Sample | Boot Camp for MAAP Algebra I

Boot Camps for Mississippi End of Course Why schedule a MAAP Algebra I Boot Camp?

• Authentic, up-to-date practice questions • Students review exactly what they need in the “final hours” before the test.

• Improves student confidence • Easy to schedule, during the school day or on the weekend • Makes test prep fun and less overwhelming for students

In just three hours students will: • Core skills for success in algebra • Pacing and time management • Test-taking and guessing strategies that really work • How to overcome test anxiety and put their best foot forward on test day

What’s included: Our Boot Camps provide test prep that fits your schedule, even at the last minute. We take care of everything. No hassle, no stress, and no attendance limits.

• Virtual or In-Person instruction by an expert MasteryPrep instructor.

• A workbook for each student with exercises to complete during the event and additional practice leading up to test day.

Boot Camps for Mississippi EOC Workbook

Table of Contents Chapter 1: MAAP AlgebrA I OvervIew ................................................................................7 Chapter 2: IntrOductOry AlgebrA .......................................................................................13 Introductory AlgebrA overvIew ........................................................................................14 Plug In PoInts on A grAPh ..................................................................................................19 dIstrIbutIve ProPerty: show your work ...........................................................................21 word Problem trAnslAtIon ...............................................................................................25 substItutIon.........................................................................................................................26 negAtIve PArAnoIA ..............................................................................................................29 Process of elImInAtIon .......................................................................................................30 equAtIons of lInes ..............................................................................................................34 try numbers ........................................................................................................................ 37 Chapter 3: FunctIOns...............................................................................................................49 functIons overvIew............................................................................................................50 creAte A vIsuAl ................................................................................................................... 53 trAnslAtIons & reflectIons ...............................................................................................54 Process of elImInAtIon ....................................................................................................... 59 use the Answer choIces....................................................................................................60 Plug It In ..............................................................................................................................63 don’t overthInk It..............................................................................................................64 reAd the questIon .............................................................................................................. 67 drAw It out ........................................................................................................................68 Chapter 4: stAtIstIcs & PrObAbIlIty ................................................................................... 77 stAtIstIcs & ProbAbIlIty overvIew .....................................................................................78 fIndIng PercentAges ...........................................................................................................83 Process of elImInAtIon .......................................................................................................85 box-And-whIsker Plot boot cAmP .................................................................................87 Wrap-Up ...................................................................................................................................... 95 FUrther praCtiCe .......................................................................................................................99 PrActIce set one ..............................................................................................................100 PrActIce set two .............................................................................................................103 PrActIce set three ...........................................................................................................107 PrActIce set exPlAnAtIons.................................................................................................111

Schedule Fill in the times following your instructor’s directions. This is the agenda we will follow throughout the day. There will be breaks throughout the session. Next to each section name in the schedule, you’ll find the corresponding page number where it begins in this workbook.

Time

Section

Page Number

MAAP Algebra I Overview

7

Introductory Algebra

13

Break

—

Functions

49

Break

—

Statistics & Probability

77

Boot Camp Wrap-Up

95

MAAP AlgebrA I boot CAMP | 5

WORKKEYS OVERVIEW

Boot Camps for Mississippi EOC Workbook

Boot Camps for Mississippi EOC Workbook

Chapter 1 MAAP Algebra I Overview

MAAP AlgebrA I boot CAMP | 7

Boot Camps for Mississippi EOC Workbook MAAP AlgebrA I OvervIew

What Is End-of-Course Testing?

End-of-course testing measures your aptitude in a given subject after you have finished a course.

Consider it a subject understanding checkup. Teachers use it to identify both your strengths and areas where improvement is needed. This helps ensure you are on track in developing the knowledge and skills needed for the next grade and, eventually, college and a career.

In this Boot Camp, we’ll focus on the three most common concepts in Algebra I: Introductory Algebra, Functions, and Statistics & Probability. Your understanding of each of these concepts will help you pass the MAAP Algebra I test.

Why Should You Care?

•

Some schools require the MAAP Algebra I test as part of your final grade in the course.

•

If your school uses the MAAP Algebra I test as a final exam for the course, then doing well on this test can boost your GPA.

•

A good MAAP Algebra I test score is a positive indicator that you are on track for college.

•

Mastering the foundational skills taught in this Boot Camp will help you succeed in more difficult math courses in the future.

•

Put in the effort now and save yourself from repeating a course or taking summer school.

NOTES:

8 | MAAP AlgebrA I boot CAMP

Boot Camps for Mississippi EOC Workbook MAAP AlgebrA I OvervIew

Orientation The three most common conceptual categories evaluated on the MAAP Algebra I test are Introductory Algebra, Functions, and Statistics & Probability.

Introductory Algebra makes up 52% of the test.

Functions makes up 33% of the test.

Statistics & Probability makes up 11% of the test.

Here is a breakdown of possible ways the three main categories will be covered on the test.

Introductory Algebra tests equations, expressions, and inequalities in the following ways: •

Evaluate problems with one or two variables.

•

Create models to describe real-life situations and relationships.

•

Understand and apply basic mathematical principles.

Functions measures your ability to interpret, understand, and build functions.

Statistics & Probability assesses how well you can summarize, represent, and interpret categorical and quantitative data and interpret linear models.

NOTES:

MAAP AlgebrA I boot CAMP | 9

Boot Camps for Mississippi EOC Workbook MAAP AlgebrA I OvervIew

Orientation The MAAP Algebra I test is a computer-based test that lasts approximately 4.5 hours. It is administered in two sessions, sometimes over a two-day period. Calculator use is permitted on the entire test.

