FSA Countdown
Algebra 2

Conversions
Florida Standards Assessments Test Item Descriptions
The Florida Standards Assessments (FSA) are composed of test items that include traditional multiplechoice items, items that require students to type or write a response, and technology-enhanced items
(TEI). Technology-enhanced items are computer-delivered items that require students to interact with
test content to select, construct, and/or support their answers. Currently, there are nine types of TEIs
that may appear on computer-based assessments for FSA
Mathematics.
Technology-Enhanced Item Types – Mathematics
1. Editing Task Choice – The student clicks a highlighted word or phrase, which reveals a drop-down menu
containing options for correcting an error as well as the highlighted word or phrase as it is shown in the
sentence to indicate that no correction is needed. The student then selects the correct word or phrase from
the drop-down menu. For paper-based assessments, the item is modified so that it can be scanned and
scored electronically. The student fills in a circle to indicate the correct word or phrase.
2. Editing Task – The student clicks on a highlighted word or phrase that may be incorrect, which reveals a text
box. The directions in the text box direct the student to replace the highlighted word or phrase with the
correct word or phrase. For paper-based assessments, this item type may be replaced with another item type
that assesses the same standard and can be scanned and scored electronically.
3. Hot Text –
a. Selectable Hot Text–Excerpted sentences from the text are presented in this item type. When the student
hovers over certain words, phrases, or sentences, the options highlight. This indicates that the text is
selectable (“hot”). The student can then click on an option to select it. For paper-based assessments, a
“selectable” hot text item is modified so that it can be scanned and scored electronically. In this version,
the student fills in a circle to indicate a selection.
b. Drag-and-Drop Hot Text–Certain numbers, words, phrases, or sentences may be designated “draggable”
in this item type. When the student hovers over these areas, the text highlights. The student can then
click on the option, hold down the mouse button, and drag it to a graphic or other format. For paperbased assessments, drag-and-drop hot text items will be replaced with another item type that assesses the
same standard and can be scanned and scored electronically.
4. Open Response–The student uses the keyboard to enter a response into a text field. These items can usually
be answered in a sentence or two. For paper-based assessments, this item type may be replaced with
another item type that assesses the same standard and can be scanned and scored electronically.
5. Multiselect – The student is directed to select all of the correct answers from among a number of options.
These items are different from multiple-choice items, which allow the student to select only one correct
answer. These items appear in the online and paper-based assessments.
6. Graphic Response Item Display (GRID)- The student selects numbers, words, phrases, or images and uses the
drag-and-drop feature to place them into a graphic. This item type may also require the student to use the
point, line, or arrow tools to create a response on a graph. For paper-based assessments, this item type may
be replaced with another item type that assesses the same standard and can be scanned and scored
electronically.
7. Equation Editor – The student is presented with a toolbar that includes a variety of mathematical symbols
that can be used to create a response. Responses may be in the form of a number, variable, expression, or
equation, as appropriate to the test item. For paper-based assessments, this item type may be replaced with
a modified version of the item that can be scanned and scored electronically or replaced with another item
type that assesses the same standard and can be scanned or scored electronically.
8. Matching Item – The student checks a box to indicate if information from a column header matches
information from a row. For paper-based assessments, this item type may be replaced with another item
type that assesses the same standard and can be scanned and scored electronically.
9. Table Item – The student types numeric values into a given table. The student may complete the entire table
or portions of the table depending on what is being asked. For paper-based assessment, this item type may
be replaced with another item type that assesses the same standard and can be scanned and scored
electronically.
Statistics, Probability, and
Number Systems (28%)
Functions and Modeling (36%)
Algebra and Modeling (1.36%)
Algebra 2 Standards
Domain
Standard
A-APR.1.1
A-APR.2.2
A-APR.3.4
A-APR.4.6
A-CED.1.1
A-CED.1.2
A-CED.1.3
A-CED.1.4
A-REI.1.1
A-REI.1.2
A-REI.2.4
A-REI.3.6
A-REI.3.7
A-REI.4.11
A-SSE.1.1
A-SSE.1.2
A-SSE.2.3
G-GPE.1.2
N-CN.3.7
A-APR.2.3
A-SSE.2.4
F-BF.1.1
F-BF.1.2
F-BF.2.3
F-BF.2.4
F-BF.2.a
F-IF.2.4
F-IF.2.5
F-IF.2.6
F-IF.3.7
F-IF.3.8
F-IF.3.9
F-LE.1.4
F-LE.2.5
F-TF.1.1
F-TF.1.2
F-TF.2.5
F-TF.3.8
N-CN.1.1
N-CN.1.2
N-RN.1.1
N-RN.1.2
S-CP.1.1
S-CP.1.2
S-CP.1.3
S-CP.1.4
S-CP.1.5
S-CP.2.6
S-CP.2.7
S-ID.1.4
S-IC.1.1
S-IC.1.2
S-IC.2.3
S-IC.2.4
S-IC.2.5
S-IC.2.6
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IP
Semester
# times
reviewed
A-APR.1.1
1. Rewrite the expression −3𝑎(𝑎 + 𝑏 − 5) + 4(−2𝑎 + 2𝑏) + 𝑏(𝑎 + 3𝑏 − 7) to find the coefficients of
each term. Enter the coefficients in the appropriate boxes.
2. Simplify the expression
(3𝑞 7 + 3𝑞 2 + 2𝑞) − (−𝑞 7 − 5𝑞 3 − 𝑞 2 )
3. For h(x) = 4x2 – x – 5 and k(x) = 2x2 + 5x – 8, find 2h(x) – 3k(x).
A. 14x2 – 17x + 14
B. 2x2 – 13x - 14
C. 2x2 – 17x – 34
D. 2x2 – 17x + 14
4. Rectangular prism A has edges with lengths x+5, x+2, and x+1. Rectangular prism B has edges
with lengths x+3, x+3, and x+2. Given that x  0, which rectangular prism has the greater volume,
and why?
5. Which expression is the expansion of (x + 1)4 ?
A. x4 + 4x3 + 6x2 + 4x + 1
B. x4 + 4x3 + 6x2 + 4x + 4
C. 4x4 + 4x3 + 6x2 + 4x + 1
D. 4x4 + 4x3 + 6x2 + 4x + 4
6. What is the product of (x + 5) and (4x2 – 3x – 4)?
A. 4x3+ 20x2 – 8x – 20
B 4x3+ 20x2 – 22x – 20
C. 4x3+ 17x2 – 12x – 20
D. 4x3+ 17x2 – 19x – 20
7. The rectangle shown is enlarged so that the horizontal length will be multiplied by 2x and its
width will be multiplied by ½x. What is the difference in the perimeters between the original and
enlarged rectangles?
5
3
A. x3 – 7x2 + 2
B.- x2 – 25x + 6
C. 5x3 – 14x2 + 4
D. 5x3 – 10x2 + 4x
2
2
8. Is the set {-3x2, 0, 2x2} closed under subtraction, and why?
A. Yes, the difference of any two elements is also in the set.
B. No, the difference of any two elements is also in the set.
C. No, two elements of this set have a difference that is not in the set.
D. Yes, two elements of this set have a difference that is not in the set.
9. An isosceles trapezoid has bases 6x2 – 4 inches and 12x2 + 2 inches as shown. The height is 3
inches, and the legs each have lengths of 4x inches. Find the area of the trapezoid?
A. 27x2 – 9 sq inches
B. 27x2 – 3 sq inches
C. 36x2 – 4 sq inches
D. 54x2 – 6 sq inches
A-APR.2.2
1. If k is constant, what is the value of k such that the polynomial k2x3 -6kx + 9 is divisible by x – 1?
2. Suppose p(x) = x3 – 2x2 + 13x + k. The remainder of the division of p(x) by (x +1) equals – 8.
What is the remainder of the division of p(x) by (x -1)?
A. – 8
B. 8
C. 16
20. 20
3. What is the remainder when P(x) = x4 – 7x2 + x – 15 is divided by x – 3?
A. 6
B. 0
C. – 18
D. - 120
4. Gloria attempted to find the remainder when P(x) = x3 – x2 – 30x + 72 is divided by (x – 3). Her
work is shown below. What error did she make, and how should she correct it?
A. Gloria should have found P(3) using the Remainder Theorem. The remainder should be 0.
B. Gloria should have written the third step as -27 + 9 + 90 + 72. The remainder should be 144.
C. Gloria should have found P(8) using the Remainder Theorem. The remainder should be 280.
D. Gloria should have written the second step as P(-3) = (-3)3 – (-3)2 – 30(3) + 72. The remainder
should be -54.
5. Which statement describes how to find the remainder of P(y) = (y3 + 6y2 + 11y + 6) ÷ (y + 1) using
the Remainder Theorem?
A. Find p(-1) = (-1)3 + 6(-1)2 + 11(-1) + 6 to get a remainder of 0.
B. Find p(1) = (1)3 + 6(1)2 + 11(1) + 6 to get a remainder of 24.
C. Use synthetic division to divide the coefficients of y3 + 6y2 + 11y + 6 by 1 to get a remainder of 0
D. Use long division to divide y3 + 6y2 + 11y + 6 by y – 1. The remainder is 24.
6. Given that the zeros of P(x) = x4 – x3 – 9x2 – 11x -4, according to the Remainder Theorem, which
statement must be true?
A. P(4) = 4, P(1) = -1
B. P(4) = -4, P(- 1) = 1
C. P(4) = 0, P(- 1) = 0
D. P(4) = 4, P(1) = 0
A-APR.3.4
1. Below is an algebraic proof that
(𝑥 2 + 1)2 = (𝑥 2 − 1)2 + (2𝑥)2 .
Is the proof valid, if not what step is invalid in the proof?
Step 1
Step 2
Step 3
Step 4
Step 5
Step 6
A.
B.
C.
D.
E.
F.
G.
(𝒙𝟐 + 𝟏)𝟐
= (𝒙𝟐 + 𝟏)(𝒙𝟐 + 𝟏)
=𝑥 4 +𝑥 2 +𝑥 2 + 1
=𝑥 4 +2𝑥 2 + 1
=𝑥 4 +2𝑥 2 + 1 − 2𝑥 2 + 2𝑥 2
=(𝑥 4 −2𝑥 2 + 1) + 4𝑥 2
= (𝑥 2 − 1)2 + (2𝑥)2
The proof is valid.
Step 1 isn’t valid.
Step 2 isn’t valid.
Step 3 isn’t valid.
Step 4 isn’t valid.
Step 5 isn’t valid.
Step 6 isn’t valid.
2. Which statement is an example of using the identity
to generate the Pythagorean triple 24, 70, 74?
3. Which statement shows an example of using the identity
expand the binomial?
4. Dylan incorrectly found f (3) below.
What is the correct value of f(3)?
A. 5
B. 10
C. 25
D. 50
5. Consider the equation
8x3 – 27y3 = (2x – 3y)(4x2 + Axy + 9y2)
What is the value of the constant A in the listed equation?
to
6. Find the value of x in the diagram to make the equation true for a2 + b2 = c2.
7. If (a2 – 1)2 = a4 + 1 + k, what is the value of k?
A. – a2
B. a2
C. 2a2
D. -2a2
8. Zach is proving the polynomial identity (x – y)2 using the diagram below.
A. x2 – y2 –y(x + y)
B. x2 – y2 –y(x - y)
C. x2 – y2 –2y(x + y)
D. x2 – y2 –2y(x - y)
9.
A-APR.4.6
1. A rational expression is shown,
2. The expression
the expressions q(x) and r(x)?
A. q(x) = x2 + 1
C. q(x) = -2
x4 – 1.
x+1
What is the quotient?
is equivalent to the expression
r(x) = 2
B. q(x) = 2
r(x) = x2 + 1
What are the values of
r(x) = x2 + 1
D. q(x) = x2 + 1 r(x) = - 2
3. When you divide to simplify the expression
quotient?
A. – 5
B.
C.
D. 3x2 – 2x – 4
what is the fractional part of the
4. Giselle made an error when she rewrote the expression
shown. What was her mistake, and what should the answer be?
in the form
as
5. Luke wants to analyze the graph of
but is having trouble determining the
important characteristics of the graph. How should he rewrite the expression
so that he can analyze the graph algebraically?
6. How can you rewrite the expression
in the form
in the form
7. What is the result of
8. Given a polynomial and its factor, what is the quotient q(x) and remainder r(x) of the following
equation?
3x4 + 7x3 – 4x – 25 by (x + 3)
9.
A-CED.1.1
1. Rebecca records the amount of money, f(x), in her bank account each month, x, as shown in the
table.
Create a function that models this relationship.
2. National Cell charges a flat $5 fee for a text messaging plan and $0.15 per text. World Wireless
doesn’t charge a flat fee, but it charges $0.19 per text. Which inequality and solution represent the
number t of texts for which World Wireless is cheaper than National Cell?
A. 19t > 15t + 5
B. 0.19t > 0.15t + 5
C. 19t < 15t + 5
D. 0.19t < 0.15t + 5
t> 1.25
t> 125
t< 1.25
t< 125
3. At a yearly basketball tournament, 64 different teams compete. After each round of the
tournament, half of the teams remain, as shown in the accompanying table. Which equation
models the relationship between the round and the number of teams remaining?
A.
B.
C.
D.
𝑡
𝑡
𝑡
𝑡
= 64(0.5)𝑟
= 64(2)𝑟
= 64(0.5)𝑟−1
= 64(2)𝑟−1
4. The length of the shortest side of a triangle is 8 inches. The lengths of the other two sides are
represented by consecutive odd integers. Which equation could be used to find the lengths of the
other sides of the triangle?
