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Kevin Jimbi K12 Homeschool > Kevin’s Cards about 7th and 8th Grade Math > Flashcards

Kevin’s Cards about 7th and 8th Grade Math Flashcards

1
Q

What is the solution to a linear equation in 2 variables

A

A solution to a linear equation in 2 variables is a point: (x,y) or ordered pair

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2
Q

How many solutions does a linear equation in two variables have

A

Linear equations in 2 variables have infinitely many solutions and each solution is a point that lies on the same line as all the other solutions

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3
Q

Ax + By = C is what equation

A

Ax + By = C is a linear equation in 2 variables

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4
Q

How do you find the solution to linear equations with 2 variables

A

To find solutions to linear equations, chose a value for x, substitute the value into the equation , and solve for y. Do the same thing to solve for x with y

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5
Q

What is the standard form of a linear equation

A

The standard form of a linear equation is: Ax + By = C, where A,B, and C are integers, A is positive and B is non-zero

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6
Q

What is the names of the point of where a line crosses the x-axis and y-axis

A

The x-intercept of a graph is the x-coordinate of the point where the line intersects the x-axis. The y-intercept is the y-coordinate of the point where the graph intersects the y-axis

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7
Q

What is a Proportional Relationship

A

Proportional Relationships are a special type of linear equation when the ratio between two quantities is constant, the quantities have a proportional relationship

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8
Q

Rate Definition

A

A ratio of two quantities measured in different units

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9
Q

In a proportional relationship between two variables increases at a constant what

A

In a proportional relationship between two variables increases at a constant rate (also called a unit rate) as the other variable increases by one

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10
Q

Ratio Definition

A

A comparison of two quantities by division

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11
Q

A proportional relationship can be modeled as what

A

y = mx

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12
Q

When is the slope (m) on a graph positive

A

The slope (m) is positive if the line rises from left to right

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13
Q

When is the slope (m) on a graph negative

A

The slope (m) is negative if the line falls from left to right

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14
Q

What is the slope (m) on a graph equal to 0

A

The slope (m)is equal to 0 when the line is horizontal

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15
Q

What is a slope

A

The slope of a line is the ratio of the vertical change between any two point on the line to the horizontal change

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16
Q

What is another name for the vertical change and the horizontal change of a line’s slope

A

The vertical change is called the rise and the horizontal change is call the run

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17
Q

What is the format for the equation for slope

A

Vertical change/ Horizontal change or Rise/ Run

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18
Q

What directions do you move when moving in a positive or negative direction on a graph

A

When you move up or right you move in a positive direction. When you move down or left, you move in a negative direction

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19
Q

What is the Formula for Slope

A

y2 - y1/ x2 - x1

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20
Q

What is the slope of a vertical line on a graph

A

A slope is undefined if the line is vertical

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21
Q

What is a hypotenuse

A

The hypotenuse of a right triangle is the longest side of the triangle which is always opposite of the right angle (90 degrees)

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22
Q

Any two points on a line are what

A

Any two points on a line are the end points of a segment that, together with the rise and run, form a right triangle

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23
Q

What can the slope of the line tell you about the rate

A

The greater the slope of the line, the greater the rate. So when you compare lines, the line with the greater slope has the greater rate

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24
Q

What does the steepness of a line on a graph tell you

A

The steeper the line, the greater the slope

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25
Q

Each form of a linear equation communicates what

A

Each form quickly communicates specific information

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26
Q

What is the point - slope form of a line useful for

A

Communicating the slope of a line and one-point on the line

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27
Q

What is Point Slope Form

A

y - y1 = m(x - x1)

