OF COURSE FINAL EXAM SPRING 2018 REVIEW FOR …

REVIEW FOR INTEGRATED MATH 1 ENDOF COURSE FINAL EXAM SPRING 2018

Teacher Edition

REVIEW FOR INTEGRATED MATH 1 END OF COURSE FINAL EXAM SPRING 2018 (Teacher Edition) Assessment ID: ib.1482214

Generated On April 10, 2018, 11:01 AM PDT Illuminate Itembank™

1 TEACHER READS:

Read the question to yourself and select the best answer.

The number of math homework problems given each night for 18 nights is shown below.

8, 9, 9, 9, 10, 11, 11, 11, 11, 14, 14, 15, 15, 16, 17, 17, 17, 18

Which box plot correctly displays the given data?

A. B. C. D.

Master ID: 449960 Revision: 1

Correct: BRationale:

A. Student(s) may have added the median value of 12.5 into both halves of the data set when determiningthe lower and upper quartile values.

B. Correct answerC. Student(s) may have used the 9th term as the median (since 9 is half of 18) and may have found the

lower and upper quartiles by excluding this value.D. Student(s) may have used the most frequent value of 11 as the median and the next most frequent

values of 9 and 17 as the lower and upper quartiles.Standards:

MA.9-12.S-ID.1


Directions: Answer the following question(s).

Illuminate Itembank™ Continue: Turn to the next page.Generated On April 10, 2018, 11:01 AM PDT Page 1

2 TEACHER READS:


Twenty babies were born in one week in the maternity ward of a hospital. The weight of each baby tothe nearest pound is listed below.

5, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10

Which of the following dot plots represents the distribution of the babies' weights that week?

A.

B.

C.

D.



A. Student(s) may not have counted all categories. Student(s) may have chosen this option afterrecognizing the first two counts are correct.

B. Correct answerC. Student(s) may have chosen this option because it is a symmetric distribution, although it does not

accurately reflect this data.D. Student(s) may have chosen this option because it is a uniform distribution, although that does not

accurately reflect this data.Standards:

MA.9-12.S-ID.1




3 TEACHER READS:

Read the question to yourself and select the best answer(s).

The amount of miles that Janice and David have each driven over the past 5 days is shown below.

Janice 46 49 50 44 41

David 2 84 49 86 21

Which of the following statements are true? Select two that apply.

A. David's set of datahas a higher standarddeviation thanJanice's.

B. David's set of datahas a higher meanthan Janice's.

C. Janice's set of datahas a higher medianthan David's.

D. Janice's set of datahas a higherinterquartile rangethan David's.


Correct: ABRationale:

A. Correct answerB. Correct answerC. Student(s) may have forgotten to put the data sets in order when finding the median.D. Student(s) may not have understood the concept of interquartile range.

Standards:MA.9-12.S-ID.2




4 TEACHER READS:


Which of the following measures of center and spread would be most appropriate to use for thehistogram shown below? Select two that apply.

A. mean B. median C. standard deviation D. interquartile range


Correct: BDRationale:

A. Student(s) may have forgotten that the mean is a more appropriate measure of center for symmetricdistributions.

B. Correct answerC. Student(s) may have forgotten that the standard deviation is a more appropriate measure of spread for

symmetric distributions.D. Correct answer





5 TEACHER READS:


The data distributions for the math test scores and science test scores of a group of students areshown below.

Which of the following statements correctly explains the summary statistics that should be used tocompare the math and science test scores?

A. The data sets are skewed, so the mean and standard deviation should be used to compare the scores.

B. The data sets are skewed, so the median and interquartile range should be used to compare the scores.

C. The data sets are normally distributed, so the mean and standard deviation should be used to compare thescores.

D. The data sets are normally distributed, so the median and interquartile range should be used to comparethe scores.


Correct: CRationale:

A. Student(s) may have confused normal distribution and skewed distribution but may have identified thecorrect summary statistics.

B. Student(s) may have thought that the data sets are skewed because the distribution of the math scoresdoes not completely overlap with the distribution of the science scores.

C. Correct answerD. Student(s) may have thought that the median and interquartile range should be used regardless of the

data distribution.Standards:

MA.9-12.S-ID.2




6 TEACHER READS:


Jessica selected 8 books from the library. The number of pages of the first 7 books is listed below. Jessica noticed that adding the 8th book would change the mean number of pages, but the mediannumber of pages would remain the same. Which of the following could be the number of pages ofthe 8th book? Select two that apply.

125, 172, 194, 219, 219, 283, 356

A. 203 B. 219 C. 224 D. 236


Correct: BDRationale:

A. Student(s) may not have realized that this value would decrease both the mean and the median.B. Correct answerC. Student(s) may not have realized that this is exactly the value of the mean number of pages of the first

7 books and that adding an 8th book of this size will not change the mean.D. Correct answer


7 TEACHER READS:


The Yellow Taxi Company's charges are based on the function y = 2x + 4, where x is the number ofmiles traveled and y is the cost of the trip in dollars.

What is the best interpretation of 2 in this equation?

A. the base fee chargedfor the trip before anymiles are traveled

B. the speed of the taxi C. the cost per miletraveled

D. the number of milestraveled



A. Student(s) may have confused the slope with the y–intercept and interpreted 2 as the base fee.B. Student(s) may have recognized that 2 is a slope but were unsure how to interpret it. Student(s) may

have chosen this option because speed is a common interpretation of slope.C. Correct answerD. Student(s) may have mixed up the meaning of 2 and x in the linear term.