A. 82 + (𝑥 + 1) = 𝑥 2
B. 𝑥 2 + 82 = (𝑥 + 1)2
C. 82 + (𝑥 + 2)2 = 𝑥 2
D. 𝑥 2 + 82 = (𝑥 + 2)2
5. Paolo can mow the lawn at his family’s home in two hours. His younger sister Roberta needs 3
hours to mow the lawn. Paola and Roberta would like to have two lawnmowers so they can both
mow at the same time. The siblings need to know how much time working together would save to
help convince their parents to get another lawnmower. What equation can the siblings use to
determine the time t, in hours, need to mow the lawn they work together?
X+1
6
6. On his tenth birthday, Joe received a silver dollar from his Aunt Betty. The next year she gave him
two silver dollars and said he would continue to receive twice as many silver dollars each birthday
until he was 21.
a) Write an equation that would model this situation to find the number of silver dollars he would get
for any given birthday, using x for Joe’s age.
b) How many silver dollars will he get when he turns 16?
7. Albert cuts lawn for neighbors and charges $25 per week for his 15 customers. In the summer, he
cuts every week for 12 weeks and in the fall, he cuts every other week for 12 weeks.
a) Write an equation to solve how much Albert earned cutting lawns in this 24 week period.
b) How much did Albert earn cutting lawns in the 24 weeks?
8. A scientist has 600 grams of a substance that is being used at a rate of 50 % per month.
a) Which equation can be used to find the length of time t (in whole months) until 75 grams are left?
b) How many months does it take?
9. Javy is attending a carnival this weekend and has $45 saved up to spend on admission and rides.
Admission is $8 and each ride costs $0.75.
a) Write an inequality that represents the number of rides, r
b) Find the maximum number of rides Javy can ride with the money he has
10.
A-CED.1.2
1. The table shows the number of people who have participated in an annual conference since it
began in 2007. Which function represents this situation?
Year since 2007, n
1
2
3
Participants, p(n)
12
36
108
1
𝑛
A. 𝑝(𝑛) = (4)
3
B. 𝑝(𝑛) = 4(3)𝑛
1 𝑛
C. 𝑝(𝑛) = 4 (3)
D. 𝑝(𝑛) = 3(4)𝑛
2. Mike’s class is going on a field trip to the museum. The total cost of the trip includes the cost of the
tickets to the museum and a parking fee. Each ticket costs $10, and the parking fee is $20.
a) Select all the equations that represent this situation, where C is the total cost and t is the number of
tickets sold.
b) graph the situation
3. Suppose the maximum height jumped by the high jumper is 2 meters. Assuming that the jumper left
the ground at the origin and followed a parabolic path, which system could be used to write an
equation of the parabola that models the path followed by the high jumper in the form
f(x) = ax2 + bx + c
4. Marge has a landscaping business with a contract to plant trees in a new housing development. She
billed the developer $2400 for 5 bottlebrush trees and 4 palm trees on the Pine St lot and $4140 for 7
bottlebrush trees and 8 palm trees on Sago Square.
Which equation could be used to find the amount Marge charged the builder for each bottlebrush tree
and each palm tree?
A. 2400 + 4140 = (5B + 7B) + (4P + 8P)
B. 2400 + 4140 = (5B + 7B) - (4P + 8P)
C. 2400 = 5B – 4P ; 4140 = 7B - 8P
D. 2400 = 5B + 4P ; 4140 = 7B + 8P
5. A sample of gas has a volume of 100 cubic centimeters when the pressure is 150 kPa. Boyle’s Gas
Law states that the product of the pressure in (kPa) and volume (in cubic centimeters) is constant.
a) Which graph best shows this relationship
b) What is the equation
P =100v
6. The centripetal acceleration, a, of an orbiting object is calculated as the ratio of the square of the
velocity, v, of the object to the radius, r, of its orbit. Which equation shows this relationship?
7. The owner of a local coffee shop is designing a rectangular sign board to display the coffee specials.
She decides to make the height of the board one-third its width, x. The printing costs depends upon
the area of the board, f(x). For this reason, the owner tries different sizes for the board and records the
areas. Use the coordinate plane to graph the relationship between the width and area when the
domain is x> 0.
8. A certain population of bacteria doubles in number every two hours. A scientist starts with 1,000
bacteria. The graph models the growth of bacteria over time.
Write an equation that models the relationship between, t the time in hours, and b, the number of
bacteria.
9.
A-CED.1.3
1. During the 2010 season, football player McGee’s earnings, m, were 0.005 million dollars more
than those of his teammate Fitzpatrick’s earnings, f. The two players earned a total of 3.95 million
dollars. Which system of equations could be used to determine the amount each player earned, in
millions of dollars?
A. {
𝑚 + 𝑓 = 3.95
𝑚 + 0.005 = 𝑓
B. {
𝑚 − 3.95 = 𝑓
𝑓 + 0.005 = 𝑚
C. {
𝑓 − 3.95 = 𝑚
𝑚 + 0.005 = 𝑓
D. {
𝑚 + 𝑓 = 3.95
𝑓 + 0.005 = 𝑚
2. Edith babysits for x hours a week after school at a job that pays $4 an hour. She has accepted a
job that pays $8 an hour as a library assistant working y hours a week. She will work both jobs. She
is able to work no more than 15 hours a week, due to school commitments. Edith wants to earn at
least $80 a week, working a combination of both jobs. Determine and state one combination of
hours that will allow Edith to earn at least $80 per week while working no more than 15 hours.
3. A farmer has 160 meters of fencing to make two enclosures, one for his goats and one for his
pigs. The farmer plans to make a circular enclosure for his goats and a rectangular enclosure for his
pigs. He plans to use between 20 meters and 30 meters of fencing to make the pig enclosure. Based
on the constraints, which describes the possibilities for the area A of the goat enclosure? Round to
the nearest whole number as needed.
A. 21m2 < A < 22m2
B. 1345m2 < A < 1560m2
C. 130m2 < A < 140m2
D. 5380m2 < A < 6240m2
4. A baker is baking cookies and brownies. It takes 12 minutes to bake a batch of cookies and 20
minutes to bake a batch of brownies. Each batch of cookies uses 1 cup of flour and each batch of
brownies uses 5 cups of flour. The baker has 10 hours available and 100 cups of flour. The baker makes
a profit of $8 on each batch of cookies and $10 on each batch of brownies.
How many batches of cookies and brownies should the baker make in order to maximize profits?
A. 0 batches of cookies and 0 batches of brownies
B. 0 batches of cookies and 20 batches of brownies
C. 50 batches of cookies and 0 batches of brownies
D. 25 batches of cookies and 15 batches of brownies
5. A principal wants to order 800 math books. The company has 500 math books in their warehouse.
They also have 600 math books in a storage unit. It costs $3 to ship a math book from a warehouse. It
costs $5 to ship a math book from the storage unit. Let x represent the number of math books shipped
from the warehouse and y represent the number of math books shipped from the storage unit.
Which system of linear inequalities represent the constraints of this situation?
A. x + y > 800
x < 600
y < 500
B. x + y < 800
x < 500
y < 600
C. x + y > 800
x < 500
y < 600
D. x + y > 800
x > 500
y > 500
6. If x is age and y is heart rate, the general guidelines for a person’s maximum heart rate (in beats per
minute) is 220 – x. The target heart rate is 50 % to 85 % of the maximum heart rate. Which
inequalities can be used to generate a table of suggested average heart rates depending on a person’s
age?
7. The tables shows the prices of attending the school’s spring musical and the total tickets sales for
each day. Which equations can determine how many tickets of each type were sold?
A-CED.1.4
1
1. The formula for the area of a trapezoid is 𝐴 = 2 ℎ(𝑏1 + 𝑏2 ). Express b1 in terms of A, h, and b2.
1
2. Caroline knows the height and the required volume of a cone-shaped vase (𝑉 = 3 𝜋𝑟 2 ℎ) she is
designing. Which formula can she use to determine the radius of the vase? Select the correct
answer.
𝑉
A. 𝑟 = √3𝜋ℎ
3𝑉
B. 𝑟 = √𝜋ℎ
C. 𝑟 =
√3𝑉
𝜋ℎ
3𝑉
D. 𝑟 = ±√𝜋ℎ
3. A small object with mass m is attached to a ceiling by a string. The string is pulled straight down and
released so that the object begins to oscillate up and down. The period T of the object’s oscillation is
given by the formula
where k is the spring constant, which describes the stiffness of the
spring. Which of the following gives k as a function of m and T?
4. What is the value of x if h + 5 - 3 = 12?
x
A. x =
C. x =
ℎ
B. x =
10
ℎ
3
+
1
3
D. x =
ℎ
3
ℎ
15
+
1
3
5. Which shows the following equation solved for m?
A. m =
C. m =
𝑝
2𝑛
–5
𝑝
2𝑛−5
B. m =
𝑝
2𝑛
D. m =
+5
𝑝
2𝑛+5
6. In the formula
, B is the balance , in dollars, of an account with initial balance rate r
compounded continuously for t years. How can you rewrite this formula to use it to find the number
of years needed to attain a certain balance?
7. Newton’s Law of Universal Gravitation explains the gravitational force between two objects. The
formula is expressed as
where
is the force between two objects, G is the
gravitational constant, m1 and m2 are the masses of the two objects and d represents the distance
between the centers of the two objects. Solve the equation for m1, the mass of the first object.
A-REI.1.1
1. The sum of two quadratic expressions is 3 times the difference of the expressions.
The first expression is shown.
4x2 – 6x + 10
Marci’s steps for finding the second expression are shown
Create an equation that shows the next step used to find B.
2. Which step below is the first incorrect step to solve 2√𝑥 + 1 = 7?
A. Step 1
B. Step 2
C. Step 3
D. Step 4
3. Which property is NOT used to justify a step taken in solving the rational equation?
A. Zero product property
B. Addition/Subtraction property of equality
C. Multiplication/Division property of equality
D. Distributive Property
4. Sonya and Alex shared their work on the equation |2x + 3|= 13 as shown.
Which statement is true?
A. Alex solved the equation correctly
B. Sonya solved the equation correctly
C. The only solution for the equation is 5
D. Neither Alex nor Sonya solved the equation correctly
5. The first two steps Ria uses to solve the equation
Which properties did she apply during these steps?
A. Addition/Multiplication property of equality
B. Addition/Division property of equality
C. Subtraction/Division property of equality
D. Subtraction/Multiplication property of equality
are shown.
6. Which sequence of steps solves the following equation for x?
4x – 2 = 6
A. Step 1: Add 2 to both sides: Addition property of equality
Step 2:Replace each side with its logarithm-base 4: Exponential property of equality
B. Step 1: Add 2 to both sides: Commutative property of equality
Step 2:Take the fourth root of both side; Powers property of equality
C. Step 1: Subtract 2 to both sides: Commutative property of subtraction
Step 2:Replace each side with its logarithm-base 4: Exponential property of equality
D. Step 1: Subtract 2 to both sides: Commutative property of subtraction
Step 2:Take the fourth root of both side; Powers property of equality
7. Judy solved the quadratic equation 𝑥 2 − 16 = 0 using the following steps.
Step 1:
𝑥 2 − 16 = 0
(𝑥 − 2)(𝑥 + 8) = 0
Step 2:
Step 3:
𝑥 − 2 = 0 or 𝑥 + 8 = 0
Step 4:
𝑥 = 2 or 𝑥 = −8
Which statement is true about Judy’s method?
A.
B.
C.
D.
8.
8. 4.
Judy made a mistake between Steps 1 and 2.
Judy made a mistake between Steps 2 and 3.
Judy made a mistake between Steps 3 and 4.
Judy solve the equation correctly.
A-REI.1.2
1. What extraneous solution arises when the equation √𝑥 + 3 = 2x is solved for x by first squaring both
sides of the equation?
2. Consider the equation.
A. -2
C. - ½
E. 1
Which values are solutions to the equation?
B. -1
D. ½
F. 2
3. What is the solution of the equation 2m2 + 3m – 5 = 4?
m2 + 4m – 5
4. An equation is shown
What is the solution to the equation?
A. 1
B. 7
C. 8
D. 34
5. Which set of values of x make this equation true?
A. -1 + 6i, - 1 – 6i
B. 1 + 6i, 1 – 6i
C. 1 + √6i, 1 – √6I
D. -1 + √6i, -1 – √6i
6. Which equation has an extraneous solution that is negative?
7. What is the solution(s) to the following equation
8. What are the solutions of the equation below?
A. 0, 4, -6
B. 1, 5, -5
C. -2, 3
D. -1, 6
A-REI.2.4
1. A juggler throws a ball into the air from a height of 5 ft with an initial vertical velocity of 16 ft/s.
a) Write a function that can be used to model the height h of the ball in feet t seconds after the ball is
thrown.
b) How long does the juggler have to catch the ball before it hits the ground?
2. The height h in feet of a baseball hit from home plate can be modeled by the function
h(t) = −16t2 + 37t + 5.7, where t is the time in seconds since the ball was hit. The ball is descending
when it passes 7.5 ft over the head of a 6 ft player standing on the ground.
a) To the nearest tenth of a second, how long after the ball is hit does it pass over the player's head?
The ball will take
seconds.
b) The horizontal distance between the player and home plate is 140 ft. Use your answer from part 1
to determine the horizontal speed of the ball to the nearest foot per second.
The horizontal speed of the ball is
ft/s
3. A quadratic equation is shown. 4(x + 7)2 = 11
Solve the equation and create a possible solution in radical form.
4. Becky throws a ball into a air. The function f(t) = -16t2 + 40t + 6 models the path of the ball.
What is the height of the ball, in feet, 2 seconds after Becky throws it?
5. Kelly is completing the square to solve the equation 2x2 – 32x = 10.
Which equation could be the result of completing the square?
A. (x – 8)2 = 5
B. (x – 8)2 = 69
C. 2(x – 8)2 = 10
D. 2(x – 8)2 = 74
6. Solve the equation 9x2 + 12x = 5 by any method. What are the solutions?
7. The cross section of a wedge is a triangle with height 2x inches and base 6x + 1 inches. It has an
area of 120 inches. What is the length of the base to the nearest hundredth?
