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Praxis Elementary Math
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Gravity
Key Concepts:
Terms in this set (65)
Complex number
Ordinal number vs Cardinal number
Cardinal Number
a number that says how many of something there are
one, two, three, four, five
Ordinal Number
a number that tells the position of something in a list
1st, 2nd, 3rd, 4th, 5th
Roots of quadratic equation
7! (Seven factorial)
7 x 6 x 5 x 4 x 3 x 2 x 1
Equation for circle
x^2 + y^2 = a
Equation for straight line
xy = a
Equation for hyperbola
x^2 - y^2 = a (opens left and right)
y^2 - x^2 = a (opens up and down)
Area of Circle
Circumference of Circle
Surface area of Cylinder
Surface area of Cone
Surface Area of Sphere
Volume of Cone
Volume of Sphere
orthogonal
of or involving right angles; at right angles.
hypotenuse
Sq Root ( a^2 + b^2 )
Area of Triangle
Area of Trapezoid
Volume of Pyramid
Supplementary angles
sum of angles equals 180º
may or may not be adjacent
if adjacent, always form a straight line
corresponding angles
Alternate interior angles
circle inscribed in a polygon
circle circumscribe a polygon
polygon inscribed in circle
polygon circumscribe circle
diagonal in polygon
Number of diagonal in n-sided polygon
d = n ( n - 3 ) / 2
Sum of interior angles in polygon
scalene triangle
has no congruent sides
angle with the largest measure is opposite to longest side
Triangle Inequality Theorem
sum of two sides is always greater than the third side
Similar triangles
corresponding angles are congruent to each other
Congruent triangles
corresponding sides are congruent to each other
Side-side-side (SSS)
if all three sides of one triangle are equal to all three sides of another triangle, they are congruent by SSS
Side-angle-side (SAS)
if two sides and the adjoining angle in one triangle are equal to two sides and the adjoining angle of another triangle, they are congruent by SAS
Pythagorean Theorem
can only be used for right angle triangles
Law of Sines
c^2 = a^2 + b^2 - 2ab (cos C)
can be used for all triangles
Reflection symmetry
Rotational symmetry
Probability
likelihood of something taking place
P(A) = Number of acceptable outcomes / Number of possible outcomes
Event
situation that produces results of some sort
coin toss
Compound Event
event that involves two or more independent events
rolling a pair of dice
Outcome
possible result in an experiment or event
heads or tails in coin toss
Desired outcome/Success
outcome that meets a certain criteria
a roll of 1 or 2 if we are looking for less than 3
Independent Events
two or more events whose outcomes do not affect one another
two coin toss at the same time
Dependent Events
two or more events whose outcomes affect one another
two cards drawn consecutively from the same deck
Certain Outcome
probability of outcomes 100% or 1
Impossible Outcome
probability of outcome is 0% or 0
Mutually Exclusive Outcomes
two or more outcomes whose criteria cannot all be satisfied in a single event
a coin coming up heads and tails at the same time
Permutation
arrangement of a specific number os a set of objects in a specific order
r = no. of items
n = given set of items
Combination
a specific number of set objects but not in any specific order
Calculating how many different 5-card hands can be drawn from a deck of 52 cards
C = n! / r! (n-r)!
Possibility of getting exactly k heads out of n flips of a fair coin
n! / k! (n-k)!
Complement of an Event
probability that A does not happen
Addition Rule
probability of a compound event
Conditional probability
probability of an event occurring once another event has already occurred
Given event A and dependent event B
Out of 10 lottery balls, the probability of pulling ball 7 in two pulls
Multiplication Rule
Two independent events occurring
P (A and B) = P(A) x P(B)
Two dependent events occurring
P (A and B) = P(A) x P(B/A)
P(B/A) is the probability of the second event occurring after the first event has already occurred
Expected Value
determining expected outcome in a random situation
Theoretical vs Experimental (Empirical) Probability
Theoretical: what should happen, possible outcomes
Experimental: same except that actual outcomes are used instead
They don't always line up with one another.
Data
Quantitative
measurements that provide info about quantities in numbers
Qualitative
info that cannot be measured in numbers
Discrete
info that can be expressed only by a specific value such as whole or half numbers (e.g. number of people)
Continuous
info that can be expressed by any value within a given range (e.g. time and temperature)
Primary
info collected directly from a survey, investigation or experiment
Raw
primary data that has not yet been organized or analyzed
Secondary
info that has already been collected, sorted and processed by the researcher
Ordinal
info that can be placed in numerical order (e.g. age, weight)
Nominal
info that cannot be placed in numerical order (e.g. names, places)
Measures of Central Tendency
Mean
arithmetic mean or average
Median
middle value of a data set that is in numerical order
Mode
value that occurs most frequently in a data set
Measures of Dispersion
Standard deviation
expresses how spread out the values of a distribution are from the mean
High standard deviation means the values are very spread out and vice versa
The increase/decrease of every value in the distribution results in the same amount of increase/decrease in mean, median, mode, BUT the standard deviation stays the same
Multiply/divide every value of the distribution will result in the same amount of multiplication/division of mean, media, mode AND standard deviation
Range of distribution
difference between highest and lowest values
Stem-and-leaf plot
Vector
Magnitude of a vector
Adding vectors
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