8 TEACHER READS:

Read and complete the task that follows.

A plumber charges a $50 service fee for house visits and $50 an hour for each hour that it takes todo the repairs. He uses the linear model y = 50x + 50, where x is the number of hours of work and yis the total charge. He decides to change his hourly fee to $75 an hour. Select the linear model theplumber can use to calculate the total charge with his new hourly fee.

A. y = 50x + 75 B. y = 50x + 125 C. y = 75x + 50 D. y = 125x + 50



A. Student(s) may not have interpreted the stem correctly and may have switched the slope (hourly fee)with the y–intercept (service fee) of the linear model. Student(s) may not have understood that it wasthe plumber's hourly rate that was changing.

B. Student(s) may have believed they needed to add the original $50 to the new $75 hourly rate.Student(s) may have also incorrectly determined this was the new y–intercept, or service fee, of thelinear model.

C. Correct answerD. Student(s) may have believed they needed to add the original $50 fee to the new $75 hourly fee.

Student(s) may have then assumed that this was the plumber's new per hour rate.Standards:

MA.9-12.S-ID.7




9 TEACHER READS:


A triangle is drawn on the coordinate plane below.

On the coordinate plane, draw the image of the triangle after a reflection over the y–axis.

Explain how you determined your answer.




Master ID: 338015 Revision: 1Rubric: 2 Point(s)

2 The student demonstrates thorough understanding of drawing a transformed figure given a figure and a transformation with theuse of appropriate tools. The student draws a correct transformed figure and provides an appropriate reasoning for the response.

From each vertex of the triangle, I counted the number of spaces (along the horizontal grid line on which the vertex was located)to the y–axis, and then placed the image point the same number of spaces on the other side of the y–axis along the samehorizontal line.

1 The student demonstrates partial understanding of drawing a transformed figure given a figure and a transformation with the useof appropriate tools. The student draws a correct transformed figure or provides an appropriate reasoning that would have led toa correct response.

0 The student demonstrates little or no understanding of drawing a transformed figure given a figure and a transformation with theuse of appropriate tools. The student does not draw a correct transformed figure and does not provide an appropriate reasoningfor the response.

Standards:MA.9-12.G-COMA.9-12.G-CO.5




10 TEACHER READS:


A student states the following two conjectures.

Conjecture 1: If the corresponding angles of two triangles are congruent, then the triangles arecongruent since a sequence of rigid motions carries one triangle onto the other.

Conjecture 2: If two triangles are congruent, then the corresponding angles are congruent since asequence of rigid motions carries each angle onto its corresponding angle.

Which statement correctly classifies the student's conjectures?

A. Both Conjecture 1and Conjecture 2 arealways true for anypair of triangles.

B. Both Conjecture 1and Conjecture 2 aretrue for some pairs oftriangles, but not all.

C. Conjecture 1 isalways true, butConjecture 2 is truefor only some pairs oftriangles.

D. Conjecture 1 is truefor only some pairs oftriangles, whileConjecture 2 isalways true.


Correct: DRationale:

A. Student(s) may not have realized that Conjecture 1 is only true for some pairs of triangles.B. Student(s) may not have realized that Conjecture 2 is true for all pairs of triangles.C. Student(s) may have confused the meanings of Conjecture 1 and 2.D. Correct answer


11 TEACHER READS:


Which of the following is a valid Triangle Congruence Theorem?

A. AAA B. SSA C. ASA D. None of the above



A. Student(s) may have confused the 'SSS' theorem with this answer. There are infinitely many trianglesthat have the same three angle measurements.

B. Student(s) may have been confused, as this is a commonly used example of what DOES NOT count asan acceptable triangle congruence theorem.

C. Correct answerD. Student(s) may not have recognized that ASA is valid.




12 TEACHER READS:


Which of the following could be the equation of a line perpendicular to the line 2x – 5y = 7?

A. 2x – 5y = 9 B. 5x + 2y = 3 C. –5x + 2y = –4 D. 2x + 5y = 5



A. Student(s) may have thought the question asked for a parallel line to the given line.B. Correct answerC. Student(s) may have thought the slope of a perpendicular line was the reciprocal of the slope of the

given line.D. Student(s) may have thought slope of a perpendicular line was the negative of the given line's slope.

Standards:MA.9-12.G-GPEMA.9-12.G-GPE.5

13 TEACHER READS:


Which of the following could be the equation of a line parallel to the line 3x + 2y = –4?

A. 2x + 3y = 7 B. –3x + 2y = 5 C. 3x + 2y = 3 D. 2x – 3y = 4



A. Student(s) may have thought the slope of a parallel line was the reciprocal of the given line's slope.B. Student(s) may have thought slope of a parallel line was the negative of the given line's slope.C. Correct answerD. Student(s) may have thought the question asked for a perpendicular equation to the given equation.





14 TEACHER READS:


Is the line passing through the points (–4, 5) and (1, 10) parallel to the line passing through thepoints (–18, –6) and (–8, 4)?

A. No, because theslopes of the lines arethe same, but the y–intercepts aredifferent.

B. No, because theslopes of the lines aredifferent.

C. Yes, because theslopes of the lines arethe same, but the y–intercepts aredifferent.

D. Yes, because theslopes of the lines aredifferent.



A. Student(s) may have correctly determined that the slopes of the lines passing through the given pointsare the same and the y–intercepts are different, but they may have misinterpreted what this means.