A. 4.39 inches
B. 8.78 inches
C. 13.67 inches
D. 27.34 inches
8. What is the solution(s) to the equation:
9. What values of x satisfy 2x2 – 4x + 5 = 0?
10. Dylan and Maebry each used completing the square to find the roots of a quadratic equation. Both
of them made at least one mathematical error. See their work below.
a) Identify at least one mathematical error in each of their work shown.
b) Use completing the square to solve the equation correctly.
A-REI.3.6
1. Given the following system of equations, what number should you multiply the first equation by so
that the system will be eliminated when the first equation is added to the second equation?
2x – y + 7z = 65
-3x + 4y – 2z = - 5
X + 9y – 5z = - 24
A. -
3
C. -
2
2
3
B.
2
D.
3
3
2
2. Chocos is a dish made from wheat, sugar and cocoa. Bertha is making a large pot of chocos for a
party. Wheat (w) costs $5 per pound, sugar (s) costs $3 per pound, and cocoa (c ) costs $4 per pound.
She spends $48 on 12 pounds of food. She buys twice as much cocoa as sugar.
How much wheat, sugar, and cocoa will she use (in pounds) in her dish?
A. wheat: 6 lb, sugar: 3 lb, cocoa 3 lb
B. wheat: 3 lb, sugar: 3 lb, cocoa 6 lb
C. wheat: 3 lb, sugar: 6 lb, cocoa 3 lb
D. wheat: 6 lb, sugar: 2 lb, cocoa 4 lb
3. The following combinations are available at Mike’s Carryout.
Assume the price of a combo meal is the same price as purchasing each item separately. Find the price
of a pizza, a coke and a bag of chips.
A. pizza $2: coke $4; bag of chips $3
B. pizza $2: coke $3; bag of chips $4
C. pizza $3: coke $2; bag of chips $4
D. pizza $4: coke $3; bag of chips $2
4. Emma needs to develop prints of digital pictures she took at a party. She has two options to choose
from. An online digital photo lab charges $0.15 per print and $2.50 for shipping. Another local photo
lab charges $0.35 per print, but there will be no shipping charge.
a) Graph the system that represents the situation
b) Determine the solution to the system
5. A local business was looking to hire a landscaper to work on their property. They narrowed
their choices to two companies. Flourish Landscaping Company charges a flat rate of $120 per
hour. Green Thumb Landscapers charges $70 per hour plus a $1600 equipment fee. Write a
system of equations representing how much each company charges. Determines and state the
number of hours that must be worked for the cost of each company to be the same.
A-REI.3.7
1. What is the distance between the points of intersection of the graphs of y = x2 and y = 6 – x?
A. √26
B. 5√2
C. 2√37
D. √170
2. A circular pond is modeled by the equation x2 + y2 = 225. A bridge over the pond is modeled by a
segment of the equation x – 7y = - 75. What are the coordinates of the points where the bridge meets
the edge of the pond?
A. (9, 12) and (-12, 9)
B. (9, 12) and (12, 9)
C. (9, -12) and (-12, -9)
D. (-9, 12) and (12, -9)
3. Which graph represents shows the solutions of the system of equations y = x2 + 2 and y = x + 4?
A.
B.
C.
D.
4. At what points do the graphs of y = 2x + 1 and y = -(x - 1)2 + 3 intersect?
A. (-3, 5) and (1, 3)
B. (-2, -6) and (2, 2)
C. (-1, -1) and (1, 3)
D. (3, 7) and (1, 3)
5. Refer to the two equations.
y = 5x – 3
y = 2x2 – 2x – 6
Describe the value and type of roots for the system.
6. Consider the circle centered at the origin with a diameter of 4. Now consider the line: x + y = 2
What are the x-values of the two points of intersection from the system described?
7. Use the two equations given.
Describe the value of the discriminant, the corresponding types of solutions, and the two values for x
when the line crosses the parabola.
De
De
De
A-REI.4.11
1. An online music sharing club has 5,060 members. The membership is increasing at a rate of 2%
per month. In approximately how many months will the membership reach 10,000?
A. 3.7 months
B. 34.4 months
C. 48.8 months
D. 98.8 months
2.
𝑦 = 𝑥 2 − 2𝑥 − 5
𝑦 = 𝑥 3 − 2𝑥 2 − 5𝑥 − 9
When the solutions to each of the two equations shown are graphed in the xy-coordinate plane,
the graphs of the solutions intersect at a point. What is the y-coordinate of the point of
intersection? Enter your answer in the box.
𝑦=
3. Use the graph below to determine which of the following is the best approximation of the equation
f(x) = g(x)
A. x = - 1, 5
B. x = -0.5, 2.5
C. x = 0.5, 4.5
D. x = 1, 3
4. Use the table below to determine which of the following is the best approximation of the solution
of the equation
A. x = 2.5
B. x = 2
C. x = 1.5
D. x = 1
5. Shae works at a box manufacturer and is required to design a box with different dimensions. She
uses the formula V(x) = 4x3 – 100x2 + 600x to find the volume of a particular box, where x represents
the side length in cm of each square cut from the cardboard to make the box. Another box uses the
formula W(x) = 4x3 – 100x2 + 625x. Shae believes that there are two values for which the volumes of
the boxes will be the same because the graphs intersect the x-axis at two points. Which is true, and
why?
A. The graphs have to intersect for the boxes to have equal volumes. Both boxes have a volume of 0
cubic cm at x = 0, 10 and 12.5, so there are 3 values for which the volumes are equal.
B. The graphs have to intersect for the boxes to have equal volumes. The volumes of the boxes only
intersect at x= 0 cubic cm, so the volumes of the boxes are never the same.
C. The graphs have to intersect for the boxes to have equal volumes. Both boxes have a volume of 0
cubic cm at x = 10, so there is only 1 value for which the volumes are equal.
D. The graphs have to intersect for the boxes to have equal volumes. Both boxes have a volume of 0
cubic cm at x = 10 and 12.5, so there are 2 values for which the volumes are equal which means she is
correct.
6. Two toy rockets are fired into the air at the same time. One has a height modeled by the function
f(t) = -16t2 + 100t + 200, where t is time in seconds. The other has a height modeled by the function
g(t) = -16t2 + 128t. Approximately how long will it take for the rockets to reach the exact same height?
A. 6.6 seconds
B. 6.9 seconds
C. 7.1 seconds
D. 7.4 seconds
7. The graphs of two functions f(x) and g(x) are shown. There is one solution to f(x) = g(x). Which
equation can be solved to represent this situation?
A. |x + 5| = x3 – 2x + 1
B. |5 - x| = x3 + 1
C. |5 - x| = x3 + 2x - 1
D. |x - 5| = x3 – 2x + 1
8. Given two functions f(x) = |x + 2| + 4 and g(x) = e2x, use the blank grid to find the approximate
solution to the equation f(x) = g(x)
A-SSE.1.1
1. The expression x2(x – y)3 – y2(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?
2. Four cattle ranches plan to increase the size of their herds. The expressions shows the predicted
herd size for each ranch after n years.
Which ranch has the herd with the fastest growth rate?
A. Bar 2
B. Flying T
C. Lazy J
D. TC
3. Elephant Population Estimates – Namibia
Combined estimates for Etosha National Park and the Northwestern Population
The elephant population in northwestern Namibia and the Etosha National Park can be predicted
by the expression 2,649(1.045)𝑏 , where b is the number of years since 1995. What does the value
2,649 represent?
A. The predicted increase in the number of elephants in the region each year
B. The predicted number of elephants in the region in 1995
C. The year when the elephant population is predicted to stop increasing
D. The percentage the elephant population is predicted to increase each year
4. Two pipes are being used to fill a water, pipe A and pipe B. Pipe A can fill half of a water tank in t
hours. It takes pipe B one hour less than pipe A to fill the same water tank completely. What does the
expression
represent?
A. the time taken by both pipes to fill the tank
B. the amount of the tank filled by both pipes in time t
C. the amount of the tank filled by both pipes in time 2t
D. the rate at which both pipes can fill the tank working together
5. In a triathlon, Agnes swims 400 meters, bikes 30 kilometers, and runs 6 kilometers. She bikes 12
times as fast as she swims and runs 5 times as fast as she swims. The expression below represents the
time it took her to complete the triathlon.
Which expression represents the time it took her to complete the swimming and biking portions of the
triathlon?
6. A concert is being held to raise money for charity. The function p(x) = -25x2 + 3000x – 18000 can
be used to determine the dollar amount raised for the charity, dependent on the ticket price. The
function
represents the number of concert tickets sold, dependent on the ticket
price. What does the numerator of the function n(x) represent in this context?
A. the cost of the concert
B. the amount of profit per concert ticket sold
C. the total amount of money brought in by the ticket sales
D. the total profit of the concert if an additional $18,000 was donated
7. Tatiana deposits $500 in a bank account that pays 3.25 % interest compounded annually. The
expression (1 + 0.0325)t represents the number of dollars in the account after t years for every dollar
in the original balance. Which of the following is a reasonable interpretation of the expression 500(1 +
0.0325)t in this context?
A. The amount of interest the account earns after one year
B. The amount of interest the account earns after 500 years
C. The amount of money in the account after one year
D. The amount of money in the account after t years
8.
A-SSE.1.2
1. A square has side length x.
A new square is created by subtracting y from each side of the original square.
Create an expression for the area of the new square in expanded form.
2. Which expression is equivalent to 𝑥 4 − 12𝑥 2 + 36?
A. (𝑥 2 − 6)(𝑥 2 − 6)
B. (𝑥 2 + 6)(𝑥 2 + 6)
C. (6 − 𝑥 2 )(6 + 𝑥 2 )
D. (𝑥 2 + 6)(𝑥 2 − 6)
3. Which of the following statements present(s) valid reasoning? Select all that apply.
A. x6 + 81 can be written as (x2)3 + (3)3 and factored as a sum of two cubes.
B. 49c2 – 154c + 121 can be rewritten as (7c)2 – 2(7c)(11) + (11)2 and factored as a perfect square
trinomial.
C. 36p4 + 96p + 64 can be rewritten as (6p2)2 + 2(6p2)(8) + 82 and factored as a perfect square
trinomial.
D. x4 + 16 can be written as (x2)2 - (-4)2 and factored as a difference of squares.
E. x18 - 8 can be written as (x6)3 - (2)3 and factored as a difference of two cubes.
F. x9 + 64 cannot be factored as the sum of two cubes because x9 is a perfect cube and 64 is a perfect
square.
4. Create an expression that represents the complete factorization of 2x2 + 16x + 32
5. Consider the rational expression
Which expression is equivalent to this one?
6. Which expression is equivalent to
7. How can the following expression be rewritten so it is equal to a2 + b2, where a and b are
binomials?
5x2 + 14xy + 26y2
8. The expression below can be rewritten in several ways.
If this expression can be represented by (a + b)3, where a and b are algebraic terms, what is the value
of k?
A. – 40
B. – 20
C. 9
D. 40
9. What are the factors of the following expression:
A-SSE.2.3
1. What are factors and values of the zeros for the following quadratic equation?
2x2 + 5x = 12
2. The functions f and g are defined by f(x) = x2 + 2x − 2 and g(x) = (x + 1)2 − 3. Use algebra to
prove that f and g represent the same function. Complete the explanation.
Complete the square to write
in vertex form.
(x) = x2 + 2x − 2
(x) = x2 + 2x +
(x) =
−2−1
3. An expression is given. x2 – 8x + 21
a) Determine the values of h and k that make the expression (x – h)2 + k equivalent to the given
expression.
b) An equation is given. x2 – 8x + 21 = (x – 4)2 + 3x – 16
Find one value of x that is a solution to the given equation.
4. A ball is thrown up into the air. Its height h above the ground in feet is modeled by the equation
h = -16t2 + 24t + 5, where t is the time in seconds after the ball is thrown. Complete the square to
determine the ball’s maximum height and the amount of time the ball takes to reach that height. Could
this ball land on the roof of a 20-foot-tall building?
5. The population of a colony doubles every 8 hours. If the number of bacteria starts at 80, the
population P after t hours is given as
What is the equivalent form of P(t) that shows the approximate hourly growth factor for the bacterial
population?
6. The landscaper wants to design a rectangular patio for a client. The function A(w) = 54w – 3w2
gives the area A (in square feet) of the patio for any width w (in feet). Which form of the function can
be used to determine the maximum area?
7. The population of a town after 1990 can be modeled by the expression I(1.045)t, where t represents
the number of years since 1990 and I represents the population of the town in 1990. Which expression
represents the monthly growth rate?
8. The population of a colony of bacteria is growing at 6.2 % per day. This growth can be
modeled by the expression P0e0.062t, where P0 represents the initial population and t is the time in
days. What expression is the equivalent for the approximate per-hour growth rate of the
population?
A. P0e0.0026t
B.
P0e0.0026(24t)
C. P0e0.062(24t)
B.
P0e0.062(60t)
G-GPE.1.2
1. Find the equation of a parabola with focus F(4, 0) and directrix x = - 3.
A. y2 = 14(x - ½)
B. x2 = 14(y - ½)
C. (y - ½)2 = 14x
D. (x - ½)2 = 14y
2. The cross section of a TV antenna dish is a parabola. The receiver is located at the focus, 4 feet
above the vertex.
a) Find an equation for the cross section of the dish. Assume the vertex is at the origin.
b) If the dish is 8 feet wide, how deep is it?
3. Which focus and directrix correspond to a parabola described by y =
1 2
x
16
?
A. Focus (0, - 4) Directrix y = - 4
B. Focus (0, 4) Directrix y = 4
A. Focus (0, - 4) Directrix y = 4
A. Focus (0, 4) Directrix y = - 4
4. The cross section of a satellite dish traces a parabolic curve. Let x represent horizontal distance in
inches and y represent vertical distance in inches. The graph shows the focus and directrix of the
parabola.
