Running head: ALGEBRA 2 ASSESSMENT

Psychometric Properties of a Computer-Based Algebra 2 Assessment

Michael Mazzarella

George Mason University

ALGEBRA 2 ASSESSMENT

Psychometric Properties of a Computer-Based Algebra 2 Assessment

Research Questions

The purpose of this study is to analyze the psychometric properties, including validity,

Classical Test Theory analysis, and Rasch analysis, of the Mazzarella (2015) Algebra 2

assessment. The following research questions will address that purpose:

1. What are the psychometric properties, particularly validity, of a computer-based Algebra

2 assessment?

2. Are there differences in these properties between the different versions of the assessment

based on item format and question type?

Method

Participants

The participants of this study will be 148 high school students (n = 148) currently

enrolled in an on-level Algebra II course in a large suburban school district during the 2014-2015

school year. These students will be selected based on a sample of convenience. The 148 students

will come from a total of nine on-level high school Algebra II classes, four of which are taught

by the researcher and five of which are taught by three other teachers in the same school. The

three teachers assisting the researcher with this study are on-level Algebra II teachers at the same

school. These teachers have two, seven, and twenty years of experience teaching within the same

school, while the researcher has four years of teaching experience within the same school. The

present study has been fully explained to the other three teachers, and they have agreed to help in

the data collection process and allow their students to participate in the study.

The sample will consist of 61 females (n = 61) and 87 males (n = 87). The ages of the

students at the time of the study will range from fifteen years to nineteen years. The ethnicity of

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the students is expected to be similar to that of the school demographic: About 33% of students

will be Hispanic, 25% of students will be Asian, 24% of students will be white (not of Hispanic

origin), 18% of students will be African-American (not of Hispanic origin), and 2% of students

will be listed as “other.” Approximately twenty students will be categorized as limited English

proficiency. About 55% of students will receive free or reduced lunch on a daily basis.

Approximately 5% of students will be categorized as special education. The school at which the

data is being collected is a public school within a large, diverse, suburban community. The

school has approximately 2,300 students, and the ethnicity of those students will be

approximately the same as that of the sample (source not cited to ensure confidentiality).

Measure

Students will be given a set of thirty mathematics items on the computer through the

program Horizon, which is a commonly used computer-based assessment program in the county

in which the present study will be being conducted. This program allows teachers to create items

of different formats, and teachers will receive the students’ results for each question when the

assessment is complete. The items for this measure can be found in Appendix A.

The curriculum used to create these mathematics items aligns with the standards set forth

by the county in which this study will be conducted. These standards also match the standards

used to create the end-of-year state assessment that students in Algebra II are required to take.

Some examples of standards included in the mathematics measure are solving radical, absolute

value, and rational equations, finding the domain and range of various functions, simplifying

rational and radical expressions, identifying properties of a normal distribution, and recognizing

and solving permutations and combinations. According to the state in which the study will be

taking place, there are four strands (i.e. standards) that categorize Algebra II test questions:

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Expressions and Operations, Equations and Inequalities, Functions, and Statistics (Virginia

Department of Education, 2012). It is also worthwhile to note that Sstudents in the county are

required to complete and pass Algebra II in order to graduate. Thus,This is important to keep in

mind because it implies that students with a variety of skill levels will be measured in the present

study, rather than only students who choose to enroll in an Algebra II course without it being

required.

Procedure and Research Design

In order to obtain assent from students and consent from the students’ parents or

guardians, the researcher will speak with all classes about the purpose of this study, the measure

being used, the students’ optional participation in this study, and the confidential data being

collected. Students will then be given the consent and assent forms, and they will be instructed to

read and sign the assent forms and have their parents read and sign the consent forms. Once the

forms have been read and signed, the students will be instructed to return both forms to their

teacher. The signed forms will be kept in a secure file cabinet in the researcher’s room until the

study has been completed.

After the teacher has received the signed consent and assent forms, students will then

take a measure of mathematics achievement. Students will have one full class period (90

minutes) to complete this test. Once students complete the test, the responses and scores will be

linked to a student ID number that matches that written on the survey. A teacher other than the

researcher will match the responses of the survey and the math measure, enter the data into a

Microsoft Excel file, replace the student ID numbers with a different unidentifiable ID number,

and give the data to the researcher. As an incentive, all students participating in the study will be

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entered into a raffle to win one of four $25 Target gift cards. Each of the three teachers assisting

with the study will also receive a $25 Target gift card.

