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Algebra II – Chapter 1 Test Review STANDARDS/GOALS:

A.1.a.: I can identify properties of real numbers and use them and the correct order of operations to simplify expressions.

A.1.b.: I can multiply monomials and binomials. A.1.c.: I can solve single-step and multistep equations and inequalities in one variable. A.1.h.: I can find the distance and midpoint between two points in the coordinate plane. S.MD.6.: I can use determine the mean, median, and mode for a data set. I can identify outliers from a data set. S.MD.7.: I can determine measures of ‘spread’ such as range, quartiles and the inter quartile range. S.ID.4.: I can find the variance and standard deviation of a set of data.

o I can recognize when a distribution is a normal distribution. o I can analyze data that comes from a normal distribution. o I can make decisions about populations based on random samples from those populations.

H.1.a.: I can use the fundamental counting principle to count the number of ways an event can happen. H.1.b./S.CP.9.: I can use permutations and combinations to compute probabilities of compound events

and solve problems. H.1.c.: I can find the probability of mutually exclusive and non-mutually exclusive events. H.1.d.: I can find the probability of independent and dependent events. H.1.e.: I can use unions, intersections, and complements to find probabilities. H.1.f./S.CP.6.: I can solve problems involving conditional probabilities. A.REI.10.: I can identify patterns that describe linear functions. I can distinguish between dependent and independent variables. F.IF.3.: I can recognize an arithmetic sequence.

G.1.c.: I can identify arithmetic sequences and patterns in a set of data. TWO WAY TABLES & PROBABILITIES:

A survey of adults living in a suburb of a large city was selected. The age and annual income of each adult in the sample were recorded. The resulting data are summarized in the table below:

Annual Income

Age Category $25,000-$35,000 $35,001-$50,000 Over $50,000 TOTAL 21-30 8 15 27 50 31-45 22 32 35 89 46-60 12 14 27 53

Over 60 5 3 7 15 TOTAL 47 64 96 207

Find the following probabilities of someone being randomly selected from this sample, based on the following criteria: #1. P(Over 60 category) #2. P(earn $25,000-$35,000) #3. P(31-45 years old) #4. P(NOT 21-30 years old) #5. P(earns over $35,001) #6. P(is 60 years old or younger) #7. P(does NOT earn Over $50,000) #8. P(Over 60 years old ⎸ earns over $50,000) #9. P(earns $35,001-$50,000 ⎸ 46-60 years old) #10. P(31-45 years old ⎸ earns $25K to $35K)

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#11. Graham has sales of $1280, $1125, $965, and $1210 the first four days of the week. How much must he have in sales on the fifth day in order to average $1150 for the week? #12. Find each theoretical probability based on ONE roll of TWO die:

a. P(sum of 3)

b. P(sum < 2)

c. P(sum ≤ 6) #13. A standard deck of playing cards has 52 cards. The deck has the same number of black and red cards and has 4 of each numbered or face card; two red and two black of each.

a. What is the probability of randomly picking a red card?

b. What is the probability of randomly picking a 4, 5, or 6?

c. What is the probability of randomly picking a black 7?

d. What is the probability of randomly picking a red Queen or Ace?

e. What is the probability of randomly picking a Queen or a Black card from a standard deck?

#14. Rancho High School has 98 seniors, 145 juniors, 160 sophomores, and 158 freshmen. Three student names are chosen randomly without replacement. What is the probability of a senior being chosen first, followed by a sophomore, and followed by a junior? Round to the nearest thousandth of a percent.