Which is the equation of the parabola?
5. The cross section of a mirror traces a parabolic curve. If x represents horizontal distance in feet and y
represents vertical distance in feet, the focus of the parabola is located at (5, 5) and the directrix of the
parabola is x = - 5. Which is the equation of the parabola?
6. What is the equation of a parabola with a focus of (2, 5) and directrix y = 1?
7.
N-CN.3.7
1. Solve 2x2 – 4x + 9 = 0. What are the solutions?
2. Solve 90x2 – 18 = 0. Which statement is true?
3. What is the solution for the following equation?
3x2 = 4x – 12
4. How many solutions does the quadratic equation x2 + 4x + 8 = 0?
A. one solution
B. one complex solution
C. two complex solutions
D. two real solutions
5. Which equation has x = - i and x = 2i√3 as two of its solutions?
A. y = x4 + 37x2 + 36
B. y = x4 - 37x2 + 36
C. y = x4 - 13x2 + 12
D. y = x4 + 13x2 + 12
6. For what values of x is the equation below true?
X2 + 4x + 5 = 0
A. x = -4, 0
B. x = -1, -3
C. x = - 2 ± 2i
D. x = - 2 ± i
7. Which shows a solution of
A-APR.2.3
1. A polynomial is shown. y = 4x3 – 12x2 – 4x + 12
Locate all the zeros and plot on the graph.
2. Which could be the graph of the polynomial function f(x) = (x – 2)(x + 4)(x2 + 4)?
A.
B.
C.
D.
3. The graph of a polynomial function with a degree of 5 is shown below. Which function could fit the
graph?
A. f(x) = (x – 2)2(x – 3)(x + 1)2
B. f(x) = (x – 2)2(x – 3)(x - 1)2
C. f(x) = (x – 2)2(x + 3)(x + 1)2
D. f(x) = (x + 2)2(x – 3)(x - 1)2
4. The graph of a polynomial function with a degree of 4 and its real zeros are shown below. Which
function could fit the graph?
A. f(x) = (x + 3)(x – 2)(x2 + 1)
B. f(x) = (x - 3)(x + 2)(x2 + 1)
C. f(x) = (x - 3)(x + 2)(x + 1)(x – 1)
D. f(x) = (x - 3)(x + 2) 2
5. Consider the function f(x) = x(x2 – 4)(x2 + 9)
What are the zeros of the polynomial?
A. 0 and 2
B. 0, 2, and -2
C. 0, 2, and -3
D. 0, 2, 3, -2 and -3
6. Sketch a graph of the polynomial function f(x) = x3 + x2 – 4x – 4
Label the x and y-intercepts
7. Which function best represents the graph below?
A. f(x) = (x + 1)(x – 2)
B. f(x) = x(x + 1)(x – 2)
C. f(x) = (x + 1)2(x – 2)3
D. f(x) = x(x + 1)2(x – 2)3
8. Which function has the same zeros as f(x) = x4 + x3 - 8x2 – 12x?
A. g(x) = x(x – 2)(x – 3)
B. g(x) = x(x + 2)(x – 3)
C. g(x) = (x + 2)(x – 3)
D. g(x) = (x – 2)(x + 3)
A-SSE.2.4
1. A lab technician wants to calculate the amount of a chemical remaining in a beaker of solution after
adding 225 mg of the chemical every 6 hours for 10 days. She tests solution after 6 hours and finds that
96 % of the chemical has evaporated from the solution. Which formula calculates the amount of the
chemical remaining in the beaker of solution after 10 days?
2. Which expression represents the sum of the seventh to tenth terms in the series below?
3. Which expression represents the sum of the first 14 terms in the series below?
4, Javier takes private piano lessons, which cost $400 for the first year and increases by 4 % each year
after that. What is the total dollar amount, to the nearest cent, Javier will have paid for lessons after 7
years?
5. The Sanchez family wants to go on vacation in August, and they begin saving in December. They
expect the vacation to cost $1,700. Each month they will deposit 5 % more than the previous month.
In December they deposit $100. How much will the Sanchez family have saved for their vacation after
9 months?
A. $147.75
B. $1102.66
C. $2864.73
D. $6000.00
6. A ball is dropped from a height of 100 feet. Each time it hits the ground, it bounces back up and
reaches a maximum height that is 80 % of its previous height. Which formula gives the total distance,
in feet, it would have traveled when hitting the ground for the 10th time?
F-BF.1.1
1. Currency conversions for British pounds and US dollars are shown.
1 British pound = 1.59 US dollars
1 US dollar = 0.99 Canadian dollar
The functions B(x) = 1.59x and C(y) = .99y represent these conversions, where x represents British
pounds and y represents US dollars.
Create a composite function that represents a conversion from x British pounds to y Canadian dollars.
2. Caitlin has a movie rental card worth $175. After she rents the first movie, the card’s value is
$172.25. After she rents the second movie, its value is $169.50. After she rents the third movie,
the card is worth $166.75.
A) Assuming the pattern continues, write an equation to define A(n), the amount of money on the
rental card after n rentals.
B) Caitlin rents a movie every Friday night. How many weeks in a row can she afford to rent a
movie, using her rental card only? Explain how you arrived at your answer.
3. Four friends attempted to write the explicit expression for the nth term of the sequence 2, 5, 10,
17…
If n represents the set of counting numbers, who wrote the correct expression?
A. Austin
B. Kaylee
C. Noah
D. Zoey
4. John had a math assignment to complete during his midterm break. He completed one question
on the first day, three questions on the second day, and seven questions on the third day. He
followed the same pattern every day until he completed the assignment on the sixth day. Write a
recursive rule to model the number of questions that John solved each day after the first.
5. A farmer has a crop of 2000 orange trees at the beginning of this year. Each year, the farmer plans
to plant 250 new trees. Assuming all the trees from one year live into the next, which explicit formula
can be used to determine the total number of orange trees, an, on this farm at the end of the nth year?
A. an = 2250 + 250(n – 1)
B. an = 2000 + 250(n – 1)
C. an = 2250 + 250(n + 1)
D. an = 2000 + 250(n + 1)
6. Let f(x) = 2x2 – x and g(x) = √𝑥 – 9
a) Find (f + g)(x)
b) (f · g) (4) and (f/g)(4)
7. The amount of a certain radioactive substance decreases by 15 % every hour. If a sample starts with
100 g of this radioactive substance, which function represents the amount of radioactive substance left
after x hours?
A. f(x) = 100(0.15)x
B. f(x) = 100(0.85)x
C. f(x) = 100(1.15)x
D. f(x) = 100(1.85)x
8.
.
F-BF.1.2
1. The first four terms of a sequence are 8, 12, 18, 27, … Write a recursive function for this
sequence.
2. A company purchases $24,500 of new computer equipment. For tax purposes, the company
estimates that the equipment decreases in value by the same amount each year. After 3 years, the
estimated value is $9,800. Write an explicit function that gives the estimated value of the
computer equipment n years after purchase.
3. 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 that apply.
A. an = 10 + 2(n – 1)
B. an = 10n2
C. an = 10(1.2)n - 1
D. a1 = 10, an = 1.2an-1
E. a1 = 10, an = 2 + an-1
4. The table below shows the balance b, in dollars, of Daryl’s savings account t years after he made
an initial deposit. What is an explicit formula for the geometric sequence that represents this
situation?
5. A scientist is studying the growth of a certain bacteria population in a dish. At 12:00 PM, the
scientist begins the study with 4 bacteria. After each hour of the study, the scientist records the time
and the number of bacteria in the dish. The scientist’s records for the first few hours of the study are
shown in the table below.
a) Write a recursive formula to represent the bacteria growth in this study. Ao represents the
number of bacteria at the beginning of the study, and let n represent the number of hours that have
passed since the study began.
b) Write an explicit formula to represent the bacteria growth in this study. Ao represents the
number of bacteria at the beginning of the study, and let n represent the number of hours that have
passed since the study began.
c) Use both formulas and determine the number of bacteria in the dish at 8 PM, given that growth
continues at the same rate.
d) Which formula would be best used to determine the number of bacteria in the dish at 10 AM on
the following day?
6. If A1 = 3 and A(n+ 1) = 2An, which equation represents the explicit formula for the sequence?
7. As part of his language assignment, Ken reads 12 pages from his book on the first day. After that,
he reads 6 more pages each day. Write a recursive rule for the number, an, of pages read by Ken at
the beginning of the nth day.
F-BF.2.3
1. Given 𝑓(𝑥) = |3𝑥|. If 𝑔(𝑥) = 𝑓(𝑥) − 2, how is the graph of 𝑓(𝑥) translated to form the graph of
𝑔(𝑥)?
2. Given 𝑓(𝑥) = |3𝑥|. If ℎ(𝑥) = 𝑓(𝑥 − 4), how is the graph of 𝑓(𝑥) translated to form the graph of
ℎ(𝑥)?
3. Which of the following describes a way to graph the function 𝑔(𝑥) = −2|𝑥|?
A. Stretch the graph of 𝑓(𝑥) = |𝑥| vertically by a factor of 2. Then reflect the results across the
x-axis.
1
B. Shrink the graph of 𝑓(𝑥) = |𝑥| vertically by a factor of 2. Then reflect the results across the
x-axis.
C. Translate the graph of 𝑓(𝑥) = |𝑥| down 2 units.
D. Translate the graph of 𝑓(𝑥) = |𝑥| right 2 units.
4. Consider the quadratic equation. f(x) = -2(x + 1)2. Show the transformation f(x) + 3
Show both parabolas on the graph.
5. How do you transform the graph of f(x) =
1
𝑥
to obtain the graph of
A. Shift left 5 units, horizontally stretch by a factor of 8, and shift down 7 units.
B. Shift left 5 units, vertically stretch by a factor of 8, and shift down 7 units.
A. Shift right 5 units, vertically stretch by a factor of 8, and shift down 7 units.
A. Shift left 5 units, vertically stretch by a factor of 8, and shift up 5 units.
6. Graph the function f(x) = 2x. Label the intercept.
a) On the same grid, graph f(x) = 2x + 1. Describe how it differs from the parent graph.
b) On the same grid, graph f(x) = -3(2x). Describe how it differs from the parent graph.
c) On the same grid, graph f(x) = 23x. Describe how it differs from the parent graph.
7. If the graph of f(x) = √𝑥 + 3 is translated two units right and 4 units down, which of these functions
describes the transformed graph?
A. g(x) = √𝑥 − 2 – 1
B. g(x) = √𝑥 + 2 - 1
C. g(x) = √𝑥 − 2 + 7
D. g(x) = √𝑥 + 2 + 7
8. The graph below shows two functions, f(x) and g(x).
Which of these equations describes the function g(x) in terms of the function f(x)?
A. g(x) = 2f(x)
B. g(x) = f(x) + 6
C. g(x) = f(x) + 2
D. g(x) = f(x) – 2
9.
F-BF.2.4
1. The cost to ship a package is 𝐶(𝑤) = 0.23𝑤 + 7 where w is the weight in pounds. Write an
inverse function to find the weight of a package as a function 𝑤(𝐶) of the cost.
𝐶−7
A. 𝑤(𝐶) = 0.23
𝐶+7
B. 𝑤(𝐶) = 0.23
C. 𝑤(𝐶) = 0.23𝐶 + 7
D. 𝑤(𝐶) = 0.23𝐶 − 7
2. The graph of the function above is shown below.
Which of the following statements about f(x) is true?
a)
The function f(x) does not have an inverse because its domain is
b)
The function f(x) does not have an inverse because it is not one-to-one.
c)
The function f(x) has an inverse because it passes the vertical line test.
d)
The function f(x) has an inverse because it is one-to-one.
.
3. What is the inverse function of g(x) = 3x2 – 2, x > 0?
Use f(x) to represent the inverse of g(x).
5
4. What is the inverse of f(x) = (3x – 5)4 for all x > 3 ?
2
5. What is the inverse of g(x) = √5𝑥 − 2 + 1, for all x > ?
5
6. What is f-1(x) if f(x) =
𝑥+2
, x ≠ 3?
𝑥−3
7. Given the graph of f(x), which point is guaranteed on the graph of the inverse function, f-1(x)?
A. (-10, 3)
B. (-3, 10)
C. (3, -10)
D. (10, -3)
2
8. Which expression represents the inverse of the function f(x) = 𝑒 𝑥 for x >0?
9. The table below shows the attempt made by four students to find the inverse of the function
g(x) = - √(𝑥 − 9)3 + 8
4
Which student correctly found the inverse of the function?
A. Daniel
B. Jean
C, Scott
D. Sophia
10.
W
F-IF.2.4
1. What is the domain over which the function 𝑦 = |3𝑥 + 2| is increasing?
2. What are the coordinates of the vertex of the graph of 𝑓(𝑥) = 3|𝑥 + 1| − 4?
A. (1, 4)
B. (1, -4)
C. (-1, 4)
D. (-1, -4)
3. Four functions are shown on the graph.
When x > 100, which function has the smallest y-values?
A. f(x)
C. h(x)
B. g(x)
D. j(x)
4. The function f(x) = -360(x – 4.75)2 + 3400 models the income f(x) for a skating rink that charges
patrons x dollars per hour. Which statement about the graph of f(x) is true?
