Unit
Statistics (Probability is mixed in as well)


For a statistics project, a group of students decide to collect data in order to approximate the percent of people in the town who
are left-handed. They ask every third student entering the school cafeteria whether he or she is left-handed or right-handed.
What type of method did this group use? Explain which population the group can draw a conclusion about based on their method.
Suggest a better method that would allow the students to draw a conclusion about all the residents in their town. Enter your
answers and your explanation in the space provided.
Exercise
o Part A The histograms show the distribution of heart rates of randomly selected adult males between the ages of 40 and 45
after 20 minutes of continuous exercise. The adult males were randomly assigned to use either a new elliptical machine
(Experimental Group) or a traditional treadmill machine (Control Group). What conclusion about the difference between the
distributions of the heart rates for these two groups can be drawn? Justify your answer. Enter your answer and your
justification in the space provided.
1. Statistics (M3U1)
o
Part B After the participants worked out three times per week for four weeks solely on their assigned machines, participants’
heart rates were collected again after 20 minutes of continuous exercise. The data are shown in the histograms. What
conclusion about the difference between the distributions of the heart rates for the two groups can be drawn? Justify your
answer. If the target heart rate range for adult males aged between 40 and 45 after 20 minutes of exercise is around 175
beats per minute, what recommendation would you make in terms of which machine to use? Justify your answer. Based upon
these data, what conclusion about exercise machines in general can be made? Enter your answers and your justification in the
space provided.

The heights of the male students at a college are approximately normally distributed. Within this curve, 95% of the heights,
centered about the mean, are between 62 inches and 78 inches. The standard deviation is 4 inches. Use this information to
estimate the mean height of the males. Approximate the probability that a male student is taller than 74 inches. Explain how you
determined your answers. Enter your answers and your explanation in the space provided.

Use the information provided to answer Part A and Part B for question 18.
A city plans to implement a composting program. In the composting program, food waste will be collected from residents and
sent to one of these compost collection sites.
Operating the trucks used to transport the waste costs $1.25 per mile driven.
Each truck can hold 20 tons of waste.
Part A: Based on the given information, determine which composting collection site is cheapest. Describe the steps used
to determine which composting site is cheapest and explain any assumptions made. Create a model that can be used to
find the total cost of disposing food waste based on the number of tons of composting with the cheapest composting
program. Describe the steps used to create your model. Enter your answer, model, explanation, and assumptions in the
space provided.
o Part B: During the previous year, the city sent 290,000 tons of waste to landfills. The cost of disposing waste at a landfill is
$75 per ton. This year, the composting program will send 10% of the waste to composting sites instead of sending the
waste to landfills. Determine the amount of money the city will save in waste disposal costs based on 290,000 tons of
waste using the composting site you chose in Part A. Show the process you used to determine your answer. Enter your
answer and your work in the space provided.
o

The distribution of weights (rounded to the nearest whole number) of all boxes of a certain cereal is approximately normal with
mean 20 ounces and standard deviation 2 ounces. A sample of the cereal boxes was selected, and the weights of the selected
boxes are summarized in the histogram shown.
o
Part A: If w is the weight of a box of cereal, which range of weights includes all of the weights of cereal boxes that are within
1.5 standard deviations of the mean?
 17 ≤ 𝑤 ≤ 23
 18.5 ≤ 𝑤 ≤ 21.5
 19 ≤ 𝑤 ≤ 21
 20 ≤ 𝑤 ≤ 23
o

Part B: Which of these values is the best estimate of the number of boxes in the sample with weights that are more than 1.5
standard deviations above the mean?
 2
 6
 17
 36
The two-way table shows the classification of students in a mathematics class by gender and dominant hand. A student who is
ambidextrous uses both hands equally well.
o