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COMBINATIONS/PERMUTATIONS/COUNTING TECHNIQUES: #15. The school yearbook staff includes 6 photographers. One photographer needs to cover the HOMECOMING parade, one will need to cover a school play, and another needs to cover a soccer game. In how many ways can photographers be assigned to these three different school events? #16. Guests at a charity fundraising banquet must choose 1 food item from these FOUR categories:

MAIN DISH ENTRÉE: pork BBQ; smoked salmon; Sirloin Steak; Fried Chicken; VEGETABLE: broccoli & cheese; baked beans; red potatoes; corn pudding; Asparagus SALAD: House Salad , Caesar Salad DESSERT: German Chocolate Cake; Red Velvet Cupcakes; KY Derby Pie

How many different dinner combinations are possible? #17. Blake has 6 dress shirts, 2 belts, 8 pairs of khaki pants, and 4 ties. How many different outfits, each composed of a dress shirt, a belt, a pair of khaki pants, and a tie, can he make? #18. A kindergarten teacher has 26 students in her class. She decides to randomly select the names of 4 students to see who brought their coloring homework assignment to school today. The first student displays the first piece of artwork, the second student displays the second piece of artwork, the third displays the third piece and the fourth student displays the final piece. In how many ways can the teacher assign these 26 students to the 4 pieces of artwork?

#19. A class of 100 students in a large freshman chemistry course at the University of Kentucky takes a standardized exam, where the scores can range from a 0 to a 100. The minimum score was a 12 and the highest was a 94. The mean score was a 62 and the standard deviation was 7. What is the number of standard deviations that includes all the data values? #20. Suppose the same class described above, takes a second test a few weeks later and the mean score and standard deviation are 81 and 8, respectively. As it turns out, every single student scored within 2 standard deviations of the mean. What COULD be the maximum and minimum scores on this test?

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#21. What is the standard deviation for the normal distribution shown below?

64 72 80 88 96 104 112 Consider the normal distribution shown above. After stating what the MEAN and STANDARD DEVIATION are, determine the following probabilities: DO NOT USE A CALCULATOR FOR THE FOLLOWING: Part a: P(X > 88) Part b: P(X < 104) Part c: P(X > 80) Part d: P(64 < X < 96) Part e: P(X > 96) Part f: P(X < 72) Part g: P(X <96) Part h: P(64 < X < 112) Part i: P(72 < X < 88) part j: P(96 < X < 104 #22. Consider the boxplots below.

a. What is the FIVE NUMBER SUMMARY for 1st period, approximately?

b. What is the IQR (Interquartile Range) for 6th period?

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The following table shows how many miles a distance runner ran during the course of a one week period:

Day of the week Sunday Monday Tuesday Wednesday Thursday Friday Saturday

MILEAGE 2.5 3.5 2.0 4.6 1.5 2.5 2.0

#23. Determine the Five Number Summary from the data given above. #24. Determine the IQR of the data. #25. How many modes does this data set have? #26. What values represent the following: 25th, 50th and 75th percentiles? What does it mean if a value is at the 75th percentile? #27. Between what two values does the middle 50% lie between? #28. Determine the mean, variance and standard deviation of the data using a calculator #29. Consider the following:

a. What are the next two terms in the following arithmetic sequence? 5, 12, 19, ….

b. What is the common difference in the sequence described above?

c. Write the explicit formula for the sequence.

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#30. Consider the following: a. What are the next two terms in the following geometric sequence?

3, -9, 27, ….

b. What is the common ratio in the sequence described above?

c. Write the explicit formula for the sequence Consider the following sequences. Determine if it is arithmetic or geometric. Write an explicit formula. #31. -7, -4, -1, 2, .... #32. 25, 40, 55, 70, … #33. 2, 6, 18, … #34. What is the 10th term in the sequence that is described by the following formula? A(n) = 8 – (n + 3)*6.

Solve the following equations: #35. -2(-x + 1) = 14 #36. -2(4x – 6) = 28 #37. -7(-8 + x) = -21 #38. (x – 4) – 6(3x – 2) = 4x + (x – 6) + 3 #39. 8x – 6x + 9 – x = -37

#40. Suppose you scored the following scores on a test: 68, 73, 85, and 86. You took a fifth test and do not know the score, but know that your average score among the five tests was a 72. What was your score on the fifth test?

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