Session One is comprised of individual questions, unrelated to each other.

Session Two presents data and asks questions that are related to the same set of information.

Test Section Session 1

Block 1 Block 2

Number of Questions 58

Time 78 minutes 79 minutes

Session 2

8

90 minutes

Total

66

257 minutes

NOTES:

10 | MAAP AlgebrA I boot CAMP

Boot Camps for Mississippi EOC Workbook

Chapter 2 Introductory Algebra

MAAP AlgebrA I boot CAMP | 13

Boot Camps for Mississippi EOC Workbook introdUCtory algebra: overvIew

What Are Boot Camp Mini-Tests?

During this Boot Camp you will take several mini-tests, which are small segments of an Algebra I test. While taking these mini-tests, it’s important to imagine that you are in an actual testing environment. The time limits assigned match the pace that you should try to keep during the actual test. Practice all of the skills that you have learned as you complete the mini-tests.

For these mini-tests, you have 8 minutes to answer 5 questions. Your instructor will signal when you are out of time. Try to get through all the questions within the time limit. Unless your instructor has provided you with an answer sheet, circle your answers directly in this book. The real test does not allow the use of cell phones, watches, or computers, so you shouldn’t use them on the mini-tests either.

NOTES:

MAAP AlgebrA I boot CAMP | 15

Boot Camps for Mississippi EOC Workbook

Introductory Algebra - Mini-Test One 1.

Which graph is a solution to 2x – 7y > 21? y

A.

y

12 10 8

B.

6

6

4

4

2 –12 –10 –8 –6 –4 –2 –2

C.

12 10 8

2 2 4

6 8 10 12

x

–12 –10 –8 –6 –4 –2 –2

–4

–4

–6 –8

–6 –8

–10

–10

–12

–12

y

y

12 10 8

12 10 8

D.

6

6

4

4

2 –12 –10 –8 –6 –4 –2 –2

2 4

6 8 10 12

2 4

6 8 10 12

x

2 2 4

6 8 10 12

x

–12 –10 –8 –6 –4 –2 –2

–4

–4

–6 –8

–6 –8

–10

–10

–12

–12

Introductory Algebra - Mini-Test One

16

x

GO ON TO THE NEXT PAGE.

Boot Camps for Mississippi EOC Workbook

2.

Use the steps in the table to answer the question. initial equation

4(x – 2)2 – 2x + x = –33x – 4x

step 1

4(x – 2)2 – x = –37x

step 2

4(x – 2)2 = –36x

step 3

(x – 2)2 = –9x

step 4

x2 – 4x + 4 = –9x

step 5

x2 + 5x + 4 = 0

The table shows the first 5 steps used to solve an equation.

Which statement is an incorrect explanation of one step in the process?

3.

A.

From step 1, apply the multiplication property of equality to –x and –37x to get 4(x – 2)2 = –36x in step 2.

B.

From step 2, apply the division property of equality to 4(x – 2)2 and –36x to get (x – 2)2 = –9x in step 3.

C.

From step 3, apply the distributive property to (x – 2)2 to get x 2 – 4x + 4 in step 4.

D.

From step 4, apply the subtraction property of equality to x 2 – 4x + 4 and –9x to get x 2 + 5x + 4 = 0.

A grocery store purchases crates of oranges.

•

Each crate contains 75 oranges.

•

Each crate costs $60.

How much does the grocery store have to charge for each orange to make a profit of $30 per crate?

A.

4.

$0.75

B.

$0.83

C.

$0.90

D.

$1.20

Which expression is equivalent to k 2 – 16?

A.

(k – 8)(k + 2)

B.

(k – 8)(k – 2)

C.

(k + 4)(k – 4)

D.

(k – 4)(k – 4)

Introductory Algebra - Mini-Test One

17

GO ON TO THE NEXT PAGE.

Boot Camps for Mississippi EOC Workbook

5.

Which expression is equivalent to (x – 2)(3x 2 – 5x + 9)?

A.

3x 2 – 4x + 7

B.

3x 2 – 4x + 9

C.

3x 3 – 5x 2 + 9x – 2

D.

3x 3 – 11x 2 + 19x – 18

Introductory Algebra - Mini-Test One

18

STOP! END OF TEST. YOU MAY GO BACK AND CHECK YOUR WORK.

Boot Camps for Mississippi EOC Workbook introdUCtory algebra: Plug In PoInts on A grAPh

Plug in Points on a Graph If you’re having trouble graphing a line on the coordinate plane, try plugging in points.

This is a quick and easy method for solving graph problems. If you forget what each number in the equation of a line represents, then plug in values for x and y to find coordinate points on the line.

Let’s take a look at how plugging in points can help you solve a problem on your test.

1.

Which graph is a solution to 2x – 7y > 21? y

A.

y

12 10 8

B.

6

6

4

4

2 –12 –10 –8 –6 –4 –2 –2

C.

12 10 8

2 2

4

6

8 10 12

x

–12 –10 –8 –6 –4 –2 –2

–4

–4

–6 –8

–6 –8

–10

–10

–12

–12

y

y

12 10 8

12 10 8

D.

6

6

4

4

2 –12 –10 –8 –6 –4 –2 –2

2

4

6

8 10 12

2

4

6

8 10 12

x

2 2

4

6

8 10 12

x

–12 –10 –8 –6 –4 –2 –2

–4

–4

–6 –8

–6 –8

–10

–10

–12

–12

x

MAAP AlgebrA I boot CAMP | 19

Boot Camps for Mississippi EOC Workbook introdUCtory algebra: Plug In PoInts on A grAPh First, simplify the inequality.