A. The graph has a relative max and relative min,
B. The graph has an absolute max.
C. The graph has an absolute min.
D. The graph has no relative max and relative min.
5. What is the domain, range, relative max and relative min for the function represented by the graph?
A. domain: all reals range: all reals relative max: 1.25 relative min: - 3
B. domain: all reals range: all reals relative max: 7 relative min: - 1
C. domain: -3 to 1.25 range: all reals relative max: 7 relative min: - 1
D. domain: all reals range: -3 to 1.35 relative max: ∞ relative min: - ∞
6. Corinne has a cell phone plan that includes 200 minutes for phone calls and unlimited texting. An
additional fee is charged for using more than 200 minutes for phone calls. The figure below is the
graph of C= f(m), where C is the monthly cost after m minutes used.
a) What is the minimum monthly cost for Corinne’s cell phone plan? Explain.
b) What is the value of f(150)? Explain its meaning in terms of the cell phone plan.
c) For what m is f(m) = 55? Explain its meaning in terms of the cell phone plan.
7. Which rational function is decreasing in the interval (- ∞, 1) and is symmetric over the line x = 1?
A.
C.
B.
D.
8. Which statement best describes the end behavior of the graph of the function f(x) = x3 + 2?
A. The function approaches ∞, as x approaches ± ∞
B. A. The function approaches - ∞, as x approaches ± ∞
C. The function approaches - ∞, as x approaches ∞ and the function approaches + ∞, as x approaches
-∞
D. The function approaches - ∞, as x approaches - ∞ and the function approaches + ∞, as x
approaches + ∞
9. Kelly bought a new car 5 years ago. She paid $15,000 for the car. Each year, the car depreciated in
value as shown in the table below.
A. What function could Kelly use to model the value of her car after 10 years?
B. Graph the function. List key features.
C. Kelly would prefer to sell her car for at least $4000 so that she can have a down payment for her
next car. How long can Kelly keep her car before she sells it, if she hopes to sell it for $4000 or more?
10. Given the rational function
A. Find the x and y-intercepts
B. Describe the end behavior
C. Find any horizontal and/or vertical asymptote
D. Use the key features to sketch the graph
F-IF.2.5
1. Sarah went on a bike ride. The graph below shows the distance, y, in miles, that she had
traveled after biking for x hours.
a. State the domain and range of the function shown in the graph
b. State the interval of time during which Sarah was riding the fastest, explain how you know.
2. The function ℎ(𝑡) = −16𝑡 2 + 144 represents the height, ℎ(𝑡), in feet, of an object from the
ground at t seconds after it is dropped. A realistic domain for this function is
A. −3 ≤ 𝑡 ≤ 3
B. 0 ≤ 𝑡 ≤ 3
C. 0 ≤ ℎ(𝑡) ≤ 144
D. All real numbers
3. A function is shown. h(x) =
x½ . What is the domain of the function?
4. Consider the function. What is the domain of f(x)?
5. The graph of a fourth-degree polynomial function f(x) is shown. Use the graph to determine the
domain and range of f(x).
6. Which set represents the domain of the function
7. Jeanette writes the functions below to model two different situations.
f(x) = 124(0.5)x models the depreciated value of a video game after x months
h(x) = 124(0.5)x models the number of teams left in a high school football tournament at the end of x
number of rounds
a. Describe the domain of function f(x)
b. Describe the domain of function h(x)
c. Compare the types of graphs and domains of the two functions
8. Which graph represents a function that has all real numbers less than 2 and greater than 2 as its
domain?
A.
C.
9.
B.
D.
F-IF.2.6
1. The value of an antique has increased exponentially, as shown in this graph. Based on the graph,
estimate to the nearest $50 the average rate of change in value of the antique for the following
time intervals.
A. From 0 to 20 years:
B. From 20 to 40 years:
2. Jerome is comparing average rates of change of the four functions below.
𝑓(𝑥) = (0.5)2𝑥
𝑔(𝑥) = 0.5𝑥 2
3
ℎ(𝑥) = √𝑥 + 2
𝑗(𝑥) = √3𝑥 + 7
Which function has the smallest average rate of change over the interval −1 ≤ 𝑥 ≤ 6?
A. f(x)
B. g(x)
C. h(x)
D. j(x)
3. The graphs of f(x), g(x), h(x), and k(x) are shown.
Which function changes at a constant rate per unit relative to x?
A. f(x)
B. g(x)
C. h(x)
D. k(x)
4. A toy rocket is launched from the roof of a building. The graph below shows the height of the
rocket x seconds after it was launched. What is the average rate of change of the height of the rocket
during its descent?
A. -32 ft/sec
B. – 24 ft/sec
C. -64/3 ft/sec
D. -16 ft/sec
2
5. Two functions are defined as g(x) = 4x – 3 and f(x) = 3x2 – 4.
What is the difference in the average rate of change of g and f over the interval from x = 0 to x = 3?
6. The table below shows the values of function f(x) for different values of x over the interval [-2, 2].
What is the average rate of change of the function f(x) over the interval [-2, 0]?
7. What is the average rate of change of a function f(x) = (√𝑥 + 4)2 over the interval [4, 9]?
A. 1
85
C. 13
A.
5
5
5.
B.
13
5
D. 17
F-IF.3.7
1. At an office supply store, if a customer purchases fewer than 10 pencils, the cost of each pencil is
$1.75. If a customer purchases 10 or more pencils, the cost of each pencil is $1.25. Let c be a
function for which c(x) is the cost of purchasing x pencils, where x is a whole number. Create a
graph of c(x) on the axes below.
1.75𝑥, 𝑖𝑓 0 ≤ 𝑥 ≤ 9
𝑐(𝑥) = {
1.25𝑥, 𝑖𝑓 𝑥 ≥ 10
2. Which diagram represents the set of all solutions of the equation 𝑦 = √𝑥 + 2?
A.
C.
B.
D.
3.
3
4. On the set of axes below, graph the function represented by 𝑦 = √𝑥 − 2 for the domain −6 ≤
𝑥 ≤ 10.
𝑟
5. An investment is earning 5 % interest compounded quarterly. The equation A = P(1 + )nt
𝑛
represents the total of money. A, where P is the original investment, r is the interest rate, t is the
number of years, and n represents the number of times per year the money earns interest.
Which graph represents this investment over at least 50 years?
A.
B.
C.
D.
6. A graph of an exponential function is shown.
Which equation represents the function shown in this graph?
7. What are the zeros and vertical asymptote of the graph of
A. Zeros -5 and 6: Vertical x = 4
B. Zeros -5 and 6: Vertical x = - 4
C. Zeros 5 and - 6: Vertical x = 4
A. Zeros 5 and - 6: Vertical x = - 4
8. Graph the following function and label the zeros.
F(x) = x3 – 13x2 + 36x


9. David graphs a polynomial function with a features listed below.
Zeros at x = -1, 2, 3
Y-intercept (0, -6)
 End behavior of
Which function did David graph?
A. f(x) = x3 – 4x2 + x + 6
B. f(x) = x3 + 4x2 + x - 6
C. f(x) = - x3 – 4x2 - x + 6
D. f(x) = - x3 + 4x2 - x - 6
10. Which of these coordinates would represent the intercepts of the graph of the function
f(x) = 3x – 9?
A. (0. -9) and (3, 0)
B. (0. -8) and (2, 0)
C. (0. 2) and (-8, 0)
A. (0. 3) and (-9, 0)
F-IF.3.8
1. A quadratic equation is written in four equivalent forms below.
I. y = (x - 1)2 - 9
II. y = x2 - 2x - 8
III. y = (x - 4)(x + 2)
IV. y = x(x - 2) - 8
Which of the forms shown above would be the most useful if attempting to find the vertex of the
quadratic equation?
a)
b)
c)
d)
III.
II.
I.
IV.
2. What is the axis of symmetry of the graph of f(x) = 3x2 – 6x + 6?
3. Louis throws a superball against the ground. The height of the bouncing ball in feet h is modeled by
the function h(t) = - 16t2 + 30t where t is the time in seconds after the ball bounces off the ground.
What is the vertex, and what does it describe?
15
A. (16, 16 ): after 14 seconds the ball reaches its maximum height
B. (30, 16): the ball reaches its maximum height of 30 feet after 16 seconds
15
C. (16 , 16): the ball reaches its maximum height of 16 feet after 0.9 seconds
D. (1, 16): the ball reaches its maximum height of 1 foot after 16 seconds
4. Gisella uses 24 inches of wooden molding to frame a rectangular picture. The function A = 12w –
w2 models the area in square inches of a rectangle with a width of w inches. What are the zeros of this
function, and what do they describe?
A. The zeros are 0 and -12; so the width must be less than 12 inches
B. The zeros are 6 and -6; so the greatest length of the picture is 6 inches
C. The zeros are 0 and 12; so the width must be between 0 and 12 inches
D. The zeros are 6 and -6; so the greatest area of the picture is 6 square inches
5. Which is equivalent to
6. The function P(x) = -3x2 + 48x + 174 represents the profit, in thousands of dollars, of a company
when selling x units (in thousands) per month.
a) Complete the square to transform the function into vertex form and find the vertex. Explain how it
relates to the company profit.
b) What are the zeros of P(x)? Explain how it relates to the company profit.
7. In 2008, the enrollment at Greenwood Elementary School was 865 students. The equation
N = 865(0.92)t can be used to determine the number, N, of students enrolled t years after 2008.
Which statement about the change in enrollment is true?
A. The enrollment is decaying at a rate of 0.92 % each year.
B. The enrollment is growing at a rate of 0.92 % each year.
C. The enrollment is decaying at a rate of 8 % each year.
D. The enrollment is growing at a rate of 8 % each year.
8. A scientist studied the population growth of a certain type of bacteria. He concluded that if you
start with 2 bacteria, then the population, P, would triple with each passing day, x. Which of these
equations represents the population growth of this bacteria?
F-IF.3.9
1. A function, m(x), is defined by the equation
2𝑥 𝑖𝑓 0 ≤ 𝑥 ≤ 6
𝑚(𝑥) = {
𝑥 − 4 𝑖𝑓 6 < 𝑥 ≤ 10
The graph of another function, p(x), is shown below.
The following statements about m(x) and p(x) are true except
A. Both functions have the same domain.
B. Both functions have a maximum value of 6.
C. Both functions are increasing on the interval 8 ≤ 𝑥 ≤ 10.
D. Both functions have one x-intercept.
2. A graph is shown
Which equation has the same minimum as this graph?
A. y = - x2 – 9
B. y = x2 + 9
C. y = - x2 – 6x
D. y = x2 – 6x
3. The function f(x) = 300(1.015)x, which give the total amount in an account after x years of interest
that is compounded annually. The function g(x) gives the amount in the account with the same initial
investment, but at a rate of interest of 2.3% compounded annually. How would the graph of g(x)
compare to the graph of f(x)?
A. It would have the same y-intercept, but rise more quickly over time
B. It would have the same y-intercept, but rise less quickly over time
C. It would have a greater y-intercept, but rise more quickly over time
D. It would have a greater y-intercept, but rise less quickly over time
4. Two toy rockets, A and B, are launched at the same time. The height, in feet, of toy rocket A is
modeled by the function f(x) = -16t2 + 96t + 112, where to represents the time the rocket is in the air
in seconds. The path of toy rocket B is shown in the graph.
If rocket B reaches a maximum height of 248 feet, what is the difference, in feet, between the
maximum heights of the two rockets?
5. The table below represents the x and y values of quadratic function g(x)
If compared with f(x) = -x2 + 4x + 6. Which function has a greater maximum value?
6. The population of two cultures of bacteria, A and B, after x hours are shown.
Which statement is a correct comparison of bacteria A and bacteria B?
A. The initial population of bacteria B is more than the initial population of bacteria A
B. The populations of bacteria A and B will never be equal at the same time.
C. The population of bacteria B is greater than the population of bacteria A after 3 hours
D. The rate of growth of bacteria B is less than the rate of growth of bacteria A
7. The graph and the table below represent two quadratic functions f(x) and g(x).
Which statement is true?
A. Both f(x) and g(x) have x = 0 as the axis of symmetry
B. Both f(x) and g(x) have y = 0 as the axis of symmetry
C. f(x) has x = 3 as the axis of symmetry and g(x) has x = 4 as the axis of symmetry
D. f(x) has y = -9 as the axis of symmetry and g(x) has y = -16 as the axis of symmetry
F-LE.1.4 (with F-BF.2.a)
1. An equation is shown.
X = log(20) + 2
What is the exponential form of the equation?
2. Zach is studying the behavior of a group of cells in a lab. He starts with 50 cells and observes that
the cell population triples every hour. The function shown models the number of cells after t hours.
Which equation can be used to determine how many hours it will take for the cell population to reach
50,000?
3. The population, P, of praire dogs increases according to the equation P = 2,250ert, where t is the
number of years, and r is the rate of growth. Which equation solves for r?
4.
A.
what is the value of x?
4
3
C. 12
B.-
4
3
D. – 12
5. A frozen 12 pound turkey initially has a temperature of 26˚ F. The turkey is left to thaw in a room
that has a temperature of 70˚ F. After 40 minutes the temperature of the 12 pound turkey has risen to
30˚F. After how many hours will the temperature of the turkey be 50˚F? Use the Newton Cooling
Formula
A. 4 hours
B. 14 hours
C. 16 hours
D. 20 hours
6. A researcher is interested in how quickly news travels through social media. He finds that a news
story spreads according to the exponential model P = 3·2.56.92t where P is the number of people who
read about the story t minutes after it is first reported. Based on this formula, what length of time
would it take for 1,000 people to have heard a rumor?
A. 3.68 min
B. 6.18 min
C. 6. 72 min
D. 141.53 min
7. What is the solution to the equation 2t = 14?
8. Solve the equation using change of base. Round to the nearest thousandth.
y = Log
6
40
9. Which is the equivalent form of 8(10)4x = 1600?
10.
F-LE.2.5
1. Eric is hiring a company to install carpeting in his house. The company charges a one-time
installation fee plus a certain amount per square yard of carpeting. The graph below shows the
relationship between the number of square yards of carpeting and the total cost, in dollars.
The quantity that represents the cost per square yard of carpeting is the
A.
B.
C.
D.
