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Praxis Study > Praxis Math > Flashcards

Praxis Math Flashcards

1
Q

hypotenuse

A

The hypotenuse is the longest side of any right triangle and is across from the right angle. Its length can be found using the Pythagorean Theorem, or
.

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2
Q

Ordinal Number

A

An ordinal number describes position, such as the black and orange Impala car is in 1st place.

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3
Q

How are quadrants ordered in the Cartesian plane?

A

Counterclockwise
2<–1
3—>4

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4
Q

Cardinal Number

A

A cardinal number describes quantity, how many of something there are.

The following are some other examples of cardinal numbers.

2 squirrels
10 betta fish
4 watermelons
8 pies

Fractions and decimals are NOT cardinal numbers.

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5
Q

Nominal Number

A

A nominal number is a number that is part of a name in order to identify a particular thing.

Baseball player 27
Zipcode 90210
Model number 910
Windows 10

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5
Q

Least Common Multiple

A

The least common multiple (LCM) is the smallest number that two or more numbers can divide into evenly.

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6
Q

Order of Meters

A

1000 mm = 1 meter
100 cm = 1 meter
10 decimeters = 1 meter
1 dekameter = 10 meters
1 hectometer = 100 meters
1 kilometer = 1000 meters

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7
Q

Inequalities with one variable are shown on how many axis? (i.e. 1<x<9)

A

Inequalities with one variable are shown on a single axis similar to a number line.

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8
Q

Inequalities with two variable are shown on how many axis? (i.e y=2x+5)

A

Inequalities with two variables are shown on the Cartesian plane with two axes, one axis for each variable.

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9
Q

How would you graph the one variable inequality x < 4?

A

To graph a one-variable inequality, the first step is to draw a circle on the maximum or minimum values or both if both are mentioned. If the inequality is either less than or greater than, keep the circle open, meaning do not fill in the circle.

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10
Q

How would you graph the one variable inequality?

A

To graph this type of inequality, both the maximum and minimum are found on the number line and a circle is drawn at those points. If the symbol is less than or greater than, the circle is left unfilled or open. If the symbol is less than or equal to or greater than or equal to, then the circle is filled in or closed.

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11
Q

What does a dashed line of a two variable inequality mean?

A

A dashed line means the inequality is less than or greater than.

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12
Q

What does a solid line of a two variable inequality mean?

A

A solid line means the inequality is either less than or equal to or greater than or equal to.

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13
Q

How do you determine where to shade the two variable inequality?

A

Test a value in each section of the graph to see if the inequality still holds true. If it holds true, shade that region.

If it doesn’t hold true, don’t shade that region.

If there are only two regions, if the inequality doesn’t hold true for one side, shade the other side.

An easy point here is (0, 0).

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14
Q

What is a linear relationship?

A

Any relationship that when graphed gives you a straight line.

If the line is not straight, it is NOT a linear relationship.

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15
Q

What conditions must a linear relationship meet?

A
  1. The equation must NOT have:
    a. variables beyond the first power (no squared/cubed!)
    b. any variables in the denominator
  2. The equation must graph as a straight line.
  3. There are at most only 2 variables.
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16
Q

What is the rate formula?

A
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17
Q

How do you convert F to C?

A
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18
Q

What is the currency exchange rate formula?

A
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19
Q

What is the formula to calculate AREA of a circle?

A
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20
Q

What is the formula to calculate CIRCUMFERENCE of a circle?

A
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21
Q

What is the formula for the SURFACE AREA of a cube?

A
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22
Q

What is the formula for the SURFACE AREA of a rectangular prism (box)?

A
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23
Q

What is the formula for SURFACE AREA of a cylinder?

A
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24
Q

What is the formula for SURFACE AREA of a pyramid?

A
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25
Q

What is the Pythagorean theorem?

A

The Pythagorean theorem states that the adjacent and opposite sides of a right triangle squared add up to equal the square root of the hypotenuse.

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26
Q

What does SOH-CAH-TOA stand for?

A

SOH-CAH-TOA represents the 3 trigonometry ratios that can be used along with the Pythagorean theorem.

The soh is for Sine is Opposite over Hypotenuse.
The cah is for Cosine is Adjacent over Hypotenuse.
The toa is for Tangent is Opposite over Adjacent.

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27
Q

What is the sine equation and what does it represent?

A
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28
Q

What is the cosine equation and what does it represent?

A
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29
Q

What is the tangent equation and what does it represent?

A
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30
Q

What is the Formula for the Volume of a Cone?

A

Here, r is the radius and h is the vertical height of the cone.

31
Q

What is the Formula for the Volume of a Cylinder?

A

Here, r is the radius and h is the height of the cylinder.

32
Q

What is the Formula for the Volume of a Sphere?

A

Here, r is the radius of the sphere.

33
Q

What is a scatterplot used for?

A

Creating and interpreting scatterplots is a great depiction of a correlation between two sets of data. This data is known as bivariate data, which are two sets of variables that can change and are compared to find relationships.

34
Q

What relationship between data does a bar graph show?