B. Student(s) may have correctly determined that if the slopes of two lines are different, then the lines arenot parallel, but they may have incorrectly concluded that this is the case with the lines passing throughthe given points.

C. Correct answerD. Student(s) may have correctly determined that the lines passing through the given points are parallel,

but they may have misidentified the reason why.Standards:

MA.9-12.G-GPEMA.9-12.G-GPE.5




15 TEACHER READS:


Which equation represents a line that is perpendicular to y = 2

3x – 5 and passes through the point

(6, 12)?

A.y =

2

3x – 2

B.y =

2

3x + 8

C.y = –

3

2x + 24

D.y = –

3

2x + 21



A. Student(s) may have confused the x– and y–coordinates and may have used the slope for a parallelline.

B. Student(s) may have mistakenly used the slope of a parallel line.C. Student(s) may have confused the x– and y–coordinates.D. Correct answer


16 TEACHER READS:


What is the domain of the given relation?

{(1 , 3), (0 , 4), (2 , 1)}

A. {1 , 3 , 4} B. {0 , 1 , 3} C. {1 , 2 , 4} D. {0 , 1 , 2}



A. Student(s) may have confused the domain of a relation with the range of a relation, which is given here.B. Student(s) may have thought that the domain of a relation is the first half of the given set, which in this

case is {1, 3, 0}.C. Student(s) may have thought that the domain of a relation is the second half of the given set, which in

this case is {1, 2, 4}.D. Correct answer

Standards:MA.9-12.F-IF.1




17 TEACHER READS:


Matthew claims is a function of x when x is greater than or equal to zero. Penny disagreesand offers this counterexample: when x = 4, y can be 2 or –2. Is Penny correct?

A. Penny presented avalid counterexample,and she is correct

that is NOT afunction of x.

B. Penny presented aflawedcounterexample, butshe is correct that

is NOT afunction of x.

C. Penny is wrong;

is a functionof x.

D. There is not enoughinformation to answerthis question.



A. Student(s) may have forgotten that the square root symbol means to use only the principle (positive)root of the number.

B. Student(s) may have recognized that penny's counterexample should not have used the negative rootof 4, but mistakenly still believed there was an issue with the equation such as the fact the square rootfunction is undefined for negative values of x.

C. Correct answerD. Student(s) may have misunderstood that the absence of any additional information implies that only the

principle root should be used and believed they needed to be told whether or not to include the negativeroots to make a determination.

Standards:MA.9-12.F-IF.1MA.9-12.F-IF.2




18 TEACHER READS:


Delilah thought that the domain of every function is all real numbers.

Select the graph that refutes Delilah's claim.

A.

B.

C.

D.



A. Student(s) may have thought that the domain represents y–values instead of x–values.B. Student(s) may have thought that the domain of this function is –5 ≤ x ≤ 1.C. Correct answerD. Student(s) may have thought that this relation was a function.





19 TEACHER READS:





Which of the following graphs shows a function with a domain of {2, 3, 4, 6, 8}? Select three thatapply.

A.

B.

C.

D.

E.





Correct: ACDRationale:

A. Correct answerB. Student(s) may have confused the domain with the range.C. Correct answerD. Correct answerE. Student(s) may have confused the domain with the range.


20 TEACHER READS:


Identify the functions below that have a range of ƒ(x) ≥ 0. Select two that apply.

A. ƒ(x) = (x + 2)2 B. C. ƒ(x) = x3 D. ƒ(x) = x2 + 3

E. ƒ(x) = x


Correct: ABRationale:

A. Correct answerB. Correct answerC. Student(s) may have incorrectly thought that a range of ƒ(x) ≥ 0 means that at least some of the

function values are greater than or equal to 0 instead of all of the function values being greater than orequal to 0.

D. Student(s) may have incorrectly thought that the equation was written as ƒ(x) = (x + 3)2 instead of ƒ(x)= x2 + 3.

E. Student(s) may have incorrectly thought that a range of ƒ(x) ≥ 0 means that at least some of thefunction values are greater than or equal to 0 instead of all of the function values being greater than orequal to 0.

Standards:MA.9-12.F-IF.1MA.9-12.F-IF.5




21 TEACHER READS:


The function P(x) = –0.015x2 + 1.2x – 11.5 gives the profit, in thousands of dollars, when a companysells a new product at x dollars per unit. Which of the following statements best interprets theaverage rate of change of this function from x = 50 to x = 55?

A. The profit increasesby $375 for every $1increase in the sellingprice.

B. The profit decreasesby $375 for every $1increase in the sellingprice.

C. The profit increasesby $1875 for every $1increase in the sellingprice.

D. The profit decreasesby $1875 for every $1increase in the sellingprice.



A. Student(s) may have thought that increasing the selling price always increases the profit or did notcorrectly interpret the negative value for the average rate of change.

B. Correct answerC. Student(s) may not have divided by the difference in x–values when calculating the average rate of

change and may have thought that increasing the selling price always increases the profit.D. Student(s) may not have divided by the difference in x–values when calculating the average rate of

change.Standards:

MA.9-12.F-IF.6




22 TEACHER READS:


A ball is kicked up in the air from the ground. The height of the ball can be modeled as a function oftime in seconds. This function is represented on the graph below.

Enter the average rate of change for the height of the ball, measured as feet per second, between 0seconds and 2 seconds.

feet per second

Input #1 Answers

■ 2


Correct: Standards:

MA.9-12.F-IF.6




23 TEACHER READS:


y = 2x2 – 5x – 3

Find the zeros for the graph of the above function.