2x – 7y > 21 – 7y > –2x + 21 y<

2 x–3 7

Now, plug in a value for x to find a set of coordinates on the graph of the inequality.

Let’s try x = 0. y<

2 (0) – 3 7

y < –3 Therefore, the point (0,–3) is on the graph of the inequality. Since y < –3, all the values of y below this point should be shaded. This makes choice B the only correct answer.

NOTES:

20 | MAAP AlgebrA I boot CAMP

Boot Camps for Mississippi EOC Workbook

Introductory Algebra - Mini-Test Two 1.

Which statements about the line shown in the graph below are true? y 12 10 8 6 4 2 –12 –10 –8 –6 –4 –2 –2

2

4

6

8 10 12

x

–4 –6 –8 –10 –12 Select all that apply.

2.

A.

The point (30,8) is on the line.

B.

The point (–30,8) is on the line.

C.

The point (0,2) is on the line.

D.

The point (2,0) is on the line.

E.

The graph represents the equation –x + 5y = 10.

F.

The graph represents the equation x – 5y = 10.

Seven times Hector’s age minus two times Sandra’s age equals 5. Sandra’s age is also three times Hector’s age. How old is Sandra?

3.

An artist spends d days expanding a mural. The existing mural is 6 feet long. Each day she adds 1.5 feet of the expansion. Which equation models the total length (L) of the mural over time?

A.

d = 1.5L + 6

B.

d = 1.5L – 6

C.

L = 1.5d + 6

D.

L = 1.5d – 6

Introductory Algebra - Mini-Test Two

23

GO ON TO THE NEXT PAGE.

Boot Camps for Mississippi EOC Workbook

4.

5.

Jordan drove a distance represented by the equation 3x + 2. Omar drove a distance represented by the expression 18x + 12. Which of the following describes how the distance Omar drove compares to the distance Jordan drove?

A.

The distance Omar drove is 3 times the distance Jordan drove.

B.

The distance Omar drove is 4 times the distance Jordan drove.

C.

The distance Omar drove is 5 times the distance Jordan drove.

D.

The distance Omar drove is 6 times the distance Jordan drove.

The formula for the area of a trapezoid is A = bases, and h is the height.

b1 + b2 h, where A is the area, b 1 and b 2 are the lengths of the 2

What is the area of the trapezoid below? b1 = x + 9

h=6

b2 = x – 1 A.

A = 6x + 4

B.

A = 6x + 24

C.

A = 3x 2 + 8x – 9

D.

A = 3x 2 + 24x – 27

Introductory Algebra - Mini-Test Two

24

STOP! END OF TEST. YOU MAY GO BACK AND CHECK YOUR WORK.

Boot Camps for Mississippi EOC Workbook introdUCtory algebra: worD ProbleM trAnslAtIon

Word Problem Translation The secret to solving a word problem is translating it into math.

When translating word problems to algebraic equations, it is important to know which words translate to which operations. is, equal to, is the same as → =

times, product, each, per, of → •

minus, without, less, difference, change → – plus, together, and, combined, both → +

divided into, split between or among, divvied up → ÷

Let’s take a look at how word problem translation can help you solve a problem on your exam.

2.

Seven times Hector’s age minus two times Sandra’s age equals 5. Sandra’s age is also three times Hector’s age. How old is Sandra?

Translate the sentences into algebraic equations. Let variables represent the unknown ages and use the translations above to determine what math operations to use.

7h – 2s = 5 s = 3h Substitute 3h from the second equation for s in the first equation.

7h – 2(3h) = 5 7h – 6h = 5 h=5 Hector is 5 years old. Substitute 5 for h in the second equation. s = 3(5) = 15 Sandra is 15 years old.

Remember to translate words into math! Only a one-two punch like this can knock out a word problem.

MAAP AlgebrA I boot CAMP | 25

Boot Camps for Mississippi EOC Workbook introdUCtory algebra: MInI-test exPlAnAtIons

Mini-Test Explanations MINI-TEST ONE 1. The correct answer is B. Solve the inequality for y. Remember to flip the inequality when dividing by a negative number.

2x – 7y > 21 –7y > –2x + 21 y<

2 x–3 7

The line represented by the linear inequality has a positive slope, so choices A and C are incorrect. The shaded region should be below the line represented by the linear inequality, so choice D is incorrect. The graph in choice B is the correct representation of the inequality.

2. The correct answer is A. In step 1, the addition property of equality, not the multiplication property of equality, is used to add x to both sides of the equation and cancel the left-side –x term.

3. The correct answer is D. To make $30 profit, a crate of oranges must be sold for 60 + 30 = $90. Divide $90 by the number of oranges in the crate.

90 = 1.2 75

Each orange must be sold for $1.20 to make a profit of $30 per crate.

4. The correct answer is C. The expression provided is a difference of squares with a2 – b2 = (a + b)(a – b).

Therefore, the given expression can be factored to the following: k2 – 16 k2 – 42 (k + 4)(k – 4) 5. The correct answer is D. Distribute both terms in the first parentheses to all terms in the second parentheses and combine like terms. (x – 2)(3x2 – 5x + 9) 3x3 – 5x2 + 9x – 6x2 + 10x – 18 3x3 – 5x2 – 6x2 + 9x + 10x – 18 3x3 – 11x2 + 19x – 18

40 | MAAP AlgebrA I boot CAMP

Boot Camps for Mississippi EOC Workbook introdUCtory algebra: MInI-test exPlAnAtIons

MINI-TEST TWO 1. The correct answers are A, C, and E. From the figure, notice that the graph of the line runs through points (–10,0) and (0,2). Use these points to find the slope of the line. m=

2 1 2 −0 = = 10 5 0 − ( −10 )

Use the slope

1 and the point (0,2) in point-slope form to find the equation of the line.

