1. © A Very Good Teacher 2007 Exit Level TAKS Preparation Unit Objective 10

2. © A Very Good Teacher 2007 Finding “additional information” 10, 8.14A PROCESS OF ELIMINATION! The answer must be something you do not already know. Example: Harvey jogged at a constant rate of 6 miles per hour. He speed up at a constant rate for 10 seconds. What additional information is needed to determine Harvey’s speed after 10 seconds? A. His speed prior to acceleration B. The length of time he sped up C. His average walking speed D. The rate at which he sped up = 6mph = 10 seconds

3. © A Very Good Teacher 2007 Comparative Situations Write an equation …Working Backwards Example: John has 2 more cookies than Maria. Maria has half as many cookies as Ernest. They have 14 cookies in all. How many cookies does John have? 10, 8.14A J + M + E = 14 E = ? M = ½ ? J = ½ ? + 2 (½ ? + 2) + (½ ?) + ? = 14 = 6 = 3 = 5

4. © A Very Good Teacher 2007 Money and Percent ($ & %) Write an equation and solve it Example: A manicurist works 8 hour shifts where she earns $5 per hour. She also keeps 75% of the tips she collects. How much tip money does she need to receive per shift to earn a total of exactly $60? 10, 8.14B Hourly Wage + Commission = Total (8▪5) +.75t = 60 40 +.75t = 60 -40.75t = 20.75 t = $26.67

5. © A Very Good Teacher 2007 Calculating Grades Create categories – each with a different percentage Add them up to get the total Example: In Mr. Graves class, tests count as 30% of a student’s grade and homework counts as 70%. Kevin has 3 test grades of 34, 89, and 62. What must Kevin’s homework average be in order for him to earn a grade greater than 80? 10, 8.14B 20%(tests) + 70%(homework) > Grade.70x > 67.67 x > 96.6

6. © A Very Good Teacher 2007 Using Tables to Solve Exponential Problems When a pattern isn’t constantly growing or shrinking …. Make a table –Population, half-life, anything dealing with carbon Example: Gary noticed that the population of ants in his ant farm doubles every 5 days. If the initial population was 20 ants, what will the population be after 30 days? 10, 8.14C DayAnts 020 540 1080 15160 20320 25640 301280 DayAnts

7. © A Very Good Teacher 2007 Multiple Distances Draw a Picture – use a straight line unless it tells you otherwise Example: Princess Petticoat rides in her carriage from her cottage, over the river bridge, through the Dark Forest to the Village. Her cottage is 2.3 miles from the Dark Forest. The bridge is 1.9 miles from the Village and.5 miles from the Dark Forest. How long is the princess’s journey? 10, 8.14C CBDFV 2.3 1.9.51.81.4 1.8 +.5 + 1.4 = 3.7

8. © A Very Good Teacher 2007 Doing a Problem Wrong?... Example: Vicky mistakenly divided a number by 4 and then added 12 to get 14. She realized that she should have added 12 and then divided by 4. What was the correct answer? 10, 8.14C Write out the “wrong” problem:Find x: -12 x = 8 Write out the “correct” problem:

9. © A Very Good Teacher 2007 Area on a Geoboard A geoboard is just like a coordinate plane To find the Area of a figure break it up into smaller pieces Example: The horizontal and vertical distances between each of the pegs on the geoboard shown below represent 1 unit. Which is closest to the area of the polygon modeled on the geoboard? A. 48 B. 58 C. 65 D. 70 10 x 7 = 70 70 7 5 10, 8.14C

10. © A Very Good Teacher 2007 Choosing the Correct Equation or Expression Use your formula chart! Example: Julie is examining the relationship between the Volume of a cube and its Surface Area. Which equation represents the relationship? 10, 8.15A A. B. C. D. V = (s ▪ s) ▪ s V = s³ S = 6s²

11. © A Very Good Teacher 2007 Using Substitution When dealing with confusing equations, use substitution to figure them out. Example: If x ¥ y = -2x – 3y, what is the value of 7 ¥ -4? 10, 8.15A x ¥ y = -2x – 3y 7 ¥ -4 = -2( ) – 3( ) 7 -4 7 ¥ -4 = -14 + 12 7 ¥ -4 = -2

12. © A Very Good Teacher 2007 Using Substitution, cont… Sometimes you must make up numbers to substitute. Example: 3 consecutive whole numbers add up to 30. The equation (n – 1) + n + (n + 1) = 30 represents this situation. What does the variable n represent? 10, 8.15A (n – 1) + n + (n + 1) = 30 9 + 10 + 11 = 30 (10 – 1) + 10 + (10 + 1) = 30 So, we choose numbers around 10 n represents the number in the middle

13. © A Very Good Teacher 2007 Venn Diagrams A Venn Diagram is a way of representing data that overlap Example: The results of a survey of Favorite Pizza Toppings are shown below in a Venn Diagram. 10, 8.16A Cheese Pepperoni Ham 21 19 13 8 3 14 1. How many people liked Cheese only? 2. How many people liked Cheese and Ham? 3. How many people liked Cheese, Pepperoni, and Ham?

14. © A Very Good Teacher 2007 Pascal’s Triangle Pascal’s Triangle is a pyramid of numbers that create a sequence Row 1: Row 2: Row 3: Row 4: Row 5: 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1

15. © A Very Good Teacher 2007 Finding Correct Statements about Geometric Relationships Draw a Picture Use your knowledge of Geometry to eliminate wrong answers. –Parallel Lines –Perpendicular Lines –Triangles –Polygons –Slope –Area –Supplementary Angles –Complementary Angles 10, 8.16B

16. © A Very Good Teacher 2007 Finding Correct Statements about Geometric Relationships, cont… Example: Points A and B lie on circle P. If circle P has a radius r, which of the following statements cannot be true? 10, 8.16B P A B A. AB > r B. AB > 2r C. AB = r D. AB = 2r B r