A. (0, –3) B.(

5

4, –6

1

8)

C.(

1

2, 0), (–3, 0)

D.(–

1

2, 0), (3, 0)



A. Student(s) may have misunderstood that the zeros of a function are the points on the graph where y =0, not necessarily x.

B. Student(s) may have confused the zeros of a function with the vertex of its graph.C. Student(s) may have factored the equation incorrectly into y = (2x – 1)(x + 3).D. Correct answer

Standards:MA.9-12.F-IF.7MA.9-12.F-IF.7.a

24 TEACHER READS:


Which of the following graphs show a function of the form ƒ(x) = x – c for some real number c? Select two that apply.

A. B. C. D.


Correct: ACRationale:

A. Correct answerB. Student(s) may not have realized that the graph of x – c must touch the x–axis.C. Correct answerD. Student(s) may have forgotten that an absolute value function will never go below the x–axis.




25 Which of the following graphs represents a function?

Select all that apply.

A. B. C. D.


Correct: ABCStandards:

MA.9-12.F-IF.1

26 TEACHER READS:


Select the function that is an example of a positive exponential growth function.

A. B.ƒ(x) = –

4

5 · 2x

C. D.



A. Student(s) may have thought that this was a growth function because the absolute value of – 6 is biggerthan 1.

B. Student(s) may have thought that this was a growth function because 2 is bigger than 1; however,student(s) may not have realized that there was a negative sign in front of 4/5.

C. Correct answerD. Student(s) may have thought that this was a growth function because 5 is bigger than 1.

Standards:MA.9-12.F-IF.8.b




27 TEACHER READS:


The graph of a function, ƒ(x), is plotted on the coordinate plane. Select two of the followingfunctions that would move the graph of the function to the right on the coordinate plane.

A. ƒ(x + 6) B. ƒ(x) + 4 C. ƒ(x – 3) + 1 D. ƒ(x) – 3

E. ƒ(x – 5) F. ƒ(x + 2) – 7


Correct: CERationale:

A. Student(s) may have thought that "+ 6" would move the graph to the right 6 units.B. Student(s) may have thought that "+ 4" would move the graph to the right 4 units.C. Correct answerD. Student(s) may have thought that "– 3" would move the graph to the right 3 units.E. Correct answerF. Student(s) may have thought that "+ 2" would move the graph to the right 2 units.




28 TEACHER READS:


A function f(x) is shown below.

Part A:On the same set of axes, draw the graph of f(x) – 3.

Part B:Explain how you determined your answer.





2 The student demonstrates thorough understanding of identifying the effect of replacing f(x) with f(x) + k, mapping relationships ina graph. The student provides an appropriate graph of f(x) – 3, and provides an appropriate reasoning for this response.Part A:

Part B:Replacing f(x) with f(x) + k has the effect of shifting the graph of f(x) up if k is positive and down if k is negative. Therefore, thegraph of f(x) – 3 is the graph of f(x) shifted down 3 units.

1 The student demonstrates partial understanding of identifying the effect of replacing f(x) with f(x) + k, mapping relationships in agraph. The student provides an appropriate graph of f(x) – 3, or provides an appropriate reasoning that would have led to thisresponse.

0 The student demonstrates little or no understanding of identifying the effect of replacing f(x) with f(x) + k, mapping relationships ina graph. The student does not provide an appropriate graph of f(x) – 3, and does not provide an appropriate reasoning that wouldhave led to this response.




29 TEACHER READS:


A geometric sequence is shown below.

2, –6, 18, –54, 162, ...

Part A:Write a recursive relationship for this sequence. Explain how you determined your answer.

Part B:Write an explicit formula for this sequence.


2 The student demonstrates thorough understanding of writing a geometric sequence both recursively and with an explicit formula.The student provides and explains a recursive process for the sequence, and provides an explicit formula for the sequence.Part A:A1 = 2;An = –3(An – 1) for all n > 1The initial term of the sequence is 2, so A1 = 2. Each subsequent term is –3 times the previous term, so An = –3(An – 1) for n > 1.

Part B:An = 2(–3)n – 1 for all n ≥ 1

1 The student demonstrates partial understanding of writing a geometric sequence both recursively and with an explicit formula.The student either provides and explains a recursive process for the sequence, or provides an explicit formula for the sequence.

0 The student demonstrates little or no understanding of writing a geometric sequence both recursively and with an explicit formula.The student does not provide and explain a recursive process for the sequence, and does not provide an explicit formula for thesequence.

Standards:MA.9-12.F-BFMA.9-12.F-BF.2




30 TEACHER READS:


An arithmetic sequence is given below.

–8, –6, –4, –2, 0

In this sequence, –8 is the first number in the sequence and n represents the term number. Thissequence can be written as an = 2n + m.

Enter the value of m.

m =

A. Input #1 Answers B. ■ −10


Correct: Standards:

MA.9-12.F-BFMA.9-12.F-BF.2

31 TEACHER READS:


During the month of January, Max used the equation d(m) = 10(2 + 0.15m) to determine the numberof minutes (m) that he should lift weights each day, where d(m) represents the amount of days sinceJanuary 1st.

Max claims that he is increasing the number of minutes that he lifts by the same amount each day. To prove his claim he needs to determine the value of d(m) – d(m – 1).

What is the value of d(m) – d(m – 1)?

