MATH 1 EOC REVIEW NC
Simplifying Radicals
Factor Tree List numbers under radical and circle in pairs.
Box and Whisker Plot
Find the 5 Number Summary needed to draw it with the calculator. Then put it above a number line.
What are some ways to solve a system?
Graphing, Substitution, and Elimination
When will a system have no solution?
Parallel lines
Exponent rule for dividing monomials
Subtract (big-small) and the answer goes where the bigger # is.
Midpoint formula
The point in the middle of a line segment
In the equation y=mx+b, what does "b" represent?
b= y-intercept
In the equation y=mx+b, what does "m" represent?
m=slope
What is the slope-intercept form of a line?
y=mx+b
Exponential Growth or Decay Formula for Word Problems
% increasing or decreasing b is the % KEPT Add or Subtract from 100 and change to a decimal
Factor the Difference of Squares
( + ) ( - )
What is the slope of a horizontal line?
0
Any (nonzero) number to the zero power is equal to what?
1
Standard Deviation (what does it mean?)
2/3 of data or 67% of data is under the mountain
How do you clear the memory on the graphing calculator?
2nd, +, 7, 1, 2
Definition of a function
A relation where each x is paired with exactly one y
Systems of Equations - Elimination Method
Add or Subtract the 2 equations so that one of the variables "disappears"
Translations - horizontal shift
Adding a positive # inside ( ) to the x, moves graph to the right or left
Translations-vertical shifts
Adding positive # on the end moves graph up adding negative number moves graph down
Line of best fit
Also called "regression line", "linear model", "prediction equation", or "trend line". Use calculator to find STAT, edit, input L1 and L2, Stat, -> CALC, #4 LinReg
What should the answer to a system look like?
An ordered pair (intersection point)
Definition of a relation
Any set of ordered pairs
What must you do if you multiply or divide both sides of an inequality by a negative number?
Change the inequality sign
Causation (Does the change in one variable CAUSE the change in the other or is there another reason?)
Did increased heat CAUSE the ice cream sales to increase or the crime rate to increase?
Domain of a relation
Domain: the x coordinates, input values, independent variables, on x axis
How do you find the line of best fit on a graph and from a table?
Graph-draw a line that goes through as much data as possible and splits any remaining data evenly. Table (using a graphing calculator)-STAT, enter the ordered pairs, STAT, right arrow (CALC), 4 (LinReg), Enter
Perpendicular lines & slope
Have opposite reciprocal slopes (flipped and sign changed) Ex. 3/2--> -2/3
Parallel lines and slope
Have the same or equal slopes
Quadratic equation
Highest power is 2 a, b, c are numbers
"Golden Rule" when solving Inequalities
If you multiply or divide both sides on inequality by a NEGATIVE number, FLIP the inequality sign around!!
What's the short cut for recognizing a function in ordered pair form?
If you notice that there is an x value repeated with a different answer for the y value
Correlation (Strong vs. Weak and Pos. vs. Neg.)
Imagine a line going through the dots~ pos slope or neg slope
What is the rule of multiplying two powers with the same base?
Keep the base, add the exponents
What is the rule of dividing two powers with the same base?
Keep the base, subtract the exponents
What kind of graph will y=mx+b create?
Linear Graph
Negatively Skewed
Long tail on the left
Positively Skewed
Long tail on the right
What should be the first step when you factor?
Look for a GCF
Average Rate of Change
Means SLOPE. The "m" in front of x Change in y divided by change in x
Q1
Middle number between Median and lowest number in data set
Q3
Middle number between median and largest number in Data set
Normal Distribution
Mound of data in the middle High in the middle, even on each side
NOW-NEXT (exponential)
Now = start number Next =NOW *_____
Pythagorean Theorem
Only use for Right Triangles * c is the hypotenuse
What is true about the slopes of parallel lines? Their y-intercepts?
Parallel lines have the same slopes, but different y-intercepts
Exponent rule for power raised to a power (1 base with 2 powers)
Power is outside a parenthesis
Calculator Steps for Finding Basic Stats
STAT, enter #s into L1, STAT ->Calc, choose #1 (1-Vars), ENTER
If given two points, how do you use your calculator to get the equation?
STAT, enter the ordered pairs, STAT, right arrow (CALC), 4 (LinReg), Enter
How do you find the x and y-intercepts of an equation?
Substitute 0 for y and solve for x. Substitute 0 for x and solve for y
If you are given a point and a slope, explain how to find the equation.
Substitute the x, y, and m and solve for b. Write the equation using m and b
Ways to Solve Systems of Equations
Substitution or Elimination or Graphing
"multiplying by the same amount" means...
The equation is an EXPONENTIAL function
To graph data on calc.
