Algebra 1 Math Review
x coordinate of vertex
-b/2a
transformation
A movement of a geometric figure
alternate exterior angles
Angles that lay outside the parallel lines and are on opposite sides of the transversal; They are congruent.
mean
Average
area
Length x Width
circumference
The distance around a circle
Power of a Power
multiply the exponents
Closure under multiplication and addition
they produce real numbers
subtract exponents
to divide powers having the same base,
Transforming absolute value inequalities
(expression)<c means -c<expression<c (expression)>c means expression>c or expression<-c
linear function
A function whose graph is a straight line.
constant
A value that does not change
area of a triangle
A=1/2bh
Addition Property of Equality
If x=y, then x+z=y+z
rotation
The action of rotating around an axis or center.
image
after the transformation
Pythagorean Theorem
a²+b²=c²
Parabola
the graph of a quadratic function
remote interior angles
the two nonadjacent interior angles corresponding to each exterior angle of a triangle
slope of a vertical line
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Multiplication Property of -1
-1*x=-x
slope of a horizontal line
0
Converse of the Multiplication Property of Zero
If a product of real numbers equals zero, then one of its factors equals zero. That is, for real numbers n and p, if np =0, then n=0 or p=0
Addition Property of Order
If a<b, then a+c<b+c
Square Root Property of Equality
If a=b, then square root of a= square root of b
mode
Most
volume of cone
V=1/3πr²h
perfect square
a square of a whole number
Associative Axiom for Addition
(x+y)+z=x+(y+z)
Like terms
Expressions that contain the same variables to the same power
negative exponents
For any nonzero number a^-n is the reciprocal of a^n
volume of triangular prism
V=(1/2bh)h
abscissa
x-axis
Associative Axiom for Multiplication
(xy)z=x(yz)
completing the square
1. Take half of the coefficient of X. 2. Square it. 3. add the result.
simple radical form
1. There are no radicals in the denominator 2. The radicand(s) in the numerator are as small as possible
Splitting the middle term
1. multiply a by c 2. Look for two factors of ac whose sum is b 3. split the middle term and factor by grouping (If not factors then it is prime)
Three Major Things Done in Algebra
1. write an expression representing something in the real world 2. find the value of an expression when you know what x equals. 3. find the value of x when you know what the expression equals.
Names for large numbers
10^3= thousand 10^6= million 10^9= billion 10^12= trillion 10^15= quadrillion 10^18= quintillion
Quadrants of Cartesian Grid
2,1,3,4
Product of Conjugate Radical Binomials
=x-y, which is a rational number
Graphs of Quadratic Inequalities
> then outside endpoints (or all of them). If < then the graph is between the endpoints
discriminant test for factorability
A Quadratic trinomial can be factored if and only if the discriminant is a perfect square
negative correlation
A finding that two factors vary systematically in opposite directions, one increasing as the other decreases.
non-linear function
A function whose graph is not a straight line
scatter plot
A graph used to determine whether there is a relationship between paired data
scatter plot
A graph with points plotted to show a possible relationship between two sets of data.
exponent
A mathematical notation indicating the number of times a quantity is multiplied by itself.
slope
A measure of the steepness of a line. Given two points with coordinates (X1,Y1) and (x2,y2) on a line the slope, m, of the line is given m = rise/run= y2-y1/x2-x1
scientific notation
A method of writing or displaying numbers in terms of a decimal number between 1 and 10 multiplied by a power of 10.
composite number
A number greater than 0 that has more than two different factors.
coefficient
A number multiplied by a variable in an algebraic expression.
coefficient
A number multiplied by a variable.