Part A: What is the probability that a randomly selected student in the class is female given that the student is right-handed?
 1/12
 12/30
 12/23
 23/30
o Part B: One student will be selected at random from the class. Consider the events: X: the selected student is female Y: the
selected student is right-handed Which statement about events X and Y is true?
 The events are independent because the number of right-handed students in the class is larger than the number of
female students.
 The events are independent because the number of categories for dominant hand is different from the number of
categories for gender.
 The events are not independent because for one of the dominant hand categories the number of female students is 0.
 The events are not independent because the probability of X is not equal to the probability of X given Y.
The manager of food services at a local high school is interested in assessing student opinion about a new lunch menu in the
school cafeteria. The manager is planning to conduct a sample survey of the student population.
o Part A: Which of the listed methods of sample selection would be the most effective at reducing bias?
 Randomly select one day of the week and then select the first 30 students who enter the cafeteria on that day.
 Post the survey on the school Web site and use the first 30 surveys that are submitted.
 Randomly select 30 students from a list of all the students in the school.
 Randomly select one classroom in the school and then select the first 30 students who enter that classroom.
o
Part B: The manager wants to know if a student’s gender is related to the student’s opinion about the menu. Which statement
best describes the study?
 This is an observational study, and therefore, the manager will be able to establish a cause-and-effect relationship
between gender and opinion.
 This is an observational study, and therefore, the manager will not be able to establish a cause-and-effect relationship
between gender and opinion.
 This is an experimental study, and therefore, the manager will be able to establish a cause-and-effect relationship
between gender and opinion.
 This is an experimental study, and therefore, the manager will not be able to establish a cause-and-effect relationship
between gender and opinion.
Complex Numbers


2. Extending the
Number System
(M2U1)

3. Quadratic
Functions:
Working with
Equations
Which expressions are equal to a real number? Select all that apply.
o (−4𝑖)11
o (−3𝑖)12
o (2 + 3𝑖)2
o (4 + 5𝑖)(4 − 5𝑖)
o (6 + 8𝑖)(8 + 6𝑖)
Which statements are true?
o √−4 = 2
o √−4 = 2𝑖
o √4𝑖 = 2𝑖
o 2(𝑖 2 )2 = 2
o 2𝑖 3 = −2𝑖
For the products listed, i represents the imaginary unit. Which of the products are real numbers? Select all that apply.
o (8 − 2𝑖)(8 + 2𝑖)
o (8 − 2𝑖)(5𝑖)
o (3)(5𝑖)
o (3)(−4)
o (𝑖)(8 + 2𝑖)
o (𝑖)(5𝑖)
Quadratic Functions

Which equation has non-real solutions?

o 2𝑥 2 + 4𝑥 − 12 = 0
o 2𝑥 2 + 3𝑥 = 4𝑥 + 12
o 2𝑥 2 + 4𝑥 + 12 = 0
o 2𝑥 2 + 4𝑥 = 0
What are the solutions to the equation 2𝑥 2 − 𝑥 + 1 = 0 ?
o
o
o
o


1
4
1
4
1
4
1
4
−
−
−
−
1
√5
√5
and 4 + 4
4
1
√7
√7
and 4 + 4
4
1
√7
√7
( ) 𝑖 and + ( ) 𝑖
4
4
4
1
√5
√5
( ) 𝑖 and + ( ) 𝑖
4
4
4
An expression is given 𝑥 2 − 8𝑥 + 21. Determine the values of h and k that make the expression (𝑥 − ℎ)2 + 𝑘 equivalent to the
given expression.
An equation is given, 𝑥 2 − 8𝑥 + 21 = (𝑥 − 4)2 + 3𝑥 − 16. Find one value of x that is a solution to the given equation.
Systems of Equations

Functions f and g are defined as
1
{
𝑓(𝑥) = 2𝑥

𝑔(𝑥) = 𝑥 2
The graphs of 𝑦 = 𝑓(𝑥) and 𝑦 = 𝑔(𝑥) intersect at point P. Determine the x-coordinate of P. Round to nearest tenth.
Let 𝑓(𝑥) = 𝑎𝑥 2 where > 0 , and let 𝑔(𝑥) = 𝑚𝑥 + 𝑏 where 𝑚 > 0 and 𝑏 < 0. The equation 𝑓(𝑥) = 𝑔(𝑥) has n distinct real
solution(s). What are all the possible values of n? Justify your answers. Enter your answers and your justification in the space
provided

What is the value of z in the solution of the system of linear equations?

