Exit Level

1. Exit Level TAKS Preparation Unit Objective 9

2. Percent% of Change • When asked to determine % of change (What percent did Ernesto save?) … • Example: The original cost of a pair of jeans is $75. Heather purchases the jeans during a sale and pays only $37.50. What percent did Heather save? 9, 8.3B

3. Problems with Proportions • Arrange your proportionsspecifically! • Example:Rodrigo types 50 words per minute and completes 12 pages each time Rachel completes 11.2 pages. Which is a reasonable estimate of Rachel’s typing speed? Rodrigo Rachel Words per min # of pages 9, 8.3B

4. Percent of a Percent … • Change percents to decimals • Remember: “of” means multiply 7.5% = .075 75% = .75 175% = 1.75 = .05 x 200 5% of 200 = 10 = .05 x .20 5% of 20% Or 1% = .01 = .05 x .20 x 80 = .8 5% of 20% of 80 9, 8.3B

5. Percent of a Percent cont… • Example: Jermaine has a photo measuring 8 inches by 10 inches that he is reducing to fit into a smaller frame. He reduces the photo by 80%, but it is not small enough. He reduces the photo again by 80%. What are the dimensions of the new image? 8 x .80 x .80 = 5.12 inches 10 x .80 x .80 = 6.4 inches 9, 8.3B

6. Writing Equations with Percents • Change percents to decimals • Convert sentences to equations • Example: Gary earns $600 per week plus a 9% commission of his sales. How much must his total weekly sales be in order for him to earn exactly $708 per week? 9% 708 =.09 108 = .09S G = 600 + .09 x S 708 = 600 + .09S 1200 = S -600 -600 9, 8.3B

7. Converting Ratios to Percents • A ratio compares quantities like wins:losses • A percent compares a quantity to a total like • To convert a ratio to percent: • Determine the total • Put specific quantity over total • Set wins Total games played 9, 8.3B

8. Converting Ratios to Percents cont… • Example: The Green Bay Packers have a regular season record of 13:3. What percentage of games did they win? 1. Determine the total 13 wins, 3 losses, Total Games Played = 16 2. Put specific quantity over total 3. Set 1300 = 16x x = 81.25% 16 16 9, 8.3B

9. Favorable outcomes Possible outcomes Simple Probability • Probability = • Example: A geometric pattern is made up of 2 squares and 1 circle grouped randomly together. What is the probability that the 2 squares are placed together? Favorable outcomes 2 squares together Possible outcomes Probability 9, 8.11A

10. Favorable outcomes Favorable outcomes Possible outcomes Possible outcomes Com∙poundProbability • Com∙poundProbability is just several Simple Probabilities multiplied together • Watch out for the words • “Replacement” • “Without Replacement” Com∙poundProbability ∙ = Means you choose an object and then put it back before you choose again Means you choose an object and hold on to it while you choose again 9, 8.11A

11. Favorable outcomes Favorable outcomes Possible outcomes Possible outcomes Com∙poundProbability cont… • Example: Jordan has a box containing 12 strips of paper. 5 of the strips contain the first 5 numbers greater than zero. Another 7 strips contain the first 7 letters of the alphabet. If Jordan draws 2 strips of paper without replacement, what is the probability that he will draw an even number and a vowel? Com∙poundProbability ∙ = 9, 8.11A

12. Making Predictions from Data • There are 2 types of questions in this section: • Questions where the data are stated • Questions with tables of data • On all questions use proportions • Example from Type 1: Steve made 15 of his last 18 field goal attempts from 35 yards. How many field goals can he be expected to make if he attempts 30? 18x = 450 x = 25 18 18 9, 8.11B

13. Making Predictions from Data, cont… • Example from Type 2: Josia surveyed 50 of his classmates to determine their choice in automobile types. The results are shown in the table below. If there are 1725 students at Josia’s school, how many can be expected to prefer trucks? 50x = 37950 50 50 x = 759 9, 8.11B

14. Measures of Central Tendency Numbers Middle Likelihood • There are 4 measures that fit this description: • Mean: • Median: • Mode: • Range: Average Middle … put numbers in order 1st *you may have to average the 2 in the middle* Most … not all data sets have a mode Biggest - Smallest 9, 8.12A

15. Measures of Central Tendency, cont… • Example: Hulan earned the following grades on his tests in Geometry this six weeks: 94, 72, 56, 81. Which measure of central tendency will give him the highest score? Mean (Average) = Median (Middle) 56, 72, 81, 94 Mode (Most) None Range (Biggest – Smallest) 94 - 56 = 38 9, 8.12A

16. Chinese 42.4˚ Pizza 63.5˚ Pizza 63.5˚ Pizza 63.5˚ Pizza 63.5˚ Burgers 105.9˚ Burgers 105.9˚ Mexican 148.2˚ Mexican 148.2˚ Mexican 148.2˚ Making Circle Graphs • To create a circle graph you must know how much of the circle to designate for each category • Example: Create a circle graph for the following data. Total # of Restaurants = 17 9, 8.12C

17. Making Conclusions from Data • PROCESS OF ELIMINATION! • Example: An internet service provider claims that its connection speed is faster than its competitors. The company uses the graph shown below to demonstrate this point. According to the graph, which statement best describes the company’s product? A. Its speed is faster than some, but much slower than others B. Its speed is much faster than others C. Its speed is about the same as others D. Its speed is somewhat slower than others 9, 8.13B