Algebra 1 EOC Review
How many solutions can a system with 2 equations have?
1) no solutions, if the lines are parallel and have the same slope. 2) one solution, if the lines intersect at one point. 3) infinite many solutions, if the two equations are the same and touch each other everywhere.
What is a system of equations or system of inequalities?
2 or more equations or inequalities graphed on the same coordinate plane
Correlation Coefficient
A number between -1 and 1 that tells you if you have a strong or weak correlation. It also lets you know if it is a positive or negative correlation.
arithmetic sequence
A sequence in which the difference between any two consecutive terms is the same.
geometric sequence
A sequence that can be generated by a multiplier
Table
A way to represent ordered pairs.
Compound Interest Formula
A=(P+r/n)^nt Common n values are 12=monthly, 4=quarterly, 2=semiannually, 1=annually. t is the time in years.
Mean (Average)
Add up all the data points, then divide by however many data points there were. Ex. 3,6,9 3+6+9= 18 /3 = 6
When do you flip an inequality symbol?
Anytime you multiply or divide by a negative number.
Mapping
Bubbles that represent the x-values and the y-values.
End Behavior
Describes what is happening to the graph overall as the x-values change. As the x-values decrease, does the graph seem to go up or down? As the x-vales increase, does the graph seem to increase or decrease? This represents the end behavior as being positive or negative.
How to solve when written in function notation.
Ex: f(x) = 3x + 4, solve for f(-2). All you do is replace the x with a (-2) and solve. 3(-2) +4 = -2
Solid or Dotted Line? Open or Closed Circle?
If it has the line under it (or equal to) it will be a closed circle or solid line.
SUBSTITUTION
If you know what one variable equals, like y=35-10x, then you can plug that value in for y in the second equation, 4x - 7y = -23 becomes 4x -7(35-10x)=-23. Distribute and solve for x. Then you can plug back in to one of the original equations to solve for y.
Quadratic Formula
In standard form, ax^2 + bx + c, where a, b, and c (Just the numbers) can be plugged into the quadratic formula to find the x-intercepts, roots, zeros, or solutions.
Rate of Change
Is another name for slope usually used in word problems.
Completing The Square
Isolate x^2 + bx on one side, move the number to the other side of the equal sign. Take b, divide by 2, then square the result. Add that number to both side. It will then factor into a perfect square.
what is a linear inequality?
It is an equation with a <, >, < or =, > or = in the place of the =.
Maximum or Minimum
Maximum is at the highest point of a parabola. Minimum is the lowest point.
Distributive Property
Multiply a number or variable to everyone inside parenthesis.
Absolute value of a negative number. IxI = -3
NO SOLUTION
variable
NOT A NUMBER. A letter or symbol that stands for a number.
How to solve absolute value inequalities?
Once the absolute value bars are on one side of the equal sign, by itself, you work two separate problems (1) Looks exactly the same as the original equation without the absolute value symbols. (2) Is the same on one side, but flip the inequality symbol and make the number negative.
What is the "rate of change" on a graph?
Slope
How to rearrange variables to solve for a specific variable.
Solve A=P+PRT for T. You perform the opposite operation on each variable until you get the one you are solving for all by itself. Subtract P, then divide by P and R.
Factoring with 4 terms
Solve by grouping. Group two sets and then factor those two groups.
The solution to a system of linear inequalities
The intersection of the two half-planes.
Mode
The number that shows up the MOST
Associative Property
The way numbers are grouped is different, but the result is the same.
y= and f(x)=
These are the same. They can be interchanged with one another. f(x) simply lets you know the equation is a function. Can also be written with other variables like g(x), p(x), etc.
How do the slopes of perdendicular lines compare?
They are opposite and fraction is flipped. Example: lines with the slopes -2 and 1/2 are perpendicular.
How do the slopes of parallel lines compare?
They are the same
Range
When talking about data sets, make sure the numbers are in order from smallest to largest, to find the RANGE you SUBTRACT the smallest from the largest.
Median
When the data is put in order from smallest to largest, it is the number in the middle. If there are two numbers in the middle, you add them together then divide by 2. (You take their average)
Piecewise-defined function Graph
When the graph is doing two (or more) different functions depending on what the x-vales are. EX. If x<-1, then y=1. If x>(or equal to) -1, then y=x^2 -3
Communitive Property
With addition and multiplication, it does not matter what order the numbers are written, you still get the same result.
Absolute Value when solving order of operations problems.
Work any math that you need to within the absolute value bars. Then always give the positive of that number as the answer.
ELIMINATION
You have to get one of the variables to eliminate by getting them to be the same number just one positive and one negative, so they zero out. Sometimes in order to do this you have to multiply one or both of the equations by a number. Then add straight down and continue to solve.
Explain each step in solving an equation.
You may have to list the steps you performed explaining what you did, step by step. Know how to justify your solutions.
coordinate plane
a plane formed by 2 perpendicular lines called axes (the x-axis goes sided to side, the y-axis goes up and down).
vertical line test
a relation is a function and passes the vertical line test if when a vertical line is drawn through the graph, it touches the graph only ONE time.
What is a quadratic equation or function?
an equation of function that has "x-squared" as its highest order exponent.
Where are the solutions of a quadratic function?
at the x-intercepts. They are also known as zeros and roots.
standard form of a quadratic equation
ax² + bx + c = 0
other names for "x"
domain, independent variable, input
Which quantity increases fastest?
exponential functions > quadratic functions > linear functions
If y=f(x) and y=g(x), then.....
f(x) = g(x) meaning you can set the two equations equal to each other in order to solve for the variable. Then to find y you plug the variable back into one of the original equations and solve.
how is slope important for linear equations and lines?
linear equations and lines have CONSTANT slopes. The slope is the SAME all the way up and down the line.
changing the "b" in the slope-intercept form of the equation of a line changes what?
moves the line up or down the y-axis.
other names for "y"
range, dependent variable, output
domain
set of all of the possible x-values. INPUTS
range
set of all the possible y-values. OUTPUTS
relation
set of ordered pairs
in y = mx + b, "m" stands for?
slope
what slope does a HORIZONTAL line have?
slope = 0
function
special relation where each x-value is paired with ONLY ONE y-value. (x-values DO NOT repeat, it passes the vertical line test)
what is the x-intercept?
the point where the graph crosses the x-axis. It has the coordinates (x, 0)
what is the y-intercept?
the point where the graph crosses the y-axis. It has the coordinates (0, y)
slope definition
the steepness of a line, vertical change/horizontal change, (y-y)/(x-x), rise over run
changing the "m" in the slope-intercept form of the equation of a line changes what?
the steepness of the line
ordered pair
the x and y coordinates of a point on the coordinate plane (x,y)
in y = mx + b, "b" stands for?
the y-intercept
what slope does a VERTICAL line have?
undefined slope
What is the SOLUTION of a system of equations?
where the lines touch or cross
axis of symmetry
x=-b/2a
vertex form of a quadratic function
y = a(x-h)^2 + k
slope-intercept form
y = mx + b
what is the linear parent function?
y = x f(x) = x