TAKS Mathematics Exit Level

Formulas, Rules & Things to Remember

Arc Length _____ =_____

360 2 r

Degree measure

of arc angle x

Degree measure

of arc angle

Arc Length represented

by xFormula for

CIRCUMFERENCE of the whole circle

Number of degrees in a circle

Set a proportion

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

r

x

Arc AreaArea of Arc, represented

by x

_____ =_____

360 r²

xFormula for AREA of the whole circle

Number of degrees in a circle

Degree measure

of arc angle

Set a proportion

r

x

Degree measure

of arc angle

Sample Data & DegreesSandwiches 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 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?

Total Number of Sandwiches sold

X represents unknown degrees

Cross-Multiply, solve for x

Answer:

150x=40(360)

x=40(360)/150

x=96

The degree measure of the angle would be 96 degrees

Sample Data

Activity Number of People

Running 30

Biking 70

Rollerblading 45

Ice Skating 55

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

x55

Total Number in Sample

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 633 students out of 2,300 that would prefer

ice skating.

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

Area

Area of Square= x²

Area of rectangle=bxh

Perimeter

Perimeter is the total of all the sides of a polygon

12

12

12

12

P=21P=48

x

x

x

x√2

x√3

2x

45, 45, 90

x, x, x √2

30, 60, 90

x, x √3,2 x

Special Right Triangles

Solving with a 30,60,90 triangle

30

2400

A

B

C

Rule: x, x √3,2 x30, 60, 90

x

2x

x√3

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

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

60

30

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

Use calculator

Finding an Equation Number of Square feet (x) Total Cost (y)

1800 630

2300 805

2900 1015

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,

•STATCALC, 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

Use calculator

Setting up Equations 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?

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

Where:y=the total amount earned

mx=80% of tips

b=hourly earnings (wage)

Volume

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

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.

FOIL- Simplified

Rules for SimplifyingExample

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

1st step: 15n²-6n-(5n²-5n-2n+2)

2nd step: 15n²-6n-5n²-7n+2

3rd step: 10n²-13n+2

FOIL

combine like terms

Finding the percent (%)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, Median, ModeMEAN 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#)

Rules Negative & Positive Numbers 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.

Things to RememberANGLES & 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 lines intersect

More things to RememberFUNCTIONS• A function is when all the x values DON’T repeatEX: (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

Notes

Notes