OAE: Middle Level Mathematics
Univariate Data
"One variable"; one type of data
Bivariate Data
"Two variable"; two types of data
Linear Equations
An equation that can be written in standard form.
Statistics
An estimate computed from a sample. Ex: The % of patients in a sample of 200 adults who are relieved by Pepcid Ac.
Divisibility Rules for 1
Any integer (not a fraction).
Acute Angles
Less than 90 degrees
Irrational Numbers
Numbers that do not have a predictable ending. Ex: pi
Whole Numbers
Numbers without fractions; an integer.
Function
For each value of x, there is exactly one y value. -Two x's can have the same y -Two y's CANNOT have the same x
Neither Even nor Odd Function
The pictures of the graphs do not match whether it's folded over the x-axis or y-axis.
Natural Numbers
The positive integers (whole numbers). Ex: 1, 2, 3....... sometimes 0
Solution Sets
The set of all solutions to an equation.
Least Common Multiples
The smallest number that is a multiple of 2 or more numbers. Ex: 3: 3, 6, 9, 12 4: 4, 8, 12 LCM: 12
Distributive Property
The sum of 2 numbers times a third number is equal to the sum of each addend times the third number.
Divisibility Rules for 3
The sum of the digits is divisible by 3. Ex. 381 (3+8+1= 12)
Divisibility Rules for 9
The sum of the digits is divisible by 9. Ex: 1629 (1+6+2+9= 18, 18/9= 2)
Closure
The sum, difference, product, or quotient of any 2 real numbers is also a real number.
Bias
The tendency of a measurement process to over- or under- estimate the value of a population parameter.
Central Tendency
mean, median, and mode
Transcendental Numbers
pi
Domain
x values in an ordered pair: independent variables; inputs.
Range
y values in an ordered pair; dependent variables; outputs.
Direct Variation
y varies directly as x; y is directly proportional to x.} y=kx
Inverse Variation
y varies inversely as x. y is inversely proportional to x.} y=k/x
Spread
1) Q(1) and Q(3) 2) Standard Deviation 3) Variance
Straight Angles
180 degrees
Right Angles
90 degrees
Ratio
A comparison of one thing to another.
Plane
A flat, two-dimensional surface that extends infinitely far.
Secant Line
A line drawn through two points on a curve.
Line
A line of points that extends infinitely in two directions.
Point
A location in geometry.
Parameter
A number that describes the population; a characteristic of a population. Ex: The % of all people who believe in capital punishment.
Polygon
A plane figure with at least 3 straight sides and angles.
Relations
A set of ordered pairs.
Sample
A subset of the population.
Scatterplot
A visual representation of a set of points.
Mixed Number
A whole number and a proper fraction.
Divisibility Rules for 11
Add and subtract digits in an alternating pattern (add, then subtract). Check if the number is divisible by 11. Ex: 1364 (+1-3+6-4= 0) 3729 (+3-7+2-9= -11)
Identity Elements
Addition- 0 Multiplication- 1
Standard Form
Ax+By=C
Terminating Decimals
Decimals that do not go on forever.
Other Decimals
Decimals that go on forever and do not repeat.
Repeating Decimals
Decimals that goes on forever, but can be predicted.
Divisibility Rules for 7
Double the last digit and subtract it from the rest of the number. The result must be divisible by 7. Ex: 672 (2x2 =4, 67-4= 63, 63/7= 3)
Base 5
Counting only using the digits 0, 1, 2, 3.
Base 3
Counting only using the digits 0, 1, 2.
Base 2
Counting only using the digits 0, 1.
Symmetry
Exactly similar parts facing each other or around an axis.
Inverse Functions
Find the inverse of a function by: 1)Interchange x and y and 2) Solve for y
Prime Factorization
Finding which prime numbers multiply together to make the original number.
Reflex Angles
Greater than 180 degrees, but less than 360 degrees
Obtuse Angles
Greater than 90 degrees, but less than 180 degrees
Vertical Line Test
If the line passes through only one point on the graph, then it's a function.
Odd Function
If you fold the graph over the x-axis, the pictures match. f(-x)= -f(x)
Even Function
If you fold the graph over the y-axis, the pictures match. f(-x)= f(x)
Real Numbers
Includes all rational and irrational numbers.
Constant Variation
The value of k.
Integers
Positive and negative numbers without fractions.
Additive Inverse
a+ (-a)= 0
Population
The entire group of individuals that we want to draw conclusions.
Greatest Common Factors
The highest number that divides exactly 2 or more numbers. 1) List the prime factors of each number 2) Multiply those factors that both numbers have in common. Ex: 18: 2x3x3 24: 2x2x2x3 GCF: 2x3= 6
Divisibility Rules for 5
The last digit is 0 or 5.
Divisibility Rules for 2
The last digit is even. Ex. 128
Divisibility Rules for 8
The last three digits must be divisible by 8. Ex: 109816 (816/8= 102)
Divisibility Rules for 4
The last two digits are divisible by 4. Ex: 1312 (12/4 = 3)
Regression Line
The line that models a set of data.
Divisibility Rules for 10
The number ends in 0.
Divisibility Rules for 12
The number is divisible by both 3 and 4. Ex: 648 (6+4+8= 18/3= 6) (48/4= 12)
Divisibility Rules for 6
The number is even and divisible by 3; has to be divisible by 2 and 3. Ex: 114 (even and 1+1+4= 6/3= 2)
Improper Fractions
The numerator is greater than or equal to the denominator.
Proper Fractions
The numerator is less than the denominator.
Congruence
Two geometric figures that have the same shape and size.
Similarity
Two geometric figures that have the same shape, but not the same size.
Commutative Property
When 2 numbers are added or multiplied together, the sum or product is the same no matter the order.
Associative Property
When 3 or more numbers are added or multiplied, the sum or product is the same no matter the grouping of the numbers.
Multiplicative Property
When the product of any number and one is that number.
Place Value
Where the digit is in the number.
Counting Numbers
Whole numbers without the 0.
Rational Numbers
Whole numbers, integers, and any number that ends/has a predicted ending. Ex: 7/8, .21, 0
Expanded Form
Writing the number by showing the value of each of the digits. Ex: 521= 500+20+1
