timss2011 g8 math

8

RELEASED MATHEMATICS ITEMS

This book contains the released Trends in International Mathematics and Science Study (TIMSS) 2011 grade 8 mathematics assessment items. This is not a complete set of all TIMSS 2011 assessment items because some items are kept confidential so that they may be used in subsequent cycles of TIMSS to measure trends.

How Can This Set of Released Items Be Used?

In Teacher-designed Assessments. The items in this book present different ways of measuring students’ understanding in various content and cognitive domains. A teacher may use these items to create an assessment according to the needs of the class after reviewing the items and selecting items of interest.

For Feedback on Student Understanding. Student responses can be scored according to the scoring information provided in the book. Items that coincide with concepts taught in class allow the teacher to gain feedback on the students’ understanding of assessed concepts. For example, a teacher might decide to examine the incorrect or partially correct responses of the class. The teacher might use the items to identify particular difficulties or misconceptions experienced by individual students, which can serve as the basis for some remedial teaching or focused practice.

To Benchmark Student Performance. The teacher might also compare the percent of students in the class who responded correctly to an item with the percent of students who responded correctly to the same item in other education systems or in the United States.

TIMSS and PIRLS are copyrighted and are registered trademarks of IEA. Released items from TIMSS and PIRLS assessments are for non-commercial, educational, and research purposes only. Translated versions of items remain the intellectual property of IEA. Although the items are in the public domain, please print an acknowledgement of the source, including the year and name of the assessment you are using. If you publish any part of the released items from TIMSS 2011, please use the following acknowledgement:

SOURCE: TIMSS 2011 Assessment. Copyright © 2013 International Association for the Evaluation of Educational Achievement (IEA). Publisher: TIMSS & PIRLS International Study Center, Lynch School of Education, Boston College, Chestnut Hill, MA and International Association for the Evaluation of Educational Achievement (IEA), IEA Secretariat, Amsterdam, the Netherlands.

38331.0513.86070312

USER’S GUIDEGrade 8

This book contains TIMSS 2011 released items for grade 8. Each item appears on a single page, on which is provided information about the item’s classification and about international student performance on the item. The items appear in the content domain order, as shown in the index on the next page.

Information about item classification

Take a look at the first item on page 1. Across the top are three boxes which identify the item’s content domain (the subject matter in mathematics that the item assesses), its main topic (the specific topic assessed within that subject matter), and its cognitive domain (the cognitive or thinking process assessed). For this item, the content domain is number, the main topic is fractions and decimals, and the cognitive domain is applying.

Below the row of boxes and above a boxed-in area of the page is the item label. For this item, it is Ann and Jenny divide 560 zeds. Below the boxed-in area is the item number, which is more commonly used to identify each item than the item label. Within the boxed-in area is the item as it appeared in student test booklets.

Correct answers are shown beneath each item. The correct answer for multiple-choice items is simply a letter code. For example, in the item M032094 on page 3, the letter code A is the correct answer. The correct answers for write-in or open-ended items are explained in a scoring guide. For example, the Ann and Jenny divide 560 zeds (page 1) provides an example of a scoring guide, indicating the general nature of correct and incorrect

responses. In some cases, partial credit may be awarded and these items will provide guidelines for fully correct, partially correct, and incorrect responses. Sample student responses are provided for some of the constructed-response items for each scoring category.

Information about international student performance

In the table along the right-hand side of the page are the percent correct statistics for the item. These consist of statistics on the percentage of students in each education system who could answer the question correctly. The lists of education systems are ordered in terms of this percentage. The international average is included as well.

To the right of some of the percent correct statistics are special symbols that indicate when an education system scored significantly higher or significantly lower than the international average. Thus, on the item Ann and Jenny divide 560 zeds as an example, an estimated 25 percent of U.S. students could correctly answer this item, a percentage that was not measurably different than the international average, after taking into account the standard of error associated with the percent correct statistic for the United States and for the international average.

38331.0513.86070312

ITEM INDEXGrade 8

Content Domain Page

NumberM032064 Ann and Jenny divide 560 zeds .................1M032094 4/100 plus 3/1000 ........................................3M032166 Best estimate of (7.21x3.86)/10.09 ..............4M032595 The percentage of caps for sale .................5M032626 36 as a product of prime factors .................6M032662 Location of N on number line ......................7M032725 Write 3 5/6 in decimal form .........................8M042002 Numbers to get greatest results ................10M042016 Express 256 X 4096 as power of 4 .............12M042024 What is K on a number line ......................13M042031 Equivalent expression ................................14M042032 Equivalent fraction for 0.125 ......................15M042041 Length of the original pipe ........................16M042059 Complete the missing boxes .....................17M042186 Next line in the pattern ..............................19M052061 Packing eggs into boxes ............................21M052214 Which number sentence is true ................22M052216 Select the decimal equal to 3/5 ...............23M052228 Method for subtracting fractions ...............24M052231 Add 42.65 to 5.748 .....................................25

AlgebraM032047 Sum of 3 consecutive whole numbers......26M032295 m boys and n girls in a parade .................27M032352 The shadow lengths of four bushes ..........28M032419 Which represents 2x plus 3x .......................29M032424 Jo has 3 metal blocks to weigh .................30M032477 Cost in zeds for taxi trip of n km .................31M032538 Find the value of y when t is 9 ...................32M032673 If t is a number between 6 and 9 ..............34M032683 Simplify 3x/8 plus x/4 plus x/2 ...................35M032738 What xy plus 1 mean .................................37M032757 Red&BlackTiles_Complete table ...............38M032760A Red&BlackTiles_Shape with 64 tiles ...........40M032760B Red&BlackTiles_Shape with 49 tiles ...........41M032760C Red&BlackTiles_Shape with 44 tiles ...........42M032761 Red&BlackTiles_Figure n ............................43M042067 What is the area of the rectangle .............45M042077 Expression to equivalent to 4(3+x) ............46M042086 What is the value of 2a + 2b + 4 ................47M042103 Solve the inequality ....................................49M042198A Next term in the pattern .............................51M042198B Term number 100 in the pattern ................53M042198C Term number n in the pattern ...................55M042226 What is the value P .....................................57M042228 Value of x in the pattern ............................59M042235 What is the value of x and y ......................61

Content Domain Page

Algebra (continued)

M042236 Simplify the expression ...............................62M042245 Equation that satisfies number pairs .........63M052002 Length of the longest wood piece ............64M052173 Area of garden’s shaded portion .............65M052302 Value of y in an expression ........................66

GeometryM032100 Shape made up of same size cubes .......67M032116 Area of a square is 144 square cm ...........68M032324 Distance between the midpoints ..............69M032331 Degrees minute hand of clock turns ........70M032397 Figure 1 transformed to 2 and 3 ................71M032398 Value of angle x in figure ...........................72M032402 Why PQR is a right angle triangle ..............73M032623 Area of the shaded region in figure ..........74M032679 Shape of cutout figure ...............................75M032692 Interior angles of pentagon ......................76M032734 View of shape directly from above ...........78M042150 Which shape has a line of symmetry ........80M042152 Half-turn around point O ............................81M042201 Length of the rectangular box ..................82M042270 Draw an isosceles triangle .........................84M042300Z Measure of angle BOC-DERIVED ...............86M052084 Calculate the area of a square ...............88M052206 Number of books to fill the box .................89M052362 What is the size of angle B .........................90M052408 Value of angle b .........................................91

Data and ChanceM032132 How likely to get pink candy .....................92M032507 Number of times spinner in red area ........93M032681A Car production graph/time cars made ...94M032681B Car production graph/avg by hour .........96M032681C Car production graph/identify time .........98M032695 Make a pie chart with labels ...................100M032721 Sales of two types of soft drink ................103M042169A Mean number of staff members .............104M042169B Median number of staff members ..........105M042169C Change in mean and median ...............108M042177 Number of regular size bottles ................110M042179 Chance of getting a button ....................111M042207 Complete and label this pie chart..........112M042260 How likely student voted for Pat ...............115M042269 Long jump competition ...........................116M052429 Probability that the marble is red ............117M052503A Age structures of country X and Y...........118M052503B Problem of taking care of elderly ............120

38331.0513.86070312

Copyright © 2013 International Association for the Evaluation of Educational Achievement (IEA). 1

TIMSS 2011 8th-Grade Mathematics Concepts and Mathematics Items

Content Domain

NUMBER

Main Topic

Fractions and Decimals

Cognitive Domain

Applying

Ann and Jenny divide 560 zeds

Ann and Jenny divide 560 zeds between them. If Jenny gets of the money, how many zeds will Ann get?

Answer: _______________

Item Number: M032064

SCORINGCorrect Response• 350

Incorrect Response• 210

•5/8• Otherincorrect(includingcrossedout,erased,straymarks,illegible,orofftask)

Overall Percent Correct

Education systemPercentcorrect

Singapore 76Korea, Rep. of 67Hong Kong-CHN 61Chinese Taipei-CHN 60Finland 48Russian Federation 48Japan 45Israel 43Hungary 40Sweden 37England-GBR 34Australia 34Italy 34Lithuania 33Malaysia 32Norway 30Kazakhstan 28Turkey 28New Zealand 28International average 27United States 25Slovenia 25Ukraine 24Armenia 23Georgia 23Tunisia 21Romania 20United Arab Emirates 17Iran, Islamic Rep. of 17Macedonia, Rep. of 16Qatar 16Chile 14Thailand 13Palestinian Nat’l Auth. 12Lebanon 10Bahrain 10Indonesia 9Saudi Arabia 8Oman 7Jordan 7Morocco 6Syrian Arab Republic 6Ghana 3

Benchmarking education system

Percentcorrect

Quebec-CAN 45North Carolina-USA 40Minnesota-USA 38Massachusetts-USA 36Ontario-CAN 31Connecticut-USA 30Colorado-USA 29Alberta-CAN 29Indiana-USA 28Dubai-UAE 25Florida-USA 23California-USA 17Abu Dhabi-UAE 15Alabama-USA 14

Percent higher than International average Percent lower than International average



Ann and Jenny divide 560 zeds (continued)M032064

Student ResponsesCorrect Response:

Answer: ________________

Incorrect Response:

Answer: ________________



Percent higher than International average

Content Domain

NUMBER

Main Topic


Cognitive Domain

Knowing

4/100plus3/1000

A. 0.043

B. 0.1043

C. 0.403

D. 0.43

1000


Correct Response: A


Education systemPercentcorrect

Singapore 92Korea, Rep. of 89Hong Kong-CHN 86Chinese Taipei-CHN 85Russian Federation 83Lebanon 81Japan 77Israel 77Italy 74Malaysia 73Slovenia 70Kazakhstan 69Lithuania 68Finland 68United Arab Emirates 68Tunisia 68Australia 68Sweden 67Armenia 66Ukraine 65Hungary 63United States 63International average 62Palestinian Nat’l Auth. 59England-GBR 57Georgia 55Romania 54Thailand 54Macedonia, Rep. of 52Qatar 52New Zealand 51Iran, Islamic Rep. of 50Turkey 50Jordan 49Norway 49Morocco 49Saudi Arabia 49Bahrain 48Syrian Arab Republic 48Oman 47Indonesia 46Chile 41Ghana 34


Percentcorrect

North Carolina-USA 77Massachusetts-USA 76Minnesota-USA 72Dubai-UAE 71Quebec-CAN 71Connecticut-USA 70Indiana-USA 70Alberta-CAN 69Abu Dhabi-UAE 67Ontario-CAN 65Florida-USA 64Colorado-USA 60California-USA 58Alabama-USA 45

Percent lower than International average



Content Domain

NUMBER

Main Topic


Cognitive Domain

Knowing

Bestestimateof(7.21x3.86)/10.09

Which of these is the BEST estimate of ?

A.

B.

C.

D.


Correct Response: B


Education systemPercent correct

Singapore 92Hong Kong-CHN 90United States 80Russian Federation 79Finland 78Lithuania 77Japan 77Chinese Taipei-CHN 73Sweden 71Norway 71Korea, Rep. of 70Slovenia 69Ukraine 66Italy 66Australia 66England-GBR 65Hungary 64Israel 61Romania 58International average 57New Zealand 56Malaysia 54Macedonia, Rep. of 53United Arab Emirates 52Armenia 52Georgia 50Thailand 49Saudi Arabia 49Turkey 47Qatar 47Kazakhstan 46Lebanon 46Tunisia 45Bahrain 43Chile 43Palestinian Nat’l Auth. 42Iran, Islamic Rep. of 39Jordan 37Indonesia 36Oman 34Morocco 30Syrian Arab Republic 26Ghana 26


Percentcorrect

Quebec-CAN 82Alberta-CAN 79Ontario-CAN 71Dubai-UAE 59Abu Dhabi-UAE 48Minnesota-USA 89Connecticut-USA 87North Carolina-USA 86Massachusetts-USA 85Indiana-USA 85Florida-USA 81Colorado-USA 80California-USA 76Alabama-USA 70




Content Domain

NUMBER

Main Topic

Ratio,ProportionandPercent

Cognitive Domain

Applying

The percentage of caps for sale

Color of Caps

The pie chart shows the percentage of caps for sale at a sporting goods store. If there are 200 caps, what is the total number of caps that are either white or green?

A. 55

B. 100

C. 110

D. 145

White30%

Green25%

Red20%

Blue10%

Black15%


Correct Response: C



Korea, Rep. of 90Singapore 89Hong Kong-CHN 87Chinese Taipei-CHN 84Finland 80Japan 79Lithuania 66England-GBR 63Hungary 63Sweden 62Slovenia 61Italy 60United States 59Israel 59Australia 58New Zealand 56Russian Federation 54Norway 54Turkey 53Ukraine 51International average 49Malaysia 46Armenia 46Chile 45Kazakhstan 42Thailand 42Iran, Islamic Rep. of 40Qatar 38United Arab Emirates 38Romania 37Indonesia 36Saudi Arabia 34Bahrain 33Georgia 33Macedonia, Rep. of 32Lebanon 28Tunisia 28Syrian Arab Republic 25Oman 23Morocco 21Palestinian Nat’l Auth. 18Ghana 14Jordan 13


Percentcorrect

Massachusetts-USA 76Minnesota-USA 73Colorado-USA 67Alberta-CAN 67Quebec-CAN 67Indiana-USA 65Connecticut-USA 65North Carolina-USA 63Ontario-CAN 59Florida-USA 58California-USA 50Dubai-UAE 42Alabama-USA 40Abu Dhabi-UAE 39




Content Domain

NUMBER

Main Topic

WholeNumbers

Cognitive Domain

Knowing

36 as a product of prime factors

Which of these shows how 36 can be expressed as a product of prime factors?

