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MATH 60 Course Overview
Beginning Algebra
176
Mathematics
Undergraduate 1
03/06/2012
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Term
MEDIAN
 Definition
The middle number in a set of ordered numbers
Term
FACTOR (n.)
 Definition
Things that are multiplied together (i.e. In the term 4yz, 4, y, and z are the three factors of the term)
Term
T/F: Division by 0 is okay.
 Definition
FALSE (i.e. 4/0, -6/0)
Term
When subtracting 2 numbers that have the same sign, the answer will be positive always/never/sometimes.
 Definition
Sometimes (i.e. 3-2=+1 but -3-(-2)=-1
Term
T/F: The following terms are NOT like terms.
3xyz, -2.5yzx
 Definition
False, they have the same variables
Term
PER means _____.
 Definition
Divide
Term
PERIMETER
 Definition
The sum of all sides (i.e. the distance around an object or shape)
Term
AREA
 Definition
How much space there is on a surface (i.e. how much space on a wall or on a table)
Term
MEAN
 Definition
The average of a set of numbers.
Term
Calculate the MEAN
 Definition
Add up all numbers in the problem and divide by how many you added together
Term
Calculate the MEDIAN
 Definition
Put the numbers in order and if there's an odd number of numbers, the middle number is the median. Otherwise, take the two numbers that are in the middle and find their mean.
Term
LIKE TERMS
 Definition
Terms that have the EXACT same collection of variables
Term
LCD
 Definition
Least Common Denominator (the LCM of the denominators)
Term
LCM
 Definition
Least Common Multiple
Term
Coefficient
 Definition
The number that is multiplied by a variable (i.e. 3 is the coefficient of 3x)
Term
RECIPROCAL
 Definition
The result of flipping a fraction (i.e. the reciprocal of 2/3 is 3/2)
Term
TERM (MONOMIAL)
 Definition
A collections of numbers and/or variables that are multiplied together (i.e. 3x + 4yz, 3x and 4yz are separate terms)
Term
MONOMIAL
 Definition
A single term (i.e., 3x, 4y, 8qw)
Term
BINOMIAL
 Definition
Two terms (i.e. 4x+7y, -9h+6R)
Term
TRINOMIAL
 Definition
Three terms (i.e. -3D-5J+4, 2x+3y+6L)
Term
T/F: 0 divided by anything is 0.
 Definition
TRUE (i.e. 0/3, 0/(-8))
Term
When dividing by a fraction you must ________.
 Definition
First flip the second fraction (get its reciprocal) and then change the division to multiplication.
Term
ORDER OF OPERATIONS
 Definition
PEMDAS
Parentheses
Exponents
Multiplications & Divisions
Additions & Subtractions
Term
In simplifying an expression, you always do it from ______ to ______.
 Definition
Left, Right
Term
EXPRESSION
 Definition
Something WITHOUT an equal sign
Term
EQUATION
 Definition
Something WITH an equal sign
Term
When multiplying 2 numbers that have the same sign (both positive OR both negative) the answer will be _______.
 Definition
Positive
Term
When multiplying 2 numbers that have different signs (one positive and one negative) the answer will be _______.
 Definition
Negative
Term
When dividing 2 numbers that have the same sign (both positive OR both negative) the answer will be _______.
 Definition
Positive
Term
When dividing 2 numbers that have different signs (one positive and one negative) the answer will be _______.
 Definition
Negative
Term
When adding 2 numbers that have the same sign, the answer will be positive always/never/sometimes.
 Definition
Sometimes (i.e.3+6=+9 but -3+(-6)=-9)
Term
T/F: -9+(-5)=-4
 Definition
False, the answer is -14
Term
T/F: -13-28=15 or -15
 Definition
False, the answer is -41
Term
T/F: The square root of -16 has no real number solution
 Definition
True, negative numbers do not have real number square roots
Term
How many terms are in the expression?
-2x+3y-4xyz
 Definition
3, Remember that addition and subtraction separate terms.
Term
NUMERATOR
 Definition
The top of a fraction
Term
DENOMINATOR
 Definition
The bottom of a fraction
Term
Before you cancel a factor out of the top and the bottom of an algebraic expression, you must first be able to _________.
 Definition
FACTOR out of the top and the bottom whatever it is you wish to cancel.
Term
When dividing by a fraction you must _________ the ________ fraction.
 Definition
Flip (get the reciprocal), Second
Term
The only time you can cancel a factor between a pair of fractions is when the two fractions are being ___________.