Classes will be randomly assigned to take one of four versions of the math measure: Test

A, Test B, Test C, or Test D. Test A and Test B have the same prompts in the same order. On

Test A, the odd-numbered questions will be multiple choice questions, and the even-numbered

questions will be technology-enhanced questions (either fill-in-the-blank or selecting multiple

correct answers). On Test B, the even numbered questions will be multiple choice questions, and

the odd numbered questions will be technology-enhanced questions. Test questions are staggered

this way so that data will be collected for every prompt in both a multiple choice and technology-

enhanced format. On both Test A and Test B, there will be twenty straightforward mathematics

problems (ten multiple choice and ten technology-enhanced) and ten real-world application

problems (five multiple choice and five technology-enhanced). Creating the assessments in this

way yields four categories: straightforward multiple choice, straightforward technology-

enhanced, word problem multiple choice, and word problem technology-enhanced. Both tests

have the same number of questions in each category. These tests were created in this way

because the data collected will provide a comparison of the same prompts with different item

formats, as well as a comparison between straightforward questions and word problems. The

items in Test A and Test B can be found at the end of this document in Appendix B.

Test C will have the same exact questions and formats as Test A, but the questions will

be in reverse order. Test D will have the same exact questions and formats as Test B, but the

questions will be in reverse order. Test C and Test D were created to account for test fatigue.

Tyrrell and colleagues (1995) support that visual and mental fatigue can occur as students take

assessments, especially when the assessments are taken on the computer. As students work

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through the thirty-question math measure, some may become less motivated or energized toward

the end of the test. Thus, it is important to test whether or not this occurs in the measure before

drawing conclusions about specific test questions or overall achievement.

As mentioned previously, the results of the mathematics measure will be available online

to the student’s teacher once the test is complete. Results will include the number of correct

answers and the responses to each multiple choice and technology-enhanced question.

Data Analysis

All data analysis will be conducted using the computer programs Microsoft Excel, SPSS,

and jMetrik. In this study, the data analysis will attempt to simultaneously answer both research

questions. The first research question asks: What are the psychometric properties, particularly

validity, of a computer-based Algebra 2 assessment? The second research question asks: Are

there differences in these properties between the different versions of the assessment based on

item format and question type? In order to answer these questions, several methods of analysis

will be used. First, two independent samples t-tests for item order will be used to determine if

there are significant differences in the results of Test A and Test C, or the results of Test B and

Test D. As mentioned before, Test A and Test C have the same exact prompts and item formats,

but are in reverse order, and Test B and Test D follow the same format. By comparing the results

of the two pairs of versions, the researcher will determine if there is an ordering effect for the

assessment.

Second, Classical Test Theory (CTT) analysis will be run. Several descriptors of each

item will be looked at. These descriptors include reliability, which is defined as the ratio of true

score variance to observed score variance; item difficulty, which is defined as the proportion of

examinees who answered the item correctly; and item discrimination, which is defined as the

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difference between the proportion of examinees in the upper group who answered the item

correctly and the proportion of examinees in the lower group who answered the item correctly

(Osterlind, pp. 122, 277-288). These CTT analyses will be applied to both student responses to

the individual items, as well as the results of the overall assessment.

Third, Rasch analysis will be applied to the data. This analysis will be used to indicate

several more characteristics about the items and the assessment. One such characteristic is fit of

items. The program jMetrik will identify misfit items, which could be an indication that the item

does not discriminate well between high and low achieving students, the item is general not a

good fit in the assessment as compared to other items, or an anomaly in the examinee’s

responses. Rasch analysis using jMetrik will also indicate the person separation index and item

separation index. The person separation index will indicate whether or not the assessment

adequately distinguishes between high and low achieving individuals, while the item separation

index will indicate whether or not the assessment adequately distinguishes between high and low

difficulty items (Dimitrov, 2014). Rasch analysis will also give three-parameter logistic (3PL)

models for each multiple choice item. The 3PL models are visual representations of student

responses based on the item discrimination, the item difficulty, the chance of randomly guessing

correctly, and the student ability level, which is based on the number of standard deviations the

students’ achievement is from the mean of a normal curve (Birnbaum, 1968; Harris, 1989).

When the 3PL model is created for multiple choice items, the chance of randomly guessing the

item correctly is .25. The researcher will be looking for curves that do not follow the normal

shape of a 3PL model or curves that are drastically different than the other curves, which may

indicate misfit items.

