exit brain dump

7/30/2019 Exit Brain Dump

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TAKS Mathematics Exit Level

Formulas, Rules & Things to Remember


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Arc Length

_____ =_____

360 2 r

Degreemeasure

of arc angle x

Degreemeasure

of arc angle

Arc Lengthrepresented

by x

Formula forCIRCUMFERENCEof the whole circle

Number ofdegrees in a circle

Set a proportion

Questions that ask about degrees, arc length, arc areaor involve circles, remember to use proportions!

r

x


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Arc AreaArea of Arc,represented

by x

_____ =_____

360 r

xFormula forAREAof the whole circle

Number ofdegrees in a circle

Degree

measure

of arc angle

Set a proportion

r

x

Degreemeasure

of arc angle


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Sample Data & Degrees

Sandwiches Sold in One day

Sandwich Sold in a Day

Turkey 40

Meat Balls 25

Ham & Cheese 60

Roast Beef 25_____ =_____

Set a proportion

360

x40

150

Based on how many sandwicheswere sold per day, if the data wasso be shown in a circle graph whatwould be the degree measure of theangle for Turkey sandwiches?

Total Numberof Sandwichessold

X representsunknowndegrees

Cross-Multiply, solve for x

Answer:

150x=40(360)

x=40(360)/150

x=96

The degree measure of the angle wouldbe 96 degrees


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Sample Data

Activity Number of People

Running 30

Biking 70

Rollerblading 45

Ice Skating 55

Sample Data

Based on the sample dataabout how many students outof a group of 2,300 are morelikely to choose ice skating?

_____ =_____

Set a proportion Sample Data proportioned to Needed Data

x55

Total Number inSample

200 2,300

Cross-Multiply, solve for x

Set a proportion

Answer:

200x=55(2,300)

x=55(2300)/200

x=632.5

There would be approximately 633students out of 2,300 that would prefer ice

skating.


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Similar ShapesSet a proportion

15

8

10

_____ =_____

Find the height of smaller triangle

hH

B b

_____ =_____h8

15 10

Cross-Multiply, solve for h

Answer:

15h=80

h=80/15

h=5.3

Big SmallBig Small

h


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Area

Area of Square= x

Area of rectangle=bxh


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x

x

x

x2

x3

2x

45, 45, 90

x, x, x 2

30, 60, 90

x, x 3,2 x

Special Right Triangles


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Solving with a 30,60,90 triangle

30

2400

A

B

C

Rule: x, x 3,2 x30, 60, 90

x

2x

x3

What is the distance from AC= (2400 3)=4156.9

What is the distance from BC= (2(2400))=4,800

60

30


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Finding the x-intercept

Given y=x+x-12

In your calculator go to y= insert the equation

2nd GRAPH and check when y=0, those are the x-intercepts

For this particular equation thex-intercept is x= -4, x= 3

Use calculator


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Finding an Equation

Number of Square feet (x) Total Cost (y)

1800 630

2300 805

2900 1015

For questions that have atable with the x and y valuesand it is asking you to find anequation that represents thedata, you need to use your

graphing calculator.

STAT, 1) Edit

Put all the xs under L1, and all the ysunder L2,

STATCALC, 4)LingReg(ax+b), ENTER

It will give you y=ax+b, the a=is your slopeand the b= is your y-intercept.

The answer for thisparticular questionswould be y=0.35x

Use calculator


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Setting up Equations

As a waiter in a restaurant, Steven works 6-hour shifts. Heearns $5 per hour and keeps 80% of his tip money. Howmuch tip money does he need to receive per shift to earn atotal of exactly $50 before taxes are deducted?

The equation will be set up as y=mx+b6(5) + .8(t)=50

30 + .8t=50

.8t=50-30

.8t=20

t=25

Where:

y=the total amount earned

mx=80% of tips

b=hourly earnings (wage)


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Volume

For volume on the formula sheetthe volume of a prism or a

cylinder is V=Bh

For the cylinderthe B, is r

For the prism theB, is lw


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Faces, Edges & Vertices

This prism has 5 faces, 8 edges, 5 vertices

The face are the flat sides.

The edges are the intersection of the flat sides.The vertices are the corners or points.


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FOIL- Simplified


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Rules for Simplifying

Example(5n-2)3n-(5n-2)(n-1)

1st step: 15n-6n-(5n-5n-2n+2)

2nd step: 15n-6n-5n-7n+2

3rd step: 10n-13n+2

FOIL

combine like terms


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Finding the percent (%)

The original price of a car is 20,000. Joe bought the car for15,000. What percent of the original cost did Joe save?

(20,000-15,000)

_____________X 100= %

(20,000)

5,000/20,000 x100= 25%

Joe saved 25% from the original price of the car.


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Mean, Median, Mode

MEAN is the average

MODE is the one that repeats the most

MEDIAN is the number in the middle when you put the numbers fromleast to greatest

RANGE is the difference between the biggest number and the smallestnumber. (big# - small#)


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Rules Negative & Positive Numbers

The bigger signindicates that thepositive number isbigger than thenegative number.

The bigger signindicates that thenegative numberis bigger than thepositive number.


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Things to Remember

ANGLES & DEGREES A Circle has 360 degrees A line is 180 degrees A triangle has180 degrees A right angle has 90 degrees

Complementary angles total 90 degrees

Supplementary angles total 180 degrees

LINES When the slope of two lines is the same

regardless of the y-intercept the lines areparallel (they dont intersect).

Solution is where two lines intersect


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More things to Remember

FUNCTIONS

A function is when all the x values DONT repeat

EX: (0,1) (1,5) (-1,3) (10,0) Function

(-10,1) (1,0) (1,1) (5,3) NOT a Function, 1s repeat

DEPENDENT & INDEPENDENT VARIABLES

Y= is the output, dependent variable

X= is the input, independent variable

DOMAIN & RANGE

Domain is all the x-values

Range is all the y-values


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Notes


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Notes

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