Pre-AP Algebra II Chapter 3 Test Revie II -- Chapter... · Pre-AP Algebra II – Chapter 3 Test Review ... Use a calculator to find the mean, mode, median, standard deviation, variance,

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Pre-AP Algebra II – Chapter 3 Test Review Standards/Goals:

S.ID.4.: o 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.

S.IC.1.: I can understand how statistics can be used as a process to make inferences and decisions regarding a population based on a random sample of data from that population.

F.IF.1: o I can understand what a relation and a function is. o I can understand that a function assigns to each element of a domain, EXACTLY one element of

the range. F.IF.2.: I can evaluate functions for input values in their domains. E.2.a./F.IF.5.: I can relate the domain of a function to its graph. C.1.d./F.BF.1b.:

o I can perform operations on functions, including: addition, subtraction, multiplication and division.

o I can determine the domain and range of functions. (Algebra I): D.2.i.: I can transform different representations of relations and functions (specifically,

with absolute value functions). (Algebra II): E.2.b.: I can use transformations to draw the graph of a relation and then determine a

relation that fits a graph. A.1.g./F.IF.7.b: I can graph a piecewise function.

Find the domain of each of the following:

#1. ( )

#2. ( ) √ #3. ( )

√

#4. Consider the following function: g(x) = | |

a. Identify the more basic, parent function that has been shifted, reflected, stretched, or compressed.

Answer: y = _____ b. Indicate how the basic function found in step 1 has been shifted, reflected, stretched,

or compressed.

Horizontal shift: ᴑ LEFT ᴑ RIGHT ᴑ NONE # of units: ______

Stretch/Compress: ᴑ STRETCH ᴑ COMPRESS ᴑ NONE By a factor of: _____

X-Axis Reflection: ᴑ yes ᴑ no

Y-Axis Reflection: ᴑ yes ᴑ no

Vertical Shift: ᴑ UP ᴑ DOWN ᴑ NONE # of units: ______

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#5. Consider the following function: g(x) = | |

a. Identify the more basic, parent function that has been shifted, reflected, stretched, or compressed.

Answer: y = _____ b. Indicate how the basic function found in step 1 has been shifted, reflected, stretched,

or compressed.

Horizontal shift: ᴑ LEFT ᴑ RIGHT ᴑ NONE # of units: ______

Stretch/Compress: ᴑ STRETCH ᴑ COMPRESS ᴑ NONE By a factor of: _____

X-Axis Reflection: ᴑ yes ᴑ no

Y-Axis Reflection: ᴑ yes ᴑ no

Vertical Shift: ᴑ UP ᴑ DOWN ᴑ NONE # of units: ______

#6. Given that f(x) = 6x – 4, find ( ) ( )

( )

Consider the following: f(x) = | |. Write an equation of a new graph, if the following occur. #7. Reflected in the x-axis, translated/shifted 4 units left and translated/shifted up 6 units.

#8. Reflected in the x-axis, translated/shifted 6 units right and translated/shifted down 10 units.

#9. Reflected in the y-axis, translated/shifted 10 units left and translated/shifted down 8 units and stretched by a factor of 4.

#10. Reflected in the x AND y axis and compressed by a factor of ½ and shifted down 12 units.

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#11. Using the graph of the relation below, answer the following: i. Is the graph a function?

ii. Name the DOMAIN and RANGE of the relation in interval notation. Function:

ᴑ yes ᴑ no DOMAIN: ____________ RANGE: ______________







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Consider the functions: ( ) and g(x) = 3x – 5 #17. Find f(g(x)) and g(f(-6)) #18. Find f(-5) + g(5)

#19. Find f(x – 1) #20. Find g(x + 8) + f(-8).

#21.

a. Use a calculator to find the mean, mode, median, standard deviation, variance, min, Q1, Q3, max and IQR of the following numbers which are the average points scored by eight members of a college women’s basketball team:

5, 11, 15, 9, 19, 22, 17, 17.

b. Suppose that each member managed to increase their average points scored by 2 points apiece the following season. Find the mean, mode, median, standard deviation, variance, min, Q1, Q3, max and IQR. Be sure to note which values changed and which ones remained the same.