Slope of the graph
Y-intercept of the graph
Domain of the function
Range of the function
2. A satellite television company charges a one-time installation fee and a monthly service charge.
The total cost is modeled by the function 𝑦 = 40 + 90𝑥. Which statement represents the meaning
of each part of the function?
A. y is the total cost, x is the number of months of service, $90 is the installation fee, and $40 is
the service charge per month.
B. y is the total cost, x is the number of months of service, $40 is the installation fee, and $90 is
the service charge per month.
C. x is the total cost, y is the number of months of service, $40 is the installation fee, and $90 is
the service charge per month.
D. x is the total cost, y is the number of months of service, $90 is the installation fee, and $40 is
the service charge per month.
3. The breakdown of a sample of a chemical compound is represented by the function 𝑝(𝑡) =
300(0.5)𝑡 , where p(t) represents the number of milligrams of the substance and t represents the
time, in years. In the function p(t), explain what 0.5 and 300 represent.
4. The value of a new car after n years is modeled by the function 𝑓(𝑛) = 21,500(0.95)𝑛 . What
does the number 21,500 represent in the given context?
5. The function A(d) = 0.45d + 180 models the amount A, in dollars, that Terry’s company pays him
based on the road-trip distance d, in miles, that Terry travels to a job site. How much does Terry’s pay
increase for every mile of travel?
A. $0.45
C. $180.45
B. $180.00
D. $180.90
6. Monica folded a paper in half to form two rectangles. Then she folded again to form 4 rectangles.
She continued in this pattern to form the greatest number of rectangles. She can use the function f(x) =
2x to model what she was doing? What is the best interpretation of the parameters of the function?
A. f(x) represents the number of times the paper was folded and x represents the total number of
people folding the paper
B. f(x) represents the number of pieces of paper that was folded and x represents the total number of
rectangles formed with those pieces of paper
C. f(x) represents the total number of rectangles formed with the paper and x represents the number of
times the paper was folded
D. f(x) represents the number of times the paper was folded and x represents the total number of
rectangles formed with the paper
F-TF.1.1
1. An angle has a measure of
A. 60 ˚
C. 240 ˚
2𝜋
radians. What is the degree measure of this angle?
3
B. 120 ˚
D. 270 ˚
2. What is the radian measure of a 144˚ angle?
𝜋
A. 36
C.
B,
4𝜋
2𝜋
5
𝜋
D, 144
5
3. A tractor wheel has a radius of 24.5 inches. The tractor moves forward by 98 inches. What is the
radian measure of the angle through which the tractor wheel turns?
A. 122.5
B. 73.5
C. 4
D. 0.25
4. A circle has a radius of 2 inches. A central angle of this circle has a measure of 5 radians. What is the
length, in inches of the arc intercepted by this central angle?
A. 0.4
B. 2.5
C. 7
D. 10
5. An arc on the unit circle is
3𝜋
4
units long.
What is the radian measure of the arc’s central angle?
A.
𝜋
4
radians
C. 3π radians
B.
3𝜋
D.
3
4
4
radians
radians
6. On the unit circle, a central angle θ in standard position intercepts an arc that is 2 units long. If you
reflect angle θ across the y-axis to create a new angle α in standard position, what is the measure of α?
A. 2 - 2π radians
B. 2 – π radians
C. π – 2 radians
D. 2π – 2 radians
7. What is degree measure of 20π radians?
8. An analog wall clock has a radius of 6 inches. What is the radian measure of the acute angle
represented by the hands of the clock at 7:00?
A.
5𝜋
6
C. 5π
B.
7𝜋
6
D. 7π
F-TF.1.2
1. An angle is shown on the unit circle.
The measure of 𝜃 is
11𝜋
6
radians. What is the value of cos 𝜃?
55𝜋
2. Determine all correct trig values for an angle of
A. sin (
55𝜋
C. cos (
55𝜋
6
)= -
1
)= -
1
6
2
2
A. sin (
D. cos (
6
55𝜋
6
55𝜋
6
radians drawn on a unit circle.
)= )= -
√3
2
√3
2
3. The cosine of 𝜃 is - ½, and the terminal side of 𝜃 is in Quadrant III. What is the value of sin 𝜃?
A. -
√3
2
B.
√3
2
C. -
3
D.
3
4
4
4. Which of the following always has the same value as sin θ?
𝜋
A. sin(θ + 2 )
C. sin(θ +
3𝜋
2
B. sin(θ + π)
)
D. sin(θ + 2π)
5. Bill put the tip of a pencil on the outer edge of a graph of the unit circle at the point (0, -1). He
4𝜋
moved his pencil tip through an angle of radians in the counterclockwise direction along the edge of
3
the circle. At what angle of the unit circle did Bill pencil tip stop?
A.
𝜋
C.
7𝜋
3
6
6. What is the exact value of cos (−
A. C.
√3
2
1
2
7𝜋
6
B.
5𝜋
D.
5𝜋
6
3
)?
1
B. -
2
√3
2
D.
7. Let point P = (0, 1). What is the value of the point in radians?
A. 0
B.
𝜋
C. π
D.
3𝜋
2
2
8. What is the point (x, y) on the unit circle that corresponds to the real number t = -
𝜋
4
?
9.
F-TF.2.5
1. Kelly rides a Ferris wheel with diameter 20 feet. The Ferris wheel makes one revolution in 40
seconds. She gets on the wheel at its lowest point, which is 5 feet from the ground. Which equation
models Kelly’s distance from the ground as a function of time t (in seconds) after she starts her ride?
A. f(t) = 10 sin
𝜋
t + 15
20
C. f(t) = - 10 cos
𝜋
20
t + 15
B. f(t) = - 10 sin
D. f(t) = 10 cos
𝜋
20
𝜋
20
t + 15
t + 15
2. Which graph represents a trig function with amplitude 4, frequency 3, and midline y = - 2?
A.
B.
C.
D.
3. The graph shown represents a trig function.
Identify the values of the amplitude, period, frequency, and midline.
4. Which graph represents f(x) = 4 sin (3x -
𝜋
2
) + 3?
A.
B.
C.
D.
5. A company analyzes wind patterns to determine whether to install windmills in Kingsport to
generate electricity. The graph shows the average monthly wind speeds in Kingsport over a two-year
period.
This function is a transformation based on a sine graph. Which value is closest to the amplitude of this
transformed function?
A. 7.2
B. 5.6
C. 3.9
D. 1.7
6. A piano string vibrates according to simple harmonic motion of p(t) = 3sin(2t – π). What is the
period of the vibration?
7. Nan draws the swinging end of a pendulum 10 cm to the left of its rest position and releases it to
swing. She wants to model the horizontal displacement of the pendulum, d, as a function of time, t,
where t = 0 at the point of release. Which function family is best for Nan to use and why?
A. cos (t), because cos(0) = 0
B. cos (t), because cos(0) is an extremum
C. sin (t), because sin(0) = 0
B. sin (t), because sin(0) is an extremum
8. The water depth of the ocean follows a periodic pattern because of high and low tides. At this
location, high tide is at 12 AM with a water depth of 8 meters. Low tide occurred at 9 AM with a
water depth of 2 meters.
a) Use the grid to graph the water depth over a 24 hour period starting at 12 AM.
b) What are the amplitude and period of the graph?
c) Express the water depth using the cosine function.
d) Find the tide height at 9 PM.
9.
F-TF.3.8
1. Given that sin θ = -
2. Given that sin θ =
5
13
and tan θ < 0, what is the exact value of cos θ?
√29
and
7
3. Given that cos θ = -
4. Given that cos θ = -
7
25
5
7
0< θ<
𝜋
2
, what is the value of cos θ rounding to the nearest hundredth?
and tan θ < 0, what is the exact value of sin θ?
and 270˚ θ < 360 ˚, what is the value of sin θ?
5. What is the value of 2sin2 34˚ + 2cos2 34˚
6. Given that sin2 x + cos2 x = 3 – x, what is the value of x?
N-CN.1.2 (with N-CN.1.1)
1. Two equations are shown
a1 =
3
a2 =
1
4
4
1
+ i
2
1
+ i
6
What is the value of a1 - a2 +
3
7
in a + bi form?
2. Which expression is equivalent to (4 – 3i)2 + (6 + i)2?
A. 30
B. 42 – 12i
C. 50
D. 62 – 12i
3. Lui simplified (1 – 7i)(10 – 8i). Her work is shown.
Which statement best describes Liu’s error?
A. The term i2 is equal to – 1, not 1.
B. Two imaginary numbers cannot be combined
C. The product of two negative numbers is positive, not negative.
D. A real number and an imaginary number cannot be combined.
4. Which is equivalent to (10 + 8i) – (-12 + 5i)?
A. 22 + 13i
B. -2i + 23i
C. 22 + 23i
D. 2i + 13i
5. Give i2 = -1, what is the value of i13?
A. 1
C. i
B. -1
D. – i
6. What is the simplified expression of
7. Simplify the expression to a complex number in the form of a + bi
4i3 · (2 + i)(5 – i)
8. Which of these is equivalent to the expression
A. 10i
B. -10i
C. 5 – 5i
D. 5 + 5i
9. Which of these is equivalent to the expression 3i(-5 + 2i) – 2(5 – 4i)
A. -16 – 23i
B. -16 – 7i
C. -10 – i
D. 21 – 4i
10.
N-RN.1.1 (with N-RN.1.2)
1. When multiplying rational exponents with the same base, how should a student apply the rules for
2
exponents to evaluate the expression (83 )
A. Multiply the exponents to give
power.
5
(83 )?
10
9
8 . Find the ninth root of 8 and raise that answer to the tenth
10
9
B. Multiply the exponents to give
power.
8 . Find the tenth root of 8 and raise that answer to the ninth
B. Multiply the exponents to give
power.
83 . Find the cube root of 8 and raise that answer to the seventh
7
7
B. Multiply the exponents to give 83 . Find the seventh root of 8 and raise that answer to the third
power.
2. Which equation best supports why
1
3. If 𝑥 3 = d, which statement is correct?
1
4. Which statement is correct about the value of
1
2
1
2
1
2
1002 ?
A. The expression
100 = 10 is correct because 100 = 102 and (102)½ = 101.
B. The expression
100 = 10000 is correct because 100 = 102 and (102)½ = 104.
C. The expression
100 = 15 is correct because 100 = 102 and (102)½ = 103/2 = 2(10).
D. The expression
1
2
3
5
100 = 25 is correct because 100 = 102 and (102)½ = 105/2 = 2(10).
5. If x and y are real numbers, what is the simplified radical form of
6. Which expression is equivalent to
7. Which expression is another way to write
8. Which expression is equivalent to
9.
S-CP.1.1
1. In a student election, four students are running for class president: two girls (April and Whitney) and
two boys (Dennis and Sam). Five students are running for vice-president: three girls (Amanda,
Stephanie, and Cara) and two boys (Dante and Carlos).
A) What is the sample space for the elected president and vice-president both being girls?
B) What is the sample space for the elected president and vice-president both being boys?
2. A game of chance at the state fair consists of three large bins filled with small rubber balls. Each bin
contains 50 red, 50 blue, and 50 white balls. If participants pull a different color from each bin, they
win a prize. What is the size of the sample space for this game?
A. 9
B. 27
C. 150
D. 450
3. From the set of natural numbers from 1 to 20, inclusive, let A represent the set of odd numbers and
let B represent the set of prime numbers. Write the set that is the complement of A ∩ B.
4. A survey asked 100 students what they prefer to do during the weekend. The results of the survey
are shown.
Which Venn diagram correctly represents the data?
A.
B.
C.
D.
5. A board game involves rolling a dodecahedron – 12 –sided figure – with the numbers 1 through 12
on its faces.
The sample space of rolling the dodecahedron consists of all the numbers from 1 through 12. Event A is
rolling a factor of 12. Event B is rolling a prime number. Which of these statements are true?
I. There are exactly 5 ways that Event A can happen
II. The complement of Event B is {2, 3, , 5, 7, 11}
III. There are exactly nine elements in A ∪ B
A. I only
B. III only
C. I and II only
D. II and III only
6. You spin a spinner with 8 equally likely landing spaces numbered 1 to 8. Event A is landing on a
prime number. Event B is landing on an odd number. What is the intersection of A and B?
A. ∅
B. {3, 5, 7}
C. {1, 2, 3, 5, 7}
D. {1, 2, 3, 4, 5, 6, 7, 8}
7. A survey was conducted to find how many high school students prefer watching comedies or action
movies or both. Let A represent the set of students who prefer comedies and B represent a set of
students who prefer action movies.
How many students like watching comedies but NOT action movies?
A. 22
B. 23
C. 27
D. 28
8.
S-CP.1.2
1. Which of these pairs of events are dependent?
A. You flip a coin and get tails. You flip it a second time and get heads.
B. You pull your friend’s name out of a hat that holds 20 different names, replace the name, then
draw out your friend’s name again.
C. You spin a spinner divided into five equal parts and is numbered 1-5. You get a 3 on the first spin,
and then spin again and get a 2 on the second spin.
D. You remove a black sock from a drawer without looking, then remove another black sock.
2. When rolling a six-sided number cube with faces labeled 1 to 6, which set of events will be
independent?
A. rolling an even number and rolling an odd number
B. rolling an even number and rolling a prime number
C. rolling a prime number and rolling a number greater than 4
D. rolling a prime number greater than 2 and rolling an odd number greater than 2
3. Two bags, bag A and bag B, each hold 3 red, 3 white, 3 blue and 3 green marbles. The bags are
shaken, and one marble is taken from each bag. Both marbles are green.
Is this an independent event?
4. Jacintha was working on a math assignment. She came across the two scenarios listed below.
I. a coin is tossed 3 times, it lands on heads each time
II. a coin is tossed and a number cube labeled 1 – 6 is rolled, the coin lands on heads and the number
cube lands on 3
Which one these scenarios illustrate independent events?