5

1 (x – 0) 5 1 y–2= x 5 1 y= x+2 5

y–2=

Check the points in choices A, B, C, and D. Choices A and C are correct while choices B and D are incorrect.

Convert the equation of the line to standard form.

1 (5)(y) = (5)( x + 2) 5

5y = x + 10 –x + 5y = 10 Compare this standard form of the equation to the equations in choices E and F. Choice E is correct and choice F is incorrect.

2. The correct answer is 15 years old. Let h be Hector’s age and s be Sandra’s age. Create an equation using the first sentence, then create another equation using the second sentence.

7h – 2s = 5 s = 3h Substitute 3h from the second equation for s in the first equation.

7h – 2(3h) = 5 7h – 6h = 5 h=5 Hector is 5 years old. Substitute 5 for h back into the second equation. s = 3(5) = 15 Sandra is 15 years old.

MAAP AlgebrA I boot CAMP | 41

Boot Camps for Mississippi EOC Workbook

Chapter 3 Functions

MAAP AlgebrA I boot CAMP | 49

Boot Camps for Mississippi EOC Workbook FUnCtions: overvIew

Functions Overview The Functions conceptual category tests your proficiency over a broad range of algebra skills. The skills that will be tested on your exam include but are not limited to the following:

Interpreting Functions •

Understand the concept of a function and use function notation.

•

Interpret functions that arise in applications in terms of the context.

•

Analyze functions using different representations.

Building Functions •

Build a function that models a relationship between two quantities.

•

Build new functions from existing functions.

Linear, Quadratic, and Exponential Models •

Construct and compare linear, quadratic, and exponential models and solve problems.

•

Interpret expressions for functions in terms of the situation they model.

NOTES:

50 | MAAP AlgebrA I boot CAMP

Boot Camps for Mississippi EOC Workbook

Functions - Mini-Test One 1.

2.

ISP (Internet Service Provider) A charges a $15 installation fee and $0.10 per GB of data, x. ISP B charges $0.15 per GB of data and no installation fee. Which function below represents the difference in cost between ISP A and ISP B? A.

f(x) = –0.05x – 15

B.

f(x) = –0.05x + 15

C.

f(x) = 15x + 0.05

D.

f(x) = 15x – 0.05

The table below contains points on a quadratic function. x

f(x)

–12

0

–10

12

–8

20

–6

24

–4

24

–2

20

0

12

Which statements are true for the function represented by the table? Select all that apply.

A.

The function has a zero at (–12,0).

B.

The function has a zero at (0,–12).

C.

The values of f(x) are increasing on the interval –4 < x < 0.

D.

The values of f(x) are decreasing on the interval –4 < x < 0.

E.

The function has a minimum value between x = –6 and x = –4.

F.

The function has a maximum value between x = –6 and x = –4.

Functions - Mini-Test One

51

GO ON TO THE NEXT PAGE.

Boot Camps for Mississippi EOC Workbook

3.

Andre is testing two prototype devices for heating small mechanical components. The results are shown in the table below.

Time (minutes)

Prototype X Temperature (C°)

Prototype Y Temperature (C°)

0

6

6

1

34

12

2

59

24

3

83

48

4

108

96

5

136

192

Which statement best describes his results?

4.

A.

Prototype X resulted in temperature changing at a constant rate.

B.

Prototype Y resulted in temperature changing at an exponential rate.

C.

Both devices resulted in temperature changing at a constant rate.

D.

Both devices resulted in temperature changing at an exponential rate.

Rayan and Megan are playing a game.

•

Rayan and Megan each started with 50 points.

•

At the end of each turn, Rayan’s points increased by 250.

•

At the end of each turn, Megan’s points doubled.

At the end of which turn will Megan have more points than Rayan?

5.

Select the box or boxes that represent the transformation of each function from the parent function f(x) = x 2.

Vertical Translation

Horizontal Translation

Vertical Reflection

f(x) = –x2 f(x) = (x + 1)2 f(x) = x2 – 8 f(x) = (x – 2)2 + 3

Functions - Mini-Test One

52

STOP! END OF TEST. YOU MAY GO BACK AND CHECK YOUR WORK.

Boot Camps for Mississippi EOC Workbook FUnCtions: CreAte A vIsuAl

Create a Visual It can be difficult to visualize word problems on a math test. Many problems that involve a picture or shape don’t actually show the picture in your test booklet.

If the path to solving a question doesn’t immediately pop out at you, drawing it out can make it more obvious.

Let’s take a look at a problem that dramatically decreases in difficulty once you create a visual.

4.

Rayan and Megan are playing a game.

•

Rayan and Megan each started with 50 points.

•

At the end of each turn, Rayan’s points increased by 250.

•

At the end of each turn, Megan’s points doubled.

At the end of which turn will Megan have more points than Rayan?

Use the information given in the question to draw a table relating the turns to the number of points. Both players start out with 50 points. Megan’s points double each turn, and Rayan’s points increase by 250 each turn. Write out the number of points both girls have for each turn until Megan’s points exceed Rayan’s.

Start

Turn 1

Turn 2

Turn 3

Turn 4

Turn 5

Megan

50

100

200

400

800

1,600

Rayan

50

300

550

800

1,050

1,300

Because you created a visual, you can determine that Megan has more points than Rayan at the end of the 5th turn. You didn’t have to use any algebra at all!