A. 6 × 6

B. 4 × 9

C. 4 × 3 × 3

D. 2 × 2 × 3 × 3


Correct Response: D



Korea, Rep. of 90Chinese Taipei-CHN 88Singapore 79Hong Kong-CHN 73Hungary 69Russian Federation 68Italy 66Thailand 65United States 64Ukraine 59Jordan 58Palestinian Nat’l Auth. 56Armenia 55Turkey 53Lebanon 52Israel 52England-GBR 51United Arab Emirates 49International average 49Norway 49Tunisia 49Romania 49Georgia 48Qatar 46Slovenia 45Australia 45New Zealand 43Iran, Islamic Rep. of 43Indonesia 43Saudi Arabia 43Ghana 43Kazakhstan 41Japan 37Macedonia, Rep. of 37Oman 35Lithuania 35Malaysia 34Bahrain 32Syrian Arab Republic 31Sweden 29Finland 29Chile 29Morocco 13


Percentcorrect

Massachusetts-USA 81Minnesota-USA 72Indiana-USA 69North Carolina-USA 69California-USA 67Colorado-USA 66Dubai-UAE 60Connecticut-USA 57Florida-USA 54Alabama-USA 51Alberta-CAN 48Ontario-CAN 45Abu Dhabi-UAE 44Quebec-CAN 44




Content Domain

NUMBER

Main Topic


Cognitive Domain

Reasoning

LocationofNonnumberline

P and Q represent two fractions on the number line above.

P × Q = N.

Which of these shows the location of N on the number line?

A.

B.

C.

D.

P Q0 1 2

NP Q0 1 2

P Q0 1 2

P Q0 1 2

P Q0 1 2

N

N

N


Correct Response: D



Chinese Taipei-CHN 53Hong Kong-CHN 47Singapore 45Korea, Rep. of 44Japan 43Russian Federation 31Sweden 30England-GBR 29Finland 29Palestinian Nat’l Auth. 28Israel 27Oman 26Syrian Arab Republic 25Saudi Arabia 25Jordan 24Australia 23Hungary 23International average 23United States 22Qatar 22Slovenia 21Bahrain 21New Zealand 19Ukraine 19Lebanon 18Malaysia 18Lithuania 18Macedonia, Rep. of 17Iran, Islamic Rep. of 16Morocco 16Italy 16Norway 15Armenia 15United Arab Emirates 15Turkey 15Tunisia 14Kazakhstan 14Chile 14Georgia 13Ghana 13Romania 12Thailand 12Indonesia 10


Percentcorrect

Massachusetts-USA 44Minnesota-USA 38North Carolina-USA 36Connecticut-USA 30Quebec-CAN 29Ontario-CAN 27Alberta-CAN 24Colorado-USA 21Florida-USA 20California-USA 19Indiana-USA 19Abu Dhabi-UAE 16Dubai-UAE 14Alabama-USA 13




Content Domain

NUMBER

Main Topic


Cognitive Domain

Knowing

Write35/6indecimalform

Write in decimal form, rounded to 2 decimal places.

Answer: _______________


SCORINGCorrect Response• 3.83

Incorrect Response• 3.56• Otherincorrect(includingcrossedout,erased,straymarks,illegible,orofftask)



Hong Kong-CHN 78Singapore 73Korea, Rep. of 65Chinese Taipei-CHN 61Japan 46Tunisia 41Russian Federation 39Kazakhstan 37Australia 31Slovenia 29Hungary 29Malaysia 29Israel 29United States 29Italy 27Armenia 27Finland 25Lithuania 25International average 25Sweden 25England-GBR 24United Arab Emirates 24Ukraine 22Macedonia, Rep. of 21Norway 19Romania 19Morocco 18Georgia 18New Zealand 18Thailand 15Palestinian Nat’l Auth. 14Saudi Arabia 14Bahrain 13Qatar 12Indonesia 8Oman 8Ghana 6Chile 6Iran, Islamic Rep. of 5Jordan 5Syrian Arab Republic 4Lebanon 3Turkey 3


Percentcorrect

Minnesota-USA 42Massachusetts-USA 42Alberta-CAN 42North Carolina-USA 41Quebec-CAN 37Indiana-USA 35Florida-USA 35Connecticut-USA 34Ontario-CAN 31Dubai-UAE 26Colorado-USA 23Alabama-USA 22Abu Dhabi-UAE 21California-USA 20




Write35/6indecimalform(continued)M032725


Answer: ________________

Incorrect Response:

Answer: ________________



Content Domain

NUMBER

Main Topic

WholeNumbers

Cognitive Domain

Reasoning

Numberstogetgreatestresults

Place the four digits 3, 5, 7, and 9 into the boxes below in the positions that would give the greatest result when the two numbers are multiplied.


SCORINGCorrect Response• 93x75OR75x93

Incorrect Response• 95x73OR73x95• 97x53OR53x97• Otherincorrect(includingcrossedout,erased,straymarks,illegible,orofftask)



Hong Kong-CHN 63Singapore 55Japan 51Chinese Taipei-CHN 50Norway 47Israel 46Korea, Rep. of 42New Zealand 41England-GBR 41United States 38Russian Federation 37Sweden 36Slovenia 36Hungary 35Australia 34Finland 32Italy 31Kazakhstan 29International average 28Malaysia 25Lithuania 25Macedonia, Rep. of 24Ukraine 23Tunisia 22Iran, Islamic Rep. of 22Armenia 21United Arab Emirates 21Turkey 20Thailand 20Palestinian Nat’l Auth. 19Syrian Arab Republic 19Saudi Arabia 19Qatar 18Jordan 18Romania 17Georgia 17Lebanon 15Morocco 13Chile 13Oman 13Bahrain 12Indonesia 10Ghana 2


Percentcorrect

Quebec-CAN 51Massachusetts-USA 48Minnesota-USA 47Ontario-CAN 47North Carolina-USA 45Alberta-CAN 42Connecticut-USA 39Indiana-USA 38Florida-USA 35Colorado-USA 34California-USA 33Alabama-USA 27Dubai-UAE 24Abu Dhabi-UAE 23




Numberstogetgreatestresults(continued)M042002


X

Incorrect Response:

X



Content Domain

NUMBER

Main Topic

WholeNumbers

Cognitive Domain

Applying

Express256X4,096aspowerof4

Look at this table:

41 42 43 44 45 46

4 16 64 256 1,024 4,096

Use the table to express the value of 256 × 4,096 as a power of 4.

A. 410

B. 416

C. 420

D. 424


Correct Response: A



Hong Kong-CHN 74Lebanon 73Russian Federation 72Korea, Rep. of 70Singapore 70Chinese Taipei-CHN 69Italy 67United States 63Ukraine 63United Arab Emirates 62Israel 59Lithuania 57Kazakhstan 57Slovenia 55Hungary 53Armenia 53Qatar 52Finland 51International average 51Romania 49England-GBR 48Macedonia, Rep. of 48Australia 47Saudi Arabia 46Japan 46Iran, Islamic Rep. of 45New Zealand 45Jordan 45Thailand 45Turkey 44Malaysia 43Georgia 42Chile 42Palestinian Nat’l Auth. 42Tunisia 41Oman 41Sweden 39Syrian Arab Republic 39Morocco 39Indonesia 39Bahrain 37Norway 32Ghana 28


Percentcorrect

North Carolina-USA 70Massachusetts-USA 69California-USA 66Florida-USA 66Minnesota-USA 65Dubai-UAE 64Abu Dhabi-UAE 63Indiana-USA 61Ontario-CAN 59Quebec-CAN 56Connecticut-USA 54Alabama-USA 53Colorado-USA 52Alberta-CAN 43




Content Domain

NUMBER

Main Topic


Cognitive Domain

Knowing

WhatisKonanumberline

Which number does K represent on this number line?

A. 27.4

B. 27.8

C. 27.9

D. 28.2

26 27 K 28


Correct Response: B



Singapore 94Japan 93Hong Kong-CHN 92Korea, Rep. of 90Chinese Taipei-CHN 86England-GBR 82Sweden 79Finland 79Slovenia 74Hungary 73Lithuania 73Australia 73New Zealand 72Russian Federation 68Norway 67United States 65Israel 61Malaysia 61Italy 59Ukraine 58International average 54Thailand 48Chile 45Kazakhstan 44United Arab Emirates 43Lebanon 41Macedonia, Rep. of 40Qatar 39Romania 38Georgia 38Turkey 37Tunisia 37Bahrain 36Armenia 36Saudi Arabia 33Palestinian Nat’l Auth. 32Morocco 31Jordan 31Syrian Arab Republic 29Indonesia 29Oman 25Iran, Islamic Rep. of 22Ghana 19


Percentcorrect

Massachusetts-USA 82Quebec-CAN 81Minnesota-USA 81North Carolina-USA 75Connecticut-USA 75Indiana-USA 73Alberta-CAN 69Ontario-CAN 68Colorado-USA 66California-USA 66Florida-USA 60Dubai-UAE 52Abu Dhabi-UAE 44Alabama-USA 44




Content Domain

NUMBER

Main Topic


Cognitive Domain

Applying

Equivalent expression

The fractions and are equivalent.

What is the value of ?

A. 6

B. 7

C. 11

D. 14


Correct Response: A



Korea, Rep. of 88Singapore 83Chinese Taipei-CHN 82Hong Kong-CHN 78Japan 66Israel 63Russian Federation 62Slovenia 56United States 55Finland 55United Arab Emirates 54Lithuania 54Saudi Arabia 54Armenia 53Kazakhstan 53Sweden 52Romania 51Lebanon 51International average 50Malaysia 49Hungary 49Italy 48Chile 47Macedonia, Rep. of 45Australia 45Ukraine 44England-GBR 43Qatar 43Palestinian Nat’l Auth. 43Syrian Arab Republic 42Tunisia 42Bahrain 42New Zealand 41Norway 40Turkey 40Georgia 39Oman 39Thailand 38Iran, Islamic Rep. of 35Jordan 34Morocco 34Ghana 32Indonesia 31


Percentcorrect

North Carolina-USA 79Quebec-CAN 74Minnesota-USA 71Massachusetts-USA 68Florida-USA 59Connecticut-USA 57Colorado-USA 56Indiana-USA 54Dubai-UAE 54Ontario-CAN 54Alberta-CAN 53California-USA 49Abu Dhabi-UAE 46Alabama-USA 43




Content Domain

NUMBER

Main Topic


Cognitive Domain

Knowing

Equivalent fraction for 0.125

Which fraction is equivalent to 0.125?

A.

B.

C.

D.


Correct Response: B



Korea, Rep. of 97Singapore 93Chinese Taipei-CHN 91Lebanon 89Hong Kong-CHN 87Russian Federation 86Slovenia 80Japan 80Kazakhstan 79Finland 78United States 76Tunisia 75Lithuania 75Hungary 74Malaysia 73Italy 73Sweden 73Armenia 72Israel 72Ukraine 70International average 70Palestinian Nat’l Auth. 67United Arab Emirates 67Morocco 67Australia 67Romania 66Jordan 66Saudi Arabia 65Georgia 64Thailand 64England-GBR 62Macedonia, Rep. of 62Bahrain 61Qatar 59Turkey 59Iran, Islamic Rep. of 58New Zealand 58Norway 58Syrian Arab Republic 56Chile 54Oman 54Indonesia 53Ghana 46


Percentcorrect

North Carolina-USA 85Massachusetts-USA 84Indiana-USA 83Quebec-CAN 82Minnesota-USA 81Connecticut-USA 80Alberta-CAN 78Florida-USA 76California-USA 73Ontario-CAN 73Colorado-USA 71Dubai-UAE 69Abu Dhabi-UAE 67Alabama-USA 66




Content Domain

NUMBER

Main Topic


Cognitive Domain

Applying

Length of the original pipe

A workman cut off of a pipe. Th e piece he cut off was 3 meters long.

How many meters long was the original pipe?

A. 8 m

B. 12 m

C. 15 m

D. 18 m

15


Correct Response: C



Korea, Rep. of 96Japan 94Chinese Taipei-CHN 92Singapore 92Finland 90Hong Kong-CHN 90Sweden 89Italy 88Russian Federation 85Norway 84Slovenia 81Lithuania 81Israel 80Australia 79England-GBR 79New Zealand 79United States 73Iran, Islamic Rep. of 72Kazakhstan 72Ukraine 71Turkey 71Hungary 71International average 70Armenia 69Thailand 64Malaysia 63Macedonia, Rep. of 63Tunisia 60United Arab Emirates 60Romania 59Palestinian Nat’l Auth. 58Chile 58Georgia 58Indonesia 56Jordan 53Bahrain 53Qatar 52Lebanon 52Ghana 51Syrian Arab Republic 51Oman 49Saudi Arabia 44Morocco 43


Percentcorrect

Massachusetts-USA 88Quebec-CAN 88Alberta-CAN 85Minnesota-USA 84North Carolina-USA 82Ontario-CAN 80Connecticut-USA 79Colorado-USA 77Indiana-USA 76California-USA 70Florida-USA 69Dubai-UAE 68Alabama-USA 60Abu Dhabi-UAE 55




Content Domain

NUMBER

Main Topic

Ratio,ProportionandPercent

Cognitive Domain

Knowing

Completethemissingboxes

Peter, James, and Andrew each had 20 tries at throwing balls into a basket.