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Fourth, a Wright map will be constructed. A Wright map, also known as an item-person

map, is used to show the distribution of examinees based on ability level, alongside the

distribution of items based on difficulty. The purpose of the Wright map is to visualize these

distributions and compare them to one another. Ideally, the two distributions will be similar in

nature with the peak of each around the same part of the axis. A Wright map could also be used

as a means of reducing the number of items in an assessment, but it will not be used in that way

for the present study because each item measures a different part of the Algebra 2 curriculum

(Neumann et al., 2010; Kuo et al., 2015). The researcher will construct a Wright map for each

test version.

Finally, based on the previous analysis, the researcher will go in depth on each item that

appears to be a misfit, determine some initial effects of item format and question type, and draw

some overall comparisons and observations about each test version. By doing so, the researcher

will attempt to validate that this Algebra 2 assessment is valid and an acceptable measure for

future studies involving the same mathematical content.

Results

At the end of the study, 41 students took Test A, 41 students took Test B, 45 students

took Test C, and 21 students took Test D. Two independent samples t-tests were run to determine

if there was an ordering effect for Tests A and C, and for Test B and D. The t-test for Tests A

and C, which did not have equal variances according to Levene’s Test, showed that t(76.416) = -

3.75, p < .001. The t-test for Tests B and D, which had equal variances according to Levene’s

Test, showed that t(60) = -2.07, p < .05. Thus, both tests showed an ordering effect for the

separate versions. However, upon further examination, it was determined that one teacher’s

classes significantly skewed the data; this teacher’s students achieved significantly lower than

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the students of the other two teachers. When this teacher’s students were removed from the tests,

the t-tests for Tests A and C and Tests B and D showed that t(58,746) = -0.48, p > .05, and t(43)

= -0.53, p > .05, respectively. Thus, it is recommended by the researcher that the data for Tests A

and C and for Tests B and D can be combined, resulting in two versions: Test A and Test B.

When combined, a total of 86 students (n = 86) took Test A, while 62 students (n = 62) took Test

B.

Classical Test Theory analysis was run on the data. As mentioned before, half of the

items on each version were multiple choice items and half of the items were technology

enhanced (either multiple select or fill-in-the-blank). Table 1 shows results of CTT analysis. On

Test A, the mean score was 17.0233 (out of 30 questions). The skewedness and kurtosis values

were -0.3956 and -0.6510, respectively, indicating that the sample is normally distributed. The

overall reliability of Test A, according to the Cronbach’s alpha value, was α = .8815. The

standard error of measurement (SEM) was 2.2417. The jMetrik program also indicates the

change in reliability if any of the items were removed from the data. The Cronbach’s alpha value

would be no larger than α = .8839, and therefore it is not recommended that any of the items be

removed from this version. On Test B, the mean score was 18.3871. The skewness and kurtosis

values were -0.1075 and -0.6814, respectively, indicating that the sample is normally distributed.

The Cronbach’s alpha value of Test B was α = .7761. It is also not recommended that any items

be removed from Test B because the Cronbach’s alpha value would be no larger than α = .7903.

The difficulty of the items on Test A ranged from .2093 (Question #17) to .8837 (Question #7),

while the difficulty of the items on Test B ranged from .1774 (Question #3) to .9516 (Question

#5 and Question #10). The discrimination of the items on Test A ranged from D = .1123

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(Question #17) to D = .6226 (Question #25), while the discrimination of the items on Test B

ranged from D = -.1115 (Question #2) to D = .5279 (Question #25).

Test A Test B

n 86 62

Mean 17.0233 18.3871

Median 19 19

Standard Deviation 6.5129 4.8704

Skewness -0.3956 -0.1075

Kurtosis -0.6510 -0.6814

Cronbach’s Alpha 0.8815 0.7761

Table 1. CTT analysis of both test versions

Rasch analysis was then run on jMetrik. The standard weighted mean squares and

standard unweighted mean squares values will indicate the any misfit items in the tests.

According to this output, Test A had three potential misfit items (Question #17, Question #19,

and Question #29), and Test B also had three potential misfit items (Question #2, Question #4,

and Question #28). The item separation index of Test A is 4.1273, while the item separation

index of Test B is 3.4176. This indicates that both versions of the test can moderately but

acceptably distinguish between item difficulties. The person separation index of Test A is

2.5484, while the person separation index of Test B is 1.8852. The 3PL Rasch analysis models

for each item were run, and the most notable outcomes are displayed in Figure 1. Finally, the two

Wright maps were run for Test A and Test B, and can be found in Figure 2 and Figure 3,

respectively.

