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Question-and-Answer Service Student Guide

April QAS 4/10/18

MathTest – Calculator55 MINUTES, 38 QUESTIONS

Turn to Section 4 of your answer sheet to answer the questions in this section.

For questions 1-30, solve each problem, choose the best answer from the choicesprovided, and fill in the corresponding circle on your answer sheet. For questions 31-38,solve the problem and enter your answer in the grid on the answer sheet. Please refer tothe directions before question 31 on how to enter your answers in the grid. You may useany available space in your test booklet for scratch work.

1. The use of a calculator is permitted.

2. All variables and expressions used represent real numbers unless otherwise indicated.

3. Figures provided in this test are drawn to scale unless otherwise indicated.

4. All figures lie in a plane unless otherwise indicated.

5. Unless otherwise indicated, the domain of a given function f is the set of all real numbers x for which f (x) is a real number.

r

rr

r

w

w w

h

hh hh

b

c

a

b

A = �w

V = �wh

A = bhA = pr2

V = pr2h

c2 = a2 + b2 Special Right TrianglesC = 2pr

�

� �

12

V = pr343 V = pr2h1

3 V = �wh13

30°

60° 45°

45°

2xx s

sx√3

s√2

The number of degrees of arc in a circle is 360.The number of radians of arc in a circle is 2p.The sum of the measures in degrees of the angles of a triangle is 180.

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April QAS 4/10/18

1

If k6 • 2 = 36, what is the value of k4 − 2 ?

A) 12B) 10C) 6D) 1

2

The number of people who rode a certain bus eachday of a week is shown in the table below.

Day Number of ridersMonday 612Tuesday 798Wednesday 655Thursday 773Friday 808Saturday 480Sunday 229

Which of the following is true based on these data?

A) The bus had the most riders on Tuesday.B) Each day from Tuesday through Sunday, the

number of riders on the bus was greater than theprevious day.

C) Each day from Tuesday through Sunday, thenumber of riders on the bus was less than theprevious day.

D) The two days with the fewest number of riderswere Saturday and Sunday.

3

A physician prescribes a treatment in which a patienttakes 2 teaspoons of a medication every 6 hours for5 days. According to the prescription, how manyteaspoons of the medication should the patient takein a 24-hour period?

A) 4B) 6C) 8D) 40

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April QAS 4/10/18

4

One hundred park-district members will be selectedto participate in a survey about selecting a newpark-district coordinator. Which of the followingmethods of choosing the 100 members would resultin a random sample of members of the park district?

A) Obtain a numbered list of all park-districtmembers. Use a random number generator toselect 100 members from the list. Give the surveyto those 100 members.

B) Obtain a list of all park-district members sortedalphabetically. Give the survey to the first100 members on the list.

C) Tell all park-district members that volunteers areneeded to take the survey. Give the survey to thefirst 100 members who volunteer.

D) Obtain a list of all park-district members whoare attending an upcoming event. Give thesurvey to the first 100 members on the list.

5

x x x x2 + 1 + 2 − 22 2( ) ( )

Which of the following expressions is equivalent tothe expression above?

A) x4 2

B) x x2 + 22

C) x x2 + 23 2

D) x x x2 + 2 − 43 2

6

If x x+ 3 = 2 − 2, what is the value of x − 4 ?

A) 9B) 5C) 4D) 1

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April QAS 4/10/18

7

The functions f and g are defined by f x x= 4( ) andg x x= 2( ) . For what value of x doesf x g x− = 4( ) ( ) ?

A) −2

B) −1

C) 1

D) 2

8

The function g is defined as g xx

=23

+ 3( ) . What is

the value of g −30( ) ?

A) −27

B) −23

C) −17

D) −7

9

Year

Total Home Runs forSelected Years, 1903–2013

Num

ber o

f hom

e run

s

19031913

19231933

19431953

19631973

19831993

20032013

0500

1,0001,5002,0002,5003,0003,5004,0004,5005,0005,5006,000

The scatterplot above shows the total number ofhome runs hit in major league baseball, in ten-yearintervals, for selected years. The line of best fit for thedata is also shown. Which of the following is closestto the difference between the actual number of homeruns and the number predicted by the line of best fitin 2003?

A) 250B) 500C) 750D) 850

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April QAS 4/10/18

Questions 10-12 refer to the following information.