Complete the missing boxes below.

Name Number of Successful Shots

Percentage of Successful Shots

Peter 10 out of 20 50 %

James 15 out of 20

Andrew out of 20 80%


SCORINGCorrect Response• 75and16,bothcorrect

Partially Correct Response• Only75correct• Only16correct

Incorrect Response• Incorrect(includingcrossedout,erased,straymarks,illegible,orofftask)



Singapore 89Korea, Rep. of 76Hong Kong-CHN 76Chinese Taipei-CHN 69Japan 57Israel 57Russian Federation 55United States 54Australia 53Lithuania 53Sweden 51Finland 50Slovenia 49England-GBR 48New Zealand 46Hungary 46Italy 46Norway 42Malaysia 42International average 37United Arab Emirates 37Kazakhstan 36Lebanon 35Armenia 34Turkey 33Ukraine 33Romania 26Chile 26Qatar 24Macedonia, Rep. of 22Bahrain 22Iran, Islamic Rep. of 22Indonesia 20Georgia 20Tunisia 19Thailand 18Palestinian Nat’l Auth. 18Syrian Arab Republic 17Saudi Arabia 12Morocco 11Jordan 11Oman 10Ghana 8


Percentcorrect

Quebec-CAN 81Massachusetts-USA 79Minnesota-USA 77Alberta-CAN 75Ontario-CAN 68North Carolina-USA 62Connecticut-USA 59Indiana-USA 59Florida-USA 58Colorado-USA 51Dubai-UAE 46California-USA 41Abu Dhabi-UAE 34Alabama-USA 31




Completethemissingboxes(continued)M042059


Peter, James, and Andrew each had 20 tries at throwing balls into a basket.





James 15 out of 20


Partially Correct Response:Peter, James, and Andrew each had 20 tries at throwing balls into a basket.





James 15 out of 20


Incorrect Response:Peter, James, and Andrew each had 20 tries at throwing balls into a basket.





James 15 out of 20




Content Domain

NUMBER

Main Topic

Integers

Cognitive Domain

Reasoning

Next line in the pattern

Here is a pattern:

3 – 3 = 0

3 – 2 = 1

3 – 1 = 2

3 – 0 = 3

What will the next line in the pattern be?

Answer: _______________


SCORINGCorrect Response• 3–(–1)=4or3+1=4




Singapore 80Hong Kong-CHN 80Chinese Taipei-CHN 79Korea, Rep. of 74Japan 70Israel 67Russian Federation 61United States 58Armenia 58Australia 57England-GBR 57Hungary 52Slovenia 51New Zealand 50United Arab Emirates 49Finland 49Lithuania 48Romania 45International average 42Italy 42Kazakhstan 42Bahrain 41Ukraine 40Macedonia, Rep. of 40Jordan 39Norway 39Sweden 34Malaysia 33Turkey 33Qatar 30Georgia 27Oman 27Lebanon 27Iran, Islamic Rep. of 24Thailand 24Chile 21Palestinian Nat’l Auth. 21Saudi Arabia 21Tunisia 17Syrian Arab Republic 16Ghana 14Morocco 12Indonesia 4


Percentcorrect

Minnesota-USA 74Massachusetts-USA 72North Carolina-USA 69Quebec-CAN 65Indiana-USA 64Florida-USA 62California-USA 59Ontario-CAN 58Alberta-CAN 57Connecticut-USA 55Colorado-USA 55Dubai-UAE 54Abu Dhabi-UAE 47Alabama-USA 42




Next line in the pattern (continued)M042186


Incorrect Response:



Content Domain

NUMBER

Main Topic

WholeNumbers

Cognitive Domain

Applying

Packingeggsintoboxes

Kim is packing eggs into boxes.

Each box holds 6 eggs.

She has 94 eggs.

What is the smallest number of boxes she needs to pack all the eggs?

Answer: ______________ boxes



Incorrect Response

• 15OR15.6OR15.67OR15.7OR152/3

• Otherincorrect(includingcrossedout,erased,straymarks,illegible,orofftask)



Hong Kong-CHN 89Chinese Taipei-CHN 86Japan 75Korea, Rep. of 74Finland 66Singapore 64Lithuania 62England-GBR 61Sweden 58Hungary 58United States 56Norway 56Slovenia 54Russian Federation 54Kazakhstan 54Australia 53Ukraine 46New Zealand 46Israel 45International average 41Armenia 39Georgia 37Italy 35Romania 33Thailand 33United Arab Emirates 32Turkey 31Malaysia 29Chile 29Macedonia, Rep. of 27Lebanon 24Bahrain 23Tunisia 23Qatar 22Iran, Islamic Rep. of 22Indonesia 21Saudi Arabia 21Jordan 17Morocco 15Palestinian Nat’l Auth. 14Oman 14Syrian Arab Republic 13Ghana 12


Percentcorrect

Minnesota-USA 76Massachusetts-USA 76Indiana-USA 72Quebec-CAN 72North Carolina-USA 69Colorado-USA 63Florida-USA 62Ontario-CAN 61Alberta-CAN 59Connecticut-USA 58Alabama-USA 48California-USA 38Dubai-UAE 35Abu Dhabi-UAE 32




Content Domain

NUMBER

Main Topic


Cognitive Domain

Knowing

Whichnumbersentenceistrue

Which of these number sentences is true?

A. 3

10 of 50 = 50% of 3

B. 3% of 50 = 6% of 100

C. 50 ÷ 30 = 30 ÷ 50

D. 3

10 × 50 = 5

10× 30


Correct Response: D



Chinese Taipei-CHN 74Korea, Rep. of 68Singapore 67Hong Kong-CHN 63Russian Federation 58Hungary 53Japan 52Armenia 51Malaysia 50Lebanon 47Israel 46Ghana 44Lithuania 43Romania 43Kazakhstan 43Indonesia 41International average 41Turkey 40Georgia 40United Arab Emirates 40Iran, Islamic Rep. of 39Ukraine 38Thailand 38Palestinian Nat’l Auth. 38Qatar 37Italy 36Australia 36United States 36Morocco 34Oman 34Jordan 34Tunisia 33England-GBR 33Macedonia, Rep. of 32Finland 32Saudi Arabia 31Bahrain 31Slovenia 31Syrian Arab Republic 27New Zealand 27Chile 25Sweden 24Norway 23


Percentcorrect

North Carolina-USA 56Massachusetts-USA 46Dubai-UAE 44Minnesota-USA 43Indiana-USA 41Florida-USA 40Quebec-CAN 39Abu Dhabi-UAE 37California-USA 34Connecticut-USA 33Alberta-CAN 32Ontario-CAN 29Alabama-USA 29Colorado-USA 25




Content Domain

NUMBER

Main Topic


Cognitive Domain

Knowing

Selectthedecimalequalto3/5

Which number is equal to 35

?

A. 0.8

B. 0.6

C. 0.53

D. 0.35


Correct Response: B



Singapore 96Korea, Rep. of 96Lebanon 93Hong Kong-CHN 89Chinese Taipei-CHN 89Japan 86Russian Federation 84Sweden 83United States 83Kazakhstan 82Armenia 80United Arab Emirates 77Tunisia 75Lithuania 74Israel 74Italy 72Saudi Arabia 72Morocco 71Slovenia 71Australia 70Finland 69Qatar 69Romania 69International average 68Ukraine 68Hungary 67Palestinian Nat’l Auth. 66Macedonia, Rep. of 65Malaysia 65Georgia 65Norway 63Oman 60England-GBR 59New Zealand 56Bahrain 54Syrian Arab Republic 52Indonesia 50Thailand 50Jordan 49Turkey 48Chile 39Ghana 39Iran, Islamic Rep. of 38


Percentcorrect

North Carolina-USA 94Florida-USA 91Minnesota-USA 90Massachusetts-USA 89Quebec-CAN 87Indiana-USA 86Connecticut-USA 84Alberta-CAN 83Colorado-USA 80Dubai-UAE 77California-USA 77Abu Dhabi-UAE 74Ontario-CAN 73Alabama-USA 72




Content Domain

NUMBER

Main Topic


Cognitive Domain

Applying

Methodforsubtractingfractions

Which shows a correct method for fi nding 13

14

?

A. 1 - 14 - 3

B.1

4 - 3

C.3 - 43 × 4

D.4 - 33 × 4

—


Correct Response: D



Korea, Rep. of 86Singapore 83Chinese Taipei-CHN 82Hong Kong-CHN 77Japan 65Russian Federation 63Armenia 56Italy 51Kazakhstan 50Lebanon 49Malaysia 46Israel 45Ukraine 41United Arab Emirates 38Turkey 37International average 37Romania 36Palestinian Nat’l Auth. 35Australia 34Jordan 33Hungary 33Georgia 33Slovenia 30Thailand 29United States 29Lithuania 28England-GBR 28Saudi Arabia 28Iran, Islamic Rep. of 27New Zealand 26Macedonia, Rep. of 25Oman 24Qatar 24Bahrain 24Indonesia 21Tunisia 21Morocco 21Ghana 19Norway 19Syrian Arab Republic 18Finland 16Sweden 14Chile 12


Percentcorrect

Massachusetts-USA 44Dubai-UAE 43Abu Dhabi-UAE 40California-USA 38Minnesota-USA 35North Carolina-USA 35Colorado-USA 34Quebec-CAN 33Ontario-CAN 33Connecticut-USA 31Florida-USA 29Indiana-USA 29Alberta-CAN 28Alabama-USA 21




Content Domain

NUMBER

Main Topic


Cognitive Domain

Knowing

Add42.65to5.748

42.65 + 5.748 =

Answer: _____________


SCORINGCorrect Response• 48.398

Incorrect Response• 10,013withdecimalpointinsertedanywhereorwithoutdecimal•Otherincorrect(includingcrossedout,erased,straymarks,illegible,orofftask)



Singapore 94Malaysia 91Hong Kong-CHN 91Kazakhstan 90Lithuania 90Russian Federation 90Chinese Taipei-CHN 89United States 89Hungary 88Italy 88Korea, Rep. of 87Slovenia 85Armenia 84Tunisia 82Israel 82Australia 82Norway 81Lebanon 81Japan 81Ukraine 80United Arab Emirates 79Sweden 79England-GBR 79Finland 79International average 72Morocco 72Qatar 72New Zealand 70Romania 69Saudi Arabia 65Macedonia, Rep. of 65Georgia 64Thailand 64Chile 58Indonesia 57Palestinian Nat’l Auth. 56Oman 49Turkey 48Bahrain 43Iran, Islamic Rep. of 42Jordan 36Ghana 36Syrian Arab Republic 31


Percentcorrect

Massachusetts-USA 95Minnesota-USA 93Florida-USA 93Alabama-USA 92Connecticut-USA 91Indiana-USA 90North Carolina-USA 90Quebec-CAN 90California-USA 89Alberta-CAN 86Ontario-CAN 85Colorado-USA 82Abu Dhabi-UAE 81Dubai-UAE 80




Content Domain

NUMBER

Main Topic

AlgebraicExpressions

Cognitive Domain

Applying

Sumof3consecutivewholenumbers

What is the sum of the three consecutive whole numbers with 2n as the middle number?

A. 6n + 3

B. 6n

C. 6n − 1

D. 6n − 3


Correct Response: B



Korea, Rep. of 78Chinese Taipei-CHN 76Finland 70Hong Kong-CHN 69Japan 68Singapore 64Lithuania 63Romania 62Israel 57Kazakhstan 57Italy 56Lebanon 56Hungary 56Morocco 55Syrian Arab Republic 55Georgia 54Russian Federation 53Tunisia 52Palestinian Nat’l Auth. 52International average 52Thailand 52Armenia 51Turkey 51Ukraine 49Iran, Islamic Rep. of 49Macedonia, Rep. of 48Jordan 48Ghana 47England-GBR 46Sweden 46Indonesia 46Australia 45Malaysia 45United Arab Emirates 44Bahrain 44New Zealand 43Oman 40Chile 40Saudi Arabia 39Norway 39Slovenia 39United States 37Qatar 36


Percentcorrect

Quebec-CAN 61Massachusetts-USA 54North Carolina-USA 47Abu Dhabi-UAE 45Ontario-CAN 44Alberta-CAN 43Connecticut-USA 43Dubai-UAE 43Minnesota-USA 40Florida-USA 38Colorado-USA 36California-USA 36Alabama-USA 35Indiana-USA 34




Content Domain

ALGEBRA

Main Topic


Cognitive Domain

Knowing

mboysandngirlsinaparade

Th ere were m boys and n girls in a parade. Each person carried 2 balloons. Which of these expressions represents the total number of balloons that were carried in the parade?

A. 2(m + n)

B. 2 + (m + n)

C. 2m + n

D. m + 2n


Correct Response: A



Singapore 95Hong Kong-CHN 94Chinese Taipei-CHN 93Korea, Rep. of 91Japan 90Russian Federation 90United States 88Lebanon 86Lithuania 86Slovenia 85Israel 82Finland 82Italy 82Ukraine 81Hungary 80Romania 77Kazakhstan 76United Arab Emirates 75England-GBR 74Australia 73International average 73Georgia 72Malaysia 71New Zealand 71Tunisia 70Armenia 69Macedonia, Rep. of 67Jordan 67Qatar 65Sweden 65Indonesia 63Turkey 62Iran, Islamic Rep. of 62Thailand 62Bahrain 62Palestinian Nat’l Auth. 62Chile 60Ghana 60Norway 59Morocco 58Oman 58Syrian Arab Republic 48Saudi Arabia 48


Percentcorrect

Massachusetts-USA 92California-USA 91Minnesota-USA 91North Carolina-USA 90Quebec-CAN 90Florida-USA 87Indiana-USA 87Connecticut-USA 83Dubai-UAE 83Colorado-USA 82Alabama-USA 81Alberta-CAN 76Ontario-CAN 76Abu Dhabi-UAE 75




Content Domain

ALGEBRA

Main Topic

Patterns

Cognitive Domain

Applying

Theshadowlengthsoffourbushes

Bush height (cm)

Shadow length (cm)

20 1640 3260 4880 64

Th e table above shows the shadow lengths of four bushes of diff erent heights at 10 a.m. What is the shadow length at 10 a.m. of a bush that has a height of 50 centimeters?