A. Input #1 Answers B. ■ 1.5 C. ■ 1.50


Correct: Standards:

MA.9-12.F-LE.1.a




32 TEACHER READS:


Matt sets up a stand to sell pretzels. He sells each pretzel for $3.00. The amount of money he earnsselling pretzels is represented by the function y = 3n, where y represents the money he earns indollars and n represents the number of pretzels he sells.

He uses this equation to show that for every 5 additional pretzels he sells he earns an additional $15. His work is shown below.

Number of Pretzels:If n1 = a and n2 = a + 5, then n2 – n1 = 5.

Additional Money Earned:If n1 = a, then y1 = 3a.If n2 = a + 5, then y2 = 3(a + 5)y2 – y1 = 3(a + 5) – 3(a)= 3a + 15 – 3a= 15.

Which of the following conclusions can be made about the additional money Matt will earn for every5 additional pretzels he sells? Select two that apply.

A. He will always earnan additional $15because y2 – y1 is notdependent on a.

B. The additional moneyhe will earn dependson the initial numberof pretzels he hassold because y2 – y1is dependent on a.

C. The additional moneyhe will earn is not aconstant amountbecause the functionincreases by differentamounts for every 5additional pretzelssold.

D. The additional moneyhe will earn is aconstant amountbecause the functionincreases by an equalamount for every 5additional pretzelssold.


Correct: ADRationale:

A. Correct answerB. Student(s) may not have recognized that a was subtracted out when the difference y2 − y1 was being

solved.C. Student(s) may have incorrectly interpreted the function that was represented by the equation.D. Correct answer

Standards:MA.9-12.F-LE.1.a




33 TEACHER READS:


A company has determined approximately how long it takes for two people to install certain amountsof wood flooring in a home. The table below shows the amount of flooring installed after a certainamount of time.

Elapsed Time (min.) Amount of Flooring Installed (sq ft)

30 42

90 126

120 168

The company wishes to use the table above to model how much flooring can be installed withincertain time frames. This will allow the company to better estimate the amount of time various jobswill take. Complete the table below to determine the amount of flooring installed after variousamounts of time.

Elapsed Time (min.) Amount of Flooring Installed (sq ft)

210

450

720

A. Input #1 Answers B. ■ 294 C. Input #2 Answers D. ■ 630E. Input #3 Answers F. ■ 1008 G. ■ 1, 008


Correct: Standards:

MA.9-12.F-LE.1.aMA.9-12.F-LE.1.b




34 TEACHER READS:


Tae'von currently has $1000 in his savings account and wishes to increase the amount of money inhis account by a constant rate per month. To do this, he is looking at three different options.

Option 1: Put $10 in during the 1st month and double this amount during each subsequent month.

Option 2: Put $25 in per month.

Option 3: Put 3% of his paycheck in per month and increase this by 1% every 3 months.

Write an equation that models the option that increases the amount of money in Tae'von's accountby a constant rate per month. Assume that m represents the number of months and d representsthe amount of money in his account.

A. Input #1 Answers B. ■ d = 1000 + 25m C. ■ 1000 + 25m = d D. ■ 25m + 1000 = d

E. ■ d = 25 m + 1000 F. ■ d = 25 m + 1000 G. ■ d = 1000 + 25 m H. ■ d = 1000 + 25 m

I. ■ 1000 + 25 m = d J. ■ 1000 + 25 m = d K. ■ 25 m + 1000 = d L. ■ 25 m + 1000 = d

M. ■ d = 25 ⋅ m + 1000 N. ■ d = 25 ⋅ m + 1000 O. ■ d = 25 × m + 1000 P. ■ d = 25 × m + 1000Q. ■ d = 1000 + 25 ⋅ m R. ■ d = 1000 + 25 ⋅ m S. ■ d = 1000 + 25 × m T. ■ d = 1000 + 25 × m

U. ■ 1000 + 25 ⋅ m = d V. ■ 1000 + 25 ⋅ m = d W. ■ 1000 + 25 × m = d X. ■ 1000 + 25 × m = d

Y. ■ 25 ⋅ m + 1000 = d Z. ■ 25 ⋅ m + 1000 = d AA. ■ 25 × m + 1000 = d AB. ■ 25 × m + 1000 = d

AC. ■ d = 25m + 1000


Correct: Standards:

MA.9-12.F-LE.1.b




35 TEACHER READS:


Which of the following equations could be used to predict the value, V(t), after t years, of a $1000investment expected to appreciate by 5% each year?

A. V(t) = 1000(0.5)t B. V(t) = 1000(1 + 0.5)t C. V(t) = 1000(0.05)t D. V(t) = 1000(1 + 0.05)t



A. Student(s) may have misrepresented 5% with 0.5, and may not have realized that appreciating by 5% isrepresented mathematically as multiplying by 105%.

B. Student(s) may have misrepresented 5% with 0.5.C. Student(s) may not have realized that appreciating by 5% is represented mathematically as multiplying

by 105%.D. Correct answer

Standards:MA.9-12.F-LE.1.c




36 TEACHER READS:


The table below shows the number of runners registered for the local Valentine's Day 5K Run over a4–year period. The equation y = 85(1.3)x describes the curve of best fit for the number of registeredrunners each year (y). Let x represent the number of years since 1999.

Valentine's Day 5K Race

Year Runners

1999 85

2000 111

2001 144

2002 186

Using this equation, what would be the approximate number of runners who register for the 5K racein the year 2006?

A. 243 B. 410 C. 533 D. 595



A. Student(s) may have misunderstood how to find the y value associated with the year 2006 and simplyfound the next value if the table was extended.