NOTES:

MAAP AlgebrA I boot CAMP | 53

Boot Camps for Mississippi EOC Workbook FUnCtions: ProCess of elIMInAtIon

Process of Elimination When you get stuck on a question and need to make a guess, always try to avoid making a random guess when you can. Instead, narrow down the choices to increase your chance of guessing correctly.

1.

The table below shows the weight of an algae bloom after several days of growth.

Time (days)

Weight (lb)

2

0.13

3

0.17

4

0.23

5

0.32

6

0.51

What is the average rate of change in weight of the algae bloom from day 2 to day 6?

A.

0.032 pound per day

B.

0.095 pound per day

C.

0.190 pound per day

D.

0.380 pound per day

Looking at the table, you can see that the rate of growth increases slightly each day.

The lowest growth rate is between the first two days, days 2 and 3, when the plant grows 0.17 – 0.13 = 0.040 lb.

The highest growth rate is between the last two days, days 5 and 6, when the plant grows 0.51 – 0.32 = 0.190 lb.

Since the question asks for the average rate of change and an average is a way of measuring the “middle” of a set of data, you can eliminate answer choices that do not reflect a number between 0.040 and 0.190 lb per day.

Choice A can be eliminated because 0.032 is less than 0.040. Choices C and D can be eliminated because 0.190 and 0.380 are equal to or greater than 0.190. Since choice B, 0.095 lb per week, is the only option that falls between the highest and lowest rates of change, it is the best guess and also the correct answer.

MAAP AlgebrA I boot CAMP | 59

Boot Camps for Mississippi EOC Workbook FUnCtions: use the Answer ChoICes

Use the Answer Choices You have learned that when you get stuck, you can try plugging numbers into the given equation to see what happens. This process is far more effective when you don’t have to pick those numbers yourself. When the answer choices give numbers, use them!

2.

Clayton throws a stone from the edge of a cliff into a lake below. The height of the stone, in meters, is modeled by the function h(s) = –s 2 + 6s + 27, where s represents how far the stone is from the cliff. How far from the cliff will the stone be when it touches the surface of the lake below?

A.

0 meters

B.

3 meters

C.

9 meters

D.

27 meters

When the stone touches the surface of the lake, its height, h(s), will be 0. To solve this problem, you would need to set the equation equal to 0 and solve for s. If you struggle with factoring polynomials, though, an easier and faster method would be to plug each of the answer choices into the equation and see which one results in a height of 0.

When your numbers come from the answer choices, start in the middle and move to higher or lower numbers if necessary.

0 = –(9)2 + 6(9) + 27 0 = –81 + 54 + 27 0 = –81 + 81 0=0 The stone is 9 meters from the cliff when it touches the surface of the lake.

NOTES:

60 | MAAP AlgebrA I boot CAMP

Boot Camps for Mississippi EOC Workbook FUnCtions: MInI-test exPlAnAtIons

Mini-Test Explanations MINI-TEST ONE 1. The correct answer is B. Create expressions for the costs for ISP A and ISP B, then subtract.

ISP A: 0.10x + 15 ISP B: 0.15x f(x) = ISP A – ISP B f(x) = 0.10x + 15 – 0.15x f(x) = –0.05x + 15 2. The correct answers are A, D, and F. A zero occurs when the graph of the function intersects the x-axis, so the function has a zero at (–12,0). The value of the function goes down from 24 to 12 on the interval –4 < x < 0, so the function is decreasing on this interval. The greatest value of the function x > 24 occurs between x = –6 and x = –4, so the function has a maximum between these values.

3. The correct answer is B. For Prototype X, temperature increased neither at a constant nor an exponential rate.

For Prototype Y, temperature increased exponentially.

4. The correct answer is the 5th turn. Rayan’s points are increased by 250 each turn and Megan’s points are doubled each turn. Consider the points for both Rayan and Megan over the course of several turns: Start

Turn 1

Turn 2

Turn 3

Turn 4

Turn 5

Megan

50

100

200

400

800

1,600

Rayan

50

300

550

800

1,050

1,300

At the end of the 5th turn, Megan has more points than Rayan.

5.

Vertical Translation

Horizontal Translation

Vertical Reflection ✓

f(x) = –x22 ✓

f(x) = (x + 1)22 f(x) = x22 – 8

✓

f(x) = (x – 2)22 + 3

✓

✓

A vertical translation occurs when a value is added or subtracted outside of the parentheses, as in the 3rd and 4th functions. A horizontal translation occurs when a value is added or subtracted inside of the parentheses, as in the 2nd and 4th functions. A vertical reflection occurs when the function is multiplied by –1, as in the 1st function.

MAAP AlgebrA I boot CAMP | 71

Boot Camps for Mississippi EOC Workbook

Chapter 4 Statistics & Probability

MAAP AlgebrA I boot CAMP | 77

Boot Camps for Mississippi EOC Workbook statistiCs & probability: overvIew

Statistics & Probability Overview The Statistics & Probability conceptual category tests your proficiency over a broad range of algebra skills. The top skill that will be tested on your exam includes the following:

Interpreting Categorical and Quantitative Data •

Summarize, represent, and interpret data on a single count or measurement variable.

•

Summarize, represent, and interpret data on two categorical and quantitative variables.

•

Interpret linear models.

NOTES:

78 | MAAP AlgebrA I boot CAMP

Boot Camps for Mississippi EOC Workbook

Statistics & Probability - Mini-Test One 1.

The table below shows the amount of sugar in several beverages.