𝑥 − 9𝑦 + 4𝑧 = 1
{−2𝑥 + 9𝑦 − 4𝑧 = −3
2𝑥 + 𝑦 − 4𝑧 = −3
How many points of intersection does the given system of equations have?
𝑦 = 1 − 𝑥2
{
𝑦 =2−𝑥
o None
o One
o Two
o

Infinitely many
Given 𝑦 = 4𝑥 2 + 12𝑥 + 9, solve if 𝑥 + 𝑦 = 12.
4. Comparing
Functions and
Modeling (M2U5)
5. Representing
Functions (M3U4)
Polynomial Functions

The expression 𝑥 4 − 81 can be rewritten in this form where a, b, and c are real numbers.
(𝑥 2 + 𝑎)(𝑥 + 𝑏)(𝑥 + 𝑐)
o
What are the values of a, b, and c?

Which expression is equivalent to 𝑎2 𝑥 2 − 2𝑐𝑥 2 + 𝑎2 𝑦 − 2𝑐𝑦
o (𝑥 2 − 𝑦)(𝑎2 − 2𝑐)
o (𝑥 2 − 𝑦)(𝑎 + 𝑐)
o (𝑥 2 + 𝑦)(𝑎2 − 2𝑐)
o (𝑥 2 + 𝑦)(𝑎 + 𝑐)

Simplify the following expression so that it is written without parentheses: 𝑗 4 − 16 + (𝑗 2 − 2)2

The polynomial 𝑝(𝑥) = 2𝑥 3 + 13𝑥 2 + 17𝑥 − 12 has (𝑥 + 4) as a factor. Factor the polynomial into three linear terms.
Describe the steps you would use to sketch the graph of the function defined by this polynomial. Identify all intercepts and
describe the end behavior of the graph. Enter your factored polynomial, your description, and your answers in the space
6. Polynomial and
Rational:
Representations
and Modeling
provided.

If k is a constant, what is the value of k such that the polynomial 𝑘 2 𝑥 3 − 6𝑘𝑥 + 9 is divisible by 𝑥 − 1?

Consider the equation (𝑥 2 + 2𝑥𝑦 + 𝑦 2 )(𝑥 + 𝑦) = 64
o Part A: What is the value of x + y?
 2
 4
 8
 32
o Part B: If 𝑧 > 0 𝑎𝑛𝑑 𝑧 𝑥 𝑧 𝑦 = 81, what is the value of z?

The expression 𝑥 2 (𝑥 − 𝑦)3 − 𝑦 2 (𝑥 − 𝑦)3 can be written in the form (𝑥 − 𝑦)𝑎 (𝑥 + 𝑦), where a is a constant. What is the
value of a?

Consider the expression 6𝑥 3 − 5𝑥 2 𝑦 − 24𝑥𝑦 2 + 20𝑦 3
o Part A: Which expression is equivalent to 6𝑥 3 − 5𝑥 2 𝑦 − 24𝑥𝑦 2 + 20𝑦 3?
 𝑥 2 (6𝑥 − 5𝑦) + 4𝑦 2 (6𝑥 + 5𝑦)
 𝑥 2 (6𝑥 − 5𝑦) + 4𝑦 2 (6𝑥 − 5𝑦)
 𝑥 2 (6𝑥 − 5𝑦) − 4𝑦 2 (6𝑥 + 5𝑦)
 𝑥 2 (6𝑥 − 5𝑦) − 4𝑦 2 (6𝑥 − 5𝑦)
o Part B: Which expression are factors of 6𝑥 3 − 5𝑥 2 𝑦 − 24𝑥𝑦 2 + 20𝑦 3 ? Select all that apply.
 𝑥 2 + 4𝑦 2
 6𝑥 − 5𝑦
 𝑥 + 2𝑦
 6𝑥 + 5𝑦
 𝑥 − 2𝑦

Consider the polynomial function 𝑓(𝑥) = (2𝑥 − 1)(𝑥 + 4)(𝑥 − 2).
o Part A: What is the y-intercept of the graph of the function in the xy-coordinate plane?
o Part B: For what values of x is 𝑓(𝑥) > 0? Select all that apply.
 𝑥 < −4
1
 −4 < 𝑥 < 2