 Definition
Multiplied
Term
DEGREE OF A TERM (Monomial)
 Definition
The sum of the exponents on the variables (i.e. -4xyz has degree 3, 15xQ^5 has degree 6)
Term
DEGREE OF A POLYNOMIAL
 Definition
Find the degree of each term and whichever one is the biggest is the degree of the entire polynomial.
Term
When you add or subtract, you must have _________.
 Definition
Like Terms
Term
When you add or subtract fractions, you must have ___________.
 Definition
Common denominators AND like terms
Term
T/F: The sign in front of a number (just to the left of it) stays with that number.
 Definition
True
Term
PRIME NUMBER
 Definition
A number that can only be divided by 1 and itself.
Term
COMPOSITE NUMBER
 Definition
A number that can be divided by at least 1 other integer besides 1 and itself
Term
INTEGER
 Definition
A number in the following set:
...,-3,-2,-1,0,1,2,3,...
Term
GCF
 Definition
Greatest Common Factor
Term
GREATEST COMMON FACTOR
 Definition
The largest integer that divides into both numbers (i.e. The GCF of 16 and 24 is 8)
Term
LEAST COMMON MULTIPLE
 Definition
The smallest integer that both numbers divide into (i.e. The LCM of 6 and 16 is 32)
Term
VOLUME
 Definition
How much room there is inside of something (i.e. inside a box or a freezer)
Term
When plugging a number into an expression, it's a good idea to put ________ around the number.
 Definition
Parentheses
Term
LINEAR EXPRESSION
 Definition
An expression whose highest power of x is 1
Term
"Twenty less than a number" translates into___________.
 Definition
x-20 (NOTE: The answer is NOT 20-x)
Term
COMPLIMENTARY ANGLES
 Definition
Angles that add up to 90 degrees
Term
SUPPLEMENTARY ANGLES
 Definition
Angles that add up to 180 degrees
Term
The angles of a triangle always add up to _______.
 Definition
180 degrees
Term
When doing operations on mixed numbers it is a good idea to first _________.
 Definition
Convert all mixed numbers to improper fractions
Term
T/F: When evaluating the square root of a fraction you MUST first rewrite the problem as the square root of the numerator divided by the square root of the denominator.
 Definition
False, you can do that but you don't have to
Term
ORIGIN
 Definition
Where the x-axis and y-axis intersect
Term
The coordinates of the origin are _____.
 Definition
(0,0)
Term
FUNCTION
 Definition
A rule wherein x-values are NOT repeated (used more than once)
Term
DOMAIN
 Definition
All the numbers that when plugged into a function for x, yield an answer
Term
RANGE
 Definition
All the y-values that a function uses
Term
X-INTERCEPT
 Definition
Where the graph of a function intersects (touches) the x-axis.
Term
To find the x-intercept of a function you must _________.
 Definition
set y = 0 and then solve
Term
Y-INTERCEPT
 Definition
Where the graph of a function intersects (touches) the y-axis.
Term
To find the y-intercept of a function you must _________.
 Definition
set x = 0 and then solve
Term
Why do I set x=0 to find the y-intercept of a function?
 Definition
Because y-intercepts are on the y-axis and every point on the y-axis has an x-coordinate = 0
Term
Why do I set y=0 to find the x-intercepts of a function?
 Definition
Because x-intercepts are on the x-axis and every point on the x-axis has a y-coordinate = 0
Term
ACUTE ANGLE
 Definition
Angle that is less than 90 degrees
Term
OBTUSE ANGLE
 Definition
Angle that is more than 90 degrees
Term
RIGHT ANGLE
 Definition
A 90 degree angle (i.e. like the angle formed where the wall and the floor meet)
Term
POINT
 Definition
A single dot on a graph
Term
LINE
 Definition
A straight, one-dimensional figure extending forever in BOTH directions
Term
RAY
 Definition
A straight, one-dimensional figure extending forever in one direction from a single point; in other words, half a line
Term
PLANE
 Definition
A flat, two-dimensional surface extending forever in all dimensions (kind of like a super-huge piece of paper that goes on forever)
Term
PARALLEL LINES
 Definition
Lines that never touch
Term
CONGRUENT ANGLES
 Definition
Angles that have the same measure (are equal)
Term
PERPENDICULAR LINES
 Definition
Lines that meet at a right angle (like the crossbeams of a standard kite)
Term
RIGHT TRIANGLE
 Definition
A triangle with ONE right angle
Term
ACUTE TRIANGLE
 Definition
A triangle with THREE acute angles
Term
OBTUSE TRIANGLE
 Definition
A triangle with ONE obtuse angle
Term
EQUILATERAL TRIANGLE
 Definition
A triangle with all sides equal and all angles equal (in this case the angles will all be 60 degrees)
Term
On the coordinate plane, the first quadrant is found in the ________corner.