B. Student(s) may have found the value when x = 6 instead of 7.C. Correct answerD. Student(s) may have misunderstood how to find the income in 2009 and simply added 85 people each

year or computed 85(7).Standards:

MA.9-12.F-LE.1.c




37 TEACHER READS:


A school district currently has 12,000 students. Based on declining enrollment figures, the numberof students in the school district is expected to decline by 5% each year. Which of the followingfunctions represents the number of students, S, in the school district after n years?

A. S(n) = 12,000(–5)n B. S(n) = 12,000(0.95)n C. S(n) = 12,000(1.05)n D. S(n) = 12,000(–0.05)n



A. Student(s) may have expressed "decline by 5% "as having a common ratio of –5.B. Correct answerC. Student(s) may have expressed a 5% increase per year, rather than a 5% decrease.D. Student(s) may not have taken into account the 1 in the exponential decay formula, i.e. expressed S(n)

= S1 (–r)n rather than S(n) = S1 (1 – r)n.Standards:

MA.9-12.F-LE.2

38 TEACHER READS:


Ben puts $3000 in a bank account that pays 2% interest, which is compounded yearly.

Complete the equation that represents the amount of money, A, Ben will have in his bank accountafter n, number of years.

A =

A. Input #1 Answers B. ■ 3000 1 + 0.02 n C. ■ 3000 1.02 n D. ■ 3000 1 + .02 n

E. ■ 3, 000 1 + 0.02 n F. ■ 3, 000 1 + .02 n G. ■ 3, 000 1.02 n


Correct: Standards:

MA.9-12.A-CED.2




39 TEACHER READS:


Which graph represents the solution to the following system of equations?

A.

B.

C.

D.






A. Student(s) may have incorrectly dropped the negative sign in front of 2y after subtracting x from bothsides of the equation x – 2y = 4 resulting in 2y = –x + 4 instead of –2y = –x + 4. Student(s) may havealso incorrectly added 2x instead of subtracting 2x from both sides of the equation 2x + y = –7 resultingin y = 2x – 7 instead of y = –2x – 7.

B. Student(s) may have incorrectly dropped the negative sign in front of 2y after subtracting x from bothsides of the equation x – 2y = 4 resulting in 2y = –x + 4 instead of –2y = –x + 4.

C. Correct answerD. Student(s) may have incorrectly added 2x instead of subtracting 2x from both sides of the equation 2x +

y = –7 resulting in y = 2x – 7 instead of y = –2x – 7.Standards:

MA.9-12.A-REI.6

40 TEACHER READS:


Where do the lines defined by the following system intersect?

x = 2y3x – 4y = 8

A. (8, 4) B. (4, 2) C.(

8

3, –2)

D. (–4, –2)


Correct: ARationale:

A. Correct answerB. Student(s) may have solved for y correctly, but then mistakenly used that value as x and recalculated an

incorrect value of y from the top equation.C. Student(s) may have used a flawed strategy to solve the system and believed they could drop the –4y

from the second equation and solve for x then drop the 3x from the equation and solve for y.D. Student(s) may have tried to solve for y by simply dropping the 3x from the second equation and then

used that value in the top equation to find x.Standards:

MA.9-12.A-REI.6




41 TEACHER READS:


If Jess wants to graph the solution to the system of equations below, which of the following graphswould represent the solution?

A.

B.

C.

D.






A. Correct answerB. Student(s) may have incorrectly dropped the negative sign in front of y after subtracting 3x from both

sides of the equation 3x – y = –1 resulting in y = –3x – 1 instead of –y = –3x – 1.C. Student(s) may have incorrectly added x instead of subtracting x from both sides of the equation x + y =

5 resulting in y = x + 5 instead of y = –x + 5.D. Student(s) may have incorrectly dropped the negative sign in front of y after subtracting 3x from both

sides of the equation 3x – y = –1 resulting in y = –3x – 1 instead of –y = –3x – 1. Student(s) may havealso incorrectly added x instead of subtracting x from both sides of the equation x + y = 5 resulting in y= x + 5 instead of y = –x + 5.

Standards:MA.9-12.A-REI.6

42 TEACHER READS:


At school athletic events you can buy 3 drinks and 2 hot dogs for $4.80 or you can buy 1 drink and 1hot dog for $2.00. How much does 1 hot dog cost?

A. $0.80 B. $0.96 C. $1.00 D. $1.20



A. Student(s) may have mistakenly chosen this option not realizing it was the price of a drink.B. Student(s) may not have recognized this problem should be solved using a system of equations and

divided the $4.80 by 5 thinking all the items were the same price.C. Student(s) may not have recognized this problem should be solved using a system of equations and

divided the $2.00 by 2 thinking all the items were the same price.D. Correct answer





43 TEACHER READS:


Which graph best represents the solution to this system of inequalities?

y ≥ –2x – 4y ≥ x – 1

A.

B.

C.

D.



A. Correct answerB. Student(s) may have misinterpreted the "greater than or equal to" sign as meaning "less than or equal

to."C. Student(s) may have made an error when determining which sides of the lines should be shaded.D. Student(s) may have considered it a mistake to have both equations as "greater than or equal to" and

changed it to be y is LESS than or equal to two x minus four.Standards:

MA.9-12.A-REI.12




44 TEACHER READS:


Which of these inequalities is graphed below?

A.y < –

3x

2 + 12

B.y ≤ –

3x

2 + 12

C.y > –

3x

2 + 12

D.y ≥ –

3x

2 + 12



A. Student(s) may have incorrectly determined the direction of the inequality sign, and they may have notrealized that a solid line indicates less–than–or–equal or greater–than–or–equal, while a dotted ordashed line indicates less–than or greater–than.