Beverage

Sugar (teaspoons)

Lemonade Soda Sweet tea Fruit punch Orange juice Coconut water Hot chocolate Sports drink

6 13 8 12 8 2 6 2

An energy drink contains 19 teaspoons of sugar. Which of the following is true if an energy drink is added to the data set?

2.

A.

The range stays the same.

B.

The median decreases.

C.

The standard deviation increases.

D.

The interquartile range decreases.

Use the table below to answer the question.

Photo Booth Price Statistics for Two Companies

Company

Median

Mean

Interquartile range

Memories Made Fun Photos

$80.75 $90.99

$82.00 $60.90

$61.21 $33.50

Which statement about the prices of renting photo booths at Memories Made and Fun Photos is best supported by the data?

A.

The fact that the median and mean are very close at Memories Made means that all of the photo booths cost under $85.

B.

Comparing the interquartile range of the companies shows that photo booths at Fun Photos are about half the cost of photo booths at Memories Made.

C.

Comparing the mean prices of both companies shows that most photo booths are more expensive at Memories Made.

D.

Some low-priced photo booths at Fun Photos make the mean lower than the median.

Statistics & Probability - Mini-Test One

79

GO ON TO THE NEXT PAGE.

Boot Camps for Mississippi EOC Workbook

3.

The table below shows the orders at an ice cream shop during the month of June.

Ice Cream Shop Sales - June Chocolate Syrup

Sprinkles

No Topping

Total

Mint Chocolate

101

0

45

146

Café Mocha

89

60

27

176

Cookie Dough

60

44

99

203

Total

250

104

171

525

Which statements about the ice cream shop sales for the month of June are true? Select all that apply.

A.

The percentage of mint chocolate sales was less than the percentage of café mocha sales.

B.

The percentage of sales of cookie dough with chocolate syrup was greater than 25% of all sales.

C.

The percentage of sales of a café mocha with no topping was less than 1% of all sales.

D.

The number of sales of cookie dough ice cream with sprinkles was 44.

E.

The number of ice cream sales with no topping was less than the number of mint chocolate ice cream sales.

Statistics & Probability - Mini-Test One

80

GO ON TO THE NEXT PAGE.

Boot Camps for Mississippi EOC Workbook

4.

The number of games each student in Ms. Costela’s class has on his or her phone is 5, 3, 2, 0, 1, 2, 6, 3, 2, 1, 25, 0, 2, 4. The data is represented by one of the figures below.

Figure 1

0

2

4

6

8 10 12 14 16 18 20 22 24 26 Figure 2

0

2

4

6

8 10 12 14 16 18 20 22 24 26 Figure 3 X

0

2

4

6

8 10 12 14 16 18 20 22 24 26 Figure 4 X

0

2

4

6

8 10 12 14 16 18 20 22 24 26

Select the answers that best complete the following statement.

O

Figure 1

O

Figure 2

1

O

2

, and

The data in the table is best represented by

Statistics & Probability - Mini-Test One

O

represents the center of the data.

O

Figure 3

O

4

O

Figure 4

O

6

81

GO ON TO THE NEXT PAGE.

Boot Camps for Mississippi EOC Workbook

5.

Rodrigo’s biology class planted tomato seeds as part of an experiment. Each week, a student measured the height of any one of the tomato vines. The data in the scatter plot shows the findings from weeks 3 through 13.

Height (in)

y

Tomato Vine Growth

80 72 64 56 48 40 32 24 16 8 0

1 2 3 4 5 6 7 8 9 10 11 12 13 Number of Weeks

x

Which function, h(x), approximates the height of the tomato vines after x weeks?

A.

h(x) = 0.16x + 4.34

B.

h(x) = 0.16x – 7.99

C.

h(x) = 6.02x + 15.79

D.

h(x) = 6.74x – 16.81

Statistics & Probability - Mini-Test One

82

STOP! END OF TEST. YOU MAY GO BACK AND CHECK YOUR WORK.

Boot Camps for Mississippi EOC Workbook statistiCs & probability: MInI-test exPlAnAtIons

Mini-Test Explanations MINI-TEST ONE 1. The correct answer is C. Use the process of elimination. 19 is larger than any number in the data set, so the range will increase, making choice A incorrect. Choice B is incorrect because if a number larger than the median is introduced to the data set, the median would increase, not decrease. Choice D is incorrect because the interquartile range does not decrease but rather increases. The interquartile range is the median of the upper half of the data minus the median of the lower half of the data. Before the energy drink is added to the data, the interquartile range is 10 – 4 = 6. After the energy drink is added in, the interquartile range becomes 12.5 – 4 = 8.5. Standard deviation is a measure used to quantify how data in a given set is dispersed, that is, the amount of variation in a set of data values. Adding a number to the data that is higher than all the other values will increase the range for the set of values. If standard deviation is a measure of how much each data point varies from the middle of the data, having a larger range of data implies the inclusion of numbers that are further away from the middle will deviate more. If the range increases, the standard deviation will also increase, so choice C is the best answer.

2. The correct answer is D. Using only the table, it is impossible to know the total number of values in the data set used to find the median, mean, and interquartile range for each company. Therefore, there are some generalizations that cannot be made. Choice A is incorrect because the data could have very high prices, well over $85, and still have a median and mean in the low 80s. Choice B is incorrect because the interquartile range is the difference between certain quartile values in the data set and does not give insight about the highest or lowest values themselves. Therefore, the given interquartile ranges show that the upper half of the data is closer in value to the lower half of the data for Fun Photos than for Memories Made, not that the overall pricing is always half as much for Fun Photos as it is for Memories Made. Choice C is incorrect because the mean does not provide evidence about the number of photo booths that are priced higher at Memories Made than at Fun Photos. Choice D is correct because lower values can always lower the mean and cause it to be lower than the median.