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INSERT FIGURE 1 HERE

Discussion

The purpose of this study was to analyze the items and results of the Algebra 2

assessment given to students in a large, diverse, suburban school district. The results of the

analysis show insight into the nature of the items based on item format or question type, or

differences in the two test versions. Both test versions were found to be fairly reliable (α = .8839

and α = .7761). It is worthy to note that the reliability of Test B is likely lower than that of Test

A due to the smaller number of students who took Test B. Nevertheless, both versions have an

acceptable level of reliability. Both versions had two questions with a difficulty less than .25. On

Test A, one of these questions was a straightforward multiple choice item (Question #17) and the

other was a multiple select word problem item (Question #24). On Test B, one question was a

straightforward multiple select item (Question #3) and the other was a multiple select word

problem item (Question #29). Further research is necessary to determine if there are significant

differences between achievement on different item formats and question types.

It is also worthwhile to discuss specific items with notable discrimination values. The

lowest discrimination of either version is Question #2 on Test B. This item is a straightforward

multiple choice question asking students to find a specific term in a recursive sequence. The item

has a negative discrimination, which is problematic because it indicates that students in the

lowest ability group answered this question more accurately than students in the highest ability

group. However, it should be noted that the content in this item was one of the last topics to be

taught in the Algebra 2 curriculum, so it is possible that one or more teachers did not fully teach

topic at the time of the study. The lowest discrimination item on Test A was Question #17. This

item, which was a straightforward multiple choice item, asks students to select the correct end

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behavior of a rational function. Based on the data, there seems to be an observable relationship

between discrimination and item format; that is, low discrimination items seem to be more often

than not multiple choice items. This additional observation supports the need for further research

regarding item format.

INSERT FIGURE 2 HERE

As mentioned previously, each version had three potential misfit items, but none of the

prompts are misfits on both versions. This suggests that none of the prompts themselves are the

cause of the items being misfits. The strongest misfit on either version is Question #2 on Test B.

The cause of this item is likely the negative discrimination, which was discussed in the previous

paragraph. Due to the large misfit value, it is recommended that this item be removed from the

analysis.

DISCUSSION OF 3PL MODELS

INSERT FIGURE 3 HERE

DISCUSSION OF WRIGHT MAP

Limitations

There are several limitations of this analysis that must be considered. First, the results of

the study cannot be generalized in several ways. Socioeconomically, the school was in a large

suburban school district with a number of resources to provide students. The results of this study

may be different if it were replicated in an urban or rural school setting. Additionally, the

students who participated in this study were in an on-level algebra class with a specific

curriculum and pacing guide. This prevents the researcher from stating that these results would

be similar in an honors or below-level setting. Finally, since the material in this assessment was

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from an Algebra 2 curriculum, one cannot assume that similar psychometrics would occur for a

geometry test, for example.

Another limitation of this study is the imbalance of participants who took each type of

test. Based on the procedures of the study and the abilities of the software on which the test was

administered, each class had to take the same test version. Since there were an odd number of

classes who participated in the study, there were more students that took Test A than those who

took Test B. This provided a limitation because some statistical results may have been altered.

For instance, Test A had a higher reliability than Test B, which may have been caused by the

lower number of students who took Test B. Also, the separation indices for Test B were

unfavorably low, most likely due to a low number of participants. The researcher suggests

replicating this study with a larger number of students to determine if these statistics are a result

of sample size.

Next, the fact that students came from three different teachers also causes a limitation. In

particular, one teacher’s students scored significantly lower than the students of the other two

teachers. This was problematic in that these students’ scores were inconsistent with the scores of

other students. Having students from different teachers participate can also generally cause some

noticeable differences. For example, some teachers may be more effective at teaching some

material than others, but ineffective at teaching other content. Additionally, the pacing of some

teachers may be different based on their teaching styles or how they feel their students are

performing. It is suggested that additional studies be conducted using students from only one

teacher.

Finally, further research is needed to determine if there are significant differences in

items based on item format or question type. The present study made some general observations

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regarding these variables, but more analysis is needed to study to what extent they impact student

achievement. In addition to simply analyzing the results of the different item format and question

types, it is also important to study what motivational constructs impact achievement on these

items. Characteristics such as motivation, task value, and interest all have been shown to increase

math achievement (Wigfield, Tonks, & Eccles, 2004); however, do these constructs predict

achievement on each item type differently? Further research is needed to answer this question.