B. Student(s) may have incorrectly determined the direction of the inequality sign.C. Student(s) may have correctly determined the direction of the inequality sign, but they may have not

realized that a solid line indicates less–than–or–equal or greater–than–or–equal, while a dotted ordashed line indicates less–than or greater–than.

D. Correct answerStandards:

MA.9-12.A-REI.12




45 TEACHER READS:


A linear inequality is shown below.

6 ≤ –x + 2y

Which of the following graphs represents the solution to this linear inequality?

A.

B.

C.

D.



A. Student(s) may have shaded below the boundary line.B. Correct answerC. Student(s) may not have divided by 2.D. Student(s) may not have divided by 2 and may have shaded below the boundary line.





46 TEACHER READS:


Square 1 and Square 2 are shown in the coordinate plane below.

Audrey claims that Square 1 can be mapped to Square 2. Which of the following transformations orsequences of transformations can be used to support her claim? Select all that apply.

A. a rotation of 180°about the point(–1, –2)

B. a translation of 6 unitsright and 4 units up

C. a reflection over theline y = –2 followed bya translation of 10units right

D. a reflection over theline y = –1 followed bya reflection over theline x = –2

E. a translation of 8 unitsup followed by arotation of 180° aboutthe point (–1, 0)

F. a rotation of 90°clockwise about theorigin followed by arotation of 180° aboutthe point (–1, 4)


Correct: ACFRationale:

A. Correct answerB. Student(s) may have mapped the upper right corner of Square 1 to the lower left corner of Square 2.C. Correct answerD. Student(s) may have confused line y = –1 with x = –1 and line x = –2 with y = –2.E. Student(s) may have thought that a rotation of 180° about point (–1, 0) has the same effect as a

reflection over line x = –1.F. Correct answer





47 TEACHER READS:


Which of the following graphs shows the reflection of JKLM across the y–axis?

A.

B.

C.

D.






A. Student(s) may have confused a translation across the y–axis with a reflection across the y–axis.B. Student(s) may have confused a rotation with a reflection.C. Student(s) may have confused the x and y–axes.D. Correct answer


48 TEACHER READS:


The diagram below shows two triangles.

Based on the diagram, which statements are true? Select three that apply.

A. The two triangles arecongruent since allisosceles righttriangles arecongruent.

B. The two triangles arecongruent since thecorresponding sidesand angles arecongruent.

C. The two triangles arecongruent since arotation can carry onetriangle onto the othertriangle.

D. The two triangles arecongruent since areflection can carryone triangle onto theother triangle.


Correct: BCDRationale:

A. Student(s) may have confused the concept of isosceles right triangles with that of SAS.B. Correct answerC. Correct answerD. Correct answer





49 TEACHER READS:


Triangles PQR and STU are congruent. Select each statement that is true for all such triangles PQRand STU.

A. The correspondingsides of the twotriangles arecongruent.

B. The correspondingangles of the twotriangles arecongruent.

C. There is a set of rigidmotions that takesone triangle to theother.


Correct: ABCRationale:

A. Correct answerB. Correct answerC. Correct answer


50 TEACHER READS:


The vertices of parallelogram ABCD are A(2 , 1), B(3 , 4), C(5 , 3), and D(4 , 0). ABCD is reflected overthe x–axis to create parallelogram QRST. What are the coordinates of QRST?

A. Q(–2 , 1), R(–3 , 4),S(–5 , 3), T(–4 , 0)

B. Q(–2 , –1), R(–3 , –4),S(–5 , –3), T(–4 , 0)

C. Q(1 , 2), R(4 , 3),S(3 , 5), T(0 , 4)

D. Q(2 , –1), R(3 , – 4),S(5 , –3), T(4 , 0)



A. Student(s) mistakenly reflected the parallelogram over the y–axis.B. Student(s) mistakenly made all coordinates negative, creating a reflection over the origin.C. Student(s) switched all of the x and y coordinates, creating a reflection over the x = y line.D. Correct answer





51 The distribution of the test scores for Classroom A and Classroom B are shown in the graphs

below.

Select the descriptions of the summary statistic that apply to the two data sets represented by thegraphs above.

A. The standarddeviation should beused to compare thespread of the datasets because they arenormally distributed.

B. The interquartilerange should be usedto compare thespread of the datasets because they areskewed.

C. The mean should beused to compare thecenter of the datasets because they arenormally distributed.


Correct: ACStandards:

MA.9-12.S-ID.2




52 The age distribution of girls and boys on different sports teams are represented by the graphsbelow.

Determine which sets of summary statistics are correctly used to compare the two data sets shownabove.

A. The interquartilerange and medianshould be used tocompare data sets 1and 2 because bothare normallydistributed.

B. The standarddeviation and meanshould be used tocompare data sets 1and 2 because bothare normallydistributed.

C. The interquartilerange and medianshould be used tocompare data sets 3and 4 because bothare skewed.

D. The standarddeviation and meanshould be used tocompare data sets 3and 4 because bothare skewed.


Correct: BCStandards:

MA.9-12.S-ID.2




53 Look at the three graphs and determine which statement is true.

A. Graph A defines y asa function of x.

B. Graph B defines y asa function of x.

C. Graph C defines y asa function of x.


Correct: CStandards:

MA.9-12.F-IF.1

54 Let V(t) represent the value of a bank account, in thousands of dollars, t years after the account isopened at the bank.