3. The correct answers are A and D. Choice A is correct because the percentage of mint chocolate sales is 146 176 · 100 ≈ 28%, which is less than the percentage of café mocha sales, · 100 ≈ 34%. Choice D is 525 525 correct because the value in the row labeled Cookie Dough under the column Sprinkles is 44. Choices B, C, and E do not accurately describe the data. The percentage of cookie dough with chocolate syrup is 60 27 · 100 ≈ 11%, which is not over 25%. The percentage of café mocha with no topping is · 100 ≈ 5%, 525 525 which is not less than 1% of all sales. The number of ice cream sales with no topping is 171, which is not less than the number of mint chocolate ice cream sales, 146.

4. The correct answers are Figure 4 and the number 2. The median of a set of data is the middle value when all the values are listed in numerical order. The median of this data is 2 and represents the center of the data. This also rules out Figures 2 and 3, which show a median value other than 2. Figure 1 can be eliminated because it incorrectly shows 25 as the maximum rather than as an outlier. A value is defined as an outlier when it is more 3 than the value of the upper quartile plus times the upper quartile. In the correct plot, the upper quartile is 4, and 2

92 | MAAP AlgebrA I boot CAMP

Boot Camps for Mississippi EOC Workbook statistiCs & probability: MInI-test exPlAnAtIons 3 (4) = 10. Since 25 is greater than 10, it should be depicted as an outlier. This makes Figure 4 the correct 2 answer.

4+

5. The correct answer is D. Sketching a line in the direction of the data shows that a line of best fit would cross the y-axis at a negative value. Since the equations listed in the answer options are in slope-intercept form, this eliminates choices A and C, both of which show a positive value for the y-intercept. Next, examine the slopes of choices B and D. The slope of choice B is 0.16, or

4 . Sketching out a line with this slope, beginning with 25

the first point on the graph, gives a line that falls far below the data points and is therefore unlikely to be the 7 . Sketching a line with this slope, beginning with the 1 first point on the graph, gives a line that is much closer to the location of the data points plotted on the graph, line of best fit. The slope of choice D is 6.74, or around

making choice D the best approximation.

MINI-TEST TWO 1. The correct answers are Figure 2 and the number 1. Use the process of elimination. The median is defined as the middle value when all the numbers in a data set are listed in numerical order. The median, or center of the data, for this set of data is 1. Figures 3 and 4 show a median of 2 and can therefore be eliminated. An 3 times the upper quartile plus the value of the upper quartile. The upper 2 3 quartile for this set of data is 2, so an outlier is any number greater than 2 + (2) = 5. Since 16 is greater than 2 5, it should be marked as an outlier. This means Figure 1 can be eliminated, and Figure 2 is the correct answer. outlier for a set of data is defined as

2. The correct answers are Club 1 and $178.80. Find the mean fundraising amount for each club by adding the fundraising totals per club and dividing by the number of fundraisers, 5.

The mean fundraising amount for Club 1 is

148 + 200 + 80 + 300 + 166 = $178.80.

5

The mean fundraising amount for Club 2 is

275 + 200 + 75 + 253 + 70 = $174.60.

5

The mean fundraising amount for Club 3 is

60 + 355 + 131+ 220 + 99 = $173.00.

5

The club with the highest average fundraising amount is Club 1, which had a mean fundraising value of $178.80.

MAAP AlgebrA I boot CAMP | 93

Boot Camps for Mississippi EOC Workbook

Maap algebra i

Wrap-Up

Boot Camps for Mississippi EOC Workbook

WORKKEYS OVERVIEW

Wrap-Up

Wrap-Up Remember These Key Test-Taking Techniques •

Process of Elimination

•

Plug It In

•

Word Problem Translation

•

Negative Paranoia

•

Draw It Out

•

Don’t Overthink It

•

Read the Question

NOTES:

96 | MAAP AlgebrA I boot CAMP

Boot Camps for Mississippi EOC Workbook

Maap algebra i

Further Practice

Boot Camps for Mississippi EOC Workbook FUrther praCtiCe: PrACtICe set one

Practice Set One 1.

2.

Which of the following expressions is equivalent to 5x 2 – (x + 3) 2 + 8x – 12?

A.

4x 2 + 2x – 21

B.

4x 2 + 2x – 3

C.

4x 2 + 14x – 21

D.

4x 2 + 14x – 3

The graph represents the change in internal temperature of a pie as it bakes in an oven for one hour. y Pie Internal Temperature

Temperature (°F)

200 150 100 50 0

15

30 45 Time (min)

60

x

Which unit would be appropriate for the rate of change in the graph?

A.

degrees hour

B.

degrees minute

C. D.

3.

hours degree minutes degree

Which of the following is a zero of the polynomial expression 4x + 32?

A.

–32

B.

–8

C.

4

D.

8

100 | MAAP AlgebrA I boot CAMP

Boot Camps for Mississippi EOC Workbook FUrther praCtiCe: PrACtICe set one 4.

5.

Which equation could be used to find the zeros of the function 15x 2 – 3x – 12?

A.

(x – 4)(x + 3) = 0

B.

(x + 5)(x + 3) = 0

C.

(3x + 5)(4x – 3) = 0

D.

(5x + 4)(3x – 3) = 0

Three times Sasha’s age plus two times Paulo’s age equals 52. Paulo’s age is also five times Sasha’s age.