Finally, gender differences were not explored in the present study. Additional research should

compare the assessment results based on gender, both at an overall level and looking only at

specific types of prompts and entry methods.

Educational Implications

Given the current emphasis on standardized testing, theThe results of this study carry

strong educational implications, especially in an era in which there is so much emphasis on

standardized testing. TheAs mentioned previously, the questions on the Mazzarella (2015)

assessment used in this study were modeled of the Virginia Algebra 2 SOL exam. Therefore,

these results can be used to assessdetermine whether or notthe reliability and validity of this type

of exam and identify potential issues. is valid and fair. This is immensely important because of

the Vvast number of students who take this difficult standardized test every year. For teachers,

these results can be used to help understand what students struggle with most, whether it is a a

substantive factor such as a particular mathematical skill or concept, the way a question was

asked, or the way that students enter their answer. For test makers, these results can help shape

the way that statewide assessments are created. If items are found to be legitimate misfits, it is

important for test makers to determine why they are misfits and how they can be improved.

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Psychometrics studies like the present study should constantly consisently be conducted so that

tests are always being scrutinized and improved.

Overall, the present study sheds light on the characteristics of a specific computer-based

mathematics assessment. The in-depth features of the test and its items provide valuable

information to teachers, students, test makers, and researchers. It is the hope of the researcher

that this study will be used to create better tests, lead to more research on computer-based math

assessments, and ultimately lead to fair tests that accurately represent students’ understanding

and can help them meet their full potential.rultimately help students succeed to their full

potential.

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References

Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee’s ability. In

F.M. Lord and M.R. Novick (Eds.), Statistical theories of mental test scores. Reading,

MA: Addison-Wesley.

Dimitrov, D. (2014). Topic 4 – Classical Test Theory [PowerPoint Slides]. Retrieved from

https://mymasonportal.gmu.edu.

Dimitrov, D. (2014). Topic 8 – Item Response Theory Part 4: Rasch model- Data fit, item/test

information, and jMetrik Rasch Analysis [PowerPoint Slides]. Retrieved from

https://mymasonportal.gmu.edu.

Harris, D. (1989). Comparison of 1-, 2-, and 3-parameter IRT models. Educational

Measurement: Issues and Practice, 8(1), 35-41. doi:10.1111/j.1745-3992.1989.tb00313.x

Kuo, C., Wu. H., Jen, T., & Hsu, Y. (2015). Development and validation of a multimedia-based

assessment of scientific inquiry. International Journal of Science Education, 37(14),

2326-2357. doi:10.1080/09500693.2015.1078521

Mazzarella, M. (2015). Algebra II Review. Unpublished mathematics assessment, George Mason

University, Fairfax, VA.

Neumann, I., Neumann, K., & Nehm, R. (2010). Evaluating instrument quality in science

education: Rasch-based analysis of a nature of science test. International Journal of

Science Education, 33(10), 1373-1405. doi:10.1080/09500693.2010.511297

Osterlind, S. J. (2010). Modern measurement: Theory, principles, and applications of mental

appraisal. Boston, MA: Allyn & Bacon.

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Tyrrell, R., Holland, K., Dennis, D., & Wilkins, A. J. (1995). Coloured overlays, visual

discomfort, visual search and classroom reading. Journal of Research in Reading, 181,

10-23.

Virginia Department of Education (2015). Standard of learning (SOL) and testing. Retrieved

from Virginia Department of Education website: http://www.doe.virginia.gov.

Wigfield, A., Tonks, S., & Eccles, J. S. (2004). Expectancy value theory in cross-cultural

perspective. In D. M. McInerney & S. Van Etten (Eds.), Big theories revisited (pp. 165-

198). Greenwich, CT: Information Age.

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Appendix A: Mathematics Measures

Test A

Question 1 :What is the solution set for this equation?

A:

B:

C:

D:

Question 2 :Type your answer into the box. You must give your answer in integer form.

The following sequence is given in recursive form.

What is the value of the fourth term of this sequence?

Question 3 :Which of the following situations involves a permutation?

A: Determining how many different groups of 3 employees can be chosen from 9 employees.

B: Determining how many different ways 7 runners can be assigned lanes on a track for a race.

C: Determining how many different ways to choose 10 students to attend a field trip from a group of 25 students.

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D: Determining how many different ways 4 cashiers can be chosen to work from a group of 7 cashiers.