To enter data: STAT, edit, input#s, ENTER To make scatterplot: turn on Plot 1, graph, ZOOM 9
How many solutions should x²=16 have?
Two (4 and -4)
What is the slope of a vertical line?
Undefined
No Solution vs. Infinitely Many Solutions (all real #'s)
When solving if all variables disappear, "No Solution": when 5=21 "Infinitely Many Solutions": when 5=5
x-intercepts
X intercept: (#, 0) let y = 0, then solve for x
y-intercepts
Y intercept: (0. #) let x = 0, then solve for y
What is the slope formula?
Y2-Y1/X2-X1
What keys do you press on your graphing calculator to solve a system?
Y=, enter equations, 2nd TRACE (Calc), 5 (intersection), ENTER, ENTER, ENTER. If graph does not show intersection point, adjust the window
Find the slope from a table of values
change in Y divided by change in X
Graphing a line
solve for y first b = starting point on y axis m= rise/run
Quadratics in flight
vertex = maximum height x-intercept = when it hits the ground or how long it was in the air y-intercept = starting height
What is the standard form of an exponential equation?
y=ab^x
What is the standard form of a quadratic equation?
y=ax^2+bx+c
What is the difference between an arithmetic and geometric sequence?
Arithmetic sequences add the same number each time, and geometric multiplies by the same number each time
How do you use the vertical line test to tell if a graph is a function?
As the vertical line passes over the graph, the vertical line can only intersect the graph one time
What is the standard form of a line?
Ax+By=C
y=mx+b
Equation for a line: m= slope and b= y-intercept
Exponential DECAY graphs
Exponential decay graphs curve down
Exponential GROWTH graph
Exponential growth graphs curve up
Factoring a quadratic (the first step is . . .)
Find the GCF GCF ("leftovers")
How do you tell if a parabola opens up/down?
If "a" is positive: opens up. If "a" is negative: opens down.
How will you know if its growth or decay from looking at the equation? Graph?
In equation form: if b is greater than one, it is growth. If b is less than one and greater than zero, it is decay. In graph form: The graph of growth will increase from left to right ( a plane taking off). For decay, the graph decreases from left to right (a plane landing).
What is the rule for taking a power to a power?
Keep the base, multiply the exponents
5 Number summary
Lowest Number, Q1, Median, Q2, Largest number
What is the rule for changing a negative exponent into a positive?
Move it to the opposite location (numerator/denominator) of the fraction bar and make the exponent positive
Exponent rule for negative exponents
Moves the term and changes the sign of the exponent. If it's in the top, it goes to the bottom. If it's in the bottom, it goes to the top.
How to eliminate fractions in equations
Multiply the ENTIRE equation (every term) by the common denominator
Solve by factoring
Must = 0 first, then factor and set each ( ) = to zero and solve
NOW-NEXT (linear situation)
Now = start number Next = NOW (+ or -) ____
Graphing Inequalities
Pay attention to whether there is a solid line or dotted line Find the intercepts Test (0,0) to determine TRUE Side
What is true about the slopes of perpendicular lines? Their y-intercepts?
Perpendicular lines have slopes that are both opposite and reciprocal and can have the same or different y-intercepts
Systems of Equations - Substitution Method
Put one equation into the other equations. Works best when one equations starts with a "y=" or "x="
IQR (Interquartile range)
Q1 - Q3
Range of a relation
Range: the y coordinates, output values, dependent variable, on the y axis
Slope is the ratio of ____ over ___
Rise, Run
Function Notation What does f(x) mean?
Same as Y Just plug in the number into x and simplify
"zeros of the function"
Same as x- intercepts, roots, solutions to equations
When will a system have infinitely many solutions?
Same line (coinciding lines)
Correlation Coefficient
The closer "r" is to 1, the better the fit. In Calc - go to catalog, turn Diagnostics on, then do LinReg.
What is a correlation coefficient and what does it tell you about the scatter plot/ line of best fit?
The correlation coefficient is "r," and it tells you how closely your data fits the line of best fit. The r values range between -1 through +1.
"adding or subtracting by the same amount" means...
The equation is an LINEAR function
When the problem says "Consecutive integers"...
Use X, X+1, X+2, X+3..
When the problem says "Consecutive Even or Odd integers" ...
Use X, X+2, X+4, X+6 ...
How do you find the vertex point of a parabola?
Use formula to find the x, then plug the x into the original equation to find the y.
Exponent rule for multiplying monomials (2 of the same base - what do the exponents do?)
When bases are the same, add exponents
When is it best to use your graphing calculator to solve a system?
When both equations are in slope-intercept form
Form of Exponential Equation
a= starting number b= rate x= time y=ending amount
