THE ALGEBRA III MIDTERM EXAM REVIEW

Name ______________________________

This review MUST be turned in when you take the midterm exam

ALG III Midterm Review

Solve and graph on a number line.

1. 2 6 14x 2. 3 12 5 14x x 3. 4(2 1) 2(4 3)x x

Find the slope, then calculate the slope-intercept form of the line through the two points.

4. (1, 4),(16, 11) 5. ( 13,10),( 15,2) 6. (4, 2),(5,2)

Write the equation of the line that passes through the given point, parallel to the given equation.

7. 1

(4,5), 12

y x 8. 1

( 9,3),4

y x 9. 2

(3, 3), 15

y x

Write the equation of the line that passes through the given point, perpendicular to the given equation.

10. ( 1,3), 3 4y x 11. 5

(5, 2), 24

y x 12. ( 2,5), 4y

Solve the following system of equations by graphing.

13. 7 2 8

2 8

x y

x y

14.

3 2 8

4 12

x y

x y

15.

2 2

3 9

x y

x y

Solve the following system of equations by elimination.

16. 10 17

4 5 2

x y

x y

17.

30 70 0

24 56 0

x y

x y

18.

5 9 13

6 8 10

x y

x y

Solve the following system of equations by substitution.

19. 6 9

7 11

y x

x y

20.

3

7 4 21

x y

x y

21.

6 3 15

6 1

x y

x y

Solving the following word problem using systems of linear equations.

22. Dennis mowed his next door neighbor’s lawn for a handful of dimes and nickels, 80 coins in all. Upon completing the

job he counted out the coins and it came to $6.60. How many of each coin did he earn?

23. On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50. It turns out that the

doughnuts were more popular than the coffee. On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of

$14.25. How much was each cup of coffee?

24. The perimeter of a rectangular garden is 62 feet. The length is 1 foot more than twice the width. Find the dimension

of the garden.

Graph the following system of linear Inequalities.

25. 2 4

3 3

x y

x y

26.

3 6

2

x y

x y

27.

4 3 3

3 6

x y

x y

Factor Completely

28. 23 39 90x x 29.

22 2 112x x 30. 25 35 40x x

31. 23 19 40x x 32.

27 45 18x x 33. 25 6 1x x

34. 380 24 48x x 35.

8 7 67 70 37x x x 38. 23 27x x

39. 3 220 35 4 7x x x 40.

3 228 8 49 14x x x 41. 3 23 21 5 35x x x

42. 3 216 20 24 30x x x 43.

3 23 2 12 8x x x 44. 3 215 12 25 20x x x

Solve by factoring

45. 23 6x x 46.

2 5 24x x 47. 22 56 6x x

Solve by taking the square root

48. 240 8 12x 49.

29 9 396x 50. 225 5 4x

Solve by using the quadratic formula

51. 24 17 4x x 52.

26 9 6 0x x 53. 27 12 2x x

Solve by completing the square

54. 2 18 87 10x x 55.

2 10 61 5x x 56. 2 14 39 0x x

Find the Axis of Symmetry, the vertex, find the x-intercepts if possible, find the y-intercept. Graph the equation, be sure to

have 2 points on either side of the vertex.

57. 2 2 3y x x 58.

22 4 2y x x 50. 2 4y x x

Graph the following Exponential function, make a table to show the points you graphed. Is the graph growth or

decay?

51. 5xy 52. 1

23

x

Write the exponential function for the function that passes through the 2 given points.

53. (0,3),( 1,6) 54. (0, 18),( 2, 2) 55. (0,7),(2,63)

Simplify

56.

2

2

4 4

4

57.

3

4 3

2

2 2 58.

1

3

3 3

3

59.

4

3 1

2

2 2 2 60.

2

4 5

4

4 4 61.

4 3

2 5

7 7

2 2

Solve using common bases

62. 1 2 310 100x x 63.

2 136 216x x 64. 2 19 27x x

65. 2 5 88 4x x 66.