A

Bar graphs are ideal for showing how two categories compare, like how athletic individuals burn more calories than non-athletic individuals.

35
Q

True/False. The percentage of a pie circle slice must correspond with the percentage of degrees within a circle.

A

True

36
Q

How do you determine the total number of degrees a slice of a pie chart should take up if you have the percentage that slice represents?

A

Because a circle has 360 degrees, the percentage is multiplied by 360 to determine the total number of degrees a slice should take up.

A slice that encompasses 70% of the data should encompass 252 degrees of the circle as seen here.

37
Q

Ordinal Number

A

Ordinal numbers are used to help describe which person is being talked about, as in their postion in a group.

1st, 2nd, 3rd, 4th, 5th

An easy way to remember an ordinal number is to think about the first three letters of the word ordinal, ord-. Those three letters are also the first three letters of the word order. So ordinal numbers tell the order.

38
Q

What is a transversal?

A

A transversal is a third line that intersects two other lines, creating special types of angles.

The blue line is the transversal.

39
Q

Alternate Interior Angles

A

Alternate interior angles are the angles between the two lines being intersected and on opposite sides of the transversal.

The green angles c and f form one pair of alternate interior angles and the purple angles d and e form the second pair of alternate interior angles.

40
Q

Alternate Exterior Angles

A

Alternate exterior angles are alternate angles that are outside the two lines being intersected by the transversal.

One pair of alternate exterior angles are the green angles a and h. Another pair of alternate exterior angles are the purple angles b and g.

Both pairs are outside of the two black lines with each angle being on the opposite side of the blue transversal.

41
Q

Corresponding Angles

A

Corresponding angles are the angles that are in the same location at each intersection.

The pair of red angles a and e are corresponding angles.

The other corresponding angles are angles b and f, d and h, and c and g.

42
Q

Consecutive Interior Angles

A

Consecutive interior angles are interior angles that are on the same side of the transversal.

These angles are NOT on opposite sides of the transversal.

The orange angles d and f make up a consecutive interior angle pair.

The angles c and e make up that other pair.

43
Q

Consecutive Exterior Angles

A

Consecutive exterior angles are exterior angles that are on the same side of the transversal.

The orange angles a and g make up a consecutive exterior angle pair.

The other pair are the angles b and h.

44
Q

Vertical Angles

A

Vertical angles are the angles that are opposite each other at an intersection.

“Kissing V’s”

Standing at an intersection, the vertical angle is the one that is diagonally on the other side.

At this intersection, the orange angles make one vertical pair and the purple angles make another vertical pair.

Vertical angles are always congruent.

45
Q

When are angles congruent?

A

Angles are congruent when they have the same measurement.

two angles measure 63 degrees = congruent

one angle is 64 degrees, the other is 62 degrees = not congruent

46
Q

What makes angles consecutive?

A

Consecutive means “following in order, unbroken.”

This means that angles that are consecutive are “unbroken/uninterrupterd” by the transveral.

They are on the SAME SIDE OF THE LINE.

47
Q

What is the only type of angle that does not need a transveral to exist?

A

A vertical angle. This will involve only the intersection of 2 lines. No third “transveral” line is needed.

48
Q

Complementary Angles

A

To be complementary, means to be “complete.”

Complementary angles are two angles whose measures add up to 90 degrees.

They make a “complete” right angle.

49
Q

Explain the difference between consecutive, complementary, and congruent angles.

A

Consecutive Angles are next to each other and share a side.

Complementary Angles add up to 90 degrees.

Congruent Angles have the same measure, regardless of their position relative to each other.

50
Q

Supplementary Angles

A

Two angles whose measures add up to 180 degrees are supplementary angles.

One way to help remember this is that the “s” in supplementary almost looks like the “8” in 180.

51
Q

Adjacent Angles

A

Adjacent angles are angles that are next to each other.

52
Q

What is the formula to convert kilograms to pounds?

Kg–>lbs

A

Kg–>lbs
lb= kg x 2.2046

“I weighed 2 grams in the year I was born 2046.”

53
Q

What is the formula to convert kilometers into miles?

Km–>m

A

Km–>m
m= km x 0.6214

“I can run 62 miles in 14 minutes.”

54
Q

How do you find the surface area of a cube?

A

SA=6a^2

55
Q

How do you find the volume of a cube?

A

V=a^3

56
Q

Create an algabraic expression.

A

An equation includes an equal sign (“=”) and shows that two expressions are equal.

6x = 4

57
Q

Create an algebraic equation.

A

6x−4

An algebraic expression is made of constants, variables, and algebraic operations.

58
Q

What is a monomial? Give an example.

A

A monomial is an algebraic expression that consists of only one term. It can be a constant, a variable, or a product of constants and variables raised to non-negative integer powers.

Examples of monomials:

59
Q

What is a binomial? Give an example.

A

A binomial is an algebraic expression that consists of exactly two terms separated by either addition or subtraction.

60
Q

What is a linear algebraic equation?

A

A linear equation is one that usually only has two variables ‘x’ and ‘y’.