Question 4 :Click on a box to choose each y-coordinate you want to select. You must select all correct answers.

What are the y-coordinates for the solution to this system of equations?

A: y = -9

B: y = -3

C: y = -2

D: y = 1

E: y = 2

F: y = 6

G: y = 8

H: y = 9

Question 5 :The number of combinations of 7 objects taken 2 at a time is

A: 3B: 7

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C: 21D: 42

Question 6 :Type your answer into the box. You must enter your answer in integer form.

The shoe sizes of a large population are normally distributed with a mean of 8.9 inches and a standard deviation of 0.705 inches. What percentage of the population has a shoe size greater than 9.8 inches? ROUND TO THE NEAREST INTEGER.

Question 7 :

Factor: 

A: (2x+3) (3x-7)

B: (2x-3) (3x+7)

C: (3x+2) (2x-7)

D: (3x-2) (2x+7)

Question 8 :Select a box for each correct part of the expression. You must select each correct expression.

Select each part of the simplified expression   .

A:

B:

C:

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D:

E:

F:

Question 9 :The area of a triangle varies jointly with the product of the base and the height. A triangle has a base of 12 feet, a height of 3 feet, and an area of 18 square feet. What is the base of a triangle with a height of 4 feet and an area of 36 square feet?

A: 0.5 feet

B: 9 feet

C: 12 feet

D: 18 feet

Question 10 :Type the answer into the box.The number of permutations of 9 objects taken 3 times is

Question 11 :

Which is a solution of   ?

A: x = -5

B:x

= C: x = -

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1

D: x = 1

Question 12 :Click on the box to select the value. You must select each correct value.

Two baseballs were thrown on a field as the same time. One ball follows the

path of the function  , and the other ball follows the path of

the function  , where x is the time in seconds, and f(x) and g(x) are the heights in feet. At what two times, in seconds, are the two balls the same height?

A: 0.7 seconds

B: 1.0 seconds

C: 4.0 seconds

D: 5.14 seconds

E: 5.45 seconds

F: 7.13 seconds

Question 13 :What is the sum of this infinite series?

72 - 36 + 18 - 9 + ...

A: -144

B: -48C: 48

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D: 144

Question 14 :Type your answer into the box. You must enter your answer in integer form.

Let   and  , what is  ?

Question 15 :A new rollercoaster at an amusement park follows the path of the

function  , where x is the time, in seconds, after the rollercoaster begins, and f(x) is the height of the rollercoaster, in yards. Between which two times, in seconds, is the rollercoaster increasing in height?

A:

B:

C:

D:

Question 16 :Select each expression that is equivalent. You must select all correct expressions.

Identify each expression that is equivalent to 1.

A:

B:

C:

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D:

E:

F:

G:

H:

Question 17 :

Which of the following describes the end behavior of   as x approaches infinity?

A: y approaches negative infinity

B: y approaches -2

C: y approaches 3

D: y approaches infinity

Question 18 :Type your answer into the box. You must enter your answer in integer form.

The heights of Galapagos penguins are normally distributed with a mean of 49 cm and a standard deviation of 1.82 cm. If a scientist measures the heights of 300 penguins, how many penguins are expected to be between 48.4 cm and 50.1 cm tall? ROUND YOUR ANSWER TO THE NEAREST INTEGER.

Question 19 :Which is the equation of an asymptote of the graph of the following equation?

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A: x = -3

B: y = 3

C: x = 6

D: y = 6

Question 20 :Click on the box to select an interval. You must select each correct interval.

Indicate each intervals where the graph   is only increasing.

A:

B:

C:

D:

E:

F:

G:

H:

Question 21 :A mathematics class consists of 10 girls and 8 boys. The teacher

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wants to choose 2 girls and 2 boys to go on a trip. How many different groups could the teacher choose?

A: 73

B: 146

C: 1260

D: 5040

Question 22 :Type your answer into the box. You must enter your answer in integer form.

If y varies directly with the square root of x, what is the constant of variation if y = 36 when x = 9?

Question 23 :

What are the zeros of the function   ?

A: x = -16 and x = 0

B: x = -16, x = -8, and x = 2

C: x = -8 and x = 2

D: x = -2 and x = 8

Question 24 :Click on the box to select the correct equation. You must select each correct equation.

A baseball was thrown by a player, and hit the ground after exactly 5 seconds. If x represents the time in seconds and y represents the height of the ball, which of the following functions could represent the path of the

ALGEBRA 2 ASSESSMENT

ball?