A. 36 cm

B. 38 cm

C. 40 cm

D. 42 cm


Correct Response: C



Korea, Rep. of 86Singapore 84Chinese Taipei-CHN 83Japan 82Hong Kong-CHN 80Russian Federation 72England-GBR 72Slovenia 70United States 69Australia 69Finland 68Israel 67New Zealand 66Italy 66Lithuania 65Hungary 65Sweden 64Malaysia 63International average 60Norway 59Thailand 59United Arab Emirates 59Ukraine 58Kazakhstan 57Turkey 56Lebanon 56Romania 54Chile 54Bahrain 53Armenia 52Qatar 52Ghana 51Iran, Islamic Rep. of 51Indonesia 51Morocco 49Macedonia, Rep. of 49Jordan 49Georgia 48Saudi Arabia 47Palestinian Nat’l Auth. 47Syrian Arab Republic 47Oman 46Tunisia 44


Percentcorrect

Massachusetts-USA 81Minnesota-USA 80Quebec-CAN 74North Carolina-USA 74Connecticut-USA 71Florida-USA 71Colorado-USA 70Ontario-CAN 69Indiana-USA 68California-USA 67Alberta-CAN 65Dubai-UAE 64Alabama-USA 62Abu Dhabi-UAE 57




Content Domain

ALGEBRA

Main Topic


Cognitive Domain

Knowing

Which represents 2x plus 3x

Which of these could represent the expression 2x + 3x?

A. Th e length of this segment:

B. Th e length of this segment:

C. Th e area of this fi gure:

D. Th e area of this fi gure:

x 5

x2 3

x

2 3

5

x x


Correct Response: C



Chinese Taipei-CHN 81Singapore 73Japan 73Hong Kong-CHN 72Korea, Rep. of 71Russian Federation 63Israel 58Lithuania 57Finland 55United States 53Hungary 51England-GBR 49Turkey 49Slovenia 49Australia 47International average 44Malaysia 43Ukraine 42New Zealand 42Kazakhstan 41Sweden 40Armenia 40United Arab Emirates 40Qatar 39Palestinian Nat’l Auth. 39Macedonia, Rep. of 39Lebanon 38Georgia 38Chile 38Norway 37Romania 35Bahrain 35Oman 33Iran, Islamic Rep. of 33Indonesia 33Tunisia 32Thailand 32Italy 31Jordan 31Morocco 30Saudi Arabia 29Syrian Arab Republic 28Ghana 25


Percentcorrect

Colorado-USA 66Minnesota-USA 64Massachusetts-USA 63Connecticut-USA 61North Carolina-USA 59California-USA 58Alberta-CAN 55Quebec-CAN 53Indiana-USA 51Florida-USA 50Ontario-CAN 47Alabama-USA 45Dubai-UAE 44Abu Dhabi-UAE 36




Content Domain

ALGEBRA

Main Topic

Equations/Formulasand Functions

Cognitive Domain

Reasoning

Johas3metalblockstoweigh

Jo has three metal blocks. Th e weight of each block is the same. When she weighed one block against 8 grams, this is what happened.

When she weighed all three blocks against 20 grams, this is what happened.

Which of the following could be the weight of one metal block?

A. 5 g

B. 6 g

C. 7 g

D. 8 g

1g

1g

1g

5g

10g 10g


Correct Response: C



Korea, Rep. of 79Japan 76Singapore 75Finland 74Chinese Taipei-CHN 74Hong Kong-CHN 68Russian Federation 67England-GBR 62Australia 62Sweden 62Lithuania 61Hungary 58Slovenia 58Israel 58United States 57New Zealand 57Norway 55Ukraine 54Italy 51Georgia 50Turkey 47International average 47Thailand 46Chile 45Kazakhstan 43Romania 40Armenia 38United Arab Emirates 37Iran, Islamic Rep. of 37Malaysia 36Macedonia, Rep. of 35Lebanon 34Jordan 33Tunisia 32Qatar 32Bahrain 30Palestinian Nat’l Auth. 26Saudi Arabia 24Syrian Arab Republic 22Oman 22Morocco 18Indonesia 18Ghana 9


Percentcorrect

Massachusetts-USA 69Quebec-CAN 67Minnesota-USA 66Connecticut-USA 61Indiana-USA 61North Carolina-USA 60Florida-USA 60Alberta-CAN 59Colorado-USA 59Ontario-CAN 59California-USA 49Dubai-UAE 48Alabama-USA 42Abu Dhabi-UAE 35




Content Domain

ALGEBRA

Main Topic


Cognitive Domain

Knowing

Costinzedsfortaxitripofnkm

Th e taxi company has a basic charge of 25 zeds and a charge of 0.2 zeds for each kilometer the taxi is driven. Which of these represents the cost in zeds to hire a taxi for a trip of n kilometers?

A. 25 + 0.2n

B. 25 × 0.2n

C. 0.2 × (25 + n)

D. 0.2 × 25 + n


Correct Response: A



Chinese Taipei-CHN 77Singapore 76Hong Kong-CHN 70Russian Federation 70Israel 66Korea, Rep. of 65Lithuania 62United States 61Slovenia 56Japan 55Norway 53Ukraine 52Tunisia 52Italy 50Hungary 50Finland 49Georgia 49Macedonia, Rep. of 49Sweden 48Australia 47United Arab Emirates 47New Zealand 46International average 46England-GBR 45Kazakhstan 44Jordan 44Armenia 43Romania 43Oman 40Turkey 39Saudi Arabia 36Bahrain 36Palestinian Nat’l Auth. 35Syrian Arab Republic 33Qatar 32Lebanon 32Iran, Islamic Rep. of 31Morocco 30Chile 29Malaysia 28Ghana 28Indonesia 24Thailand 24


Percentcorrect

Massachusetts-USA 82North Carolina-USA 73Minnesota-USA 72Florida-USA 66Colorado-USA 65Indiana-USA 65Quebec-CAN 64Connecticut-USA 64California-USA 60Ontario-CAN 57Alberta-CAN 56Dubai-UAE 50Abu Dhabi-UAE 45Alabama-USA 42




Content Domain

ALGEBRA

Main Topic


Cognitive Domain

Knowing

Findthevalueofywhentis9

Use the formula to fi nd the value of y when t = 9.

Answer: _______________



Incorrect Response• 10• Otherincorrect(includingcrossedout,erased,straymarks,illegible,orofftask)



Singapore 84Chinese Taipei-CHN 82Russian Federation 80Korea, Rep. of 74Hong Kong-CHN 73Japan 69Kazakhstan 66Ukraine 58Israel 57Lithuania 56United States 55Italy 54Armenia 54Finland 54Slovenia 53Hungary 51Macedonia, Rep. of 50Romania 47Australia 47England-GBR 45International average 43Lebanon 42United Arab Emirates 39Georgia 39New Zealand 32Tunisia 31Malaysia 31Qatar 30Turkey 29Palestinian Nat’l Auth. 29Bahrain 28Jordan 26Indonesia 24Norway 24Thailand 24Syrian Arab Republic 23Iran, Islamic Rep. of 22Oman 21Saudi Arabia 20Chile 16Ghana 16Morocco 11Sweden —


Percentcorrect

Massachusetts-USA 74Minnesota-USA 70North Carolina-USA 65Indiana-USA 63California-USA 59Florida-USA 58Connecticut-USA 55Colorado-USA 54Quebec-CAN 51Dubai-UAE 49Ontario-CAN 47Alabama-USA 44Alberta-CAN 40Abu Dhabi-UAE 37


—Notapplicable



Findthevalueofywhentis9(continued)M032538


Answer: ________________

Incorrect Response:

Answer: ________________



Content Domain

ALGEBRA

Main Topic


Cognitive Domain

Knowing

Iftisanumberbetween6and9

If t is a number between 6 and 9, then t + 5 is between what two numbers?

A. 1 and 4

B. 10 and 13

C. 11 and 14

D. 30 and 45


Correct Response: C



Korea, Rep. of 87Chinese Taipei-CHN 81Singapore 80Hong Kong-CHN 78Japan 75Hungary 64England-GBR 64United States 61Russian Federation 61Australia 59Slovenia 56New Zealand 55Italy 54Sweden 53Finland 52Georgia 49Israel 49Romania 48International average 47Turkey 47Ukraine 44Lithuania 43Thailand 43United Arab Emirates 41Lebanon 40Malaysia 39Jordan 39Chile 39Qatar 38Kazakhstan 38Norway 37Iran, Islamic Rep. of 36Tunisia 35Macedonia, Rep. of 34Palestinian Nat’l Auth. 34Armenia 33Bahrain 33Saudi Arabia 33Syrian Arab Republic 32Oman 31Morocco 27Indonesia 24Ghana 21


Percentcorrect

Massachusetts-USA 76North Carolina-USA 71Minnesota-USA 70Quebec-CAN 67Indiana-USA 66Colorado-USA 64Connecticut-USA 63Florida-USA 60Ontario-CAN 58Alberta-CAN 57California-USA 52Alabama-USA 51Dubai-UAE 48Abu Dhabi-UAE 40




Content Domain

ALGEBRA

Main Topic


Cognitive Domain

Knowing

Simplify3x/8plusx/4plusx/2

Simplify the expression . Show your work.

Answer: ______________________________


SCORINGCorrect Response

•98x or

118x withworkshown

Partially Correct Response

•98x or

118x withnoworkshown

•Anytwotermscombinedcorrectlyorthreetermswithacommondenominator

Incorrect Response

•

• Anyotherexpressioninvolving5x or 14• Otherincorrect(includingcrossedout,erased,straymarks,illegible,orofftask)



Singapore 75Chinese Taipei-CHN 63Japan 63Korea, Rep. of 61Hong Kong-CHN 53Lebanon 44Kazakhstan 41Armenia 41Russian Federation 35Hungary 34Ukraine 33Romania 29Georgia 28Italy 27Jordan 26Turkey 25Malaysia 25International average 24Palestinian Nat’l Auth. 24Lithuania 22United States 19Israel 19Syrian Arab Republic 19United Arab Emirates 18Slovenia 18Tunisia 18Australia 14Macedonia, Rep. of 14Iran, Islamic Rep. of 11Qatar 11Bahrain 11Ghana 11Thailand 11Indonesia 10Oman 9Finland 9England-GBR 9Morocco 8New Zealand 8Saudi Arabia 8Norway 6Sweden 5Chile 4


Percentcorrect

Dubai-UAE 30Massachusetts-USA 29Quebec-CAN 29California-USA 28Minnesota-USA 25Connecticut-USA 20Indiana-USA 19North Carolina-USA 18Colorado-USA 17Florida-USA 15Abu Dhabi-UAE 15Ontario-CAN 9Alabama-USA 6Alberta-CAN 3




Simplify3x/8plusx/4plusx/2(continued)M032683

Student ResponsesCorrect Response:Simplify the expression . Show your work.

Answer: ______________________________

Partially Correct Response:Simplify the expression . Show your work.

Answer: ______________________________

Incorrect Response:Simplify the expression . Show your work.

Answer: ______________________________



Content Domain

ALGEBRA

Main Topic


Cognitive Domain

Knowing

What does xy plus 1 mean

What does xy + 1 mean?

A. Add 1 to y, then multiply by x.

B. Multiply x and y by 1.

C. Add x to y, then add 1.

D. Multiply x by y, then add 1.


Correct Response: D



Hong Kong-CHN 94Korea, Rep. of 91Singapore 91Chinese Taipei-CHN 90Russian Federation 89Japan 87Ukraine 81United States 80Armenia 79Slovenia 76Lithuania 75Israel 74Kazakhstan 73Hungary 73Finland 72England-GBR 72Georgia 71Australia 71Jordan 69United Arab Emirates 66International average 65Italy 65Romania 65Macedonia, Rep. of 63Bahrain 62New Zealand 60Thailand 60Lebanon 59Turkey 58Chile 58Saudi Arabia 57Palestinian Nat’l Auth. 56Qatar 55Iran, Islamic Rep. of 55Sweden 53Tunisia 49Indonesia 48Syrian Arab Republic 48Oman 47Malaysia 43Morocco 41Ghana 36Norway 36


Percentcorrect

Massachusetts-USA 91Minnesota-USA 88Florida-USA 88Indiana-USA 86North Carolina-USA 84Connecticut-USA 83Ontario-CAN 81California-USA 79Alberta-CAN 78Alabama-USA 77Colorado-USA 76Dubai-UAE 72Quebec-CAN 68Abu Dhabi-UAE 63




Content Domain

ALGEBRA

Main Topic

Patterns

Cognitive Domain

Reasoning

Red&BlackTiles_Completetable

Pat has red tiles and black tiles. Pat uses the tiles to make square shapes.

Th e table below shows the number of tiles for the fi rst three shapes Pat made. Pat continued making shapes using this pattern. Complete the table for the 6 × 6 and 7 × 7 shapes.

Shape Number of Black Tiles

Number of Red Tiles

Total Numberof Tiles

3 × 3 1 8 9

4 × 4 4 12 16

5 × 5 9 16 25

6 × 6 16

7 × 7 25

The 3 × 3 shape has 1 black tile and 8 red tiles.

The 4 × 4 shape has 4 black tiles and 12 red tiles.

= Red tile

B

R

= Black tile

R

R

R

R R R

R R RR

R

RB B

B B

B

R R R

R

R R

R

R

Questions for Red and Black Tiles continue.