These variables will never be in the denominator and there will be no exponents in these equations and therefore always have a degree of 1.

Linear equations will only have one line when graphed.

61
Q

What is a quadratic algebraic equation?

A

A quadratic equation is a type of polynomial equation of the second degree, meaning it includes a term with the variable raised to the power of two as its highest degree.

A general form of a quadratic equation is:

ax^2+bx+c = 0

62
Q

What is a cubic algebraic equation?

A

A cubic equation is a polynomial equation of the third degree in which there are three ‘x’ variables with one that is raised to the third power, one raised to the second power and one that does not have an exponent.

The general form of a cubic equation is:

ax^3+bx^2+cx+d=0

63
Q

When do I know to use the slope equation?

A

You should consider using the concept of slope in a problem when you need to determine the rate of change or the relationship between two variables that change in a linear manner. Here are specific scenarios where using the slope would be appropriate:

  1. Analyzing a Relationship Between Two Variables:
    When you have two variables that are related in a way that one variable depends on the other (like distance and time, cost and quantity, or temperature and time).

You want to understand how a change in one variable (the independent variable, (𝑥,x) affects the other variable (the dependent variable, 𝑦,y).

64
Q

When is it ideal to use a double bar graph to compare data?

A

A double-bar graph is a concise and structured way to visually display data by using bars to represent data within two different categories. This type of graph is common when comparisons are needed to analyze data.

65
Q

When is it ideal to use a scatterplot to compare data?

A

When creating a scatterplot, you will be looking at two sets of data. This data is known as bivariate data, which are two sets of variables that can change and are compared to find relationships.

Creating and interpreting scatterplots is a great depiction of a correlation between two sets of data.

66
Q

When is a stem and leaf display? Why is it useful?

A

A stem-and-leaf display is a visual representation of data where the stem, the data on the left side of the chart, shows one part of the value while the leaves, the data on the right side of the chart, show the other.

Not only can we see the frequency of our data in a stem-and-leaf display, but we can also get each specific value from our data set.

67
Q

When is it ideal to use a circle graph to compare data?

A

A pie chart is used to represent the spread of response variables for a given data type. By quickly viewing a pie chart, readers can observe what the most common response type is by identifying the largest slice.

68
Q

When is it ideal to use a bar graph to compare data?

A

Bar graphs are used for showing how many items in certain categories, how often events occur, or how values change over time.

Bar graphs show information, or data, visually. The graph has bars that run either vertically from the x-axis or horizontally from the y-axis. The bars are sorted into categories based on the data collected, and the length of each bar represents a number.

69
Q

When is it ideal to use a histogram to compare data?

A

Histograms are an excellent way to group and visualize data distributions.

Histograms are very similar to bar graphs.

Histograms show us how frequently certain numbers appear in a set of data. You can use histograms to show the popularity, or modes, of certain types of data.

To create a histogram, first put the type of data on the horizontal axis. The vertical axis represents the frequency of each choice.

A histogram can show when data is skewed, which is where the shape of a graph peaks to the left or the right of the center.

70
Q

What do you use a box plot for?

A

A box plot shows where a data set might be skewed or if the data set is symmetrical. Specifically, a box plot marks and illustrates the minimum value, maximum value, median, first and third quartiles, and the interquartile range.

71
Q

When should you use a double line graph?

A

In real life double line graphs have lots of uses: whenever two things must be compared, consider drawing a double line graph to show the comparison.

Some real-world examples are:

Comparing the monthly temperatures in two cities.
Comparing monthly prices of an item for two different years.

72
Q

What is a frequency distribution? Give an example of its use and how it can be graphed.

A

The term frequency defines the number of times some observed event of interest happened. When studying a population, frequency distribution lists how often an event of interest occurred.

The primary graphs for frequency distribution are a histogram (aka bar graph) and a pie chart.

In a histogram, bars visually represent the data for the frequency for every class or class limit. The shape, central tendency, and variability of a histogram will show which classes in the population occur most and least frequently in a population.

On the other hand, a pie chart requires the relative frequency percentage calculation and displays them as percentages in a round pie-shaped image with slices.

73
Q

What is relative frequency and how do you calculate it?

A

Relative frequency is the proportion of times a specific event occurs relative to the total number of observations. It is calculated by dividing the frequency of the event by the total number of observations and is often expressed as a fraction, decimal, or percentage.

74
Q

What does a histogram skewed to the left and right mean? Where is the mode represented?

A

Data sets that are skewed to the right have fewer observations, or numbers, that are higher values, while data sets that are skewed to the left have fewer observations, or numbers, that are lower values.

The tallest peak of a histogram will give you the mode, or the most popular choice, in the data set.

75
Q

How do you create a circle graph?

A

To create a pie chart, the percentage of responses each response variable makes up is needed. This is accomplished by dividing the number of responses of a particular type by the total number of responses and multiplying it by 100. The percentage of response types are then multiplied by 360, which is the total number of degrees within a circle. The resulting calculation corresponds with the number of degrees of the interior angle of the response type’s corresponding slice.

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