Integers { , 3, 2, 1, 0, 1, 2, 3,} · 2013-05-14 · EOC Review.notebook May 14, 2013 Unit 1 –...

EOC Review.notebook May 14, 2013

Rational and Irrational Numbers

Rational Numbers

Ex. .6767... Ex. .5 .03 a decimal that terminates

a decimal that repeats indefinitely positive and negative whole numbers

Integers ..., 3, 2, 1, 0, 1, 2, 3,...

Whole numbers and their negatives.Not DecimalsNot Fractions

INTEGERS = RATIONAL NUMBERS

5, -8, 9, -25, 0, -12, 2

.6, -.08, 2/5, -1.2, 1/9


Nonterminating (never stops) Nonrepeating decimals (never repeats)

Irrational Numbers

Examples of irrational numbers


Unit 1 – Equaons

• Equaons

To solve an equaon, use your calculator.

STEPS:

1. Menu

2. Algebra (#3)

3. Numerical Solve (#1)

4. Type in equaon

5. Put a comma (,) at the end, and then the variable aerwards


Ex 1: 2x + 5 = 6x – 3

Ex 2: 6(x + 1) = 2/3(9x + 12)

Ex 3: 4x + 10 = 2(2x + 5)

Ex 4:


Solve: cd = f + gh for h


Dimensional Analysis

• Must Know Conversions!!!!

Dimensional Analysis:

Ex 1: The sea horse swims at a rate of 52.68 feet per hour. Use dimensional analysis to convert this speed to inches per minute.


Ex 2: A car is traveling at 50 miles per hour. How many feet per second is the car traveling?

• Inequalies:

o Solve the same as equaons

o If there is a negave with the variable, flip the sign

o Variable must always be on the le, the answer must be on the right

o > and < are open circles on the number line

o ≤ and ≥ are closed circles on the number line

o > and ≥ are to the right on the number line

o < and ≤ are to the le on the number line


Ex 1: y ≤ 4y + 18

Ex 2: 4m – 3 < 2m + 6


Ex 3: 2(k – 3) > 6 + 3k – 3


Relation: Any set of ordered pairsRelations can be represented as the following:

set of ordered pairs tablegraph mapping

(1,2)(2,4)(0,3)

x y 12 0

2 43

12 0

2 43

Function:

• A relation where there is only one x for every y

• the x's cannot repeat!


"x" and "y" coordinates in each ordered pair are switched .**The Domain becomes the Range in the inverse.**

RELATION INVERSE RELATION

Inverse Relation

(2,5)(3,2)(6,7)(5,1)

(5,2)(2,3)(7,6)(1,5)

Example 1:Express the relation (3,2), (-1,4), (0,-3), (-3,4), and (-2,-2)as a table, graph, and a mapping. Tell the domain and range.

x yx y

A. What is the domain of the relaon?

B. What is the range of the relaon?

C. Is the relaon a funcon? Explain your answer.

D. What is the inverse of the relaon as ordered pairs?

E. Is the inverse of the relaon a funcon? Explain your answer.


linear function:

• a function whose graph is linear and a non vertical line

• a table or scenario that has a constant rate of change

• any equation set equal to y that does not have any variables

• raised to a power, does not have any variables in a

• denominator and does not have any variables being multiplied


The xintercept is where the graph crosses the xaxis.

The ycoordinate is always 0.

The yintercept is where the graph crosses the yaxis.

The xcoordinate is always 0.

Try These:

Find the x and y intercepts of the following equations.

ex1. 9x 6y = 18

ex2. 5x + 4y = 15

ex3. 21x + 42y = 63


Definitions of Slope:

1. Constant Rate of Change

2. RISE

3. The increase or decrease of a graph, table, ordered pairs or a situation

4.The change in y's

RUN

The change in x's


Slope – Intercept Form

y = mx + b

m represents the slope (rate of change)

b represents the yintercept

yintercept: Where the graph crosses the

yaxis


Ex 1: What is the equaon 4x + 6y = ‐12 in slope intercept from?

Ex 2: What is the equaon of the line that passes through the point with

coordinates (‐5, 3) and has a slope of


Ex 3: What is the equaon of this line?

Ex 4: Use funcon notaon to represent the funcon shown in this graph:


Ex 5: Which equaon has this graph?

Ex 6: Which is the graph of


Ex 7: Which is the graph of the line that passes through the point with the coordinates of (1, 3) and has a slope of ½?

Point‐Slope Form:

1. What is the equaon for point‐ slope form?__________________________________

2. What two things do you need to write an equaon in point‐slope form?__________________________________


3. Where do you plug in the slope?__________________________________

4. Where do you plug in the point?___________________________________


Parallel Lines: The equations have the same slope; the graphs never intersect

Perpendicular Lines: The equations have slope that are opposite reciprocals; The graphs cross to form a right angle

Example 1: Write an equaon of a line in slope‐intercept form that is parallel to y = ‐3x ‐ 2 and goes through (‐1, ‐2)

Example 2: Write the equaon of a line in slope‐intercept form that is perpendicular to x + 4y = 12 and passes through (0, ‐3)


Example 3: Which of the lines whose equaons are given below is perpendicular to y = 4x + 3?

Scaer Plots:

Steps:

1. Enter your data into the lists and spreadsheets on the home screen of the calculator (looks like excel sheet)

2. Go back to the home screen and open data and stascs (looks like a bar graph)

3. Add your x and y variables

4. Press menu; pick analyze (#4) recession (#6) and y = mx + b (#1)


Translaons:

What affect does slope have on a graph?

m > 1_____________________________________________

0<m<1____________________________________________

m < 0_____________________________________________


Steps:

1. Get rid of outside exponent

2. Move negative exponents

3. Combine like bases and whole numbers

mult by allinside exponents

neg on top→ move to bottomneg on bottom → movet to top

• If variables are on same level, (x 4x5), add exponents• If variables Are on different levels, subtract exponents• If numbers are on same level, multiply them• if numbers are on different levels, divide them


Equation: y = kx

SetUp: y = yx x

Graph:

goes thruthe point(0, 0)

Variables:

When the x's increase, the y's increase

When the x's decrease, the y's decrease

K is the Slope, Rate of change, or the constant of variation

Integers { , 3, 2, 1, 0, 1, 2, 3,} · 2013-05-14 · EOC Review.notebook May 14, 2013 Unit 1 –...

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