Ave

rage

pric

e of o

ne m

etric

ton

of o

rang

es (U

S do

llars

)

889873857841825809793

761

Month

777

745729

FebruaryMarc

hApril May June

JulyAugust

The line graph above shows the average price of onemetric ton of oranges, in dollars, for each of sevenmonths in 2014.

10

Between which two consecutive months shown didthe average price of one metric ton of orangesdecrease the most?

A) March to AprilB) May to JuneC) June to JulyD) July to August

11

Which of the following is closest to the median price,in dollars, of the seven recorded prices of one metricton of oranges?

A) 834B) 808C) 783D) 768

12

In 2014, the average price of one metric ton oforanges decreased by 2.36% from January (notshown) to February. Which of the following is closestto the price of one metric ton of oranges inJanuary 2014?

A) 700B) 770C) 790D) 830

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April QAS 4/10/18

13

Single story

Two story

Total

Roof type

9

20

29

4

10

14

2

3

5

15

Asphaltshingle Slate Cedar

shake Total

33

48

The table above shows the distribution ofsingle-story and two-story houses in a neighborhoodclassified according to roof type. If one of the housesis selected at random, what is the probability that itwill be a single-story house with a slate roof?

A)448

B)415

C)414

D)1448

14

x yx y2 − = −42 + = 4

For the solution of the system of equations above,what is the value of x ?

A) −4

B) −2

C) 0

D) 2

15

The load capacity of a certain washing machine is12 pounds. What is the approximate load capacity ofthe same washing machine, in kilograms?(1 kilogram = 2.2046 pounds)

A) 2.2B) 5.4C) 9.8D) 26.5

16

20 5

2129

B

C FD

E

A

Triangles ABC and DEF above are similar. Howmuch longer than segment EF is segment DE ?

A) 1B) 2C) 4D) 8

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April QAS 4/10/18

17

Data set A 25,550 40,430 49,150 62,590 73,670 118,780 126,040Data set B 22,860 55,020 173,730 300,580 358,920 456,170 603,300

Which of the following is true about the standard deviations of the twodata sets in the table above?

A) The standard deviation of data set B is larger than the standarddeviation of data set A.

B) The standard deviation of data set A is larger than the standarddeviation of data set B.

C) The standard deviation of data set A is equal to the standarddeviation of data set B.

D) There is not enough information available to compare the standarddeviations of the two data sets.

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April QAS 4/10/18

18

The velocity v, in meters per second, of a fallingobject on Earth after t seconds, ignoring theeffect of air resistance, is modeled by the equationv t= 9.8 . There is a different linear relationshipbetween time and velocity on Mars, as shown in thetable below.

Time(seconds)

Velocity onMars (metersper second)

0 04 14.88 29.6

If an object dropped toward the surface of Earth hasa velocity of 58.8 meters per second after t seconds,what would be the velocity of the same objectdropped toward the surface of Mars after t seconds,ignoring the effect of air resistance?

A) 15.9 meters per secondB) 22.2 meters per secondC) 36.2 meters per secondD) 88.8 meters per second

19

In the xy-plane, the graph of line has slope 3.Line k is parallel to line and contains thepoint 3, 10( ). Which of the following is an equationof line k ?

A) y x= −13

+ 11

B) y x=13

+ 9

C) y x= 3 + 7

D) y x= 3 + 1

20

A certain colony of bacteria began with one cell, andthe population doubled every 20 minutes. What wasthe population of the colony after 2 hours?

A) 6B) 12C) 32D) 64

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April QAS 4/10/18

21

The circumference of Earth is estimated to be40,030 kilometers at the equator. Which of thefollowing best approximates the diameter, in miles,of Earth’s equator? (1 kilometer ≈ 0.62137 miles)

A) 3,205 milesB) 5,541 milesC) 7,917 milesD) 13,004 miles

22

The budget for a school band was $8,000 in 2010.The budget decreased by 15% from 2010 to 2011 andthen increased by 22% from 2011 to 2012. Which ofthe following expressions represents the budget, indollars, for the school band in 2012?

A) (1.15)(1.22)(8,000)B) (0.85)(1.22)(8,000)C) (1.15)(0.78)(8,000)D) (0.85)(0.78)(8,000)

Questions 23 and 24 refer to the followinginformation.

