Chapter 0: Preparing for Advanced Algebra


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1 Lesson 01: Representing Functions Date: Example 1: Locate Coordinates Name the quadrant in which the point is located. Example 2: Identify Domain and Range State the domain and range of each relation. Then determine whether each relation is a function. a. {(, ), (, ), (, ), (, )} b. x y c. d. Example 3: Identify Functions Label each of the following functions. a. b. c. d. e. f.
2 Example 4: Solving Equations Solve each equation. a. b. c. d. e. f.
3 Lesson 02: FOIL Date: Example 5: Use the FOIL Method Find each product. a. b. Lesson 03: Factoring Polynomials Example 6: Use the Distributive Property Factor
4
5 Example 7: Use Factors and Sums Factor each polynomial. a. b. c. d. e. f. g. h.
6 Lesson 07: Congruent and Similar Figures Date: Example 8: Congruence Statements The corresponding parts of the two congruent triangles are marked on the figure. Write a congruence statement for the two triangles. W B C Y X A Example 9: Determine Similarity Determine whether the polygons are similar. Justify your answer. a. b Example 10: Solve a Problem Involving Similarity The city of Mansfield plans to build a bridge across Pine Lake. Use the information in the diagram at the right to find the distance across Pine Lake.
7 Lesson 08: The Pythagorean Theorem Example 11: Find Hypotenuse/Leg Measures Find the length of the missing side of each triangle. a. b. 8 in. c in. 12 m 15 in. 20 m a m Example 12: Using Trig Functions Find the values of the six trigonometric functions for the identified angle.
8 Lesson 04: Counting Techniques Date: An is the result of a single trial of a process involving chance. The set of all possible outcomes is called a. Example 13: Fundamental Counting Principal BICYCLES A bicycle manufacturer makes five and tenspeed bikes in seven different colors and four different frame sizes. How many different bicycles does the manufacturer make? An arrangement of a group of distinct objects in a certain order is called a. Example: Example 14: Permutations of n Objects BAND There are 8 finalists in a band competition. In how many different ways can the bands be ranked if they cannot receive the same ranking?
9 Example 15: Permutations of n Objects Taken r at a Time Refer to example 14. In how many different ways can 1 st, 2 nd, and 3 rd place be awarded? A selection of distinct objects in which the order is not important is called a. Example: When selecting 3 out of 4 books for a book report, selecting books 1, 2, and 3 is the same as selecting books 3, 2, and 1. Example 16: Combinations of n Objects Taken r at a Time CARDS How many ways are there to choose 5 cards from a standard deck of 52 playing cards? Example 17: Permutations or Combinations Twentyfive students write their names on slips of paper. Then three different names are chosen at random to receive prizes. Determine whether each situation involves permutations or combinations. a. choosing 3 people to each receive a no homework coupon b. choosing 3 people to each receive one of the following prizes: 1 st prize, a new calculator; 2 nd prize, a no homework coupon; 3 rd prize, a new pencil
10 Lesson 05: Adding Probabilities Date: is a measure of the chance that a given event will occur. If each event is equally likely, we use probability. When using outcomes obtained by actually performing trials, we use probability. Example 18: Theoretical and Experimental Probability The graph shows the results of several trials of an experiment in which a single die is rolled. a. What is the experimental probability of rolling a 6? b. What is the theoretical probability of rolling a 6?
11 An event that has a single outcome is called a event. (example: rolling a die) An event which consists of two or more simple events is called a event. Events that cannot occur at the same time are said to be, that is they have no outcomes in common. (example: you cannot draw a card from a standard deck that is both a king and a queen) Example 19: Add Probabilities Determine whether the events are mutually exclusive or not mutually exclusive. Then find the probability. a. Keisha has a stack of 8 baseball cards, 5 basketball cards, and 6 hockey cards. If she selects a card at random from the stack, what is the probability that it is a baseball or a hockey card? b. Suppose that of 1400 students, 550 take Spanish, 700 take biology, and 400 take both Spanish and biology. What is the probability that a student selected at random takes Spanish or biology?
