of the variables.

Front 226

means

Back 226

The middle terms of the proportion.

Front 227

mixture problem

Back 227

Problems in which two or more parts are combined into the whole.

Front 228

multi–step equations

Back 228

Equations with more than one operation.

Front 229

number theory

Back 229

The study of numbers and the relationships between them.

Front 230

percent of change

Back 230

When an increase or decrease is expressed as a percent.

Front 231

percent of decrease

Back 231

The ration of an amount of decrease to the previous amount, expressed as a percent.

Front 232

percent of increase

Back 232

The ration of an amount of increase to the previous amount, expressed as a percent.

Front 233

Proportion

Back 233

An equation of the form a/b =c/d stating that two ratios are equivalent.

Front 234

ratio

Back 234

A comparison of two numbers by division.

Front 235

rate

Back 235

The ratio of two measurements having different units of measure.

Front 236

scale

Back 236

The ratio or rate used when making a model of something that is to large or to small to be conviently shown at actually size.

Front 237

solve an equation

Back 237

The process of finding all values of the variable that make the equation a true statement.

Front 238

uniform motion problems

Back 238

Problems in which an object moves at a certain speed, or rate.

Front 239

weighted average

Back 239

The sum of the product of the number of units and the value per unit divided by the sum of the number of units, represented by M.

Front 240

monomial

Back 240

a number, a variable, or a product of a number and one or more variables

Front 241

constants

Back 241

monomials that are real numbers

Front 242

Product of Powers

Back 242

to multipy two powers that have the same base, add the exponents

Front 243

Power of a power

Back 243

to find the power of a power multipy the exponents

Front 244

Power of a Product

Back 244

to find the power of a product, find the power of each factor and multiply.

Front 245

Simplifying Monimial Expressions

Back 245

To simplify an expression involving monimials, write an equivalent expression in which:
Eaach base appears only once,
There are no power of powers, and
All fractions are in simplest form

Front 246

Variable (p. 6)

Back 246

A letter or symbol used to represent a value that can change.

Front 247

Constant (p. 6)

Back 247

A value that does not change.

Front 248

Numerical Expression (p. 6)

Back 248

Contains only constants and/or operations.

Front 249

Algebraic Expression (p. 6)

Back 249

Contains variables, constants, and/or operations.

Front 250

Evaluate (p. 7)

Back 250

To find the value of an expression.

Front 251

Replacement Set (p. 7)

Back 251

A set of numbers that can be substituted for a variable.

Front 252

Real Numbers (p. 14)

Back 252

The set of all numbers that can be represented on a number line.

Front 253

Absolute Value (p. 14)

Back 253

The distance of a number from zero on a number line.

Front 254

Opposites (p. 15)

Back 254

Two numbers that have the same absolute value but have different signs.

Front 255

Additive Inverse (p. 15)

Back 255

A number and its opposite that are the same distance from zero.

Front 256

Reciprocal (p. 21)

Back 256

The product of two numbers that are equal to 1.

Front 257

Multiplicative Inverse (p. 21)

Back 257

A number and its reciprocal.

Front 258

Power (p. 26)

Back 258

An expression written with an exponent and a base.

Front 259

Base (p. 26)

Back 259

The number that is used as a factor.

Front 260

Exponent (p. 26)

Back 260

The number that indicates how many times the base is used as a factor.

Front 261

Square Root (p. 32)

Back 261

A number that is multiplied by itself to form a product.

Front 262

Principal Square Root (p. 32)

Back 262

The positive square root of a number that is represented by √.

Front 263

Perfect Square (p. 32)

Back 263

A number whose positive square root is a whole number.

Front 264

Cube Root (p. 32)

Back 264

A number that is raised to the third power to form a product.

Front 265

Natural Numbers (p. 33)

Back 265

All counting numbers.

Front 266

Whole Numbers (p. 33)

Back 266

All natural numbers and zero.

Front 267

Integers (p. 33)

Back 267

All whole numbers and their opposites.

Front 268

Rational Numbers (p. 33)

Back 268

Numbers that can be expressed in the form a/b, where a and b are both integers and b ≠ 0.

Front 269

Terminating Decimal (p. 33)

Back 269

Has a finite number of digits after the decimal point.

Front 270

Repeating Decimal (p. 33)

Back 270

Has a block of one or more digits after the decimal point that repeat continuously.

Front 271

Irrational Numbers (p. 34)

Back 271

All numbers that are not rational.

Front 272

Counterexample (p. 43)

Back 272

An example that disproves a statement, or shows that it is false.

Front 273

Closure (p. 44)

Back 273

A set of numbers is said to be closed under an operation if the result of the operation on any two numbers in the set is also in the set.

Front 274

Order of Operations (p. 48)

Back 274

Tells you which operation to perform first.

Front 275

Terms (p. 49)

Back 275

The parts of an expression that are added or subtracted.

Front 276

Like Terms (p. 49)

Back 276

Terms with the same variables raised to the same exponents.