−4 < 𝑥 < 2
1
<𝑥<2
2

𝑥>
1
2


 𝑥>2
o Part C: What is the end behavior of the graph of the function?
 As x → −∞, f x( ) → ∞, and as x → ∞, f x( ) → ∞.
 As x → −∞, f x( ) → ∞, and as x → ∞, f x( ) → −∞.
 As x → −∞, f x( ) → −∞, and as x → ∞, f x( ) → ∞.
 As x → −∞, f x( ) → −∞, and as x → ∞, f x( ) → −∞
o Part D: How many relative maximums does the function have?
 None
 One
 Two
 Three
Factor the expression 6𝑥 4 + 24𝑥 3 − 72𝑥 2
Write the expression 𝑥 − 𝑥𝑦 2 as the product of the greatest common factor and a binomial. Then, determine the complete
factorization of 𝑥 − 𝑥𝑦 2 . Enter your answers in the boxes.
o Product of greatest common factor and binomial:
o Complete factorization:
Rational Functions

7. Radicals,
Logarithms and
Exponents:
Representations
and Modeling
Determine the solution(s) of the equation. Select all that apply.
2𝑚2 + 3𝑚 − 5
=4
𝑚2 + 4𝑚 − 5
o -5
o -15/2
o -5/2
o 0
o 1
Radical Functions

Solve for x. −√𝑥 + 10 = −7

Which expression is equivalent to (√27) ?
o 12
o 92
o 814
3
4
3


o 274
What extraneous solution arises when the equation √𝑥 + 3 = 2𝑥 is solved for x by first squaring both sides of the equation?
Given that 𝑥 > 0, which expression is equivalent to 5√𝑥𝑦 + 25√𝑥?
o 5(𝑥𝑦)−1 + 25𝑥 −1
1
o
25𝑥 2 (√𝑦 + 5)
o
√𝑥 (25𝑦 2 + 5)
o
5𝑥 2 (𝑦 2 + 5)
1
1
1
3

If √ √(𝑥 + 1)5 = (𝑥 + 1)𝑎 , for 𝑥 ≥ −1, and a is a constant, what is the value of a?


o 3/10
o 5/6
o 5/3
o 10/3
Solve √𝑥 2 − 4𝑥 + 4 = 𝑥 − 2
What extraneous solution arises from solving the equation √𝑎 = 𝑎 − 6 ?

What is the extraneous solution that arises from solving the equation√ 4 − 𝑥 = 𝑥 ?
15
Exponential Functions


27𝑥 = 9𝑥−3
3
81𝑥 can be written as (3𝑎𝑥 )3 . What is a?

Consider the equation
2
o
o
4𝑥
2𝑥
=2
Which equation is equivalent to the equation shown?
2
 2𝑥 = 2
2
 2𝑥 −𝑥 = 2
 22𝑥 = 2
2
 22𝑥 −𝑥 = 2
Which values are solutions to the equation?
 -2
 -1

 -1/2
 ½
 1
 2
During a 1-year period, a population of tropical insects grew according to the model = 𝑃0 (1.46)𝑡 , where P is the population, 𝑃0 is
the initial population, and t is time in years. Which equation can be used to model the approximate weekly growth rate? (Assume
52 weeks in a year.)
o 𝑃 = 𝑃0 (1.0073)52𝑡
o 𝑃 = 𝑃0 (1.0088)52𝑡
o 𝑃 = 𝑃0 (1.0281)52𝑡
o 𝑃 = 𝑃0 (1.0371)52𝑡

Comparing Interest
o A bank offers a savings account that accrues simple interest annually based on an initial deposit of $500. If 𝑆(𝑡) represents
the money in the account at the end of t years and 𝑆(5) = 575, write a function that could be used to determine the
amount of money in the account over time. Show your work or explain your reasoning. Enter your equation and your
reasoning in the space provided.
o Another bank offers a savings account that accrues compound interest annually at a rate of 3%. What is the initial
amount needed in this account so that it will have the same amount of money at the end of 10 years as the account in
Part A at the end of 10 years? Show your work or explain your reasoning. Enter your answer and your reasoning in the
space provided.