SCORINGCorrect Response• BothrowscompletelycorrectShape6x6:20,36Shape7x7:24,49

Partially Correct Response• Entriesforonerowcorrectbutnotboth

Incorrect Response• EntriesforonecolumncorrectbutnotbothRedTiles:20,24ORTotalTiles:36,49•Otherincorrect(includingcrossedout,erased,straymarks,illegible,orofftask)



Korea, Rep. of 90Japan 86Singapore 86Chinese Taipei-CHN 85Hong Kong-CHN 79Russian Federation 67Hungary 66Italy 64Israel 63England-GBR 63Slovenia 61Finland 60Australia 59New Zealand 58Lebanon 57Lithuania 57United Arab Emirates 57United States 57Kazakhstan 54International average 54Malaysia 54Turkey 52Sweden 51Iran, Islamic Rep. of 50Ukraine 50Bahrain 50Qatar 48Tunisia 48Chile 46Thailand 45Saudi Arabia 45Palestinian Nat’l Auth. 45Jordan 44Norway 42Romania 41Indonesia 40Georgia 40Morocco 39Oman 37Armenia 37Macedonia, Rep. of 35Ghana 31Syrian Arab Republic 29


Percentcorrect

Massachusetts-USA 78Minnesota-USA 69Ontario-CAN 69Colorado-USA 69North Carolina-USA 68Quebec-CAN 66Alberta-CAN 63Dubai-UAE 62Indiana-USA 58Florida-USA 58Connecticut-USA 57Abu Dhabi-UAE 55California-USA 53Alabama-USA 37




Red&BlackTiles_Completetable(continued)M032757





Number of Red Tiles


3 × 3 1 8 9

4 × 4 4 12 16

5 × 5 9 16 25

6 × 6 16

7 × 7 25



= Red tile

B

R

= Black tile

R

R

R

R R R

R R RR

R

RB B

B B

B

R R R

R

R R

R

R


Partially Correct Response:




Number of Red Tiles


3 × 3 1 8 9

4 × 4 4 12 16

5 × 5 9 16 25

6 × 6 16

7 × 7 25



= Red tile

B

R

= Black tile

R

R

R

R R R

R R RR

R

RB B

B B

B

R R R

R

R R

R

R

Questions for Red and Black Tiles continue.Incorrect Response:




Number of Red Tiles


3 × 3 1 8 9

4 × 4 4 12 16

5 × 5 9 16 25

6 × 6 16

7 × 7 25



= Red tile

B

R

= Black tile

R

R

R

R R R

R R RR

R

RB B

B B

B

R R R

R

R R

R

R




Content Domain

ALGEBRA

Main Topic

Patterns

Cognitive Domain

Reasoning

Red&BlackTiles_Shapewith64tiles

Use the patterns in the previous table to answer the following questions.

A. Pat made a shape with a total of 64 tiles. How many were black and how many were red?

Answer: ____________ black tiles ____________ red tiles

Red and Black Tiles (Continued)

Item Number: M032760A

SCORINGCorrect Response• 36blackand28red

Partially Correct Response• 36black,redincorrect• 28red,blackincorrect

Incorrect Response•Incorrect(includingcrossedout,erased,straymarks,illegible,orofftask)



Chinese Taipei-CHN 75Singapore 74Korea, Rep. of 74Japan 66Hong Kong-CHN 62Russian Federation 42Israel 38England-GBR 38Australia 35United States 34Finland 32Slovenia 32New Zealand 32Hungary 31Italy 31Turkey 28International average 27Sweden 27Lithuania 27Kazakhstan 25United Arab Emirates 24Malaysia 23Thailand 23Qatar 20Iran, Islamic Rep. of 20Ukraine 19Norway 19Bahrain 18Romania 16Lebanon 16Chile 16Georgia 16Macedonia, Rep. of 15Jordan 15Saudi Arabia 14Armenia 14Palestinian Nat’l Auth. 12Tunisia 12Oman 9Indonesia 8Syrian Arab Republic 7Morocco 7Ghana 3


Percentcorrect

Massachusetts-USA 54Minnesota-USA 47Ontario-CAN 46North Carolina-USA 41Quebec-CAN 39Connecticut-USA 37Colorado-USA 37Alberta-CAN 34Dubai-UAE 32Indiana-USA 30Florida-USA 30California-USA 28Abu Dhabi-UAE 22Alabama-USA 16




Content Domain

ALGEBRA

Main Topic

Patterns

Cognitive Domain

Reasoning



B. Pat made a shape that used 49 black tiles. How many red tiles did Pat use in that shape?

Answer: ____________ red tiles


Item Number: M032760B





Singapore 65Chinese Taipei-CHN 60Korea, Rep. of 58Hong Kong-CHN 53Japan 50Russian Federation 33England-GBR 29Australia 26Israel 26Hungary 25New Zealand 25Finland 24United States 24Slovenia 24Italy 22International average 20Sweden 20Lithuania 20Turkey 20Thailand 18Kazakhstan 16Qatar 15Malaysia 15Iran, Islamic Rep. of 15United Arab Emirates 14Norway 13Armenia 13Ukraine 12Romania 11Macedonia, Rep. of 11Bahrain 11Jordan 10Georgia 9Lebanon 9Indonesia 8Saudi Arabia 8Chile 8Palestinian Nat’l Auth. 8Tunisia 7Oman 7Syrian Arab Republic 5Morocco 5Ghana 3


Percentcorrect

Massachusetts-USA 44Ontario-CAN 36North Carolina-USA 35Minnesota-USA 33Colorado-USA 30Quebec-CAN 28Connecticut-USA 28Alberta-CAN 25Indiana-USA 22Dubai-UAE 20Florida-USA 19California-USA 18Abu Dhabi-UAE 13Alabama-USA 11




Content Domain

ALGEBRA

Main Topic

Patterns

Cognitive Domain

Reasoning



C. Next, Pat made a shape using 44 of the red tiles. How many black tiles would Pat need to complete the black part of the shape?

Answer: ____________ black tiles


Item Number: M032760C





Korea, Rep. of 57Chinese Taipei-CHN 55Singapore 53Hong Kong-CHN 39Japan 37Russian Federation 23England-GBR 21Turkey 19Israel 18Australia 17United States 17New Zealand 17Kazakhstan 16Hungary 15International average 15Slovenia 14Finland 13Lithuania 12Sweden 12Italy 11Thailand 10United Arab Emirates 10Malaysia 10Qatar 10Macedonia, Rep. of 9Armenia 9Georgia 8Romania 8Bahrain 8Ukraine 7Norway 7Iran, Islamic Rep. of 7Palestinian Nat’l Auth. 6Jordan 6Lebanon 5Chile 5Saudi Arabia 4Indonesia 4Oman 4Tunisia 3Morocco 2Syrian Arab Republic 1Ghana 1


Percentcorrect

Massachusetts-USA 33Minnesota-USA 28North Carolina-USA 25Ontario-CAN 25Quebec-CAN 21Connecticut-USA 20Colorado-USA 19Alberta-CAN 16Florida-USA 16Dubai-UAE 14California-USA 14Indiana-USA 13Abu Dhabi-UAE 10Alabama-USA 8




Content Domain

ALGEBRA

Main Topic


Cognitive Domain

Reasoning

Red&BlackTiles_Figuren

Pat wanted to add a line to the table showing how to fi nd the number of tiles needed to make a square of any size. Use the patterns in the table on the oppositepage to help you complete the line for shape n × n in the table below.


Number of Red Tiles

Total Number of Tiles

n × n (n – 2)2


SCORINGCorrect Response• BothexpressionscorrectinsimplifiedformRedtiles:4(n–1);4n–4;orcorrectverbalexpressionTotal tiles: n2,nxn;orcorrectverbalexpression,suchas“squarethenumber”or“multiplybyitself”• Bothexpressionscorrectwithexpressionforredtilesintheformoftotalnumberoftilesminusnumberofblacktilese.g.,n2–(n–2)2 or equivalent.

Partially Correct Response• Expressionforredtilescorrectasin20butnotexpressionfortotaltiles• Expressionfortotaltilescorrectasin20butnotexpressionforredtiles

Incorrect Response• Incorrectexpressionincludingnforredtilesortotalorboth(includesincorrectattemptstoexpress

red tiles as difference from total tiles)• Otherincorrect(includingcrossedout,erased,straymarks,illegible,orofftask)



Chinese Taipei-CHN 53Singapore 47Korea, Rep. of 45Hong Kong-CHN 40Japan 36Russian Federation 21Hungary 14Israel 14England-GBR 13Kazakhstan 13Australia 12Turkey 11Slovenia 11International average 11Italy 9New Zealand 9United States 8Finland 7Lithuania 7Ukraine 7Romania 6Lebanon 6Armenia 5United Arab Emirates 5Qatar 5Macedonia, Rep. of 5Thailand 4Sweden 4Georgia 4Iran, Islamic Rep. of 4Bahrain 3Palestinian Nat’l Auth. 3Tunisia 3Malaysia 3Jordan 2Oman 2Morocco 2Norway 2Saudi Arabia 1Syrian Arab Republic 1Chile 1Indonesia 1Ghana 1


Percentcorrect

Massachusetts-USA 24Quebec-CAN 11Colorado-USA 11Connecticut-USA 10Ontario-CAN 9Minnesota-USA 9North Carolina-USA 9California-USA 9Florida-USA 8Dubai-UAE 7Indiana-USA 7Alberta-CAN 7Abu Dhabi-UAE 5Alabama-USA 3




Red&BlackTiles_Figuren(continued)M032761


Pat wanted to add a line to the table showing how to fi nd the number of tiles needed to make a square of any size. Use the patterns in the table on the oppositepage to help you complete the line for shape n × n in the table below.


Number of Red Tiles


n × n (n – 2)2

Partially Correct Response:Pat wanted to add a line to the table showing how to fi nd the number of tiles needed to make a square of any size. Use the patterns in the table on the oppositepage to help you complete the line for shape n × n in the table below.


Number of Red Tiles


n × n (n – 2)2

Incorrect Response:Pat wanted to add a line to the table showing how to fi nd the number of tiles needed to make a square of any size. Use the patterns in the table on the oppositepage to help you complete the line for shape n × n in the table below.


Number of Red Tiles


n × n (n – 2)2



Content Domain

ALGEBRA

Main Topic


Cognitive Domain

Applying

What is the area of the rectangle

What is the area of this rectangle?

A. x2 + 2

B. x2 + 2x

C. 2x + 2

D. 4x + 4

x

x + 2


Correct Response: B



Chinese Taipei-CHN 83Singapore 79Russian Federation 72Hong Kong-CHN 69Korea, Rep. of 67Kazakhstan 55Armenia 55Ukraine 52Israel 49Japan 48Romania 48Georgia 45Turkey 42Lithuania 42Thailand 41International average 40Macedonia, Rep. of 39Lebanon 39United States 37Indonesia 36England-GBR 35Syrian Arab Republic 34Palestinian Nat’l Auth. 34Qatar 33Iran, Islamic Rep. of 33Finland 32Slovenia 32Italy 31Tunisia 30United Arab Emirates 30Hungary 30Bahrain 30Norway 28New Zealand 28Morocco 28Ghana 27Australia 26Malaysia 25Chile 24Sweden 24Saudi Arabia 24Oman 23Jordan 21


Percentcorrect

California-USA 53North Carolina-USA 45Minnesota-USA 44Colorado-USA 44Massachusetts-USA 43Florida-USA 42Dubai-UAE 39Connecticut-USA 38Indiana-USA 34Alberta-CAN 26Abu Dhabi-UAE 25Alabama-USA 25Quebec-CAN 24Ontario-CAN 23




Content Domain

ALGEBRA

Main Topic


Cognitive Domain

Knowing

Expressionequivalentto4(3+x)

Which expression is equivalent to 4(3 + x)?

A. 12 + x

B. 7 + x

C. 12 + 4x

D. 12x


Correct Response: C



Singapore 89Hong Kong-CHN 86Korea, Rep. of 86Chinese Taipei-CHN 85Japan 82Russian Federation 81Lebanon 75Israel 72Ukraine 68Kazakhstan 63Armenia 62Romania 62Lithuania 58Hungary 57United States 53Italy 52Jordan 51International average 51Turkey 50Qatar 49Georgia 49Syrian Arab Republic 48Bahrain 47Oman 46Macedonia, Rep. of 45Finland 44Ghana 42England-GBR 41United Arab Emirates 40Australia 40Morocco 39New Zealand 39Palestinian Nat’l Auth. 38Tunisia 37Malaysia 37Iran, Islamic Rep. of 36Indonesia 36Slovenia 34Thailand 33Saudi Arabia 28Sweden 24Chile 18Norway 16


Percentcorrect

California-USA 72Minnesota-USA 67Massachusetts-USA 63Dubai-UAE 60North Carolina-USA 59Quebec-CAN 57Florida-USA 55Indiana-USA 54Colorado-USA 48Connecticut-USA 47Alabama-USA 39Abu Dhabi-UAE 35Ontario-CAN 23Alberta-CAN 23




Content Domain

ALGEBRA

Main Topic


Cognitive Domain

Applying

Whatisthevalueof2a+2b+4

a + b = 25. What is the value of 2a + 2b + 4?

Answer: _______________






Singapore 76Chinese Taipei-CHN 75Korea, Rep. of 68Hong Kong-CHN 65Russian Federation 54Hungary 47Sweden 44Japan 43England-GBR 42Israel 42Kazakhstan 40Armenia 36Italy 34Romania 34Australia 34New Zealand 33Slovenia 33United States 33Georgia 33International average 32Lebanon 32Finland 32Lithuania 31Turkey 30Norway 29United Arab Emirates 27Macedonia, Rep. of 27Ukraine 26Chile 22Malaysia 22Palestinian Nat’l Auth. 20Syrian Arab Republic 19Thailand 18Tunisia 17Qatar 17Jordan 16Bahrain 16Morocco 14Oman 13Iran, Islamic Rep. of 13Saudi Arabia 12Indonesia 12Ghana 6


Percentcorrect

Massachusetts-USA 56Minnesota-USA 47North Carolina-USA 42Quebec-CAN 42Ontario-CAN 40Connecticut-USA 38Indiana-USA 37Alberta-CAN 36Colorado-USA 36Dubai-UAE 33California-USA 28Alabama-USA 25Florida-USA 25Abu Dhabi-UAE 24




Whatisthevalueof2a+2b+4(continued)M042086

Student Responses

Correct Response:

Answer:

Incorrect Response:

Answer:



Content Domain

ALGEBRA

Main Topic


Cognitive Domain

Knowing

Solve the inequality

Solve this inequality.

