math isu vals version[1]

8/8/2019 Math ISU Vals Version[1]

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Integers

- An Integer is a Positive orNegative, Whole num

- Ex. 9, +25, 0.- Rules for Adding, Subtracting, Multiplying, and

Integers

- Adding a Positive plus a Positive = aNegative

- Negative plus a Negative = a Positive

- Positive plus a Negative = Positive/Negative dep

the greater amount

- Subtracting (+8) +(-2)= 6

- Multiplying two Integers with same sign will resu

Positive answer


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- Product of two Integers with different signs will

Negative answer

- Dividing, When dividing the rules apply in the sa

multiplying (ex. positive x positive=positive)

Ratios, Rate, Proportions

Ratio is a fraction comparing2 numbers orquantities with the sa

(ex .cm : cm)

Rate is a fraction that compares numbers or quantities with diffe

(Ex liters: miles)

Proportion is a statement that equates 2 ratios.

Ratios: 25:100 =1:4 etc always reduce to lowest terms when usi


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Conversions of Decimals Percents and Fractions

- To convert a Fraction to a Decimal divides theN

by the Denominator.

- Convert to a Percent by moving the decimal placspots to the left

Ex. 1.20 = 120%

- Find the LCD (Lowest Common Denominator)

- Use the same rules as when using integers

- To convert from a decimal to a fraction find the a

that is expressed (how many numbers there are o

side) ex. 1.20=1000 1.200=10000 Etc.


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Number Classifications

Natural numbers: any number starting from one

Whole numbers: any number starting from 0

Integers: negative or positive numbers including 0

Rational numbers: any numbers that are fractions, integers, and/

numbers

Irrational numbers: almost any number including square root of


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Fractions

Rules of Dividing and Multiplying Fraction

-To divide simply multiply the Reciprocal of the second fraction

-To multiply, multiply numerator and denominator by each othe-To Subtract find a common denominator and then subtract

-To Add find a common denominator and then add(ex.3 + 2

1 3

=1x3,3x3

=9 + 2

3 3)


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Bedmas-Bedmas is the order of operations of which to do calculations in

-It goes in order of Brackets (9+3x(5-2) )

-Exponents 92= 81

-Division 90/10

-Multiplication 90x270

-Addition 7+6

-Subtraction 90-35


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Relationships

Linear and Non-Linear Relations

- A Linear relationship is when the exponent above all the

is 1

A N Li l i hi i h h b h


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- A Non-Linear relationship is when the exponent above th

is not 1

- A Linear relationship between 2 variables forms a straig

they can be approximated with a Line of Best Fit

- A Non-linear relationship doesnt form a straight line, thapproximated by a curve of best fit

Distance and Time Graphs

-A Distance and Time graph is a type of graph that measures the

over a period of time of an objectIndependent/Dependant Variables

A I d d i bl i h i bl h ff h D


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- An Independent variable is the variable the affects the D

variable, it goes along the X axis

- The Dependant Variable is affected by the Independent v

goes along the Y axis

Outliers

- An Outlier is a piece of data that varies significantly from

of the data, sometimes it can be removed from the data

C l ti T


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Correlation Types

- A Positive Correlation is when the Line of Best Fit point

to the right of the data

- A Negative Correlation is when the Line of Best fit poin

and to the right of the data- No Correlation is when there is little or no correlation be

data

Correlation Coefficient

A C l ti C ffi i t i i l b b t 1


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- A Correlation Coefficient is a single number between 1

describes the strength of the relationship between two va

Correlation Strong Weak

Positive 0.7 to 1.0 0.3 to 0.7

Negative -1.0 to 0.7 -0.7 to 0.3Little or no Correlation 0.3 to 0.3

Relationship Definitions

- Primary Data- Data collected by you (you count the amo

people eating healthy vs. non healthy)

- Secondary Data- Data collected by someone else (you fin

that says there are only 7 pandas in the world)

- Sample- A small portion of the population (all the Asian

Toronto)- Census- The whole population (everyone in Canada)


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Unit 3 Polynomials

- Terms- A product of numerical expression and a variable

- Like Terms have the same variable and exponent ex. 5y

Polynomial one or more terms added together ex 5nm+7y


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-Polynomial, one or more terms added together ex. 5nm+7y