Rational Number
A number that can be written as a fraction
rational number
A number that can be written as a fraction
Irrational Number
A number that cannot be written as a quotient of two integers.
corresponding angles
A pair of angles which are on the same side of the transversal, one must be interior, one must be exterior, and they must be nonadjacent
ordered pair
A pair of numbers that can be used to locate a point on a coordinate plane
ordered pair
A pair of numbers that give the location of a point on a x and y grid. for example graph (3, 2)
Vertex
A point where two or more lines meet.
vertex
A point where two or more straight lines meet.
function
A prewritten formula that makes it easy to perform common calculations
Radical Equation
A radical equation is an equation with a variable under the radical sign.
system of equations
A set of equations with the same variables
inequality
A statement that compares two quantities using <, >, ≤,≥, or ≠
radius
A straight line from the center to the circumference of a circle or sphere.
diameter
A straight line passing from side to side through the center of a circle or sphere.
reflection
A transformation that "flips" a figure over a mirror or reflection line.
translation
A transformation that "slides" each point of a figure the same distance in the same direction.
linear relationship
A type of relationship that exists between two variables whose graphed data points lie on a straight line
area of a rectangle
A=lw
area of a circle
A=pie r squared
Subtraction
Adding a number's opposite
real number
All rational and irrational numbers
Integer
All whole numbers (both positive and negative) and zero.
integer
All whole numbers (both positive and negative) and zero.
obtuse angle
An angle between 90 and 180 degrees
acute angle
An angle that is less than 90 degrees
identity
An equation that is true for all values of the variable.
irrational number
Any real number which cant be expressed as a fraction of two integers
Exponentiation
Arithmetic operator that raises to a power
standard form
Ax+By=C
associative property
Changing the grouping of numbers will NOT change the value. For example: (7 + 4) + 8 = 7 + (4 + 8) also works with multiplication
output
Data that has been processed into a useful format.
input
Data that is to be entered into a worksheet
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Denominator equals zero
quadrants
Four regions into which a coordinate plane is divided by the x-axis and the y-axis
Statistics
Given data resulting from a random experiment, predict something about the real-world situation from which the data comes.
Probability
Given information about something in the real world, predict the results of a random experiment.
congruent
Having the same size and shape
Common factor
If in an expression each term has the same factor.
Multiplication Property of Order
If x<y then xz<yz if z is positive xz>yz if z is negative xz=yz if z is zero
Quotient of two powers with equal bases
If you divide two powers, and they have equal bases, then you can subtract the exponents and use that same base.
pythagorean theorem
In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs
interior angles
Inside angles of two lines intersected by a transversal
Prime
Is a positive integer that has no positive integers as factors other than 1 and itself. The number 1 is not considered to be prime.
Division
Multiplying by its reciprocal, besides zero.
negative exponents
Negative exponents always have to SWITCH positions in their fractions. [If you don't see a fraction, make one by drawing a bar over 1, then switch 3^(-1)=1/3
Probability Equation
Number of favorable outcomes/total number of outcomes= Number of elements in the event space/ number of elements in the sample space
Terms
Numbers that are added to each other or subtracted from each other.
Factors
Numbers that are multiplied together.
Order of Operations
Parentheses, powers, multiply and divide from left to right, and add and subtract from left to right.
negative exponents
Raising a number to a negative exponent is the same as raising the number's reciprocal to the equivalent positive exponent
slope
Rise over run
order of operations
Rules describing what sequence to use in evaluating expressions
slopes of perpendicular lines
Slopes are negative reciprocals or each other
Square Root of a Quotient
Square root distributes over division
Square root of a product
Square root distributes over multiplication.
Power, Base, and Exponent
The base is the number on the bottom, the exponent is the number on top, and together they form a power.
absolute value
The distance a number is from zero on a number line. ALWAYS POSITIVE
perimeter
The distance around a figure
distance formula
The distance d between any two points with coordinates
Domain
The domain of a function is the set of permissible values of the independent variable.
independent variable
The experimental factor that is manipulated; the variable whose effect is being studied.