4000

0.2

0.4

0.6

0.8

1.0

500 600

Phase Diagram forAluminosilicate Polymorphs

Temperature (°C)Pr

essu

re (G

Pa)

sillimanite

kyanite

andalusite

(350, 0.19)

(500, 0.38)

(795, 1.0)

(760, 0)

700 800

During mineral formation, the same chemical compoundcan become different minerals depending on thetemperature and pressure at the time of formation.A phase diagram is a graph that shows the conditionsthat are needed to form each mineral. The graph above isa portion of the phase diagram for aluminosilicates, withthe temperature T, in degrees Celsius (°C), on thehorizontal axis, and the pressure P, in gigapascals (GPa),on the vertical axis.

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April QAS 4/10/18

23

P T= −0.00146 + 1.11

An equation of the boundary line between theandalusite and sillimanite regions is approximated bythe equation above. What is the meaning of theT-intercept of this line?

A) It is the maximum temperature at whichsillimanite can form.

B) It is the temperature at which both andalusiteand sillimanite can form when there is nopressure applied.

C) It is the increase in the number of degreesCelsius needed to remain on the boundarybetween andalusite and sillimanite if the pressureis reduced by 1 GPa.

D) It is the decrease in the number of gigapascals ofpressure needed to remain on the boundarybetween andalusite and sillimanite if thetemperature is increased by 1°C.

24

Which of the following systems of inequalities bestdescribes the region where sillimanite can form?

A) P TP T≥ 0.0021 − 0.67≥ 0.0013 − 0.25

B) P TP T≤ 0.0021 − 0.67≥ −0.0015 + 1.13

C) P TP T≤ 0.0013 − 0.25≥ −0.0015 + 1.13

D) P TP T≤ 0.0013 − 0.25≤ −0.0015 + 1.13

25

y xy x x= 2 + 4= − 3 + 2( )( )

The system of equations above is graphed in thexy-plane. At which of the following points do thegraphs of the equations intersect?

A) −3, −2( )

B) −3, 2( )

C) 5, −2( )

D) 5, 14( )

26

The gas mileage M s( ), in miles per gallon, of a cartraveling s miles per hour is modeled by the functionbelow, where s20 ≤ ≤ 75.

M s s s= −124

+ 4 − 502( )

According to the model, at what speed, in miles perhour, does the car obtain its greatest gas mileage?

A) 46B) 48C) 50D) 75

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April QAS 4/10/18

27

x h(x)−1 12 74 11

The table above shows selected values for thefunction h. In the xy-plane, the graph of y h x= ( ) isa line. What is the value of h 8( ) ?

A) 15B) 19C) 21D) 22

28

The front row of an auditorium has 10 seats. Thereare 50 rows in total. If each row has 2 more seats thanthe row before it, which expression gives the totalnumber of seats in the last row?

A) 10 + 2 50 − 1( )

B) 10 + 2 50( )

C) 50 10 + 2( )

D) 10 + 250

29

An ecologist selected a random sample of 30 prairiedogs from a colony and found that themean mass of the prairie dogs in the sample was0.94 kilograms (kg) with an associated margin oferror of 0.12 kg. Which of the following is the bestinterpretation of the ecologist’s findings?

A) All prairie dogs in the sample have a massbetween 0.82 kg and 1.06 kg.

B) Most prairie dogs in the colony have a massbetween 0.82 kg and 1.06 kg.

C) Any mass between 0.82 kg and 1.06 kg is aplausible value for the mean mass of the prairiedogs in the sample.

D) Any mass between 0.82 kg and 1.06 kg is aplausible value for the mean mass of the prairiedogs in the colony.

30

A poster has an area of 432 square inches. Thelength x, in inches, of the poster is 6 inches longerthan the width of the poster. Which of the followingequations can be solved to determine the length, ininches, of the poster?

A) x − 6 = 4322

B) x x− 6 = 4322

C) x + 6 = 4322

D) x x+ 6 = 4322

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April QAS 4/10/18

2

34

56

789

2

34

56

789

2

34

56

789

2

34

56

789

Grid inresult.

Fractionline

Writeanswerin boxes.

For questions 31-38, solve the problem and enter your answer in the grid, as describedbelow, on the answer sheet.