4 1 2100 1000x x 67. 2 327 243x x

Solve the following word problems using exponential growth or decay.

68. The number of mosquitoes at the beach has tripled every year since 1999. In 1999, there were 2,500 mosquitoes.

Write a model for this situation. How many mosquitoes would you predict were at the beach in 2005?

69. I bought a car for $25,000, but its value is depreciating at a rate of 10% per year. How much will my car be worth

after 8 years?

70. From 2000 - 2010 a city had a 2.5% annual decrease in population. If the city had 2,950,000 people in 2000,

determine the city’s population in 2008.

Probability

12-1 Counting Principle

1) The Breakfast Special at the Country Pantry, customers can choose their eggs scrambled, fried, or poached, whole

wheat, or white toast, and either orange, apple, tomato or grapefruit juice. How many different breakfast specials can a

customer order?

State whether the events are independent or dependent.

2) choosing a president, secretary and treasurer for the French Club, assuming a student could only hold one office.

3) choosing an ice-cream flavor and choosing a topping for it.

4) choosing a marble from a bag and then choosing another marble from the bag

5) rolling a die and getting a 4, then rolling the die and getting a 2

Solve:

6) The Palace of Pizza offers small, medium and large pizzas, with fourteen different toppings.

How many different one-topping pizzas do they serve?

7) Alicia brought 8 t-shirts and 6 pairs of shorts to soccer camp. How many different outfits consisting of a t-shirt and a

pair of shorts does she have?

12-2 Permutations and Combinations

nPr= n!/( n-r)! nCr= n!/ (n-r)!r! permutation/repetition= n!/p!q! Evaluate:

1a) 8P2 1b) 7P5 1c) 10C4 1d) 12C7

2) How many four-person committees can be formed from a set of 20 people? 3) Annette has rented a summer house. She wants to select four roommates from six friends. How many combinations of four friends will she have? 4) Find the number of possibilities for putting an algebra book, a geometry book, a chemistry book an English book and a health book on a shelf. 5) How many different ways can the letters in the word MISSISSIPPI be arranged? 12-3 Probability Odds of success = sucess:fail Probability = success/total

1) Find the odds of an event given the probability a) 8/9 b) 3/8 c) 11/12 d) 4/11 2) Find the probability of an event given the odds a) 6:1 b) 1:8 c) 4:5 d) 3:7 3) Eight out of 100 males and 1 out of 1000 females have some form of color blindness. a) What are the odds of a male being color-blind? b) What are the odds of a female being color-blind? 4) Rachel has 4 male kittens and 7 female kittens. She picks up 2 kittens to give to a friend. Find the probability of each selection. a) P(2 male) b) P(2 female) c) P(1 of each)

12-4 Multiplying Probability P(A and B)= P(A) P(B) P(A and B) = P(A) P(B following A) 1)Three dice are rolled to determine the number of moves in a board game for the players. a) What is the probability of the first die being a 4, the second die a 4 and the third die not a 4? b) What is the probability of the first die being a 2, the second die a 3 and the third die a 4? 2) The 20 prizes are each listed on a chip. The contestant picks a chip from the bag. There are 11 that say laptop, 8 say trip and 1 says truck. a) Drawing at random without replacement, what is the probability of picking a laptop and then a truck? b) Drawing at random without replacement, what is the probability of picking two trips?