Characteristic
The factor on the right power of ten
Intersection
The intersection of sets A and B, abbreviated A Upside down U B, is the set of numbers that are in both sets
least common multiple (LCM)
The least number that is a common multiple of two or more numbers.
median
The middle number in the set (if two numbers are in the middle, find the average of the two numbers)
nth root
The number that must be multiplied times itself n times to equal a given value.
dependent variable
The outcome factor; the variable that may change in response to manipulations of the independent variable.
commutative property
The property that says that two or more numbers can be added or multiplied in any order without changing the result.
Range
The range of a function is the set of values of the dependent variable corresponding to all values of the independent variable in the domain.
Sign of a Product
The sign of a product will be: NEGATIVE, if it has an ODD number of negative factors. POSITIVE, if it has an EVEN number of negative factors.
Union
The union of sets A and B, abbreviated A U B, is the set of numbers that are either in set A or in set B
no correlation
There is no relationship between data sets.
Relatively prime
Two numbers are relatively prime if their greatest common factor is 1
Additive Inverses or Opposites
Two numbers whose sum is 0 are additive inverses of one another.
volume of rectangular prism
V=lwh
exterior angles
When the sides of a triangle are extended, the angles that are adjacent to the interior angles.
repeating decimal
a decimal that repeats a digit or group of digits forever
Property
a fact that is true concerning the system.
Event
a favorable outcome of a random experiment
linear function
a function in which the graph of the solutions forms a line
Function
a function is a set of ordered pairs for which there is never more than one value of y for any one given value of x
cluster
a grouping of a number of similar things
transversal
a line that intersects two or more coplanar lines at different points
scientific notation
a method of writing very large (34,200,000) or very small (0.0000029) numbers using powers of 10
rational number
a number that can be expressed as a ratio (fraction) of two integers - terminating and repeating decimals are considered rational
Common multiple
a number that is a multiple of two or more numbers
square root
a number that when multiplied by itself equals a given number
axiom
a property that forms the base of the mathematical system. It is assumed to be true without proof.
System of Equations
a set of equations with the same variables
Linear Function
a set of ordered pairs that are related by an equation of the form
Pythagorean theorem
a squared+ b squared= c squared
radical sign
a symbol to indicate the square root
dilation
a transformation created proportionally by enlarging or reducing a figure ( multiply x and y by scale factor)
the sign above the radical sign
a viniculum
distributive property
a(b + c) = ab + ac
Random Experiment
an action in which there is no way to tell beforehand just which of several possible things will happen
linear regression
an algorithm to find a precise line of fit for a set of data
fractional equation
an equation in which a variable occurs in a denominator
conditional equation
an equation that has one or more answers that may or may not satisfy the equation
linear equation
an equation whose graph is a straight line
Open Sentence
an equation with one or more variables
Solution of a system
an ordered pair that satisfies all equations in the system
alternate interior angles
angles are on opposite sides of the transversal and on the inside of the given lines
zero exponent
any nonzero number raised to the zero power is 1
Pythagorean theorem
a²+b²=c²
The Discriminant
b squared minus 4ac
pre-image
before the transformation
conjugate binomials
binomials that are the same except for the sign between the terms
run
change in x
rise
change in y
expressions
consist of numbers, variables and operations
identity property
describes the results of adding the number zero to another number or multiplying a number by one - the results are identical
Fundamental Theorem of Arithmetic
each positive integer has exactly one set of prime factors
Outcomes
equally likely results of a random experiment
Power of a Quotient
exponentiation distributes over division
Power of a Product
exponentiation distributes over multiplication.
First step in factoring
factor the GCF of the terms from the polynomial
slopes of parallel lines
have to have same slope
Square root Property of order
if a>b then the square of a > than the square of b
Transitive Axiom of Equality
if x=y and y=z then x=z
Symmetric Axiom of Equality
if x=y then y=x
Multiplication Property of Equality
if x=y, then xz=yz
equations of a horizontal and vertical lines
if y is constant, the graph is a horizontal line. If x is constant, than the graph is a vertical line.