9x – 6 < 4x + 4

Answer: _____________


SCORINGCorrect Response• x<2or2>x Note:5x<10iscodedasincorrect

Incorrect Response• x=2•x>2OR2<x• Otherincorrect(includingcrossedout,erased,straymarks,illegible,orofftask)



Korea, Rep. of 60Chinese Taipei-CHN 52Armenia 47Russian Federation 46Singapore 44Israel 41Lebanon 40Hungary 38Kazakhstan 38Romania 34Macedonia, Rep. of 26Georgia 23Lithuania 23United States 21International average 17Hong Kong-CHN 16Oman 15Bahrain 13Ghana 13Morocco 13Turkey 10Japan 9Jordan 9Finland 8Australia 8United Arab Emirates 7Syrian Arab Republic 7Qatar 6Ukraine 6England-GBR 5Italy 5Palestinian Nat’l Auth. 4Saudi Arabia 4Indonesia 3Malaysia 3New Zealand 2Thailand 2Slovenia 2Norway 1Tunisia 1Chile 1Iran, Islamic Rep. of #Sweden —


Percentcorrect

North Carolina-USA 38California-USA 35Minnesota-USA 33Massachusetts-USA 33Indiana-USA 33Connecticut-USA 22Florida-USA 19Colorado-USA 13Dubai-UAE 10Alabama-USA 9Abu Dhabi-UAE 8Quebec-CAN 1Ontario-CAN 1Alberta-CAN #


—Notapplicable# Rounds to zero



Solve the inequality (continued)M042103



9x – 6 < 4x + 4

Answer: _____________

Incorrect Response:


9x – 6 < 4x + 4

Answer: _____________



Content Domain

ALGEBRA

Main Topic

Patterns

Cognitive Domain

Knowing

Next term in the pattern

, , , ,

A. What is the next term in this pattern?

Answer: _______________


SCORINGCorrect Response•6/7




Japan 94Singapore 94Korea, Rep. of 92Hong Kong-CHN 92Chinese Taipei-CHN 92Finland 91Australia 91Slovenia 90Hungary 90New Zealand 89England-GBR 89Sweden 88Norway 88United States 87Lithuania 86Israel 85Italy 85Ukraine 85Russian Federation 82Romania 81Kazakhstan 78Turkey 77Tunisia 76United Arab Emirates 70International average 70Iran, Islamic Rep. of 68Thailand 68Armenia 66Macedonia, Rep. of 66Bahrain 62Qatar 56Georgia 53Malaysia 53Jordan 45Syrian Arab Republic 44Lebanon 43Ghana 38Oman 37Palestinian Nat’l Auth. 36Saudi Arabia 33Indonesia 32Chile 32Morocco 15


Percentcorrect

Massachusetts-USA 94Quebec-CAN 92Ontario-CAN 92Indiana-USA 91Alberta-CAN 90Colorado-USA 90Minnesota-USA 90North Carolina-USA 89Connecticut-USA 88Florida-USA 87Alabama-USA 87California-USA 86Dubai-UAE 79Abu Dhabi-UAE 68




Next term in the pattern (continued)M042198A


, , , ,


Answer: _______________

Incorrect Response: , , , ,


Answer: _______________



Content Domain

ALGEBRA

Main Topic

Patterns

Cognitive Domain

Reasoning

Termnumber100inthepattern

, , , ,

B. What would term number 100 be?

Answer: _______________


SCORINGCorrect Response• 100/101

Incorrect Response• 99/100• Otherincorrect(includingcrossedout,erased,straymarks,illegible,orofftask)



Singapore 73Chinese Taipei-CHN 72Hong Kong-CHN 68Korea, Rep. of 65Finland 65Lithuania 61Israel 60Hungary 59England-GBR 59Japan 57Slovenia 57Norway 56New Zealand 56Australia 56Ukraine 52United States 50Turkey 49Russian Federation 48Sweden 47Thailand 44Italy 44Romania 43Macedonia, Rep. of 41International average 41United Arab Emirates 37Kazakhstan 36Georgia 36Iran, Islamic Rep. of 34Armenia 30Qatar 30Jordan 29Bahrain 23Tunisia 22Lebanon 22Malaysia 19Syrian Arab Republic 17Chile 17Oman 17Saudi Arabia 16Ghana 12Indonesia 12Palestinian Nat’l Auth. 12Morocco 5


Percentcorrect

Massachusetts-USA 67Ontario-CAN 65Minnesota-USA 61Quebec-CAN 60North Carolina-USA 57Connecticut-USA 56Alberta-CAN 55Colorado-USA 53Indiana-USA 52California-USA 49Florida-USA 48Dubai-UAE 46Alabama-USA 46Abu Dhabi-UAE 34




Termnumber100inthepattern(continued)M042198B


, , , ,


Answer: _______________



Answer: _______________



Content Domain

ALGEBRA

Main Topic

Patterns

Cognitive Domain

Reasoning

Termnumberninthepattern

, , , ,

C. What would term number n be?

Answer: _______________


SCORINGCorrect Response• n/(n+1)

Incorrect Response• (n-1)/n• Otherincorrect(includingcrossedout,erased,straymarks,illegible,orofftask)



Chinese Taipei-CHN 61Singapore 58Hong Kong-CHN 52Korea, Rep. of 50Japan 39Israel 37Russian Federation 35Romania 29Ukraine 25England-GBR 21Hungary 20Kazakhstan 20Turkey 19Armenia 19Georgia 19Slovenia 18International average 18Lithuania 17Macedonia, Rep. of 17Jordan 15Italy 15Syrian Arab Republic 13United States 13United Arab Emirates 12Iran, Islamic Rep. of 11Australia 11New Zealand 11Qatar 11Thailand 10Finland 8Sweden 8Lebanon 7Tunisia 7Oman 6Chile 5Bahrain 5Palestinian Nat’l Auth. 5Norway 4Saudi Arabia 3Morocco 2Malaysia 1Indonesia 1Ghana 1


Percentcorrect

Massachusetts-USA 34Minnesota-USA 24Connecticut-USA 19Dubai-UAE 18North Carolina-USA 18Quebec-CAN 17Colorado-USA 15Ontario-CAN 12California-USA 11Indiana-USA 10Florida-USA 10Abu Dhabi-UAE 10Alberta-CAN 6Alabama-USA 4




Termnumberninthepattern(continued)M042198C

Student ResponsesCorrect Response: , , , ,


Answer: _______________



Answer: _______________



Content Domain

ALGEBRA

Main Topic


Cognitive Domain

Knowing

What is the value P

and . What is the value of P when ?

Answer: _______________






Singapore 88Hong Kong-CHN 87Russian Federation 83Korea, Rep. of 81Chinese Taipei-CHN 77Japan 72United States 70Kazakhstan 69Armenia 62Lebanon 57Ukraine 56Israel 54United Arab Emirates 53Romania 52Lithuania 50Slovenia 49Macedonia, Rep. of 47Australia 46Hungary 46Italy 46International average 44England-GBR 40Qatar 39Georgia 39Bahrain 38Saudi Arabia 37Finland 36Palestinian Nat’l Auth. 36Jordan 35New Zealand 30Turkey 29Oman 28Malaysia 28Syrian Arab Republic 28Iran, Islamic Rep. of 27Indonesia 23Tunisia 22Thailand 21Morocco 17Sweden 16Chile 11Ghana 10Norway 7


Percentcorrect

North Carolina-USA 83Minnesota-USA 83Massachusetts-USA 81Indiana-USA 77Florida-USA 76California-USA 70Alabama-USA 65Connecticut-USA 62Colorado-USA 60Dubai-UAE 57Quebec-CAN 50Abu Dhabi-UAE 49Ontario-CAN 48Alberta-CAN 41




What is the value P (continued)M042226


Answer:

Incorrect Response:

Answer:



Content Domain

ALGEBRA

Main Topic

Patterns

Cognitive Domain

Reasoning

Value of x in the pattern

What is the value of x in this pattern?

Answer: _______________

2 4 6 8

6 10 14

16 x

40






Korea, Rep. of 77Singapore 66Chinese Taipei-CHN 63England-GBR 58Finland 58Japan 57Hong Kong-CHN 55Turkey 51Italy 44Israel 43Hungary 43Norway 42New Zealand 42Australia 41Sweden 40Russian Federation 39Lithuania 38Kazakhstan 38Slovenia 37United States 37Macedonia, Rep. of 36International average 35Chile 35Armenia 33United Arab Emirates 28Romania 28Lebanon 27Ukraine 27Palestinian Nat’l Auth. 27Iran, Islamic Rep. of 27Indonesia 27Thailand 24Georgia 22Tunisia 21Malaysia 20Qatar 19Morocco 18Bahrain 18Oman 15Jordan 15Saudi Arabia 13Syrian Arab Republic 12Ghana 10


Percentcorrect

Massachusetts-USA 50North Carolina-USA 50Quebec-CAN 47Minnesota-USA 45Colorado-USA 43Connecticut-USA 43Ontario-CAN 43Indiana-USA 40Florida-USA 39Alberta-CAN 38California-USA 35Dubai-UAE 33Abu Dhabi-UAE 28Alabama-USA 26




Value of x in the pattern (continued)M042228


Answer:

Incorrect Response:

Answer:



Content Domain

ALGEBRA

Main Topic


Cognitive Domain

Knowing

What is the value of x and y

x + y = 12 and 2x + 5y = 36.

What are the values of x and y?

A. x = 2, y = 10

B. x = 4, y = 8

C. x = 6, y = 6

D. x = 8, y = 4


Correct Response: D



Korea, Rep. of 87Singapore 84Hong Kong-CHN 82Chinese Taipei-CHN 81Japan 79Russian Federation 72United States 70Israel 65Australia 60Finland 58England-GBR 58New Zealand 57Hungary 57Lithuania 56Ukraine 54Armenia 54United Arab Emirates 54Kazakhstan 53Slovenia 53Sweden 52Romania 51Jordan 50International average 50Macedonia, Rep. of 48Georgia 47Turkey 47Italy 47Lebanon 43Qatar 41Malaysia 39Palestinian Nat’l Auth. 39Thailand 37Bahrain 35Iran, Islamic Rep. of 35Saudi Arabia 34Syrian Arab Republic 31Norway 30Oman 30Tunisia 29Chile 25Morocco 20Indonesia 20Ghana 18


Percentcorrect

Massachusetts-USA 82Minnesota-USA 75Indiana-USA 74North Carolina-USA 73California-USA 70Ontario-CAN 67Florida-USA 66Connecticut-USA 63Colorado-USA 62Alberta-CAN 62Quebec-CAN 61Dubai-UAE 58Abu Dhabi-UAE 53Alabama-USA 50




Content Domain

ALGEBRA

Main Topic


Cognitive Domain

Knowing

Simplify the expression

Which of these is equal to 3p2 + 2p + 2p2 + p?

A. 8pB. 8p2

C. 5p2 + 3p

D. 7p2 + p


Correct Response: C



Singapore 93Hong Kong-CHN 88Japan 87Korea, Rep. of 85Chinese Taipei-CHN 84Russian Federation 81Lebanon 70Finland 67Armenia 64Kazakhstan 64Hungary 63Italy 62Lithuania 62Israel 62Slovenia 62Romania 60United States 58England-GBR 57Australia 56Ukraine 56International average 56New Zealand 56Malaysia 51Sweden 51Indonesia 50Qatar 49Turkey 48United Arab Emirates 46Macedonia, Rep. of 46Georgia 45Syrian Arab Republic 45Norway 45Jordan 44Morocco 43Ghana 42Palestinian Nat’l Auth. 42Iran, Islamic Rep. of 41Tunisia 41Thailand 40Bahrain 38Oman 36Chile 35Saudi Arabia 26


Percentcorrect

Quebec-CAN 68California-USA 68North Carolina-USA 68Massachusetts-USA 65Minnesota-USA 64Dubai-UAE 61Colorado-USA 59Indiana-USA 56Connecticut-USA 53Florida-USA 51Alabama-USA 46Abu Dhabi-UAE 41Ontario-CAN 41Alberta-CAN 32




Content Domain

ALGEBRA

Main Topic


Cognitive Domain

Applying

Equationthatsatisfiesnumberpairs

(0, −1), (1, 3)

Which equation is satisfi ed by BOTH of these pairs of numbers (x, y)?

A. x + y = −1

B. 2x + y = 5

C. 3x − y = 0

D. 4x − y = 1


Correct Response: D



Chinese Taipei-CHN 66Korea, Rep. of 64Russian Federation 53Singapore 52Japan 48Hong Kong-CHN 47Israel 38United States 38Turkey 33Romania 31Kazakhstan 31Macedonia, Rep. of 30Ukraine 29Hungary 29Italy 28Armenia 27International average 26Georgia 26Jordan 25England-GBR 24Finland 24Slovenia 24Australia 22United Arab Emirates 22Lithuania 21Qatar 20New Zealand 20Iran, Islamic Rep. of 20Palestinian Nat’l Auth. 19Thailand 19Saudi Arabia 18Ghana 17Oman 17Bahrain 16Malaysia 16Tunisia 15Syrian Arab Republic 15Indonesia 14Chile 11Lebanon 11Morocco 10Norway 10Sweden 8


Percentcorrect

North Carolina-USA 49Massachusetts-USA 45California-USA 43Minnesota-USA 41Indiana-USA 39Connecticut-USA 38Florida-USA 36Colorado-USA 36Alabama-USA 29Dubai-UAE 24Alberta-CAN 24Abu Dhabi-UAE 21Ontario-CAN 20Quebec-CAN 20




Content Domain

ALGEBRA

Main Topic


Cognitive Domain

Applying

Length of the longest wood piece

A piece of wood was 40 cm long.

It was cut into 3 pieces.