3) Two cards are drawn from a standard deck of cards. Find each probability if no replacement occurs. a) P(two diamonds) b) P(jack, then king) 4) A die rolled twice. Find the probability. a) P(2, then 3) b) P(two 4’s) 5) A bowl contains 4 apples and 5 pears. Max randomly selects one, puts it back and then randomly selects another. What is the probability that both selections were pears? 6) Jack’s wallet contains three$1 bills, four $5 bills, and two $10 bills. If he selects three bills in succession, then what is the probability of selecting a $10 bill, then a $5 bill, then a $1 bill if the bills are not replaced? 7) A spinner has three colors on it, red, blue and green. What is the probability of: a) spinning twice and getting red then green b) spinning twice and getting the same number both times 12-5 Adding Probability P(A or B)= P(A) + P(B) P(A or B)= P(A) + P(B) – P(A and B) 1) Determine whether the events are mutually exclusive or inclusive. Then find the probability. a) the probability of drawing a King or a diamond from a standard deck of cards b)the probability of drawing a 3 or a Jack c) the probability of drawing an Ace or a face card(jack, queen, king) 1) A die is rolled. Find the probability of a) rolling a prime b) rolling at least a 5

c) rolling at least a 3 d) rolling less than 4 e) rolling multiples of 2 or 3 3) Sophie has 9 rings in her jewelry box. Five are gold and 4 are silver. If she randomly selects 3 rings to wear to a party, find each probability. a) P(2 silver or 2 gold) b) P(all gold or all silver)

Statistics Review

12-6 Statistical Measure 1) A firm gives sales training to its newly hired employees. To determine how effective the training is, the firm

compared the monthly sales of a group that has completed the training with a group that has not.

Create a stem and leaf plot from the data and compare. Does the orientation program seem to be succeeding?

thousands of dollars of sales last month:

No Training : 19, 22, 34, 23 ,27, 43,42, 28, 32, 29, 41, 26, 28, 26 ,43, 40

Training : 29, 21, 39, 44, 41, 36, 37, 29, 43, 45, 28, 32, 28, 33, 36, 32

2) Find the mean temperature from the data?

Temperature (Fahrenheit) Frequency

52 4

53 6

54 3

55 8

56 4

57 5

3) Find the mean, median and mode of the data: (show work it is required on the midterm)

12,11,7,9,8,6,4,5,10,1,5

4) Create a box-and-whisker plot of ages of some of the presidents at inauguration.

42, 43, 46, 51, 51, 51, 52, 54, 55, 55, 56, 56, 56, 60, 61, 61, 64, 69

5) Create a stem and leaf plot from the number of food items collected during a 20 day period.

20, 21, 25, 25, 30, 32, 33, 33, 35, 36, 37, 40, 45, 52, 55, 60, 65, 70, 72, 75

a) What does the entry 5|2 represent in the stem and leaf plot?

b) Does the data appear to be skewed to the right, skewed to the left or normally distributed?

6) Find the mean weight from the data and the standard deviation? (Round to nearest hundredth)

Weight (lbs.) Frequency

105 4

95 6

145 3

112 8

124 4

155 5

Mean: _________ standard deviation _____________

7) Find the mean, median and mode of the data: (round to the nearest tenth)

7, 11, 3, 8, 8, 10, 12, 2, 2

Mean: _________ median: __________ mode: ___________

8) Jon’s recreational basketball team has had the following yearly numbers of wins over the past 15 years.

Create a box-and-whisker plot of this data. Include labels and values of the five summary statistics. (round to the

nearest tenth)

15, 12, 14, 5, 17, 18, 20, 18, 15, 9, 6, 12, 14, 11, 15

9) What is the difference between a sample and a population or use examples to explain it?

10) Find the mean (round to nearest tenth) and standard deviation (round to nearest hundredth) for the data below as a

sample:

15, 3, 4, 11, 6, 5, 22, 17

sample mean: _____________ standard deviation: _____

11) Find the mean(round to nearest hundredth), standard deviation (round to nearest ten thousandth)and coefficient of

variation (round to nearest tenth of a percent) for the data. Determine whether weights of the group of pre-school

children or the H.S. football players is more consistent (less variable) .

Pre-school Weight lbs. HS Football Weight lbs.

30 150

35 135

40 250

32 175

38 115

45 125

29 200

33 195

30 176

41 130

Pre-school: mean: ___________ standard deviation: ____________ High School mean: ___________ standard deviation: ____________

12) Use the data to make a histogram. Determine if the data is skewed to the right, skewed to the left or normally

distributed.