 Definition
Upper Right
Term
On the coordinate plane, the second quadrant is found in the ________corner.
 Definition
Upper Left
Term
On the coordinate plane, the third quadrant is found in the ________corner.
 Definition
Lower Left
Term
On the coordinate plane, the fourth quadrant is found in the ________corner.
 Definition
Lower right
Term
When converting a fraction to a decimal, divide the _______ by the ________.
 Definition
Numerator, Denominator
Term
To compare fractions to see which one is bigger you can either _______ or _______.
 Definition
Get common denominators, Convert both fractions to decimals
Term
To change a percent to a decimal, you must move the decimal point ______.
 Definition
To the left 2 places
Term
To change a decimal to a percent, you must move the decimal point ______.
 Definition
To the right 2 places
Term
To enter a function into the calculator you must press the button labeled _____.
 Definition
Y=
Term
(3,0) is a ___-intercept.
 Definition
X
Term
(-7,0) is a ___-intercept
 Definition
X
Term
(0,5) is a ___-intercept
 Definition
Y
Term
(0,-8) is a ___-intercept
 Definition
Y
Term
For a linear equation, when Y is by itself, we say that the equation is in __________ form.
 Definition
Slope-intercept
Term
For a linear equation, when Y is by itself, we say that the equation is in __________ form.
 Definition
Slope-intercept
Term
In a linear equation, when Y is by itself, the slope is ALWAYS the number _________ by x.
 Definition
Multiplied
Term
In a linear equation, when Y is by itself, the Y-intercept is ALWAYS the number _________ to x.
 Definition
Added
Term
A handy way to remember slope is _______ over _______.
 Definition
Rise, Run
Term
When we say "slope is rise over run" the 'rise' means the difference in the __________ from one point to another.
 Definition
Y-values
Term
When we say "slope is rise over run" the 'run' means the difference in the __________ from one point to another.
 Definition
X-Values
Term
T/F: In the expression -7-9, the two negatives can both be changed to positives.
 Definition
False, in order to be able to change them both to positives, they have to be right next to each other.
Term
T/F: In the expression -(-9), the two negatives can both be changed to positives.
 Definition
True
Term
T/F: If a fraction is negative, it doesn't matter if the negative is applied to the NUMERATOR or the DENOMINATOR or in front of the fraction.
 Definition
True
Term
INPUT
 Definition
What you plug into a function for x
Term
OUTPUT
 Definition
The result after you plug in a number for x into a function
Term
X-AXIS
 Definition
The horizontal axis of a graph
Term
Y-AXIS
 Definition
The vertical axis of a graph
Term
T/F: Addition is commutative
 Definition
TRUE (i.e. 3+2=2+3)
Term
T/F: Subtraction is commutative
 Definition
False (i.e. 2-3 does not equal 3-2)
Term
T/F: Multiplication is commutative
 Definition
True (i.e. 3*2=2*3)
Term
T/F: Division is commutative
 Definition
False (i.e. 2/3 does not equal 3/2)
Term
If a variable does not appear to be multiplied by a number, then its coefficient is ____.
 Definition
1
Term
When multiplying 2 things together, you may add their exponents only when _________.
 Definition
The bases of the exponents are the same (i.e. x^2*x^3=x^5)
Term
The only time you ever multiply 2 exponents by each other is when ______.
 Definition
One exponent is raised to the power of another (i.e. (x^2)^3=x^6)
Term
Cubic inches are used for measuring ________.
 Definition
Volume
Term
Cubic feet are used for measuring ________.
 Definition
Volume
Term
Cubic meters are used for measuring ________.
 Definition
Volume
Term
Square inches are used for measuring ________.
 Definition
Area
Term
Square feet are used for measuring ________.
 Definition
Area
Term
Square meters are used for measuring ________.
 Definition
Area
Term
Another way to write 3
 Definition
(3,7)
Term
Another way to write -4<=x<9 is____.
 Definition
[-4,9)
Term
Another way to write x>8 is ______.
 Definition
(8,infinity)
Term
If the equation for renting a jackhammer is y=35x+50, the 50 probably means ________.
 Definition
The initial rental fee (up front).
Term
If the equation for renting a jackhammer is y=35x+50, the 35 probably means ________.
 Definition
The hourly cost
Term
If an equation begins as:
3x-11=7
and changes to become:
3x=18,
what happened?
 Definition
Eleven was added to both sides
Term
After solving an equation for the given variable, a way to check your work is to ____________.