Type Of Polynomial Number of Terms Example

onomial 1 7x

inomial 2 5y+9sTrinomial 3 45y-9x+35z

Degrees of Terms and Polynomials

Term Sum of Exponents Degree

93 3 3

8yc 2 2

9xyz+ 7x8 11 11The Distributive Property

Is when you multiply all numbers on the inside of the bracket by


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Is when you multiply all numbers on the inside of the bracket by

number out side of the bracket Ex.3 (7x+8) becomes 21x+24

=x2 + 4x

Exponent RulesWhen multiplying an exponent by anotherexponent you add the

exponents, when dividing you subtract the exponents, and when

a power of a power you multiply the exponents Ex. 5n5x 7n3= 35

Multiplying and DividingMultiplying: When you multiply simply add the exponents of th

Ex: 5n5 x 4x7=20n5x7


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Ex: 5n x 4x =20n x

Dividing: Subtract the exponents of the terms

Ex: 5n7/36n7

Power-to-Power: When there is a power to beside each other an

is indicated multiply the exponents of the variable/term.Ex:(54 )(56 )= 510

Unit 4 Algebraic Equations

Equations: a mathematical statement that says two exp

equal

Solution: the value of the variable that makes an equatio

Constant Term: a term that does not include a variable (E

Changing signs: When moving numbers over the equal


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Changing signs: When moving numbers over the equal

sign changes to the opposite of what they were.

Ex: x + 4 = 13

X+4 4 = 13 -4

X=9- When solving simply equations bring the variables to on

the constant term to the other side

- LS/RS is a good way to check if your answer is correct

- LS: x+4

9+4=13

- RS: =13

LS=RS there fore x=13

Multi Step Equations


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Multi Step Equations

Multi-step equations are solved by using the exact same rule

simple equations (Bring all the variables to one side and all t

constant terms to the other)

Ex: 7-2k = 8-5k5k-2k=8-7

3k=-1

Solving Equations with Denominators #1

- Find the Lowest Common Denominator

- Multiply each term by the LCD


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- Multiply each term by the LCD

- Eliminate Denominators by reducing fractions and multi

denominator by the numerator

- Solve the remaining equation

Ex: 2/3x=-82/3x=-24/3

2/3x=6/72

x=61/72

Solving Multi-Step Denominators #2

- Eliminate Brackets Using the Distributive PropertyEx: x-1/3=x+2

Modeling with Algebra


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Slope Point Formula


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Slope Point Formula

Slope Point Formula uses 2 points (x1, y1) and (x2, y2)

M= y2-y1

x2-x1

First Differences

First Differences

X Y

5 -1

6 -2

7 -3

8 -4The differences on the x side change by +1, and the y

sides changes by +1 making the slope 1

1

Unit 6 The Line


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Unit 6 The Line

Slope Intercept Form- is y=mx+b where y is the y coordinate, m

x is the x coordinate, and b is the y-intercept.

Standard Form- Ax+By+C=0 A is equal to the slope, x is once a

coordinate, B the y-intercept, y is a y coordinate, and C is the ne

form of the sum of Ax+By.

Parallel and Perpendicular Lines- a parallel line is any line that hsame slope as another, a perpendicular line is any 2 lines which

negative reciprocals.

Unit 7 Geometry


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Unit 7 Geometry

Angle Theorems- CAT- Complementary Angle Theorem- Angle

measure up to 90 degrees

-SAT Supplementary Angle Theorem- When an angle adds up t

degrees.

-OAT Opposite Angle Theorem- States that all opposite angles a

-ALT (Z) Alternate Angles- When two parallel lines become int

by another line, resulting in a Z pattern

-COR (F) Corresponding Angles- When 2 parallel lines becomeintersected by another line, they then may form an F pattern


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-INT (C) Interior Angles- any of the angles that are on the inside

shape

-ITT Isosceles Triangle Theorem- States that the base angles are

on each side

-EATT1 Exterior Angle Theorem for a Triangle 1- Angel A + A

Angel C-EATQ Exterior Angel Theorem for a Quadrilateral- All the ang

quadrilateral add up to 360 degrees

-ASTT Angel Sum Theorem for a Triangle- Angel A+ Angel B+

C=180 degrees


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