Weeks Number of Patients

0-3.9 1

4-7.9 3

8-11.9 4

12-15.9 12

16-19.9 16

20+ 5

13) Find the mean(round to nearest tenth) and standard deviation (round to nearest hundredth) of the scores of the 20 people who took a nursing licensing test. (sample)

Score 71 75 78 82 84 93

Frequency 1 7 2 4 5 1

Mean: ____________ standard deviation: _______________

14) Find the mean, standard deviation and coefficient of variation for the data. Determine whether coffee prices or

gasoline prices were more stable in 2004.

Month Coffee $/lb. Gasoline $/gallon

Jan 2.89 1.59

Feb 2.86 1.67

Mar 2.93 1.77

Apr 2.91 1.83

May 2.83 2.01

June 2.75 2.04

July 2.88 1.94

Aug 2.87 1.90

Sept 2.84 1.89

Oct. 2.78 2.03

Nov. 2.78 2.01

Dec. 2.85 1.88

Z – Score calculations

1. IQ scores have a mean of 100 and a standard deviation of 16. Albert Einstein reportedly had an IQ of 160.

a. What is the difference between Einsteins IQ and the mean?

b. How many standard deviations is that?

c. Convert Einstein’s IQ score to a z score.

d. If we consider “usual IQ scores to be those that convert z scores between -2 and 2, is Einstein’s IQ usual or unusual?

2. Women’s heights have a mean of 63.6 in. and a standard deviation of 2.5 inches. Find the z score corresponding to a woman with a height of 70 inches and determine whether the height is unusual.

3. Three students take equivalent stress tests. Which is the highest relative score (meaning which has the largest z score value)? a. A score of 144 on a test with a mean of 128 and a standard deviation of 34.

b. A score of 90 on a test with a mean of 86 and a standard deviation of 18.

c. A score of 18 on a test with a mean of 15 and a standard deviation of 4. For the numbers below, find the area between the mean and the z-score:

a) z = 1.17

b) z = -1.37

5. For the z-scores below, find the percentile rank (percent of individuals scoring below): a) -0.47

b) 2.24

6. Scores on the SAT form a normal distribution with 500 and 100 .

a) What is the minimum score necessary to be in the top 15% of the SAT distribution?

b) Find the range of values that defines the middle 80% of the distribution of SAT scores (372 and 628).

7) Mrs. Appleby gave an exam to her 32 Alg II students at the end of the first semester. The scores were normally

distributed with a mean score of 75 and standard deviation of 6.

Draw a normal distribution. Label the distribution with the mean value, and label the distribution with the

corresponding values for +/- one standard deviation, +/- two standard deviations, +/- three standard deviations

a) About what percent of the class would you expect to have scored between 69 and 81?

b) What percent of the class would you expect to have scored between 63 and 69?

c) Approximately how many students scored between 81 and 87?

d) Approximately how many students scored between 63 and 8

e) What is the z-score for a student that scored 72?

f) Approximately what percentage of students have z-scores between 0 and 1.7?

g) Approximately what percentage of students have z-scores between 1.2 and 1.7?

h) Approximately what percentage of students have z-scores between 0 and -1.35?

i) Approximately what percentage of students have z-scores between -1.35 and 1.5?

h) What is the test score of a student that had a z-score of -1.4?

12-7 Normal distribution

8) Use the data to make a histogram. Determine if the data is positively skewed, negatively skewed or normally

distributed.

Miles run Track Team Members

0-4 3

5-9 4

10-14 7

15-19 5

20-23 2

9) The number of eggs laid per year by a particular breed of chicken is normally distributed with a mean of 225 and a

standard deviation of 10 eggs.

Use the sketch below to place the mean and the deviations in the correct locations:

About what percent of the chickens will lay between 215 and 235 eggs per year?

What percent would you expect to lay more than 245 eggs?