 Definition
Plug your solution into the ORIGINAL problem for the variable and make sure both sides of the equation are equal.
Term
If you have a function f(x)=3x-7, then f(5) means _______.
 Definition
The y-value that is paired up with the x-value, 5.
Term
If you have a function g(x)=8-6x, then g(-3) means _______.
 Definition
The y-value that is paired up with the x-value, -3.
Term
On the TI calculator, to access the graph press _______.
 Definition
Graph
Term
On the TI calculator, to access the table press _______.
 Definition
Second and then Graph
Term
On the TI calculator, to access the table setup screen, press _______.
 Definition
Second and then Window
Term
On the Table Setup screen on the TI calculator, the first number tells you _______.
 Definition
What will be the first x-value displayed on your Table
Term
On the Table Setup screen on the TI calculator, the second number tells you _______.
 Definition
What your x-values will increase by on the Table
Term
The best way to solve 3x-8=4 is to first move the ____ to the other side of the equation then move the _____.
 Definition
8, 3
Term
When you see the phrase "in terms of", the variable that comes directly before the phrase is the ________ variable.
 Definition
Dependent
Term
When you see the phrase "in terms of", the variable that comes directly after the phrase is the ________ variable.
 Definition
Independent
Term
To solve the equation:
PV=nRT for the variable R, you would need to ________ both sides of the equation by _____.
 Definition
Divide, nT
Term
To solve the equation:
A=3r^2
for the variable r, you would need to ________ both sides of the equation by _____ and then ______ of both sides.
 Definition
Divide, 3, take the square root
Term
If a relation passes the Vertical Line Test, ________.
 Definition
It is a function
Term
If a relation doesn't pass the Vertical Line Test, ________.
 Definition
It is not a function
Term
If a relation uses a value for x more than once, ________.
 Definition
It is not a function
Term
If a relation uses a value for y more than once, it ____ a function.
 Definition
May or may not be a function (how often the y-values get uses has no bearing on whether or not it is a function-only if you use an x-value more than once)
Term
T/F: The relation
(1,6),(2,6),(3,6),(4,6)
is a function.
 Definition
True
Term
T/F: The relation
(6,1),(6,2),(6,3),(6,4)
is a function.
 Definition
False
Term
Like a book, graphs are read from _____ to _____.
 Definition
Left, Right
Term
If the graph of a line goes down, from left to right, it has a ____ slope.
 Definition
Negative
Term
If the graph of a line goes up, from left to right, it has a ____ slope.
 Definition
Positive
Term
If the graph of a line is flat (horizontal), from left to right, it has a ____ slope.
 Definition
0
Term
X-intercepts of functions are found by setting ____ equal to _____ and then solving.
 Definition
Y,0
Term
Y-intercepts of functions are found by setting ____ equal to _____ and then solving.
 Definition
X,0
Term
When the equation of a line is in slope-intercept form, the number multiplied by X is the ____.
 Definition
Slope
Term
When the equation of a line is in slope-intercept form, the number added to X is the ____.
 Definition
Y-intercept
Term
Slope is represented by the variable ____.
 Definition
M
Term
Y-intercepts are represented by the variable ___.
 Definition
B
Term
When the equation of a line is in slope-intercept form, _______.
 Definition
Y is by itself/isolated.
Term
The slope of the equation y=3x-9 is ____.
 Definition
3
Term
The y-intercept of the equation y=3x-9 is ____.
 Definition
-9
Term
The slope of the equation y=3-9x is ____.
 Definition
-9
Term
The y-intercept of the equation y=3-9x is ____.
 Definition
3
Term
Two lines are parallel if their slopes are _____ AND if their y-intercepts are _____.
 Definition
Equal, Different
Term
Two lines are perpendicular if their slopes _____.
 Definition
Multiply to -1
Term
If the y-intercept of a line is -4 and the slope of the line is 6, the equation of the line is _____.
 Definition
y=6x-4 OR y=-4+6x
Term
For the equation y=4x+10, the slope can be written as a fraction. In that case it would be _____.
 Definition
4/1
Term
A 'proportion' is ________.
 Definition
A single fraction equal to a single fraction (i.e. 3/x = 2/5)
Term
There are _____ centimeters in a meter.
 Definition
100
Term
There are _____ meters in a kilometer.
 Definition
1000
Term
There are _____ millimeters in a centimeter.
 Definition
10
Term
There are about _____ centimeters in an inch.
 Definition
2.5
Term
T/F: Similar triangles have angles that are the same size.
 Definition
True
Term
T/F: Similar triangles have sides that are the same lengths.
 Definition
False, (rather they are proportional to each other)
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