1. Although not required, it is suggested that you write your answer in the boxes at the top of the columns to help you fill in the circles accurately. You will receive credit only if the circles are filled in correctly.2. Mark no more than one circle in any column.3. No question has a negative answer.4. Some problems may have more than one correct answer. In such cases, grid only one answer.

5. Mixed numbers such as must be gridded

as 3.5 or 7/2. (If is entered into the

grid, it will be interpreted as , not .)

6. Decimal answers: If you obtain a decimal answer with more digits than the grid can accommodate, it may be either rounded or truncated, but it must fill the entire grid.

Answer:

Acceptable ways to grid are:

712

312

12

3

12

3 23

Decimalpoint

10

. . . .

101

01

//7 1/ 2

Answer: 2.5

10

. . . .

2

34

56

789

1

34

56

789

012

34

56

789

012

34

56

789

//.2 5

2

10

. . . .

2

34

56

789

12

34

56

789

012

34

56

789

012

34

56

789

///2 3

10

. . . .

2

34

56

789

12

34

56

789

012

34

56

789

012

34

56

789

//66. .6

10

. . . .

2

34

56

789

12

34

56

789

012

34

56

789

012

34

56

789

//66 7

Answer: 201 – either position is correct

10

. . . .

2

3

12

3

012

3

012

3

//02 1

10

. . . .

2

3

12

3

012

3

012

3

//102

6

7777778888888

6

7777778888888

6

7777778888888

6

7777778888888

6

7777778888888

7777778888888

7777778888888

7777778888888

6

7777778888888

7777778888888

7777778888888

6

8888888

2222

33333333 33333333

2222

33333333

2222

3333333 33333333

2222

33333333

2222

33333333

2222

3333333

//

3 /1 2//

NOTE: You may start your answers in any column, space permitting. Columns you don’t need to use should be left blank.

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April QAS 4/10/18

31

If x2 + 3 = 5 and y3 − 3 = 6, what is one possiblevalue of xy ?

32

0 1 2 3 4 5 6 70

10203040506070

Reve

nue (

mill

ions

of d

olla

rs)

Year

Revenue

The scatterplot above shows the revenue, in millionsof dollars, that a company earned over several yearsand a line of best fit for the data. In Year 4, thedifference between the actual revenue and thepredicted revenue is n million dollars, where n is apositive integer. What is the value of n ? Round youranswer to the nearest whole number. (Disregard the$ sign when gridding your answer.)

33

8 m10 m 10 m

seating x m

stage

The figure above is the floor plan drawn by anarchitect for a small concert hall. The stage has depth8 meters (m) and two walls each of length 10 m. Ifthe seating portion of the hall has an area of180 square meters, what is the value of x ?

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April QAS 4/10/18

34

Jacob bought two types of pens: blue pens that cost$0.60 each and red pens that each cost d times asmuch as a blue pen. If the cost of 3 blue pens and6 red pens was $10.80, what is the value of d ?

35

George took a nonstop flight from Dallas toLos Angeles, a total flight distance of 1,233 miles. Theplane flew at a speed of 460 miles per hour for thefirst 75 minutes of the flight and at a speed of439 miles per hour for the remainder of the flight. Tothe nearest minute, for how many minutes did theplane fly at a speed of 439 miles per hour?

36

An arc of a circle measures 2.4 radians. To thenearest degree, what is the measure, in degrees, ofthis arc? (Disregard the degree sign when griddingyour answer.)

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April QAS 4/10/18

Questions 37 and 38 refer to the followinginformation.

12 in

9 in

Carrie, a packaging engineer, is designing a container tohold 12 drinking glasses shaped as regular octagonalprisms. Her initial sketch of the top view of the base ofthe container is shown above.

37

If the length and width of the container base in theinitial sketch were doubled, at most how many moreglasses could the new container hold?

38

Carrie redesigned the container because the initialsketch did not account for cushioning materialbetween the glasses. The area of the base of the newlydesigned container is 25% greater than the area of thebase in the initial sketch. What is the area, in squareinches, of the base of the newly designed container?

STOPIf you finish before time is called, youmay check your work on this section only.

Do not turn to any other section.

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Unauthorized copying or reuse of any part of this page is illegal. 55

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