Paul started to train for a marathon. The table shows the number of miles Paul ran during each of the first three weeks after he
began training.
If this pattern continues, which of the listed statements could model the number of miles Paul runs 𝑎𝑛 , in terms of the number
of weeks, n, after he began training? Select all the apply.
o 𝑎𝑛 = 10 + 2(𝑛 − 1)
o 𝑎𝑛 = 10𝑛2
o 𝑎𝑛 = 10(1.2)𝑛−1
o 𝑎1 = 10, 𝑎𝑛 = 1.2𝑎𝑛−1
o 𝑎1 = 10, 𝑎𝑛 = 2 + 𝑎𝑛−1

A scientist places 7.35 grams of a radioactive element in a dish. The half-life of the element is 2 days. After d days, the number of
𝑑
grams of the element remaining in the dish is given by the function 𝑅(𝑑) =

Which statement is true about the
equation when it is rewritten without a fractional exponent? Select all that apply.
o An approximately equivalent equation is 𝑅(𝑑) = 7.35(0.250)𝑑 .
o An approximately equivalent equation is 𝑅(𝑑) = 7.35(0.707)𝑑 .
o The base of the exponent in this form of the equation can be interpreted to mean that the element decays by 0.250 grams
per day.
o The base of the exponent in this form of the equation can be interpreted to mean that the element decays by 0.707 grams
per day.
o The base of the exponent in this form of the equation can be interpreted to mean that about 25% of the element remains
from one day to the next day.
o The base of the exponent in this form of the equation can be interpreted to mean that about 70.7% of the element
remains from one day to the next day.
Consider the expression 3𝑥 − 3𝑥−2
o Part A: Which is an equivalent form of the given expression?
 3𝑥 − 9(3𝑥 )
 3𝑥 − 2(3𝑥 )
o

1 2
7.35 (2) .

3𝑥 −

3𝑥 −
3𝑥
2
3𝑥
9
Part B: This expression can also be rewritten in the form 𝑎(3𝑥 ), where a is a constant. What is the value of a?
 1/9
 1/2
 8/9
 3/2
The population of country A was 40 million in the year 2000 and has grown continually in the years following. The population P, in
millions, of the country t years after 2000 can be modeled by the function 𝑃(𝑡) = 40𝑒 0.027𝑡 , where 𝑡 ≥ 0 .
o Part A: Based on the model, what was the average rate of change, in millions of people per year, of the population of
country A from 2000 to 2005? Give your answer to the nearest hundredth.
o Part B: Based on the model, the solution to the equation 50 = 40𝑒 0.027𝑡 gives the number of years it will take for the
population of country A to reach 50 million. What is the solution to the equation expressed as a logarithm?
 0.027ln(1.25)


ln(1.25)
0.027
1.25
ln (0.027)

o
o


0.027
ln ( 1.25 )
Part C: Based on the model, in which years will the population of country A be greater than 55 million? Select all that
apply.
 2004
 2007
 2010
 2013
 2016
 2019
Part D: For another country, country B, the population M, in millions, t years after 2000 can be modeled by the function
𝑀(𝑡) = 35𝑒 −0.042𝑡 , where 𝑡 ≥ 0. Based on the models, what year will be the first year in which the population of country
B will be greater than the population of country A?
 2009
 2012
 2021
 The population of country B will not exceed the population of country A.
DeShawn is in his fifth year of employment as a patrol officer for the Metro Police. His salary for his first year of employment was
$47,000. Each year after the first, his salary increased by 4% of his salary the previous year.
o Part A: What is the sum of DeShawn’s salaries for his first five years of service?
 $101,983
 $188,000
 $219,932
 $254,567
o Part B: If DeShawn continues his employment at the same rate of increase in yearly salary, for which year will the sum of
his salaries first exceed $1,000,000? Give your answer to the nearest integer.
To investigate housing needs in the future, a town planning committee created a model to help predict the growth of the
population of the town. The
committee created a model based on data about the population
of the town for five years. The data
are shown in the table.
o
o

Part A: Which model for 𝑃(𝑡), the population of the town t years after 1985, best fits the data?
 𝑃(𝑡) = 4.95 + 0.229𝑡