A. Only I
B. Only II
C. Both I and II
D. Neither I and II
5. According to a 2013 National Health survey of 21,000 US households, approximately 56 % of
households had a landline phone and 41 % had a cell phone, but no landline. 48 % of households had
both a landline and cell phone.
Are having a cell phone and having a landline independent? Support your answer.
S-CP.1.3
1. A basket contains 6 bottles of apple juice and 8 bottles of grape juice. You choose a bottle without
looking, put it aside, and then choose another bottle. What is the probability that you choose a bottle
of apple juice followed by a bottle of grape juice?
2. A bag contains 4 blue marbles and 4 red marbles. You choose a marble without looking, put it
aside, and then choose another marble. Is there a greater than or less than 50% choose two marbles
with different colors? Explain
3. Consider a standard deck of playing cards and the following events: A: the card is an ace; B: the
card is black: C: the card is a club. Find each probability as a fraction.
a, P(A|B)
b. P(B|A)
c. P(B|C)
d. P(C|A)
4. Jackie’s dogs are play fighting with their toys. They have a total of 10 toys, 5 of which are red.
Jackie sees one of her dogs has a red toy in its mouth. If the other dog has a toy in its mouth as
well, what is the chance that the toy is red?
A. 5
2
B.
4
1
D.
5
C. 2
9
9
5. Amy rolled two six-sided number cubes. What is the probability (rounded to the nearest
hundredth) that the sum of the numbers on the cubes is a prime number given that the number on
the first cube is even?
A. 0.19
B. 0.39
C. 0.42
D. 0.50
6. Students in a second grade classroom were surveyed to see if they have any pets. Of the students
surveyed, 68 % of them said they have a dog and 17 % said they have a dog and a cat. What is the
probability that a student has a cat given that the student already has a dog?
A. 4 %
B. 17 %
C. 25 %
D. 51 %
7. 52 % of the visitors to a museum purchase tickets to the planetarium. 24 % of the visitors to a
museum buy tickets for both the planetarium and the 3D theater. About what percent of visitors
who buy tickets for the planetarium also buy tickets for the 3D theater?
S-CP.1.4
1. Jaime randomly surveyed some students at his school to see what they thought of a possible increase
to the length of the school day. The results of his survey are shown in the table below.
a. A newspaper reporter will randomly select a Grade 11 student from this survey to interview.
What is the probability that the student selected is opposed to lengthening the school day?
b. The newspaper reporter would also like to interview a student in favor of lengthening the school
day. If a student in favor is randomly selected, what is the probability that this student is also from
Grade 11?
2. The table below shows numbers of registered voters by age in the United States in 2004
based on the census. Find each probability in decimal form.
Age
Registered Voters
Not Registered to Vote
(in thousands)
(in Thousands)
18-24
14,334
13,474
25-44
49,371
32,763
45-64
51,659
19,355
65 and over
26,706
8,033
a. A randomly selected person is registered to vote, given that the parson is between the ages of 18
and 24. _____________
b. A randomly selected person is between the ages of 45 and 64 and is not registered to vote.
______________
c. A randomly selected person is registered to vote and is at least 65 years old._
3. The table below shows the number of days that a meteorologist predicted it would be sunny, and
the number of days it was sunny. Based on the data in the table, what is the conditional probability
that it will be sunny on a day when the meteorologist predicts it will be sunny?
A. 57 %
B. 59 %
C. 90 %
D. 97 %
4. The table shows the results of a survey in which 487 students were asked if they were left-handed or
right-handed. What is the probability that a left-handed student is randomly selected, given that the
student who has chosen is male? Write solution as a fraction.
5. A recent survey was conducted on the preferred ice cream flavors. The table created separated
based on gender and ice cream type.
What is the conditional probability that a female was chosen, given that she prefers strawberry
flavored ice cream?
10
B. 146
10
D. 25
A. 146
C. 63
25
10
6. There are 30 students in a class. Whether they are involved in a varsity sport or not is recorded in
the table.
What is the probability a student is involved in a varsity sport given that the student is female?
5
B. 17
5
D. 30
A. 14
C. 30
6.
5
17
S-CP.1.5
1. 110 students are surveyed about their pets. The results are shown in the table. Which statement is
true?
A. 27 % of the boys have no pets
B. 40 % of the boys have at least one pet
C. 49 % of the girls have no pets
D. 57 % of the students have at least one pet
2. The probability that James has a baseball game this week is 2/7. The probability that James comes
home late and he has a baseball game is 1/7. What is the probability that he comes home late given
that he had a baseball game?
A. 14 %
B. 29 %
C. 50 %
D. 200 %
3. In class of 25 students, 13 have dark hair, 9 have brown eyes, and 19 have either dark hair, brown
eyes, or both. If a student was selected at random, what is the probability that the student has brown
eyes given that the student has dark hair?
A. 0.23
B. 0.36
C. 0.47
D. 0.69
4. On a given day, your car has a 0.10 probability of breaking down and your friend’s car has a 0.15
probability of the same. Given that at least one of the cars breaks down, what is the probability that it
is your car? Round to the nearest hundredth.
5. A math teacher curves a test if no students score a 100 %. If 10 new, smart, hard-working students
are added to the class, what would happen to the probability of the next test being curved and why?
A. decrease because the new students are more likely to score a 100 %
B. decrease because more students means the denominator of the probability would get bigger
C. increase because more students means the denominator of the probability would get bigger
D. increase because the students would bring up the average of the class making a curve more likely
6. The weather forecast for the day shows a 45 % chance of rain, a 45 % chance of lightning, and a
25 % chance of lightning and rain. Which statement is correct?
A. The chance of rain and the chance of lightning are independent events because 0.20 ≠ 0.25.
B. The chance of rain and the chance of lightning are independent events because 0.45 = 0.45.
C. The chance of rain and the chance of lightning are dependent events because 0.20 ≠ 0.25.
D. The chance of rain and the chance of lightning are independent events because 0.45 = 0.45.
7. Jim and Bob love to play basketball and practice together on most evenings. Jim always tells Bob
that he (Jim) does not play as well in the mornings, and he doesn’t think those games should count
that much. In fact, Jim has been keeping track of the wins in different scenarios.
What is the difference between the probability that Jim will win given that it is morning, and the
probability that Jim will win given that it is evening?
A. 6 %
B. 46 %
C. 50 %
D. 52 %
S-CP.2.6
1. 200 people took part in a study involving a new headache medicine. After one week, the subjects
were asked if they had a headache in the past week. According to the data in the two-way table, what
fraction of the people who were given the placebo did not have a headache?
A.
2
C.
3
5
5
B.
3
D.
4
4
5
2. George ordered 100 pizzas for a class party. He ordered 20 cheese pizzas, 35 pepperoni pizzas, and
rest were supreme. Isabella took the first box from the stack and noticed from the mark that it had
toppings, she just couldn’t tell which topping it was. Assuming that the pizzas were randomly
distributed, what is the probability that she grabbed a supreme pizza?
A.
C.
7
20
9
20
B.
D.
7
16
9
16
3. Katie won a large bag of candies by correctly guessing the total number of candies inside a jar. She
was then given a chance to double the amount of candy she was going to receive. She was told that 20
% of the candies are chocolate, 25 % are hard candy, 30 % are caramel and 25 % are white
chocolate. She is then asked the following:
If I pull out a random candy, and I tell you it is not chocolate, what is the probability that it is a hard
candy?
How should she respond to double her candy?
A.
C.
1
4
5
11
B.
D.
3
10
6
11
4. In a state-wide academic challenge, only a few counties made it to the final round of the
competition.
For the final round, some competition questions were based on data collected from the community.
They called 100 people in each county and asked what their favorite colors were.
a) What is the probability that a randomly selected person is from Dade County given that the person
selected red?
b) What is the probability that a randomly selected person that liked red, given that the person is from
Dade county?
Leave solutions in fraction form.
5. The table below shows the number of students in a school by grade level and by membership status
in the Volunteer Club.
The principal selects a student at random. What is the probability that the student is a member of the
Volunteer Club given that the student is a freshman? Round to the nearest thousandth.
6. A survey taken during class revealed 30 % of the students in a class bring their lunch to school. If the
probability that a randomly selected student is a boy given that the student brings their lunch is 40 %,
what is the probability that a randomly selected student will be a boy that brings his lunch to school?
A. 10 %
B. 12 %
C. 70 %
D. 75 %
7. A ticket is drawn at random from tickets numbered 1 to 20. What is the approximate probability
that the number on the ticket drawn is a prime number given that the number is greater than 12?
A. 0.15
B. 0.33
C. 0.38
D. 0.40
8. The students at a college were surveyed. The results show that 88 % of the students have a parttime job and 62 % own a car. The survey also determined that 51 % of the students have a part-time
job.
a) Find the probability that a student owns a car given that he or she had a part-time job.
Round to a whole number percent.
b) Find the probability that a student has a part-time job given that he or she owns a car.
Round to a whole number percent.
9. The table below shows the results of a survey given to a group of students about their favorite type
of sandwich.
Based on the data from the survey, if a girl is chosen, what is the approximate probability that her
favorite type of sandwich is a BLT?
A. 0.22
B. 0.46
C. 0.51
D. 0.85
S-CP.2.7
1. Of 50 students going on a class trip, 35 are student athletes and 5 are left-handed. Of the student
athletes, 3 are left-handed. Which is the probability that one of the students on the trip is an athlete or
is left-handed?
A. 0.2
C. 0.74
B. 0.5
D. 0.8
2. A geneticist is studying a population of fruit flies. Of the 1278 flies, 467 are wingless and 446 have
red eyes. There are 210 flies that are wingless whose eyes are not red. What is the approximate
probability that a fly is wingless or has red eyes?
A. 0.49
B. 0.51
C. 0.71
D. 0.88
3. Darren randomly chooses a card from a standard deck of 52 playing cards. What is the probability
that Darren chooses a club or a queen?
A. 52
4
B. 52
16
D. 52
C. 52
13
17
4. A dodecaheral solid has 12 sides numbered 1 through 12, all equally likely to appear when you roll
it. What is the likelihood that you roll an even number or a prime number?
A. It is impossible because the probability is 0.
B. It is unlikely, because the probability is less than 0.5
C. It is as likely or not, because the probability is about 0.5
D. It is likely, because the probability is greater than 0.5
5. Jeff wants to go to the mall, and he also wants to go to the movies. He has a 50 % chance of going
to the mall, and a 40 % chance of going to the movies. However, the probability of going to the mall
and to the movies is only 5 %.
What is the probability that he goes to the mall or to the movies?
A. 5 %
b. 85 %
c. 90 %
d. 95 %
6. There are 42 people in a grocery store, of which 18 are female. The total number who are 30 years
old or older is 24, of which 10 are female. If a person is randomly selected as a winner of a free
grocery giveaway, what is the probability that the person is either male or is 30 years old or older?
A. 21
17
B. 7
47
D. 3
C. 84
4
1
7. Andy calculates that out of the 100 students that signed up for a charity walk, 60 are juniors, 40 are
boys, and 35 are girls who are juniors. What is the probability that a student chosen randomly from
the group is either a junior or a girl?
8. A box contains 100 red and green light bulbs. The number of red bulbs in the box is three times the
number of green bulbs. It is found that 20 bulbs in the box are defective, of which 10 % are red. What
is the probability that a bulb selected randomly from the box is either a red bulb or a defective bulb?
A. 73 %
B. 82 %
C. 93 %
D. 95 %
S-ID.1.4
1. A town has 685 households. The number of people per household is normally distributed with a
mean, µ, of 3.67 and a standard deviation, 𝜎, of 0.34. Approximately how many households have
between 2.999 and 4.01 people?
A. 493 households
C. 558 households
A. 520 households
A. 575 households
2. The scores on a recent test are normally distributed. John’s test score of 69 was 1 standard deviation
below the mean. Betty’s test score of 99 was 3 standard deviations above the mean. What are the
mean and standard deviation for the test score distribution?
A. The mean is 76.5. and the standard deviation is 7.5.
B. The mean is 79. and the standard deviation is 10.
C. The mean is 84. and the standard deviation is 15.
D. The mean is 91. and the standard deviation is 2.5.
3. A high school is collecting data on ACT scores of its students. The mean and standard deviation of
the scores for last year’s test were 20 and 5, respectively.
Which graph best represents this data, assuming the data is normally distributed?
A.
C.
B.
4. The results of a census indicate that the average income in one town is $42,000, with a standard
deviation of $6,500.
Determine all the correct statements.
a. The z-score of the $30,000 income is 1.85.
b. The z-score of the $30,000 income is -1.85.
c. 3.2 % of the data is at or below $30,000
d. 4 % of the data is at or below $30,000
5. The sample of final grades of 15 students in an algebra class is shown below.
85,87,92,72,94,88,85,75,77,87,95,92,86,80,92
Assuming the data is normally distributed, what percentage of the students scored between 86 and 93?
A. 33 %
B. 34 %
C. 36 %
D. 46 %
6. The average ice skate size of customers at an ice rink with 200 patrons is 9.5.
Assume the data is normally distributed. If the standard deviation of this data is 0.5, how many
patrons have a skate size of 10.5 or larger? (Round to the nearest integer.)
7. The area under the normal curve below is equal to 1 unit. Each grid square has an area of 0.01 unit.
Suppose the annual rainfall in an Alaskan town is normally distributed with a mean of 150 inches per
year and a standard deviation of 36 inches per year. Use the graph to approximate the probability that
the rainfall in a given year is less than 140 inches.
A. 51 %
B. 61 %
C. 50 %
D. 39 %
8. The life expectancy of a dishwasher is 11 years and standard deviation is 1 year. The lifespan is
normally distributed. What percent of these dishwashers will last from 9 to 13 years?
A. about 47.5%
B. about 68 %
C. about 95 %
D. about 34 %
9.
