Mathematics TAKS Exit Level Review

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 x Formula 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 Area Area of Arc, represented by x _____ =_____ 360 r ² x Formula 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 & Degrees

Sandwiches Sold in One day

_____ =_____ Set a proportion 360 x 40 150 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 25 Roast Beef 60 Ham & Cheese 25 Meat Balls 40 Turkey Sold in a Day Sandwich

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 x 55 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. 55 Ice Skating 45 Rollerblading 70 Biking 30 Running Number of People Activity

Similar Shapes Set a proportion 15 8 10 _____ =_____ Find the height of smaller triangle h H B b _____ =_____ h 8 15 10 Cross-Multiply, solve for h Answer: 15h=80 h=80/15 h=5.3 Big Small Big Small h

Area Area of Square= x ² Area of rectangle=bxh

Perimeter Perimeter is the total of all the sides of a polygon 12 12 12 12 P=21 P=48

Special Right Triangles x x x x √2 x √3 2x 45, 45, 90 x, x, x √2 30, 60, 90 x, x √3,2 x

Solving with a 30,60,90 triangle 30 2400 A B C Rule: x, x √3,2 x 30, 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=x ²+x-12

In your calculator go to y= insert the equation

2 nd 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 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 Use calculator Total Cost (y) Number of Square feet (x) 1015 2900 805 2300 630 1800

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 r ² 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 Simplifying

Example

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

1 st step: 15n ²-6n- (5 n²-5n-2n+2) 2 nd step: 15n²-6n-5n²-7n+2 3 rd 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, 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 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 Remember

ANGLES & DEGREES

A Circle has 360 degrees

A line is 180 degrees

A triangle has 180 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 Remember

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

Notes

Notes

Mathematics TAKS Exit Level Review

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Notes on slide 1

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