 𝑃(𝑡) = 5.35 + 0.228𝑡
 𝑃(𝑡) = 5.24(1.030)𝑡
 𝑃(𝑡) = 5.35(1.029)𝑡
Part B: Consider the value predicted by the model for the year 2010. Which statement is true?
 The model overpredicts the actual population of the town by fewer than 1,000 people.
 The model overpredicts the actual population of the town by more than 1,000 people.
 The model underpredicts the actual population of the town by fewer than 1,000 people.
 The model underpredicts the actual population of the town by more than 1,000 people.
When approximating the age of an artifact that is less than 40,000 years old, the radioisotope carbon-14 can be used. Carbon-14 is
an element with the property that every 5,730 years the mass of the element in a sample is reduced by half. The mass of the
carbon-14 in an artifact can be modeled by an exponential function, m, of its age, x.
o Part A: Let A represent the original mass of carbon-14. Which function is an appropriate model?
 𝑚(𝑥) = 𝐴 ∙ 2−5,730𝑥
−𝑥

𝑚(𝑥) = 𝐴 ∙ 25,730

𝑚(𝑥) = 𝐴 ∙ 2 40,000
−5,730𝑥
−40,000𝑥
o
o
 𝑚(𝑥) = 𝐴 ∙ 2 5,730
Part B: Based on the situation, which interval represents the domain of the function m?
 0≤𝑥<∞
 −∞ < 𝑥 < ∞
 0 ≤ 𝑥 < 5,730
 0 ≤ 𝑥 < 40,000
Part C: Which statements describe the graph of m in the coordinate plane? Select all the apply.
 The function m is a linear function.
 The function m is a nonlinear function.
 The function m is an increasing function.
 The function m is a decreasing function.
o

 The function m is a periodic function.
Part D: At what age would the mass of carbon-14 in an artifact be one-fourth the original amount?
 1,432.5 years old
 2,865 years old
 11,460 years old
 22,920 years old
An investor deposits g dollars into an account at the beginning of each year for n years. The account earns an annual interest rate
of r, expressed as a decimal. The amount of money S, in dollars, in the account can be determined by the formula 𝑆 =
𝑔
[(1 + 𝑟)𝑛 − 1]
𝑟
o
o
Part A: Suppose the investor deposits $500 a year for 10 years into an account that earns an annual interest rate of 5%. If
no additional deposits or withdrawals are made, what will be the balance in the account at the end of 10 years?
 $6,003.05
 $6,015.06
 $6,288.95
 $6,301.52
Part B: Fill in the blank to complete the sentence. Give your answer to the nearest cent.
 Suppose the investor wanted the balance in the account to be at least $12,000 at the end of 10 years. At an
annual interest rate of 5%, the amount of the yearly deposit should be at least $______
Average Rate of Change

Find the average rate of change of the graph.

Find the average rate of change in the account that can be modeled by the equation 𝐴 = 2000𝑒 0.045𝑡 for the first two years? Find
the amount of time it will take for the account to have $4000.
Trigonometric Functions

The function 𝑓(𝑥) = cos(𝑥). Function 𝑔(𝑥) results from a transformation on the function
𝑓(𝑥) = cos(𝑥). A portion of the graph of 𝑔(𝑥) is shown. What is the equation of 𝑔(𝑥)?
o
o
o
o
𝑔(𝑥) = cos(𝑥) − 2
𝑔(𝑥) = cos(𝑥) + 2
𝑔(𝑥) = cos(2𝑥) + 0
𝑔(𝑥) = 2cos(𝑥) + 0

The graph shows 𝑓(𝑥) = cos(𝑥) on the interval 0 ≤ 𝑥 ≤ 2𝜋. Function h is a transformation of
f such that ℎ(𝑥) = −𝑓(𝑥). Which of the following statements is true?
o Function f is an even function.
o Function f is an odd function.
o Function f is neither an even nor odd function. Function h is an even function.
o Function h is an odd function.
o Function h is neither an even nor odd function.