Th e lengths in cm are

2x – 5

x + 7

x + 6

A. What is the length of the longest piece?

Answer: ______________ cm

B. Show your work. If you use a calculator, you still must describe all the steps you used to obtain your answer.


SCORINGCorrect Response• 15,with4x+8=40orequivalentalgebraicreasoningshown

Partially Correct Response• 8,withcorrectworkingshownorindicationofx=8withcorrectworking• x+7,withcorrectworkingshownorindicationofx=8• 15,withnumerical(i.e.,non-algebraic)reasoningshown

Incorrect Response• 15orx+7withno/incorrectworkshown• Otherincorrect(includingcrossedout,erased,straymarks,illegible,orofftask)



Singapore 53Chinese Taipei-CHN 50Korea, Rep. of 40Hong Kong-CHN 28Israel 27Hungary 23Russian Federation 22Lithuania 19Ukraine 16Japan 16Turkey 15Finland 11International average 11Armenia 10Georgia 10Romania 9Sweden 8United States 7Australia 7Kazakhstan 7United Arab Emirates 6Bahrain 5Italy 5New Zealand 5Qatar 4Thailand 4Lebanon 4Macedonia, Rep. of 4Slovenia 4Malaysia 3Tunisia 3England-GBR 3Chile 3Syrian Arab Republic 3Palestinian Nat’l Auth. 3Iran, Islamic Rep. of 2Oman 2Jordan 2Saudi Arabia 1Indonesia 1Ghana 1Morocco #Norway #


Percentcorrect

Quebec-CAN 16Massachusetts-USA 16North Carolina-USA 14Minnesota-USA 13Dubai-UAE 10Connecticut-USA 9Indiana-USA 9Florida-USA 9Ontario-CAN 8California-USA 6Colorado-USA 6Abu Dhabi-UAE 5Alberta-CAN 4Alabama-USA 3


# Rounds to zero



Content Domain

ALGEBRA

Main Topic


Cognitive Domain

Applying

Area of garden’s shaded portion

Th is is a diagram of a rectangular garden.

Th e white area is a rectangular path that is 1 meter wide.

Which expression shows the area of the shaded portion of the garden in m2?

A. x2 + 3x

B. x2 + 4x

C. x2 + 4x – 1

D. x2 + 3x – 1

(x + 4) m

1 m

x m path


Correct Response: A



Chinese Taipei-CHN 65Singapore 55Hong Kong-CHN 46Korea, Rep. of 46Japan 27Russian Federation 26Turkey 21Armenia 21Kazakhstan 20Israel 19Macedonia, Rep. of 18International average 16Romania 16England-GBR 15Australia 14Lithuania 14Slovenia 13Italy 13Ukraine 12Georgia 12Malaysia 11Sweden 11Oman 11Palestinian Nat’l Auth. 11New Zealand 10United Arab Emirates 10United States 10Ghana 10Iran, Islamic Rep. of 10Chile 9Syrian Arab Republic 9Saudi Arabia 9Qatar 9Finland 9Tunisia 9Hungary 9Lebanon 9Thailand 8Bahrain 8Jordan 8Indonesia 8Morocco 6Norway —


Percentcorrect

Massachusetts-USA 20Colorado-USA 16Minnesota-USA 15Connecticut-USA 15North Carolina-USA 13Ontario-CAN 11Dubai-UAE 11Indiana-USA 11Florida-USA 10Quebec-CAN 10Abu Dhabi-UAE 10Alberta-CAN 9Alabama-USA 9California-USA 8


—Notapplicable



Content Domain

ALGEBRA

Main Topic


Cognitive Domain

Knowing

Value of y in an expression

y a bc

=+

a = 8, b = 6, and c = 2

What is the value of y?

A. 7

B. 10

C. 11

D. 14


Correct Response: A



Korea, Rep. of 92Chinese Taipei-CHN 91Singapore 91Russian Federation 91United States 89Japan 86Kazakhstan 86Hong Kong-CHN 83Lithuania 83Ukraine 81Hungary 81Armenia 81Italy 80Slovenia 78Finland 78Romania 75Sweden 75England-GBR 73Israel 72Macedonia, Rep. of 71Australia 71International average 71Norway 70Georgia 68Qatar 66Turkey 66Jordan 65Indonesia 65Chile 65Syrian Arab Republic 65United Arab Emirates 64Bahrain 64Tunisia 62New Zealand 61Lebanon 60Palestinian Nat’l Auth. 59Saudi Arabia 57Thailand 56Iran, Islamic Rep. of 51Ghana 49Oman 48Malaysia 47Morocco 45


Percentcorrect

Massachusetts-USA 94Indiana-USA 93Minnesota-USA 92Florida-USA 90California-USA 89North Carolina-USA 89Connecticut-USA 88Alabama-USA 84Colorado-USA 84Ontario-CAN 78Quebec-CAN 75Dubai-UAE 73Alberta-CAN 71Abu Dhabi-UAE 64




Content Domain

GEOMETRY

Main Topic

Geometric Measurement

Cognitive Domain

Applying

Shapemadeupofsamesizecubes

Th e fi gure above shows a shape made up of cubes that are all the same size. Th ere is a hole all the way through the shape. How many cubes would be needed to fi ll the hole?

A. 6

B. 12

C. 15

D. 18


Correct Response: D



Korea, Rep. of 87Chinese Taipei-CHN 84Japan 80Singapore 77Finland 77Hong Kong-CHN 74Australia 72Lithuania 70New Zealand 68England-GBR 66Hungary 65Slovenia 64Russian Federation 63United States 60Norway 58Sweden 57Italy 57Chile 52Ukraine 50Israel 48Turkey 47International average 47Malaysia 40Kazakhstan 39Macedonia, Rep. of 38Thailand 38Romania 38Georgia 35United Arab Emirates 35Armenia 35Iran, Islamic Rep. of 30Qatar 30Oman 28Bahrain 27Saudi Arabia 26Indonesia 24Lebanon 23Palestinian Nat’l Auth. 20Tunisia 20Morocco 19Jordan 19Syrian Arab Republic 14Ghana 11


Percentcorrect

Massachusetts-USA 74Minnesota-USA 72Quebec-CAN 71Indiana-USA 68North Carolina-USA 67Colorado-USA 67Alberta-CAN 67Ontario-CAN 65Connecticut-USA 57Florida-USA 55California-USA 53Alabama-USA 48Dubai-UAE 38Abu Dhabi-UAE 35




Content Domain

GEOMETRY

Main Topic


Cognitive Domain

Applying

Area of a square is 144 square cm

Th e area of a square is 144 cm2. What is the perimeter of the square?

A. 12 cm

B. 48 cm

C. 288 cm

D. 576 cm


Correct Response: B



Singapore 79Chinese Taipei-CHN 75Korea, Rep. of 69Italy 67Hong Kong-CHN 66Russian Federation 62Israel 55Lithuania 53Romania 52Slovenia 51Hungary 49Armenia 48Australia 48Turkey 48Ukraine 47Japan 47Georgia 47England-GBR 47United States 46Norway 46International average 45New Zealand 45Macedonia, Rep. of 45Kazakhstan 45Sweden 44Malaysia 43Finland 42Tunisia 41United Arab Emirates 39Chile 39Iran, Islamic Rep. of 38Palestinian Nat’l Auth. 37Syrian Arab Republic 36Bahrain 36Thailand 35Jordan 34Qatar 33Lebanon 33Oman 32Saudi Arabia 31Morocco 27Ghana 27Indonesia 25


Percentcorrect

Massachusetts-USA 61Colorado-USA 58Indiana-USA 57North Carolina-USA 55Ontario-CAN 54Quebec-CAN 51Connecticut-USA 50Minnesota-USA 48Alberta-CAN 45Dubai-UAE 44Florida-USA 44California-USA 42Alabama-USA 41Abu Dhabi-UAE 36




Content Domain

GEOMETRY

Main Topic

Geometric Shapes

Cognitive Domain

Reasoning

Distancebetweenthemidpoints

Points A, B, and C lie on a line and B is between A and C. If AB = 10 cm andBC = 5.2 cm, what is the distance between the midpoints of AB and BC?

A. 2.4 cm

B. 2.6 cm

C. 5.0 cm

D. 7.6 cm


Correct Response: D



Chinese Taipei-CHN 69Korea, Rep. of 68Singapore 65Japan 63Russian Federation 60Ukraine 50Hong Kong-CHN 48Armenia 48Lithuania 45Georgia 44Finland 44Lebanon 44Kazakhstan 42Hungary 41Sweden 41Slovenia 40Australia 40Italy 39International average 39Romania 38Norway 38England-GBR 38Israel 37Turkey 36Palestinian Nat’l Auth. 35Malaysia 35Macedonia, Rep. of 34Tunisia 33Morocco 32New Zealand 31United Arab Emirates 31Iran, Islamic Rep. of 30Jordan 30United States 29Bahrain 28Syrian Arab Republic 28Saudi Arabia 27Thailand 26Oman 26Qatar 25Chile 25Ghana 19Indonesia 18


Percentcorrect

Quebec-CAN 54Massachusetts-USA 40Ontario-CAN 39Alberta-CAN 38Indiana-USA 35Minnesota-USA 35North Carolina-USA 34Colorado-USA 33Dubai-UAE 32Connecticut-USA 31Abu Dhabi-UAE 30California-USA 29Florida-USA 29Alabama-USA 21




Content Domain

GEOMETRY

Main Topic

Geometric Shapes

Cognitive Domain

Applying

Degreesminutehandofclockturns

How many degrees does a minute hand of a clock turn through from 6:20 a.m. to 8:00 a.m. on the same day?

A. 680°

B. 600°

C. 540°

D. 420°


Correct Response: B



Korea, Rep. of 63Japan 58Singapore 57Chinese Taipei-CHN 56Hong Kong-CHN 51Finland 32Sweden 31England-GBR 31Slovenia 31Morocco 30Hungary 30Syrian Arab Republic 30Palestinian Nat’l Auth. 29International average 29Russian Federation 29Saudi Arabia 28Macedonia, Rep. of 28Turkey 27Israel 27Australia 27New Zealand 26Iran, Islamic Rep. of 26Tunisia 26Malaysia 26Ukraine 25Armenia 25Italy 25Jordan 25Lebanon 24Bahrain 24Romania 23Norway 23Kazakhstan 23United Arab Emirates 23United States 22Qatar 22Oman 21Lithuania 21Ghana 21Georgia 19Indonesia 19Thailand 16Chile —


Percentcorrect

Quebec-CAN 30Minnesota-USA 29Ontario-CAN 26North Carolina-USA 26Massachusetts-USA 25Dubai-UAE 24Connecticut-USA 24Abu Dhabi-UAE 23Indiana-USA 19Alberta-CAN 19Alabama-USA 18Colorado-USA 18Florida-USA 18California-USA 17


—Notapplicable



Content Domain

GEOMETRY

Main Topic

Location and Movement

Cognitive Domain

Knowing

Figure 1 transformed to 2 and 3

Which of these transformations, taken in order, can be used so that Figure 1 above becomes Figure 2 and then Figure 3?

A. refl ection and then translation

B. refl ection and then turn rotation clockwise

C. turn rotation and then translation

D. turn rotation counterclockwise and then refl ection

Figure 1 Figure 2 Figure 3


Correct Response: B



Hong Kong-CHN 84Korea, Rep. of 83Japan 78Chinese Taipei-CHN 69Singapore 67New Zealand 65Hungary 65Australia 63England-GBR 61Finland 59United States 58Turkey 55Sweden 54Russian Federation 52Italy 50Slovenia 48Norway 47International average 43Malaysia 42Lithuania 41United Arab Emirates 40Thailand 38Ukraine 38Israel 37Qatar 33Palestinian Nat’l Auth. 33Iran, Islamic Rep. of 32Oman 32Jordan 32Georgia 32Indonesia 31Kazakhstan 31Romania 31Tunisia 30Bahrain 30Syrian Arab Republic 27Saudi Arabia 27Macedonia, Rep. of 26Chile 24Lebanon 21Armenia 20Ghana 20Morocco 18


Percentcorrect

Ontario-CAN 76Massachusetts-USA 75Alberta-CAN 69Minnesota-USA 69North Carolina-USA 67Connecticut-USA 66Florida-USA 65Indiana-USA 63Quebec-CAN 63Colorado-USA 62Alabama-USA 54California-USA 46Dubai-UAE 43Abu Dhabi-UAE 39




Content Domain

GEOMETRY

Main Topic

Geometric Shapes

Cognitive Domain

Reasoning

Valueofanglexinfigure

In the fi gure above, what is the value of x?

A. 30°

B. 40°

C. 45°

D. 65°

45˚ 30˚

65˚x


Correct Response: B



Singapore 83Japan 81Korea, Rep. of 81Hong Kong-CHN 79Chinese Taipei-CHN 76Russian Federation 58Lebanon 52Kazakhstan 50Italy 50Finland 49Malaysia 49Israel 49Hungary 49Turkey 48Lithuania 46International average 46England-GBR 44Ukraine 43New Zealand 43Australia 43Sweden 43Thailand 42United States 42Ghana 42Armenia 41Saudi Arabia 41Jordan 40Slovenia 40Iran, Islamic Rep. of 39United Arab Emirates 38Indonesia 37Chile 37Norway 36Oman 35Georgia 35Bahrain 33Qatar 33Romania 33Macedonia, Rep. of 33Morocco 32Syrian Arab Republic 32Palestinian Nat’l Auth. 31Tunisia 27


Percentcorrect

Massachusetts-USA 56Quebec-CAN 53Alberta-CAN 50North Carolina-USA 48California-USA 48Minnesota-USA 47Ontario-CAN 43Indiana-USA 43Florida-USA 42Colorado-USA 41Dubai-UAE 41Abu Dhabi-UAE 40Connecticut-USA 39Alabama-USA 38




Content Domain

GEOMETRY

Main Topic

Geometric Shapes

Cognitive Domain

Reasoning

Why PQR is a right angle triangle

Which of these is the reason that triangle PQR is a right angle triangle?