Cross multiplication
in a proportion, the product of the means equals the product of the extremes. a:b= d:c then ad=bc
Polynomial
is an expression that has no operation other than addition, subtraction, and multiplication by or of the variable (s).
regression line
line of best fit
parallel lines
lines in the same plane that never intersect
Polynomials with one, two, or three terms
monomial, binomial, and trinomial
add exponents
multiplying powers with the same base
Exponent Property of the nth root
n over the square root x= x and one nth
consecutive
numbers that follow one after the other in a sequence (1, 2, 3...x, x+1, X+2)
legs
sides that are adjacent to the right angle
180 degree rotation
switch sign of x and y to the opposite sign.
90 degree rotation
switch x and y location and use sign (-, +) to the quadrant the point will be after rotation.
radical
taking the square root of a number
Degree
the degree of a polynomial with one variable is the exponent of the highest power of that variable. Linear, Quadratic, and Cubic.
difference of two squares
the factors of a difference of two square are conjugate binomials.
least common denominator
the least common multiple of two or more denominators
hypotenuse
the longest side of a right triangle
line of best fit
the most accurate trend line on a scatter plot showing the relationship between two sets of data
significant digits
the number of significant digits is the number in the mantissa. The answer is put with the number with the least amount of significant digits.
Numerical Coefficient
the number that stands before a variable
radicand
the number you're taking the square root of
Mantissa
the power on the left side of the decimal point after the first number other than zero in an exponent
rational algebraic expression
the quotient of two polynomials
scale factor
the ratio used to enlarge or reduce similar figures
positive correlation
the relationship between two sets of data in which both sets of data increase together.
direct of variation
the relationship of two variables if there is a nonzero number
event space
the set of all favorable outcomes for an event
Sample Space
the set of all possible outcomes for a random experiment.
Real numbers
the set of all rational and irrational numbers
radical symbol
the symbol used to denote a root
Factoring by grouping
the use of the distributive property to factor some polynomials having four or more terms
volume of sphere
the volume of a sphere equals four thirds times pies times r to the third power
Canceling
to divide the numerator and denominator by the same common factor.
Multiplication property of fractions
to multiply two fractions, multiply their numerators and multiply their denominators
average speed equation
total distance/total time
system of linear equations
two or more linear equations.
nonlinear relationship
whenever one quantity is plotted with another and the resulting graph is NOT a straight line.
x intercept
where the graph crosses the x-axis
y-intercept
where the line crosses the y axis
Multiplicative Identity Axiom
x * 1 = x
Multiplicative Inverses Axiom
x * 1/x = 1
Additive Inverses Axiom
x + (-x) = 0
Factor Theorem
x -n is a factor of a polynomial if and only if the polynomial equals to 0 when n is substituted for x
Quadratic Formula
x equals the opposite of b plus or minus the square root of b square minus four a c all divided by 2a
Between and inclusive
x is between means: a<x<b x is between, inclusive means: a<(with line)x<(with line) b
Distributive axiom for multiplication over addition
x(y+z) = xy+ xz
Multiplication Property of Zero
x*0=0
Additive Identity Axiom
x+0=x
Commutative axiom for addition
x+y=y+x
Special Cases of fractions
x-5/5-x=-1, x+5/x+5=1, and nothing is special about conjugate numbers
multiplication identity axiom
x.1=x
Reflexive Axiom of Equality
x=x
Commutative axiom for multiplication
xy=yx
Ordinate
y-axis
ordinate
y-axis
point-slope form
y-y1 = m(x-x1)
Point slope form of a linear equation
y-y1=m(x-x1)
point slope form
y-y1=m(x-x1)
Quadratic Function
y=axsquared+ bx+ c
Inverse Variation Function
y=k/x
Direct Variation Function
y=kx
General Equation vs. Particular equation
y=kx or y=k/x is a general equation and y=3x or y=24/x is a particular equation
slope intercept form of an equation
y=mx + b (m is the slope, b is the y intercept point)
regression equation
y=mx+b
slope-intercept form
y=mx+b
product of two powers with equal bases
you can add the exponents