Select each statement that is true about the graph of 𝑓(𝑥) = sin(𝑥 + 3) − 2
o Amplitude: 1
o Amplitude: 2
o Midline: y = 2
o Y-intercept: (0, 2)
o X-intercept: (0, 0)

Angle  is in Quadrant II, and sin 𝜃 = 5. What is the value of cos 𝜃?
8. Trigonometric:
Representations
and Modeling
4
o
o
o
o
4/5
3/5
-3/5
-4/5

Select each statement that is true about the graph of 𝑓(𝑥) = sin(𝑥 + 2) − 2
o Amplitude: 1
o Amplitude: 2
o Midline: y = 2
o Y-intercept: (0,2)
o X-intercept: (0,0)

The London Eye, a Ferris wheel in England, has a diameter of 120 meters. The wheel completes a full rotation in 30 minutes to
allow passengers to enter a capsule at the base of the Ferris wheel without stopping the wheel. At the highest point, a capsule
reaches a height of 135 meters above the ground. The height above the ground, in meters, of a capsule after x minutes can be
𝜋
𝑥) + 𝐵
15
modeled by (𝑥) = 𝐴 ∙ cos (
o
o

, where A and B are constants.
Part A: Given the situation, what is the value of A?
Part B: Consider a capsule that begins its rotation at the base of the London Eye. For the times listed, how many
minutes after the rotation begins will the capsule be 45 meters above the ground? Select all that apply.
 15 minutes
 25 minutes
 35 minutes
 45 minutes
 55 minutes
 65 minutes
𝜋(𝑥)
)+
2
Using your knowledge of period, amplitude, and points on the midline, graph the function 𝑓(𝑥) = sin (
3 .
Average Rate of Change

The graph models the height, h, above the ground, in feet, at time t, in seconds, of a person swinging on a swing. Each point
indicated on the graph represents the height of the person above the ground at the end of each one-second interval.
Select two time intervals for which the average rate of change in the height of the person is approximately -1/2 feet per second.
o From 0 seconds to 1 second
o From 1 second to 2 seconds
o From 2 seconds to 3 seconds
o From 3 seconds to 4 seconds
o From 4 seconds to 5 seconds
o From 5 seconds to 6 seconds
o
o

From 6 seconds to 7 seconds
From 7 seconds to 8 seconds
The apothem of a regular polygon is the distance from the center to any side.
If the length of the apothem remains constant at 10 inches, the formula for the perimeter of a regular polygon as a function of the
360
number of sides n is 𝑃(𝑛) = 10 (tan ) (2𝑛).
2𝑛
As the regular polygon changes from a pentagon (5 sides) to an octagon (8 sides), what is the approximate average rate of change
in the perimeter?
o
o
o
o
9. Probability
(M2U8)
Decrease of 0.80 inches for each additional side
Decrease of 2.13 inches for each additional side
Decrease of 4.56 inches for each additional side
Decrease of 6.38 inches for each additional side
See Stats Section from Unit 1 Above
Where do these fit in????
Functions

The function f is defined as 𝑓(𝑥) = 𝑥 2 − 4𝑥.
o Write an expression that defines 𝑓(𝑥 + 5).
o Describe the transformation that maps the graph of 𝑓(𝑥) to 𝑓(𝑥 + 5). Justify your answer algebraically or by using key features of the graphs.

The functions f and g are defined by 𝑓(𝑥) = 𝑥 2 and 𝑔(𝑥) = 2𝑥 respectively, Which equation is equivalent to ℎ(𝑥) =
o
o
o
o


ℎ(𝑥) = −2𝑥 3
ℎ(𝑥) = −8𝑥 3
ℎ(𝑥) = 𝑥 2 − 2𝑥
ℎ(𝑥) = 2𝑥 2 + 2𝑥
𝑓(2𝑥)𝑔(−2𝑥)
?
2
Given the functions ℎ(𝑥) = |𝑥 − 4| + 1 and 𝑘(𝑥) = 𝑥 2 + 3, which intervals contain a value of x for which ℎ(𝑥) = 𝑘(𝑥)? Select all that apply.
o −4.5 < 𝑥 < −3
o −3 < 𝑥 < −1.5
o −1.5 < 𝑥 < 1.5
o 1.5 < 𝑥 < 3
o 3 < 𝑥 < 4.5
Consider the functions 𝑓(𝑥) and 𝑔(𝑥) described by the equations and the functions ℎ(𝑥) and 𝑘(𝑥) shown by graphs. Which of the statements are true?
Select all the apply.
o
o
F is an odd function.
F is neither an even nor odd function.
o
o
o
o
o
o