Front 277

Coefficient (p. 49)

Back 277

A number multiplied by a variable.

Front 278

Variable (p. 6)

Back 278

A letter or symbol used to represent a value that can change.

Front 279

Constant (p. 6)

Back 279

A value that does not change.

Front 280

Numerical Expression (p. 6)

Back 280

Contains only constants and/or operations.

Front 281

Algebraic Expression (p. 6)

Back 281

Contains variables, constants, and/or operations.

Front 282

Evaluate (p. 7)

Back 282

To find the value of an expression.

Front 283

Replacement Set (p. 7)

Back 283

A set of numbers that can be substituted for a variable.

Front 284

Real Numbers (p. 14)

Back 284

The set of all numbers that can be represented on a number line.

Front 285

Absolute Value (p. 14)

Back 285

The distance of a number from zero on a number line.

Front 286

Opposites (p. 15)

Back 286

Two numbers that have the same absolute value but have different signs.

Front 287

Additive Inverse (p. 15)

Back 287

A number and its opposite that are the same distance from zero.

Front 288

Reciprocal (p. 21)

Back 288

The product of two numbers that are equal to 1.

Front 289

Multiplicative Inverse (p. 21)

Back 289

A number and its reciprocal.

Front 290

Power (p. 26)

Back 290

An expression written with an exponent and a base.

Front 291

Base (p. 26)

Back 291

The number that is used as a factor.

Front 292

Exponent (p. 26)

Back 292

The number that indicates how many times the base is used as a factor.

Front 293

Square Root (p. 32)

Back 293

A number that is multiplied by itself to form a product.

Front 294

Principal Square Root (p. 32)

Back 294

The positive square root of a number that is represented by √.

Front 295

Perfect Square (p. 32)

Back 295

A number whose positive square root is a whole number.

Front 296

Cube Root (p. 32)

Back 296

A number that is raised to the third power to form a product.

Front 297

Natural Numbers (p. 33)

Back 297

All counting numbers.

Front 298

Whole Numbers (p. 33)

Back 298

All natural numbers and zero.

Front 299

Integers (p. 33)

Back 299

All whole numbers and their opposites.

Front 300

Rational Numbers (p. 33)

Back 300

Numbers that can be expressed in the form a/b, where a and b are both integers and b ≠ 0.

Front 301

Terminating Decimal (p. 33)

Back 301

Has a finite number of digits after the decimal point.

Front 302

Repeating Decimal (p. 33)

Back 302

Has a block of one or more digits after the decimal point that repeat continuously.

Front 303

Irrational Numbers (p. 34)

Back 303

All numbers that are not rational.

Front 304

Counterexample (p. 43)

Back 304

An example that disproves a statement, or shows that it is false.

Front 305

Closure (p. 44)

Back 305

A set of numbers is said to be closed under an operation if the result of the operation on any two numbers in the set is also in the set.

Front 306

Order of Operations (p. 48)

Back 306

Tells you which operation to perform first.

Front 307

Terms (p. 49)

Back 307

The parts of an expression that are added or subtracted.

Front 308

Like Terms (p. 49)

Back 308

Terms with the same variables raised to the same exponents.

Front 309

Coefficient (p. 49)

Back 309

A number multiplied by a variable.

Front 310

abscissa

Back 310

the distance along the horizontal axis in a coordinate graph.

Front 311

absolute value

Back 311

the numerical value when direction or sign is not considered. the symbol for absolute value.

Front 312

additive axiom of equality

Back 312

if a=b and c=d, then a+c=b+d.

Front 313

additive axiom of inequality

Back 313

if a>b, then a+c>b+c.

Front 314

additive inverse

Back 314

the opposite (negative) of a number. Any number plus its additive inverse equals 0.

Front 315

algebra

Back 315

arithmetic operations using letters and/or symbols in place of numbers.

Front 316

algebraic expressions

Back 316

expressions composed of letters to stand for numbers.

Front 317

algebraic fractions

Back 317

fractions using a variable in the numerator and/or denominator.

Front 318

ascending order

Back 318

basically, when the power of a term increases for each succeeding term.

Front 319

associative property

Back 319

grouping of elements does not make any difference in the outcome. Only true for multiplications and addition.

Front 320

axioms of equality

Back 320

basic rules for using the equal sign

Front 321

binomial

Back 321

an algebraic expression consisting of two terms.

Front 322

braces

Back 322

grouping symbols used after the use of brackets. Also used to represent a set. { }

Front 323

brackets

Back 323

grouping symbols used after parentheses. [ ]

Front 324

canceling

Back 324

in multiplication of fractions, dividing the same number into both a numerator and a denominator.

Front 325

cartesian coordinates

Back 325

a system of assigning ordered pairs to points on a plane.

Front 326

closed half–plane

Back 326

a half–plane that includes the boundary line and is graphed using a solid line

Front 327

closed interval

Back 327

an interval that includes both endpoints or fixed boundaries

Front 328

closure property

Back 328

when all answers fall into the original set.