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#22. A quality control engineer finds that the mean life expectancy of its best-selling model of refrigerators is 11 years and the standard deviation is 2 years. The lifespans are approximately normally-distributed.

a. Draw the vertical lines for the distribution of the refrigerators.

b. What percent of refrigerators models will last from 9 to 13 years?

c. What percent of refrigerators modes will last from 5 years to 17 years?

d. What percent of refrigerators models will last for over 13 years? For less than 13 years?

e. What percent of refrigerators models will last for less than 7 years? Between 7 and 11 years?

Multiple Choice: #24. Which of the following histograms would be best approximated by a normal distribution: (a) (b) (c) (d)

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Multiple Choice: #25. Evaluate the piecewise function at the given value of the independent variable.

#26. Be able to distinguish the following types of sampling designs:

Simple Random Systematic Voluntary Response Convenience

Know which of the above types of sample designs will provide biased results. a. A psychologist uses a computer program to randomly select names from a list

of students at a university. The members of the sample will take a survey about student housing at the university.

b. A school principal gathers an alphabetical list of all the students at her school. Then she selects every 15th student to take a survey about the cafeteria’s lunch menu.

c. The students planning the junior class party want to know what kinds of pizza to buy. They ask the pizza restaurant what kinds sell the most.

d. The county road department wants to know which roads cause the most concern among the residents of the county. They ask the local restaurants to hand out survey forms for customers to return by mail.

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EXTRA PRACTICE: #27. 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 #28. 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? #29. 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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#30. Multiple Choice: Graph the function:

( ) {

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End of Course Exam Review: THROWBACK: #1. Find the distance between the points (-9, 7) and (5, 13). #2. Explain in a complete sentence what it means if you scored at the 83rd percentile on the ACT Science test in October of 2014? #3. A 6th grade teacher must choose 4 students from a class of 19 to present a presentation to the local school board. In how many ways can the teacher choose the four students? #4. A 6th grade teacher must choose 4 students from a class of 19 to present a presentation to the local school board. One student must do the needed research, one student must be the spokesperson, one student must work the projector and one student must design a special handout. In how many ways can the teacher choose the four students? #5. 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

a. What is the sample size?

b. What is the probability of randomly selecting a person who makes $25-$35K?

c. What is the probability of randomly selecting a person who is 46-60, given that they make over $50K?

d. What is the probability of randomly selecting a person who is 21-30 and earns over $50,000?

#6. What is the value of z in the solution of the system?

3 4 2 20

4

6 2 23

x y z

x y z

x y z

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#7. Write a set of constraints and an objective function for the following situation. The Supreme Shipping Company can load its trucks with both rectangular and cylindrical containers. A rectangular container has a volume of 100 cubic ft and weighs 200lb. A cylindrical container has a volume of 200 cubic ft and weighs 100 lb. Let x denote the number of rectangular crates carried by a truck and let y denote the number of cylindrical containers. The truck can haul at most 4800 lb and has the room for 4200 cubic ft of containers. The company charges $60 to ship a rectangular container and $50 to ship a cylindrical container so how many should they haul to maximize profits? Solve and graph each absolute inequality. #8. | | #9. | |

#10. | | #11. |

|

#12. Multiple Choice:

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Write each equation in standard form using integers.

#13. y = x + 6 #14. y + 5 = -(x + 3) #15. y =

Write the following equations into slope-intercept form from standard form. #16. 5x + 8y = 17 #17. 4x – 6y = 20 #18. 10x + 20y = 100 Matrices: Find the variable in each matrix equation.

#19. [

] [

] #20. [

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Pre-AP Algebra II Chapter 3 Test Revie II -- Chapter... · Pre-AP Algebra II – Chapter 3 Test Review ... Use a calculator to find the mean, mode, median, standard deviation, variance,