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28
Q

If a number is added in point-slope form what sign is it

A

It is negative

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29
Q

A proportional relationship can be modeled as what

A

y = mx

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30
Q

When a graph intersects the origin, you can do what to find the slope

A

Use any point to find the slope

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31
Q

What is slope-intercept form

A

y = mx + b, where b the y-intercept and m is the slope

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32
Q

Rate Definition

A

A ratio that compares quantities of a different kinds of units

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33
Q

Unit Rate Definition

A

A rate in which the 2nd quantity is 1

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34
Q

Terminating Decimals Definition

A

Decimals that have a finite number of nonzero digits

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35
Q

Initial Value Definition

A

The beginning value of a linear relationship; y-intercept

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36
Q

Ratio Definition

A

The relationship between two or more quantities

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37
Q

Mph is and example of what

A

An unit rate

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38
Q

Two or more linear equations using the same variables make up what

A

A system of linear equations

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39
Q

What is the solution of a system of linear equations

A

A solution of a system of linear equations is a point where the lines of the equations intersect

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40
Q

What does percent mean

A

Per 100

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41
Q

How do you convert a fraction to a percent

A

Multiply by 100

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42
Q

How do you convert a percent to a fraction

A

Divide by 100

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43
Q

A system with at least one solution is a what

A

A consistent system

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44
Q

What is a system with exactly one solution called

A

A consistent independent system

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45
Q

The lines in a consistent independent system do what

A

They intersect at exactly one point and have different slopes

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46
Q

A system with infinitely many solutions is what

A

A consistent dependent or a coincident

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47
Q

The lines in a consistent dependent system is also called a what

A

Coincident

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48
Q

A system that has no solutions is what

A

Inconsistent

49
Q

The lines in a inconsistent system are what

A

Parallel

50
Q

What are the slopes and y-intercepts like in an inconsistent system

A

Same slopes and different intercepts

51
Q

What are the slopes and y-intercepts like in a consistent dependent system

A

Same slopes and same y-intercepts

52
Q

What are the slopes and y-intercepts like in a consistent independent system

A

Different slopes and different or same y-intercepts

53
Q

Percent Error

A

The absolute value of the Estimated value - actual value divided by actual value times 100

54
Q

What is Commission

A

Commission is a payment based on amount of sales an employee makes. It is usually calculated as a percent of the employee’s total. For this reason, the more sales an employee makes, the more money he or she makes. Many commission base companies/jobs also pay a base salary that guarantees that the employee will receive money even if there are no sales

55
Q

Commission

A

Earning = base salary + (commission% x sales)

56
Q

When putting your money in a bank what can you earn on it

A

You can earn interest on it

57
Q

What is used to solve for simple interest

A

I = Prt, I: interest earned, P: principal, r: interest rate, and t: time in years

58
Q

Interest Rate Definition

A

The percentage of the original amount of money on which on which the interest will be calculated

59
Q

Principal Definition

A

Money that earns interest at a given rate over time; the principal is the original amount of money on which interest is based

60
Q

Simple Interest Definition

A

Interest earned or paid only on the principal

61
Q

Interest Definition

A

The cost of borrowing money or the amount earned by lending money

62
Q

Annual Rate Definition

A

Something paid every year (once a year)

63
Q

Proportion Definition

A

An equation stating that two ratios are equal

64
Q

Relation Definition

A

A mapping from a set of inputs to a set outputs

65
Q

What are the inputs

A

Any x-coordinate

66
Q

What are the outputs

A

Any y-coordinate

67
Q

What are different ways a relation can be shown

A

A relation can be shown in ordered pairs, a table, and arrow diagram, or graph

68
Q

Domain Definition

A

In a relation, the set of allowable inputs (all x-coordinates)

69
Q

Range Definition

A

The set of possible outputs (all y-coordinates)

70
Q

When is the domain and range both the set of all real numbers

A

When a graph of a line that is not vertical or horizontal contains an infinite number of elements in both its range and its domain

71
Q

What is k

A

The constant of proportionality

72
Q

What is the equation for k

A

k = y/x

73
Q

Function Definition

A

A relation in which every element of the domain is assigned to exactly one element of the range

74
Q

If a x-value is repeated, is the relation a function

A

No

75
Q

Vertical Line Test Definition

A

For any relation, if a vertical line intersects the graph more than once, the relation isn’t a function