999.
4.
S-IC.1.1
1. Jean polled a random sample from a population and calculated a sample statistic. Jean can use this
statistic to draw an inference about what?
A. the corresponding sample parameter
C. corresponding population statistic
B. the population size
D. corresponding population parameter
2. Determine which sampling method is most likely to be representative of the opinions of voter in an
election race for governor of a state
A. Over the course of a week, poll every customer who comes into a car dealership and is willing to
answer questions
B. Send questionnaires to 500 randomly selected registered members of each of the recognized
political parties in the state
C. Call 1000 randomly selected registered voters and ask their opinions
D. Ask viewers of the 11:00 PM news on a local television station to register their opinions on the
station’s web site
3. Six students worked over spring break. Three of them earned $330, two of them earned $280, and
the other one earned $375. What is the variance of their earnings? Round to two decimal places.
4. Four students were asked to give an example of a survey of a population. Their answers are listed.
Olivia: The number of students in every math class in our high school is recorded.
Pedro: A semi-pro baseball team wants to compare the batting statistics of its best batters against the
batting statistics of the other batters in the league.
Quentin: Our school’s guidance counselor records the addresses of all the students in the school
Regina: A movie theater asks people to take an online survey about their favorite movies of the year
Which students correctly identified a survey of a population?
A. Olivia and Quentin
B. Olivia and Pedro
C. Pedro and Regina
D. Quentin and Regina
5. As senior class president, Grace wants to help provide more lunch items that the students like to eat.
She designs a survey that assesses the favorite foods of students. After school one day, on her way to
the bus, Grace administers the survey to 50 students waiting at the bus loop where buses meet to take
students home.
A. Will the results of this survey represent a random sample, a convenience sample or a self-selected
sample? Explain why
B. Which sampling method would be the best method?
6. Three students are to be selected to serve on a school advisory panel from a class of 35 students.
Which panel would yield data that is MOST likely to be representative of the entire class?
A, The first three names on the class roll
B, The first three students that volunteer
C, The first three students who show up for class tomorrow
D, The first three names chosen from all student names placed in a hat
7. Joe is conducting an experiment to determine the average height of students in his middle school.
He measures all the students in his first period class and averages their heights.
Which statement most accurately describes his experiment?
A. The experiment is valid since Joe can draw a valid conclusion
B. The experiment is not valid since Joe did not choose a random sample of students and cannot draw
a valid conclusion
C. The experiment is valid but Joe cannot draw a valid conclusion because he has not chosen an
appropriate math calculations
D. The experiment is not valid because Joe measured the students and not someone else
8.
S-IC.1.2
1. Ethan is playing with a single die. He figures that the probability of rolling an even number is 3 out
of 6, or 50 %. He rolls the die 50 times, and the die comes up with an even number 15 times.
Did the observed result follow the model?
a. The observed result did not follow the model because the expected result was about 25 even
numbers in 50 rolls of the die.
b. The observed result did not follow the model because there had to be 25 even numbers in a row.
c. The observed result followed the model because it is expected that the next 50 rolls will result in 15
odd numbers.
d. The observed result followed the model because eventually the results will follow the model
exactly.
2. A probability model for a spinner with 4 unequal sections labeled 1, 2, 3, and 4 is shown. Which
result is most unlikely for this model?
A. The spinner lands on 1 twice in 20 spins
B. The spinner lands on 2 twice in 5 spins
C. The spinner lands on 3 twice in 25 spins
D. The spinner lands on 4 twice in 10 spins
3. A restaurant is having a promotional event. With every order over $10, the customer picks an
envelope from a bin and opens it to reveal the discount they will receive. 5 % of the envelopes
contain the word “Free” and the customer will not pay for the order. Which statement describes how
to use a random digits table to simulate how many customers out of 20 will receive their order free?
A. Look at a random digit table, one digit at a time which represents each customer. The number 5 is
the customer receiving their order free. Look at twenty numbers and count how many are the number
5.
B. Look at a random digit table, one digit at a time which represents each customer. The number 5 is
the customer receiving their order free. Count how many digits it takes to get twenty numbers that are
5.
C. Look at a random digit table, two digits at a time which represents each customer. The numbers 01
to 05 are the customers receiving their order free. Look at twenty two-digit numbers and count how
many are between the numbers 01 to 05.
D. Look at a random digit table, two digits at a time which represents each customer. The numbers 01
to 05 are the customers receiving their order free. Count how many two-digit numbers it takes to get
twenty numbers that are between 01 to 05.
4. Janice has 4 spinners which each have 6 sectors. On each spinner, 1 sector has a dot, 2 sectors have
2 dots and 3 sectors have 3 dots. She performs 4 different sets of trials with each spinner. The results of
the trials are listed.
Based on the results, which spinner is most likely weighted evenly?
A. Spinner I
B. Spinner II
C. Spinner III
D. Spinner IV
5. Glen tosses a coin 4 times in a row and records his results. If he performs this trial multiple times,
what results would Glen expect to have with a fair coin?
I. He will get 2 heads and 2 tails more often than 1 head and 3 tails.
II. All the coins will be the same (4 heads or 4 tails) about 25 % of the time.
III. He will get 3 heads and 1 tail about 25 % of the time.
A. I and II
B. I and III
C. II and III
D. I, II, and III
6. Thirty art students each receive an identical set of markers. As part of a project, each student closes
his or her eyes and selects a marker at random.
Pat’s model predicts the probability of a student randomly picking a yellow marker is 0.1. Which result
would MOST likely cast doubt on Pat’s model?
A. Ten students pick red markers
B. Ten students pick yellow markers
C. Two students pick red markers
D. Two
students pick yellow markers
S-IC.2.3
1. A student wants to determine the most liked professor at her college. Which type of study would be
the most practical to obtain this information?
a. simulation
b. experiment
c. survey
d. observation
2. A principal wants to survey 150 students to determine which electives to offer during the next
school year. There are 1.800 students in the school. Which procedure could the principal use to select a
sample using a systematic random sample?
A. Obtain a list of students, Start with the eighth student, and select every twelfth student until 150
students have been selected.
B. Select the first 150 students who enter the school.
C. Choose the fifth student to come into the cafeteria, and then select every third student who comes
in to the cafeteria until 150 students have been selected.
D. Place students names on slips of paper and select 150 slips.
3. A group of educators wants to determine the average number of hours that high school students in
their district spend on homework each week.
Which would be the best way to carry out the study?
A. Ask all students at the performing arts high school
B. Survey a group of randomly selected students from each high school in the district.
C. Take the average from the surveys conducted by other school districts.
D. Ask the football players of each high school team in the district.
4. A radio station wants to get the opinions of listeners on the host of a new radio show. The stations’
staff emails a survey to all listeners who have subscribed to their online listening option. Is this
sampling method biased, and why or why not?
A. The sample is not biased. It is a random sample.
B. The sample is not biased. The listeners have certainly heard the show.
C. The sample is biased. Some people who listen to the radio show might not subscribe to the online
listening option.
D. The sample is not biased. There is no way to know if the online subscribers listen to the station.
5. Marsha wants to know what local people think about the new city tax. She sits in a hotel lobby and
askes the first 50 people that walk in how they about the tax. What type of sample is this?
A. stratified
B. convenience
C. self-selected
D, cluster
6. Which project would be best conducted using an observational study instead of a randomized
experiment?
A. Do cars get better mileage with premium or regular unleaded gasoline?
B. Does using a particular fertiziler increase the yield of potatoes?
C. Does a certain brand of shampoo reduce hair loss?
D. Does the sun affect the growth of moss on trees?
7.
S-IC.2.4
1. When using a c % confidence interval to estimate a population mean or proportion, how does the
interval change as the value of c changes?
A. The interval gets wider as the value of c increases
B. The interval gets narrower as the value of c increases
C. The interval depends on the sample mean or proportion, not the value of c.
D. The interval depends on the sample standard deviation, not the value of c.
2. For a thesis paper, a college student randomly surveyed 250 students concerning morning start times
for classes. Given the choice between starting classes at 8 AM or 9 AM, 189 selected the 9 AM classes. If
he creates a 99 % confidence interval, what is the margin of error for the student’s survey?
A. ± 4.5%
B. A. ± 5.0%
C. ± 7.0%
D. ± 14.0%
3. A marketing researcher wants to find a 99 % confidence interval for the mean amount of money
visitors to a theme park spend per person per day. She knows the standard deviation amounts spent
per person per day by all visitors to the park is $11. How large of a sample should the researcher select
so that the estimate will be within $2 of the population mean?
4. At a furniture store, employees keep track of the number of customers who enter the store and the
number who make a purchase. During the last month, a sample of 643 customers who entered the
store produced 285 purchases. Using the data, what would be a 99 % confidence interval for the
percentage of customers who make a purchase?
A. 39. 4 % - 49.4 %
B. 40. 5 % - 48.2 %
C. 41. 1 % - 47.5 %
D. 42.4 % - 46.3 %
5. The Green Electronics Company installs a new machine that makes a part that is used in cell phones.
A preliminary sample of 200 parts produced by the machine shows that 8 % of them are defective. To
the nearest whole number, how large a sample should the company select so that the 95 % confidence
interval is within 0.02 of the population proportion?
6. A professional sports team and city officials want to conduct a poll to see what percent of fans use
the subway system to attend games. They want to create 95 % confidence interval with a margin of
error of 2 %. What is the minimum number of fans that should be polled to create the confidence
interval?
A. 625
B.1225
C.2400
D. 4800
S-IC.2.5
1. Chris is a short distance runner for his HS varsity track team. His goal is to improve his average 100
meter race time from last year. If his times for the first four races of this year are 10.45, 10.32, 10.22,
and 10.39, what is the maximum time in his fifth and final race to beat his previous year’s average time
of 10.32? Round to the hundredths.
2. Tom is almost done figuring out if his calorie-counting diet is effective by doing a hypothesis test. He
found a p-value of 3.24 %. Which could be true about this problem?
A. He failed to reject the null hypothesis with α = 0.10.
B. He failed to reject the null hypothesis with α = 0.05.
C. He rejected the null hypothesis with α = 0.025.
D. He failed to reject the null hypothesis with α = 0.01.
3. A golf company believes its new ball will travel further than any ball they sell. The company hired
12 golf pros to conduct an experiment. Each pro hit the current and new ball in a randomized order.
The ball distances in yards were recorded in the table.
Using a null hypothesis that there is no difference between the two balls, and an alternative hypothesis
that the new ball travels further, the company then conducted a matched pairs t-test. To the nearest
thousandth, what is the p-value for this sample?
4. Ashley was almost done with her work, dealing with the amount of ice that comes in a five pound
bag. Her p-value was 0.0273. What does this p-value mean?
A. There is a 27.3 % chance that the sample size was too small.
B. There is a 27.3 % chance she will reject the null hypothesis.
C. There is a 27.3 % chance that the amount of ice in the next bag is correct.
D. There is a 27.3 % chance that she would get her sample given that the null hypothesis is true.
5. An experiment was designed to analyze the performance of students who have a study hall to those
who do not.
Group A; Students with study hall: average percent on honor roll 60 %
Group B: Students without study hall: average percent on honor roll 40 %
A simulation was run on a computer program which resulted in a mean difference of 0.5% favoring
Group A. Based on these results, is there convincing evidence that students with a study hall
outperform students without a study hall?
A. Yes, because the mean difference is not close to the simulated mean difference
B. No, because the mean difference is not close to the simulated mean difference
C. Yes, because the mean difference is close to the simulated mean difference
D. No, because the mean difference is close to the simulated mean difference
6. The local water company did a study on a new water treatment procedure. The curves represent
the new treatment (solid) and control group (dotted). The mean values are shown as vertical dashed
lines and are equal among the cases. In which case does the new treatment show the greatest effect?
S-IC.2.6
1. A physicist is testing the impact of temperature on conductivity of a new alloy. She measures the
conductivity of ten samples, once at 32° F and once at room temperature (68° F).
Which type of t-test should the physicist use on the data?
A.
B.
C.
D.
A dependent two-tailed t-test
An independent one-tailed t-test
A dependent one-tailed t-test
An independent two-tailed t-test
2. At a degree of freedom of 40, suppose t = 2.6. For 𝛼 = 0.01, can the null hypothesis be rejected on
a two-tailed test? Why or why not?
a. Yes, because there needs to be more degrees of freedom.
b. No, because the t-value is too low.
c. No, because the parameters is too high to be meaningful
d. Yes, because the t-value is high enough.
3. Researchers measured the levels of fluoride in young children and gave tests to measure their
intellectual development over several years. The results show that young children with higher exposure
to fluoride tend to have lower IQ scores later in life. What can the researchers claim based on these
results?
A. There is a relationship between fluoride levels in children and IQ scores
B. Exposure to higher levels of fluoride reduces IQ
C. There is no relationship between fluoride levels in children and IQ scores
D. Reducing exposure to fluoride can increase IQ
4. The table shows the projected population of 5 countries in 2050
Based on the table, a reporter says the US will make up more than 40 % of the world population.
Which statement best explains whether she is correct or incorrect?
A. She is correct because the projected population of the US is more than 3 times larger than the next
most populous country.
B. She is incorrect because the projected population of the other countries add up to less than the
projected population of the US.
C. She is incorrect because not all the countries in the world are listed in the table.
D. She is correct because the US has the largest projection population listed.
5. Based on the harvest data in the table, one of these harvests decreased in an exponential fashion.
Which vegetable’s data best supports this statement?
A. Broccoli
B. Cauliflower
C. Carrots
D. Cucumber
6. The table below shows the literacy rates for selected countries, per the CIA.
Based on the data, which conclusions are most likely to be valid?
I, There are more people who are literate in Greece than in China
II. The overall literacy rate for these countries is around 92 %
III. There are more females than males in Uruguay that are literate