Front 329

coefficient

Back 329

the number in front of a variable. For example: 9x, 9 is the coefficient

Front 330

common factors

Back 330

factors that are the same for two or more numbers.

Front 331

commutative property

Back 331

order of elements does not make any difference in the outcome. Only true for multiplication and addition.

Front 332

complex fraction

Back 332

a fraction having a fraction or fractions in the numerator and/or denominator

Front 333

composite number

Back 333

a number divisible by more than 1 and itself ( such as 4 ,6 ,8 ,9 ...). 0 and 1 are not composite numbers.

Front 334

conjugate

Back 334

the conjugate of a binomial contains the same terms, but the opposite sign between them. (x+y) and (x–y) are conjugates.

Front 335

coordinate axes

Back 335

two perpendicular number lines used in a coordinate graph.

Front 336

coordinate graph

Back 336

two perpendicular number lines, the x axis and the y axis, creating a plane on which each point on a coordinate is assigned a pair of numbers.

Front 337

coordinates

Back 337

the numbers that correspond to a point on a coordinate graph.

Front 338

cube

Back 338

the result when a number is multiplied by itself twice. Designated by the exponent 3 (such as x3 or x–cubed)

Front 339

cube root

Back 339

the number that when multiplied by itself twice gives you the original number. For example, 5 is the cube root of 125.

Front 340

denominator

Back 340

everything below the fraction bar in a fraction

Front 341

descending order

Back 341

basically, when the power of a term decreases for each succeeding term.

Front 342

direct variation

Back 342

when y varies directly as x or y is directly proportional to x.

Front 343

discriminant

Back 343

the value under the radical sign in the quadratic formula. [b2–4ac].

Front 344

distributive property

Back 344

the process of distributing the number on the outside of the parentheses to each number on the inside. a(b+c) = ab+ac.

Front 345

domain

Back 345

the set of all first coordinates from the ordered pairs.

Front 346

element

Back 346

a member of a set.

Front 347

empty set

Back 347

a set with no members (a null set).

Front 348

equal sets

Back 348

sets that have exactly the same members.

Front 349

equation

Back 349

a balanced relationship between numbers and/or symbols. A mathematical sentence.

Front 350

equivalent sets

Back 350

sets that have the same number of members.

Front 351

Euler circles

Back 351

a method of pictorially representing sets.

Front 352

evaluate

Back 352

to to determine the value or numerical amount.

Front 353

exponent

Back 353

a numeral used to indicate the power of a number.

Front 354

extremes

Back 354

outer terms.

Front 355

factor

Back 355

to find two or more qualities whose product equals the original quantity.

Front 356

finite

Back 356

countable. Having a definite ending.

Front 357

F.O.I.L. method

Back 357

method of multiplying binomals in which first terms, outside terms, inside terms, and last terms are multiplied.

Front 358

function

Back 358

a relation in which each element in the domain is paired with exactly one element in the range

Front 359

graphing method

Back 359

a method of slving simultaneous equations by graphing each equation on a coordinate graph and finding the common point (intersection).

Front 360

A listing from least to greatest

Back 360

Ascending

Front 361

The sum or difference of two monomials

Back 361

Binomial

Front 362

Two lines with all points shared

Back 362

Coinciding Lines

Front 363

The sum of the exponents of the variables

Back 363

Degree of a Monomial

Front 364

The greatest degree of any term

Back 364

Degree of a Polynomial

Front 365

Output of a function

Back 365

Dependent Variable

Front 366

A listing from greatest to least

Back 366

Descending

Front 367

X values in a set of ordered pairs

Back 367

Domain

Front 368

Expressing a polynomial as a product

Back 368

Factoring

Front 369

Numbers multiplied to get a product

Back 369

Factors

Front 370

A set of ordered pairs in which each element of the domain is paired with exactly one element of the range

Back 370

Function

Front 371

Input for a function

Back 371

Independent Variable

Front 372

An uncountable number of solutions

Back 372

Infinite

Front 373

A point at whcih two lines cross

Back 373

Intersection

Front 374

The number in front of the term with the highest degree

Back 374

Leading Coefficient

Front 375

Number, variable, or the product of numbers and variables

Back 375

Monomial

Front 376

Lines in the same plane with the same slope that don't intersect

Back 376

Parallel Lines

Front 377

Two lines that intersect to form right angles

Back 377

Perpendicular Lines

Front 378

The sum of four or more monomials

Back 378

Polynomial

Front 379

Of the second degree

Back 379

Quadratic

Front 380

Y values in a set of ordered pairs

Back 380

Range

Front 381

Any set of ordered pairs

Back 381

Relation

Front 382

The sum or difference of three monomials

Back 382

Trinomial

Front 383

Number that tells how many times a base is used as a factor

Back 383

Exponent

Front 384

Where a line crosses the x–axis

Back 384

x–intercept

Front 385

Where a line crosses the y–axis

Back 385

y–intercept

Front 386

Numerical value that tells how steep a line is – also rise over run

Back 386

Slope