76
Q

Linear functions are most often written in what line form

A

Slope-intercept form

77
Q

Linear functions are written in what form

A

Slope-intercept form

78
Q

What is the general form of a proportional relationship

A

y = kx

79
Q

What is another for the constant of proportionality

A

Constant of variation

80
Q

K can be everything but what

A

0

81
Q

If in a linear equation written in slope-intercept form, has an exponent other than 1 over x, is it linear

A

No

82
Q

Linear Function Definition

A

A function that when graphed forms a straight line

83
Q

Nonlinear Function Definition

A

A function that when graphed doesn’t form a straight line

84
Q

When describing Function graphs you must read from where to where

A

Left to right

85
Q

When the x-values increases and the y-values increase, the line is what

A

Increasing

86
Q

When the x-values increase but the y-values decrease, the line is what

A

Decreasing

87
Q

When is a function constant

A

If the value of the function stays the same as x increases

88
Q

What are key features when interpreting a function graph

A

Axis labels; the graph is increasing, decreasing, or constant; and if horizontal and vertical intercepts

89
Q

Two-Way Table Definition

A

A table used to compare two categorical variables

90
Q

Relative Frequency Table Definition

A

Table that describes the percent of occurrence of the values or intervals in a data set

91
Q

What is frequency

A

How many times a value occurs

92
Q

Categorical Variable Definition

A

A variable that is separable into mutually exclusive groups (For ex: boys and girls)

93
Q

Cluster Definition

A

Points that are close together on a scatter-plot

94
Q

What is an association

A

A pattern

95
Q

What does Positive association mean

A

The points are rising

96
Q

What does Negative association mean

A

The points are decreasing

97
Q

What does no association mean

A

The pattern isn’t clear

98
Q

How many solutions does a linear equation in one variable have

A

One

99
Q

What is the sum of supplementary angles

A

180 degrees

100
Q

Adjacent Angles Definition

A

Two angles in the same plane that have a common side and a common vertex, but no common interior points

101
Q

Linear Pair Definition

A

Two angles that have a common side and the same vertex, and their other sides point in opposite directions

102
Q

Vertical Angle Definition

A

The angles opposite of each other when two lines intersect to form 4 angles

103
Q

What happens to the inequality sign when multiplying or dividing by negative numbers

A

The inequality sign gets reversed when you multiply and divide by negative numbers

104
Q

Linear Inequality Definition

A

An inequality in which the variable is of degree one

105
Q

How many angles are formed when a transversal goes through two parallel lines

A

8 angles

106
Q

Alternate Interior Angles Definition

A

The inside angles on opposite diagonal sides of a transversal crossing two lines

107
Q

Alternate Exterior Angles Definition

A

The outside angles on opposite diagonal sides of a transversal crossing two lines lines

108
Q

Corresponding Angles Definition

A

Angles that lie in the same position or match up when a transversal intersects two lines

109
Q

Transversal Definition

A

A line that intersects two or more lines in a plane

110
Q

Corresponding Angles are what

A

Equivalent

111
Q

Scale Factor Definition

A

The ratio of the side length of the image to the corresponding side length of the pre-image

112
Q

Dilation Definition

A

A transformation that changes the size, but not the shape, of a figure

113
Q

Enlargement Definition

A

A dilation that increases the size of a figure; the scale factor is greater than 1 in an enlargement

114
Q

Reduction Definition

A

A dilation that reduces the size of a figure; the scale factor is less than 1 in reduction

115
Q

In a triangle, how is an exterior angle formed

A

When a side of a triangle is extended

116
Q

What does the exterior angle theorem state

A

“The measure of an exterior angle of a triangle is equal to the sun of the measures of the two no adjacent interior angles”

117
Q

Equiangular Polygon Definition

A

A polygon with all angles congruent

118
Q

Regular Polygon Definition

A

A polygon with all its sides congruent and all its angles congruent

Kevin Jimbi K12 Homeschool (37 decks)

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