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# TAKS Mathematics Exit Level - PowerPoint PPT Presentation

TAKS Mathematics Exit Level. Formulas, Rules & Things to Remember. Set a proportion. Degree measure of arc angle. Arc Length. Degree measure of arc angle. Arc Length represented by x. _____ =_____ 360 2 r. x. Formula for CIRCUMFERENCE of the whole circle. x. r.

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Formulas, Rules & Things to Remember

Degree measure

of arc angle

Arc Length

Degree measure

of arc angle

Arc Length represented by x

_____ =_____

360 2 r

x

Formula for CIRCUMFERENCE of the whole circle

x

r

Number of degrees in a circle

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

Arc Area

Area of Arc, represented by x

Degree measure

of arc angle

Degree measure

of arc angle

_____ =_____

360 r²

x

Formula for AREA of the whole circle

x

r

Number of degrees in a circle

Sample Data & Degrees

Sandwiches Sold in One day

Based on how many sandwiches were sold per day, if the data was so be shown in a circle graph what would be the degree measure of the angle for Turkey sandwiches?

X represents unknown degrees

40

_____ =_____

x

150

360

150x=40(360)

x=40(360)/150

x=96

The degree measure of the angle would be 96 degrees

Total Number of Sandwiches sold

Cross-Multiply, solve for x

Sample Data

Sample Data

Based on the sample data about how many students out of a group of 2,300 are more likely to choose ice skating?

Set a proportion Sample Data proportioned to Needed Data

55

_____ =_____

x

200x=55(2,300)

x=55(2300)/200

x=632.5

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

200

2,300

Total Number in Sample

Cross-Multiply, solve for x

Similar Shapes

Big

Small

Big

Small

8

H

h

h

_____ =_____

B

b

15

10

Find the height of smaller triangle

15h=80

h=80/15

h=5.3

8

h

_____ =_____

15

10

Cross-Multiply, solve for h

Area of Square= x²

Area of rectangle=bxh

12

12

12

P=21

12

P=48

Perimeter is the total of all the sides of a polygon

x√2

45, 45, 90

x, x, x √2

x

x

2x

30, 60, 90

x, x √3,2 x

x

x√3

B

30

30, 60, 90

60

Rule: x, x √3,2 x

2x

2400

x

30

C

A

x√3

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

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

Finding the x-intercept

Given y=x²+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 the x-intercept is x= -4, x= 3

Finding an Equation

For questions that have a table with the x and y values and it is asking you to find an equation that represents the data, you need to use your graphing calculator.

• STAT, 1) Edit

• Put all the x’s under L1, and all the y’s under L2,

• STATCALC, 4)LingReg(ax+b), ENTER

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

The answer for this particular questions would be y=0.35x

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

Where:

y=the total amount earned

mx=80% of tips

b=hourly earnings (wage)

The equation will be set up as y=mx+b

6(5) + .8(t)=50

30 + .8t=50

.8t=50-30

.8t=20

t=25

For volume on the formula sheet the volume of a prism or a cylinder is V=Bh

For the cylinder the B, is r²

For the prism the B, is lw

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.

Example

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

FOIL

1st step: 15n²-6n-(5n²-5n-2n+2)

2nd step: 15n²-6n-5n²-7n+2

3rd step: 10n²-13n+2

combine like terms

The original price of a car is 20,000. Joe bought the car for 15,000. 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.

MEAN is the average

MODE is the one that repeats the most

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

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

The bigger sign indicates that the positive number is bigger than the negative number.

The bigger sign indicates that the negative number is bigger than the positive number.

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 are parallel (they don’t intersect).

• Solution is where two linesintersect

FUNCTIONS

• A function is when all the x values DON’T repeat

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

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