A:

B:

C:

D:

E:

F:

Question 25 :A normally distributed set of numbers has a mean of 75 and a standard deviation of 7.97. What percentage of values lies between 70 and 85?

A: 11%B: 37%C: 63%D: 89%

Question 26 :Click on the correct box to select each value. You must select each correct value.

The domain of the function   is all real numbers except -

A: -7B: -4C: -3D: 0E: 3

ALGEBRA 2 ASSESSMENT

F: 4G: 7

Question 27 :In a school, 12 students are running for 4 class officers- a president, a vice president, a secretary, and a treasurer. If each position is to be held by one person and no person can hold more than one position, in how many ways can those positions be filled?

A: 48

B: 495

C: 11880

D: 20736

Question 28 :Click on each box to select each function. You must select each correct function.

Which of the following functions are in the same family as the

function   ?

A:

B:

C:

D:

E:

F:

ALGEBRA 2 ASSESSMENT

Question 29 :The steps to simplify an expression are shown below:

Step 1: 4(x+3) - 3x + 1Step 2: 4x + 12 - 3x + 1Step 3: 4x - 3x + 12 + 1Step 4: x + 13

Which of the following properties justifies getting from Step 2 to Step 3?

A: Associative Property

B: Commutative Property

C: Distributive Property

D: Transitive Property

Question 30 :Type your answer into the box. ROUND YOUR ANSWER TO THE NEAREST TENTH.

A baseball player throws a ball from one end of the field to the other. A fan measures the path of the ball and determines that it follows the

function  , where x is the time in seconds and f(x) is the height in feet. What is the maximum height of the ball, in feet? ROUND YOUR ANSWER TO THE NEAREST TENTH.

Test B

ALGEBRA 2 ASSESSMENT

Question 1 :Type your answer into the box. Enter your answer as a whole number.

What is the solution set for this equation?

Question 2 :The following sequence is given in recursive form.

What is the value of the fourth term of this sequence?

A: 29B: 33C: 61

D: 125

Question 3 :Click on the box to choose the situation. You must select all correct situations.

Which of the following situations involve a permutation?

A: Determining how many different ways to choose 3 employees from a group of 9 employees.

B: Determining how many different ways 7 runners can be assigned lanes on a track for a race.

C: Determining how many different seating charts can be made placing 6 people around a table.

D: Determining how many 5-letter passwords can be made using the

ALGEBRA 2 ASSESSMENT

word "graph."

E: Determining how many different groups of 10 students can be chosen to go on a field trip from a group of 25 students.

F: Determining how many different ways 4 cashiers can be chosen to work from a group of 6 cashiers.

Question 4 :What are the y-coordinates for the solutions to this system of equations?

A: y = 1 and y = 9

B: y = -3 and y = -9

C: y = -2 and y = 6

D: y = 2 and y = 8

Question 5 :Type the answer into the box.

The number of combinations of 7 objects taken 2 at a time is

Question 6 :The shoe sizes of a large population are normally distributed with a mean of 8.9 inches and a standard deviation of 0.705 inches. What percentage of the population has a shoe size greater than 9.8 inches? Round to the nearest integer.

A: 5%B: 10%C: 20%

ALGEBRA 2 ASSESSMENT

D: 34%

Question 7 :Click on a box for each factor you want to select. You must select all correct factors.

Select all of the factors of: 

A: (2x+3)

B: (2x-3)

C: (3x+2)

D: (3x-2)

E: (2x+7)

F: (2x-7)

G: (3x+7)

H: (3x-7)

Question 8 :

Which of the following expressions is equivalent to   ?

A:

B:

C:

ALGEBRA 2 ASSESSMENT

D:

Question 9 :Type your answer into the box. You must enter your answer in integer form.

The area of a triangle varies jointly with the product of the base and the height. A triangle has a base of 12 feet, a height of 3 feet, and an area of 18 square feet. What is the base of a triangle with a height, in feet, of 4 feet and an area of 36 square feet?

Question 10 :The number of permutations of 9 objects taken 3 times is

A: 27B: 84

C: 504

D: 729

Question 11 :Click on each solution to the equation. You must select each correct solution.

Select all the solutions of   .

A: x = -5

B:x

= 

C: x = -1

D: x = 1

ALGEBRA 2 ASSESSMENT

E:x

= 

F: x = 5

Question 12 :Two baseballs were thrown on a field as the same time. One ball

follows the path of the function  , and the other ball

follows the path of the function  , where x is the time in seconds, and f(x) and g(x) are the heights in feet. At what two times, in seconds, are the two balls the same height?