G is an even function.
G is neither an even nor odd function.
H is an even function.
H is an odd function.
K is an odd function.
K is neither an even nor odd function.
Creating Equations
o Part A: Two children sit on a seesaw, as illustrated. The mass, in kilograms, of the first child 𝑚1 s and the mass, in kilograms, of the second child
is 𝑚1 . In the diagram, 𝑑1 and 𝑑2 represent the distance, in feet, from the fulcrum (the balance point) to each child. The total distance between
the children is 10 feet.
For a seesaw to be balanced, 𝑚1 𝑑1 = 𝑚2 𝑑2 . Use the information in the table to write the function 𝑓(𝑥) that allows you to determine 𝑚1 , the
mass of the first child.
Enter your function in the space provided. Enter only your function.
o
Part B: Determine the inverse function 𝑓 −1 (𝑥) to model the distance, 𝑑2 , based on the mass of the first child. Show your work.

The graph represents the temperature, in degrees Fahrenheit (°F), of tea for the first 120 minutes after it was poured into a cup.
o
o

Part A: Based on the graph, what was the temperature of the tea when it was first poured into the cup?
 68°
 114°
 136°
 204°
Part B: Based on the graph, as the number of minutes increased, what temperature did the tea approach?
 68°
 114°
 136°
 204°
Use the information provided to answer Part A and Part B for question 13. An athletic shoe company is designing a new running shoe. The sole of the
shoe is designed with 5.0 millimeters of tread on the heel area and 4.0 millimeters of tread on the front-foot area. To test the durability of the shoe, the
designers gave test shoes to 9 people who run every day. After one week of use, the tread was measured to see how much was remaining. The results of
the test are shown in the table.
Tread Remaining after One Week
o
o

Part A: Create one model for the tread thickness of the heel and one model for the tread thickness of the front-foot that can be used to
determine the length of time the tread of the shoes will last under daily use. Describe how you determined your models and state any
assumptions you made. Use the models to determine the number of weeks the shoes will last. Enter your models, your description, and your
answer in the space provided.
Part B: Based on your models from Part A, describe how the company could modify the thickness of the tread so that the tread on the entire
shoe lasts about the same amount of time. Justify your description. Enter your description and your justification in the space provided.
A scientist is studying the cooling patterns of a particular material over time. Her research requires heating a sample of the material to 200C. She records
the temperature of the sample as it is cooled to 0C. The table shows the data collected during the first 2 minutes of the coloring process.
Time Material is
cooling (seconds)
Temperature (C)
0
40
80
120
200
141
101
74
The figure shows the scientist’s data (data points are plotted as large dots). Three possible models for the data are also shown: a linear model, a quadratic
model, and an exponential model.
o
o
o
o

Part A: Which model is linear? Which model is quadratic? Which model is exponential?
Part B: Which model is best for the range of times 0 ≤ 𝑡 ≤ 250 ?
Part C: Explain why the other models do not fit the data very well for the range of times 0 ≤ 𝑡 ≤ 250.
Part D: Construct a function using the type of model you decided is best (linear, quadratic, or exponential). Show your work and use function notation
when entering your answer.
The functions 𝑓(𝑥) = 1 − 𝑥 and 𝑔(𝑥) =
0.11
are
𝑥2
defined for all values of x > 0. The graphs are shown in the coordinate plane.
o
o
o
Part A: Explain how you can use the graph to find the solution(s) of the equation 𝑓(𝑥) = 𝑔(𝑥). In your answer, provide the approximate value(s) of the
solution(s).
Part B: Write the value(s) of 𝑓(𝑥) when x equals the solution(s) from Part A.
Part C: Let function ℎ(𝑥) be defined as ℎ(𝑥) = 𝑓(𝑥) − 𝑔(𝑥). What are the coordinates of the point(s) on the graph of ℎ(𝑥) when x equals the solution(s)
from Part A? Explain your reasoning.