How old is Paulo?

6.

Force is related to the mass of two objects by the formula F = •

G is the gravitational constant.

•

m1 and m2 are the mass of two objects.

•

d is the distance between the objects.

Gm1 m2 . d2

Which equation finds d, given F, G, m1, and m2?

7.

A.

d=

F Gm1 m2

B.

d=

Gm1 m2 F

C.

d=

F Gm1 m2

D.

d=

Gm1 m2 F

The table below shows the cost of buying protein bars from a health food store.

Protein Bars

30

60

90

120

150

Cost (in dollars)

25

50

75

100

125

What is the meaning of the slope of the linear model for the data?

A.

The cost of 5 bars is 1 dollar.

B.

The cost of 5 bars is 6 dollars.

C.

The cost of 6 bars is 1 dollar.

D.

The cost of 6 bars is 5 dollars.

MAAP AlgebrA I boot CAMP | 101

Boot Camps for Mississippi EOC Workbook FUrther praCtiCe: PrACtICe set one 8.

Use the equation to answer the question.

2x2 + 12x + 5 = 7 Valentina is completing the square to rewrite the equation. Which equation could be her result?

9.

A.

(x + 3)2 = 5

B.

(x + 3)2 = 7

C.

(x + 3)2 = 10

D.

(x + 3)2 = 13

An acrobat’s height as she jumps from a platform above a trampoline, in feet, is modeled by the function h(x) = –x 2 + 5x + 36, where x represents the distance of the acrobat from the platform. How far from the platform will the acrobat be when she reaches the trampoline?

A.

0 feet

B.

4 feet

C.

5 feet

D.

9 feet

10. Jessica wants to earn at least $145 dollars from her two jobs next week. She can work 18 hours at most.

Her first job pays $8 per hour, and her second job pays $9 per hour. Let b represent the number of hours worked at the first job and s represent the number of hours worked at the second job. Which system of linear inequalities models Jessica’s situation?

A.

b + s < 18 8b + 9s > 145

B.

b + s ≤ 18 8b + 9s ≥ 145

C.

b + s ≥ 18 8b + 9s ≤ 145

D.

b + s > 18 8b + 9s < 145

102 | MAAP AlgebrA I boot CAMP

Boot Camps for Mississippi EOC Workbook FUrther praCtiCe: PrACtICe set exPlAnAtIons

Practice Set Explanations PRACTICE SET ONE 1. The correct answer is A. Simplify the expression by using FOIL on (x + 3)2, distributing the negative sign, and combining like terms.

5x2 – (x + 3)2 + 8x – 12 5x2 – (x + 3)(x + 3) + 8x – 12 5x2 – (x2 + 6x + 9) + 8x – 12 5x2 – x2 – 6x – 9 + 8x – 12 4x2 + 2x – 21 2. The correct answer is B. In the figure, the y-axis represents temperature (°F) and the x-axis represents time (minutes). The rate of change, or slope, of the linear equation is

degrees change in y or . minute change in x

3. The correct answer is B. Find the zero of the polynomial by setting the expression equal to zero and solving for x.

4x + 32 = 0 4(x + 8) = 0 x+8=0 x = –8 4. The correct answer is D. Factor the function and use the process of elimination to quickly rule out incorrect answer options. Because 15x2 appears in the function, the x terms in the answer choices must multiply to equal this. The only answer choice where this occurs is choice D, where (3x)(5x) = 15x2.

5. The correct answer is 20. Let Sasha’s age be s and let Paulo’s age be p. Use the first sentence to create an equation. Then, use the second sentence to create another equation.

3s + 2p = 52 p = 5s Substitute 5s in for p in the first equation and solve for s.

MAAP AlgebrA I boot CAMP | 111

Boot Camps for Mississippi EOC Workbook FUrther praCtiCe: PrACtICe set exPlAnAtIons 3s + 2(5s) = 52 3s + 10s = 52 13s = 52 s=4 Sasha is 4 years old. So Paulo is p = 5(4) = 20 years old.

6. The correct answer is D. Use the formula to solve for d.

F=

Gm1m2 d2

Fd2 = Gm1m2 d2 =

Gm1m2 F

d=

Gm1m2 F

7. The correct answer is D. The slope of the linear model is in the form

bars . Take two points from the table, dollars

(25,30) and (50,60), and use the slope formula. m=

60 − 30 30 6 6 bars = = = 50 − 25 25 5 5 dollars

The cost of 6 bars is 5 dollars.

8. The correct answer is C. Isolate the x terms to the left side of the equation, simplify, and complete the square 2

 b  by adding   to both sides of the equation.  2a 

2x2 + 12x + 5 = 7 2x2 + 12x = 2 x2 + 6x = 1 2

2

 6   6  x2 + 6x +   =   + 1 2 1  ( )  2 (1)  x2 + 6x + 9 = 9 + 1 (x + 3)2 = 10 9. The correct answer is D. Set the quadratic function equal to zero. Then, factor and solve for x.

–x2 + 5x + 36 = 0 x2 – 5x – 36 = 0 (x – 9)(x + 4) = 0

112 | MAAP AlgebrA I boot CAMP

Take the next step towards transforming student outcomes.

Ready to see how MasteryPrep can revolutionize college readiness in your district?

Our team is ready to show you how our targeted solutions can significantly boost your accountability outcomes and enhance student achievement.

Don’t wait to make a difference. Get in touch now, and let’s start a conversation that changes the future of education in your district.

Contact Us: Phone: 855-922-8773 Email: info@masteryprep.com