A: 0.70 seconds and 5.45 seconds

B: 7.13 seconds and 5.14 seconds

C: 0.70 seconds and 7.13 seconds

D: 5.14 seconds and 5.45 seconds

Question 13 :Type your answer into the box.

What is the sum of this infinite series?

72 - 36 + 18 - 9 + ...

Question 14 :

Let   and  . What is   ?

A: -29B: 35C: 75

ALGEBRA 2 ASSESSMENT

D: 152

Question 15 :Click on the box to select the interval. You must select each correct interval.

A new rollercoaster at an amusement park follows the path of the

function  , where x is the time, in seconds, after the rollercoaster begins, and f(x) is the height of the rollercoaster, in yards. Between which two times, in seconds, is the rollercoaster increasing in height?

A:

B:

C:

D:

E:

F:

Question 16 :Which expression is equivalent to 1?

A:

B:

C:

D:

ALGEBRA 2 ASSESSMENT

Question 17 :Type your answer into the box. You must give your answer in integer form.

What value does y approach in the function   as x approaches infinity?

Question 18 :The heights of Galapagos penguins are normally distributed with a mean of 49 cm and a standard deviation of 1.82 cm. If a scientist measures the heights of 300 penguins, how many penguins are expected to be between 48.4 cm and 50.1 cm tall? Round your answer to the nearest integer.

A: 84

B: 107

C: 168

D: 204

Question 19 :Click on each box to choose each asymptote. You must select all correct asymptotes.

Which are the equations of the asymptotes of the graph of the following function?

A: x = -3

B: y = -3

C: x = 3

ALGEBRA 2 ASSESSMENT

D: y = 3

E: x = 6

F: y = 6

Question 20 :

Throughout which of the following intervals is   only increasing?

A:

B:

C:

D:

Question 21 :Type your answer into the box. You must enter your answer in integer form.

A mathematics class consists of 10 girls and 8 boys. The teacher wants to choose 2 girls and 2 boys to go on a trip. How many different groups could the teacher choose?

Question 22 :If y varies directly as the square root of x, what is the constant of variation if y = 36 and x = 9?

A: 1.5

B: 2C: 4D: 12

ALGEBRA 2 ASSESSMENT

Question 23 :Click on the box to select the zeros. You must select each correct zero.

Which of the following are zeros of the function   ?

A: x = -16

B: x = -8

C: x = -2

D: x = 0

E: x = 2

F: x = 8

Question 24 :A baseball was thrown by a player, and hit the ground after exactly 5 seconds. If x represents the time in seconds and y represents the height of the ball, which of the following functions could represent the path of the ball?

A:

B:

C:

D:

Question 25 :Type your answer into the box. You must enter your answer in

ALGEBRA 2 ASSESSMENT

integer form.

A normally distributed set of numbers has a mean of 75 and a standard deviation of 7.97. What percentage of values lies between 70 and 85? ROUND TO THE NEAREST INTEGER.

Question 26 :

The domain of the function   is all real numbers except -

A: -7, -4, 4

B: -7, 4

C: -4, 7

D: 4

Question 27 :Type your answer into the box. You must enter your answer in integer form.

In a school, 12 students are running for 4 class officers- a president, a vice president, a secretary, and a treasurer. If each position is to be held by one person and no person can hold more than one position, in how many ways can those positions be filled?

Question 28 :Which of the following is in the same family as the

function   ?

A:

B:

C:

ALGEBRA 2 ASSESSMENT

D:

Question 29 :Click on the box to select a property. You must select each correct property.

The steps to simplify an expression are shown below:

Step 1: 4(x+3) - 3x + 1Step 2: 4x + 12 - 3x + 1Step 3: 4x - 3x + 12 + 1Step 4: x + 13

Which of the following properties justify Step 2, Step 3, and Step 4?

A: Associative Property

B: Commutative Property

C: Distributive Property

D: Inverse Property

E: Substitution Property

F: Transitive Property

Question 30 :A baseball player throws a ball from one end of the field to the other. A fan measures the path of the ball and determines that it

follows the function  , where x is the time in seconds and f(x) is the height in feet. What is the maximum height of the ball, in feet?

A: 2 feet

ALGEBRA 2 ASSESSMENT

B: 5.4 feet

C: 6 feet

D: 9.2 feet