Determine which statements are true.

A. V(0) = 2 means thatthe value of the bankaccount when it isopened is $2000

B. V(5) = 2.2 means that2.2 years after thebank account isopened, its value is$5000

C. V(10) – V(5) = 0.4means that the bankaccount grows by$400 between 5 and10 years after itsopening


Correct: ACStandards:

MA.9-12.F-IF.2MA.9-12.F-IF.4




55 A soccer ball is kicked up into the air from the ground. The graph represents the height of the ball

as a function of time.

Part A:

What is the maximum height, in feet, the soccer ball reaches before falling back to the ground?

feetPart B:

Which of the following statements describe the soccer ball? Select all that apply.

A. At 0 seconds, the ballis on the ground.

B. At 8 seconds, the ballis on the ground.

C. The ball is in the airfor a total of 4seconds.

D. The ball is at a heightof 3 feet 6 secondsafter it was kicked.

E. Between 2 and 4seconds, the ball isfalling towards theground.


Correct: ABDStandards:

MA.9-12.F-IF.4




56 John let his remote controlled airplane fly from where he was sitting in the bleachers. After a shortperiod of time, he stopped the airplane. The graph represents the height of the airplane above theground during the time it was flying.

The height of the airplane above the ground, in feet, is a function of time, in seconds.

Part A:

How high above the ground, in feet, was the airplane at the time he released it from the bleachers?

feet Part B:

Enter the lowest height, in feet, the airplane reached.

feet

Part C:

Enter the total time, in seconds, the airplane was flying for.

seconds

A. Input #1 Answers B. ■ 24 feet 8 feet4seconds





Correct: Rubric: 3 Point(s)

3210


57 Determine whether each function represents exponential growth or exponential decay.

f(x) = 3(2/5)x

f(x) = (7/4)3x

f(x) = 1/2(3/2)2x

f(x) = (1/3)4x-1

A. Input #1 Answers B. ■ Decay, Growth,Growth, Decay


Correct: Standards:

MA.9-12.F-IF.8.b




58 TEACHER READS:


Select all expressions equivalent to –90x + 60.

A. –30(–3x + 2) B. 30(–3x + 2) C. 10(–9x + 6) D. –10(9x – 6)

E. –10(9x + 6)


Correct: BCDRationale:

A. Student(s) may have misidentified –30 as the correct value instead of 30.B. Correct answerC. Correct answerD. Correct answerE. Student(s) may have misidentified –10 as the correct value instead of 10.

Standards:MA.7.7.EE.1

59 TEACHER READS:


Which expression is the simplified form of –10 + 3x – x – 7x + 5x + 7 + 2x?

A. 4x – 3 B. 2x – 3 C. –18x – 17 D. –x



A. Student(s) may have subtracted (–x) from (–7x) to get (–6x), then added like terms.B. Correct answerC. Student(s) may have thought that all of the terms in the expression should be negative, and changed all

of the positive signs to negatives prior to combining like terms.D. Student(s) may not have understood the idea of adding together only like terms, and added 2x and –3

to get –x .Standards:

MA.7.7.EE.1

60 Select all possible solutions:

|2x - 5| = 9

A. 2 B. -2 C. 7 D. -7


Correct: BCStandards:

MA.7-12.A




61 Select all possible solutions

|5y - 8| = 1

A. 75

B. 57

C. 59

D. 95


Correct: AD

62 TEACHER READS:


A function is given on the graph below.

What is the x–intercept of this function?

A. –2 B. 0 C. 3 D. 6



A. Student(s) may have found the slope of this function.B. Student(s) may have found the y–value of the point where the function crosses the x–axis.C. Correct answerD. Student(s) may have found the y–intercept of this function.





63 TEACHER READS:


If ƒ(x) = 4x – 11, what is the value of ƒ(5)?

A. 20x – 55 B. 34 C. 9 D. 4



A. Student(s) may have mistakenly thought they should multiply the expression by 5.B. Student(s) may have interpreted ƒ(5) to mean change 4x to 45 (instead of the product of 4 and 5).C. Correct answerD. Student(s) may have misinterpreted the problem to be asking what value of x would solve 5 = 4x – 11


64 TEACHER READS:


Which of the following coordinate planes shows the graph of the function y – 3 = –2(x + 2)?

A. B. C. D.



A. Student(s) may have thought that 2 is the y–intercept and –2 is the slope.B. Correct answerC. Student(s) may have distributed and thought that –4 is the y–intercept and –2 is the slope. Student(s)

may have thought that negative slopes move downwards from right to left.D. Student(s) may have distributed and subtracted 3 from –4 and thought that –7 is the y–intercept and –2

is the slope. Student(s) may have thought that negative slopes move downwards from right to left.Standards:

MA.9-12.F-IF.7MA.9-12.F-IF.7.a




65 TEACHER READS:





Which of the following graphs represents a line whose y–intercept is equal to the y–intercept of theline given by the table? Select two that apply.

x 1 3 5 7

y 5 11 17 23

A.

B.

C.

D.

E.

F.





Correct: AERationale:

A. Correct answerB. Student(s) may have thought that the first y–entry in the table was the y–intercept.C. Student(s) may have confused the change in y in the table with the y–intercept.D. Student(s) may have confused the change in y in the table with the y–intercept.E. Correct answerF. Student(s) may have thought that the first y–entry in the table was the y–intercept.

Standards:MA.9-12.F-IF.7MA.9-12.F-IF.7.a



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