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- 1. TAKS Mathematics Exit Level Formulas, Rules & Things to Remember
- 2. 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
- 3. 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
- 4. Sample Data & Degrees <ul><li>Sandwiches Sold in One day </li></ul>_____ =_____ 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
- 5. 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
- 6. 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
- 7. Area Area of Square= x ² Area of rectangle=bxh
- 8. Perimeter Perimeter is the total of all the sides of a polygon 12 12 12 12 P=21 P=48
- 9. 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
- 10. 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
- 11. Finding the x-intercept <ul><li>Given y=x ²+x-12 </li></ul><ul><li>In your calculator go to y= insert the equation </li></ul><ul><li>2 nd GRAPH and check when y=0, those are the x-intercepts </li></ul>For this particular equation the x-intercept is x= -4, x= 3 Use calculator
- 12. 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. <ul><li>STAT, 1) Edit </li></ul><ul><li>Put all the x’s under L1, and all the y’s under L2, </li></ul><ul><li>STAT CALC, 4)LingReg(ax+b), ENTER </li></ul><ul><li>It will give you y=ax+b, the a=is your slope and the b= is your y-intercept. </li></ul>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
- 13. 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)
- 14. 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
- 15. 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.
- 16. FOIL- Simplified
- 17. Rules for Simplifying <ul><li>Example </li></ul><ul><li>(5n-2)3n- (5n-2)(n-1) </li></ul>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
- 18. 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.
- 19. Mean, Median, Mode <ul><li>MEAN is the average </li></ul><ul><li>MODE is the one that repeats the most </li></ul><ul><li>MEDIAN is the number in the middle when you put the numbers from least to greatest </li></ul><ul><li>RANGE is the difference between the biggest number and the smallest number. (big# - small#) </li></ul>
- 20. 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.
- 21. Things to Remember <ul><li>ANGLES & DEGREES </li></ul><ul><li>A Circle has 360 degrees </li></ul><ul><li>A line is 180 degrees </li></ul><ul><li>A triangle has 180 degrees </li></ul><ul><li>A right angle has 90 degrees </li></ul><ul><li>Complementary angles total 90 degrees </li></ul><ul><li>Supplementary angles total 180 degrees </li></ul><ul><li>LINES </li></ul><ul><li>When the slope of two lines is the same regardless of the y-intercept the lines are parallel (they don’t intersect). </li></ul><ul><li>Solution is where two lines intersect </li></ul>
- 22. More things to Remember <ul><li>FUNCTIONS </li></ul><ul><li>A function is when all the x values DON’T repeat </li></ul><ul><li>EX: (0,1) (1,5) (-1,3) (10,0) Function </li></ul><ul><li>(-10,1) ( 1 ,0) ( 1 ,1) (5,3) NOT a Function, 1’s repeat </li></ul><ul><li>DEPENDENT & INDEPENDENT VARIABLES </li></ul><ul><li>Y= is the output, dependent variable </li></ul><ul><li>X= is the input, independent variable </li></ul><ul><li>DOMAIN & RANGE </li></ul><ul><li>Domain is all the x-values </li></ul><ul><li>Range is all the y-values </li></ul>
- 23. <ul><li>Notes </li></ul>
- 24. Notes

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I LOVE DANE

AND SLOPPY BURGERS

EXTRA DANE

-dane