12 Lesson 06: Multiplying Probabilities Date: If the probability of one event does not affect the probability of a second event occurring, then the two events are events. (example: rolling a 6 then rolling a 5) If the probability of the first event does affect the probability of the second event occurring, then the two events are events. (example: drawing a card, not putting it back, then drawing a second card) The probability of an event A occurring given that event B has already occurred is called probability. It is represented by and read the probability of B given A. Example 20: Probability of Independent Events A coin is tossed and a die is rolled. What is the probability of the coin landing on tails and rolling a 3? Example 21: Probability of Dependent Events A bag contains 12 red, 9 blue, 11 yellow, and 8 green marbles. If two marbles are drawn at random and not replaced, what is the probability that a red and then a blue marble are drawn?
13 Example 22: Conditional Probability FOOD At a restaurant, 25% of customers order chili. If 4% of customers order chili and a baked potato, find the probability that someone who orders chili also orders a baked potato. Example 23: TwoWay Frequency Table MEDICINE A drug company conducted an experiment to determine the effectiveness of a certain new drug. Test subjects were randomly assigned to one of two groups: a treatment group, which received the drug, or a control group, which received a placebo instead of the drug. The contingency table below shows the results. a. Find the probability that a test subject s condition improved given that her or she was in the treatment group. b. Find the probability that a test subject was in the control group given that his or her condition did not improve.
14 Lesson 09: Measures of Center, Spread, and Position Date: is the science of collecting, organizing, displaying, and analyzing data in order to draw conclusions and make predictions. The entire group of interest is called a. When it is not possible to obtain data about every member of a population, a representative is selected. Data with only one variable is often summarized using a single number to represent what is average or typical (using measures of center) Example 24: Measures of Center The number of milligrams of sodium in a 12ounce can of ten different brands of regular cola are shown. Find the mean, median, and mode. 50, 30, 25, 20, 40, 35, 35, 10, 15, 35
15 Because two different data sets can have the same mean, we also use measures of spread to describe how widely the data values vary and how much the values differ from what is typical. Example 25: Measures of Spread MIDTERM EXAMS Two classes took the same midterm exam. The scores of five students from each class are shown. Both sets of scores have a mean of a. Find the range, variance, and standard deviation for the sample scores from class A. b. Use a calculator to find the range, variance, and standard deviation from the sample scores from Class B.
16 are three position measures that divide a data set arranged in ascending order into four groups, each containing about 25% of the data. The or the second quartile (Q 2 ) separates the data into upper and lower halves. The first (Q 1 ), called the, is the median of the lower half. The third (Q 3 ), called the, is the median of the upper half. The three quartiles along with the maximum and minimum values are called a. When the number of values in the set is odd, the median is not included in either half of the data when calculating Q 1 or Q 3 Example: Example 26: FiveNumber Summary PARTTIME JOB The number of hours Liana worked each week for the last 12 weeks were: 21, 10, 18, 12, 15, 13, 20, 19, 16, 18, and 14. Use a graphing calculator to find the minimum, lower quartile, median, upper quartile, and maximum of the data set.
17 The difference between Q 3 and Q 1 is called the or IQR. The IQR contains about 50% of the values. A large IQR means that the data are spread out. An is an extremely high or extremely low value when compared with the rest of the values in the set. (data values that are beyond the upper or lower quartiles by more than 1.5 times the IQR) Example 27: Effect of an Outlier The number of minutes each of the 22 students in a class spent working on the same algebra assignments is shown. 15, 12, 25, 15, 27, 10, 16, 18, 30, 35, 22, 25, 65, 20, 18, 25, 15, 13, 25, 22, 15, 28 a. Identify any outliers in the data b. Find the mean, median, mode, range, and standard deviation of the data set with and without the outlier. Describe the effect on each measure. Data Set Mean Median Mode Range Standard Deviation With outlier Without outlier
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