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