A. 32 + 42 = 52

B. 5 < 3 + 4

C. 3 + 4 = 12 − 5

D. 3 > 5 − 4

3 cm5 cm

4 cm

P

Q R


Correct Response: A



Hong Kong-CHN 87Singapore 79Chinese Taipei-CHN 76Russian Federation 71Lebanon 70Israel 66Lithuania 65Romania 63Ukraine 60United States 59Italy 59Kazakhstan 58Turkey 58Hungary 57Thailand 56Indonesia 55Macedonia, Rep. of 55Palestinian Nat’l Auth. 54United Arab Emirates 53Iran, Islamic Rep. of 52Georgia 52Malaysia 52International average 51Australia 50Armenia 50England-GBR 50Morocco 49Finland 45Jordan 45Saudi Arabia 44Qatar 44Bahrain 42Chile 41Korea, Rep. of 41Syrian Arab Republic 40Oman 34Slovenia 34Ghana 34Norway 33New Zealand 32Japan 27Sweden 23Tunisia 19


Percentcorrect

Massachusetts-USA 74North Carolina-USA 68Minnesota-USA 66Indiana-USA 64Florida-USA 63Colorado-USA 63Alberta-CAN 62Dubai-UAE 56California-USA 55Ontario-CAN 54Alabama-USA 52Connecticut-USA 51Abu Dhabi-UAE 48Quebec-CAN 29




Content Domain

GEOMETRY

Main Topic


Cognitive Domain

Applying

Areaoftheshadedregioninfigure

In the fi gure above, what is the area of the shaded region in cm2?

A. 24

B. 44

C. 48

D. 72

16 cm

6 cm

8 cm


Correct Response: D



Chinese Taipei-CHN 84Hong Kong-CHN 84Singapore 80Korea, Rep. of 79Japan 76Italy 56Israel 48Russian Federation 46Sweden 44Lithuania 42Finland 42Romania 39England-GBR 38Australia 38International average 36Hungary 36Slovenia 35United States 35Norway 35New Zealand 34Turkey 30Tunisia 29United Arab Emirates 29Malaysia 29Kazakhstan 28Ukraine 27Armenia 27Georgia 27Chile 26Iran, Islamic Rep. of 24Saudi Arabia 23Palestinian Nat’l Auth. 22Jordan 22Indonesia 22Bahrain 21Macedonia, Rep. of 21Thailand 21Qatar 21Syrian Arab Republic 19Lebanon 19Oman 17Morocco 17Ghana 14


Percentcorrect

Quebec-CAN 63Massachusetts-USA 57Colorado-USA 50North Carolina-USA 48Ontario-CAN 45Connecticut-USA 44Minnesota-USA 43Indiana-USA 42Alberta-CAN 40Dubai-UAE 34Florida-USA 29Abu Dhabi-UAE 27California-USA 24Alabama-USA 23




Content Domain

GEOMETRY

Main Topic

Geometric Shapes

Cognitive Domain

Knowing

Shapeofcutoutfigure

A piece of paper in the shape of a rectangle is folded in half as shown in the fi gure above. It is then cut along the dotted line, and the small piece that is cut is opened. What is the shape of the cutout fi gure?

A. an isosceles triangle

B. two isosceles triangles

C. a right triangle

D. an equilateral triangle

4 cm

1 cm


Correct Response: A



Hong Kong-CHN 88Chinese Taipei-CHN 87Korea, Rep. of 85Japan 85Singapore 80Russian Federation 73Italy 69England-GBR 66Israel 64Ukraine 63Australia 63Lithuania 60Hungary 59New Zealand 57Kazakhstan 57Norway 56Slovenia 56United States 55Sweden 53Finland 53International average 52Romania 51Chile 49Georgia 48Thailand 47United Arab Emirates 46Indonesia 44Iran, Islamic Rep. of 44Tunisia 44Macedonia, Rep. of 41Qatar 39Lebanon 39Turkey 39Armenia 37Syrian Arab Republic 35Palestinian Nat’l Auth. 35Morocco 35Bahrain 34Jordan 34Malaysia 33Saudi Arabia 30Oman 28Ghana 28


Percentcorrect

Quebec-CAN 69Minnesota-USA 67Massachusetts-USA 65Connecticut-USA 64Ontario-CAN 63North Carolina-USA 60Colorado-USA 59Florida-USA 58Indiana-USA 57Dubai-UAE 50Alberta-CAN 49Abu Dhabi-UAE 49California-USA 47Alabama-USA 41




Content Domain

GEOMETRY

Main Topic

Geometric Shapes

Cognitive Domain

Reasoning

Interior angles of pentagon

What is the sum of all the interior angles of pentagon ABCDE? Show your work.

Answer: _______________

A B

C

D

E


SCORINGCorrect Response• 540degreeswithworkshownExamples:3(triangles)×180o =540o

6(rightangles)×90o=540o

Partially Correct Response• 540degreeswithnoworkshown




Japan 72Chinese Taipei-CHN 70Korea, Rep. of 69Singapore 55Hong Kong-CHN 38Slovenia 31Israel 30Turkey 28Armenia 23Hungary 22Iran, Islamic Rep. of 21Kazakhstan 20International average 19Russian Federation 19Italy 18Macedonia, Rep. of 18Palestinian Nat’l Auth. 18Oman 17England-GBR 17Lithuania 16Jordan 15Ukraine 15Norway 15Australia 13Georgia 12Tunisia 12Finland 12United States 12Sweden 11New Zealand 11United Arab Emirates 10Saudi Arabia 10Qatar 10Lebanon 8Romania 8Syrian Arab Republic 7Chile 7Malaysia 6Bahrain 6Thailand 6Ghana 4Morocco 3Indonesia #


Percentcorrect

Massachusetts-USA 40Quebec-CAN 21North Carolina-USA 17Dubai-UAE 16Minnesota-USA 15Florida-USA 15Connecticut-USA 12Colorado-USA 12Indiana-USA 12Ontario-CAN 10Abu Dhabi-UAE 8California-USA 7Alabama-USA 5Alberta-CAN 4


# Rounds to zero



Interior angles of pentagon (continued)M032692


Answer: ______________


Answer: ______________

Incorrect Response:

Answer: ______________



Content Domain

GEOMETRY

Main Topic

Geometric Shapes

Cognitive Domain

Knowing

Viewofshapedirectlyfromabove

Th e shape shown above is cut out of cardboard. Th e triangle fl aps are then folded up along the dotted lines until they touch the edges of the fl aps next to them.

Complete the diagram below to show what the shape would look like when viewed from directly above.


SCORINGCorrect Response• Correctfigure(squarewithdiagonalsmeetingincenter)




Japan 89Finland 89Australia 87Korea, Rep. of 85New Zealand 84Singapore 83England-GBR 82United States 81Slovenia 81Lithuania 78Hungary 77Hong Kong-CHN 77Russian Federation 75Norway 74Chinese Taipei-CHN 74Chile 70Italy 70Israel 66Sweden 65Kazakhstan 60Ukraine 59International average 58Turkey 57Malaysia 53Thailand 51United Arab Emirates 50Bahrain 49Romania 47Macedonia, Rep. of 47Iran, Islamic Rep. of 45Tunisia 44Jordan 42Armenia 41Qatar 40Palestinian Nat’l Auth. 37Saudi Arabia 37Georgia 37Oman 36Morocco 35Indonesia 27Syrian Arab Republic 26Lebanon 22Ghana 10


Percentcorrect

Massachusetts-USA 90Minnesota-USA 89Alberta-CAN 86Ontario-CAN 86Colorado-USA 85North Carolina-USA 82Quebec-CAN 80Indiana-USA 79Florida-USA 79Connecticut-USA 79California-USA 76Alabama-USA 69Dubai-UAE 57Abu Dhabi-UAE 50




Viewofshapedirectlyfromabove(continued)M032734



Incorrect Response:




Content Domain

GEOMETRY

Main Topic

Geometric Shapes

Cognitive Domain

Knowing

Which shape has a line of symmetry

Which shape has a line of symmetry?

A.

B.

C.

D.


Correct Response: B



Chinese Taipei-CHN 81England-GBR 71Singapore 70Hong Kong-CHN 64Australia 60New Zealand 57Hungary 57Lithuania 56United States 52Iran, Islamic Rep. of 52Russian Federation 52Japan 50Slovenia 49United Arab Emirates 45Qatar 45Kazakhstan 42International average 41Italy 38Oman 38Korea, Rep. of 38Jordan 37Morocco 36Macedonia, Rep. of 36Armenia 35Palestinian Nat’l Auth. 35Israel 34Georgia 32Turkey 32Malaysia 32Ukraine 32Finland 31Saudi Arabia 31Romania 30Thailand 29Norway 29Indonesia 28Lebanon 28Bahrain 27Tunisia 27Chile 26Sweden 23Syrian Arab Republic 21Ghana 17


Percentcorrect

Massachusetts-USA 65Ontario-CAN 65Connecticut-USA 60Colorado-USA 60Florida-USA 59North Carolina-USA 52Minnesota-USA 51Quebec-CAN 48Abu Dhabi-UAE 47Indiana-USA 47Dubai-UAE 46Alabama-USA 45Alberta-CAN 41California-USA 37




Content Domain

GEOMETRY

Main Topic

Location and Movement

Cognitive Domain

Knowing

Half-turnaroundpointO

Which of these shows the result of a half-turn clockwise around point O?

A.

B.

C.

D.

O


Correct Response: D



Korea, Rep. of 79Japan 73Hong Kong-CHN 71Finland 66Chinese Taipei-CHN 64New Zealand 63Hungary 62Singapore 62Slovenia 58England-GBR 56Australia 55Italy 52Ukraine 52Israel 51Sweden 50Norway 48Russian Federation 48International average 45Lithuania 45Thailand 44Malaysia 44Saudi Arabia 43United Arab Emirates 42Jordan 40Georgia 40Indonesia 40Bahrain 40Qatar 39United States 39Chile 37Kazakhstan 36Iran, Islamic Rep. of 36Palestinian Nat’l Auth. 36Turkey 35Oman 34Tunisia 34Romania 32Syrian Arab Republic 30Armenia 28Lebanon 28Macedonia, Rep. of 27Morocco 26Ghana 26


Percentcorrect

Quebec-CAN 61Ontario-CAN 55Alberta-CAN 54Minnesota-USA 50Connecticut-USA 48Massachusetts-USA 44Dubai-UAE 42Indiana-USA 42North Carolina-USA 41Abu Dhabi-UAE 41Colorado-USA 41California-USA 39Florida-USA 38Alabama-USA 29




Content Domain

GEOMETRY

Main Topic


Cognitive Domain

Applying

Lengthoftherectangularbox

Th e volume of the rectangular box is 200 cm3. What is the value of x?

Answer: _______________

5 cm

4 cm

x cm






Singapore 92Chinese Taipei-CHN 89Hong Kong-CHN 87Japan 79Korea, Rep. of 78Russian Federation 65United States 58Kazakhstan 56Slovenia 56Lithuania 55Israel 54Australia 53Finland 51England-GBR 49Norway 48New Zealand 48Italy 44Romania 44United Arab Emirates 44Hungary 44International average 43Ukraine 43Armenia 42Malaysia 42Macedonia, Rep. of 38Turkey 35Indonesia 35Sweden 33Palestinian Nat’l Auth. 33Georgia 32Thailand 30Iran, Islamic Rep. of 28Lebanon 28Bahrain 27Qatar 26Chile 25Tunisia 22Jordan 22Oman 21Saudi Arabia 20Morocco 19Syrian Arab Republic 18Ghana 17


Percentcorrect

Massachusetts-USA 80North Carolina-USA 75Minnesota-USA 72Indiana-USA 68Connecticut-USA 67Ontario-CAN 66Colorado-USA 64Alberta-CAN 58Florida-USA 58California-USA 56Quebec-CAN 51Dubai-UAE 50Abu Dhabi-UAE 42Alabama-USA 41




Lengthoftherectangularbox(continued)M042201


Answer:

Incorrect Response:

Answer:



Content Domain

GEOMETRY

Main Topic

Geometric Shapes

Cognitive Domain

Applying

Draw an isosceles triangle

Th e length of side of each of the small squares represents 1 cm. Draw an isosceles triangle with a base of 4 cm and a height of 5 cm.


SCORINGCorrect Response• Correcttriangledrawn(anyorientation)




Japan 85Korea, Rep. of 84Hong Kong-CHN 82Chinese Taipei-CHN 82Italy 81Russian Federation 75Singapore 72Hungary 68Kazakhstan 65Slovenia 63Sweden 60Ukraine 60Romania 59Lebanon 58Lithuania 57Israel 56Norway 53Finland 52Tunisia 51Morocco 50Armenia 49International average 48New Zealand 46Macedonia, Rep. of 43Australia 41Palestinian Nat’l Auth. 40England-GBR 40Malaysia 39Turkey 39Indonesia 39Chile 39Georgia 38Syrian Arab Republic 33Jordan 32Iran, Islamic Rep. of 30Thailand 30Oman 27United States 27Bahrain 27United Arab Emirates 26Qatar 17Saudi Arabia 10Ghana 9


Percentcorrect

Quebec-CAN 62Ontario-CAN 48Massachusetts-USA 43Connecticut-USA 36North Carolina-USA 35Minnesota-USA 35Alberta-CAN 32Colorado-USA 29Abu Dhabi-UAE 29Indiana-USA 27Florida-USA 26Dubai-UAE 26California-USA 25Alabama-USA 14




Draw an isosceles triangle (continued)M042270


Th e length of side of each of the small squares represents 1 cm. Draw an isosceles triangle with a base of 4 cm and a height of 5 cm.

Incorrect Response:Th e length of side of each of the small squares represents 1 cm. Draw an isosceles triangle with a base of 4 cm and a height of 5 cm.



Content Domain

GEOMETRY

Main Topic


Cognitive Domain

Applying

MarkthepointsBandCongraph

Th e diagram shows a system for locating points

In this system, the position of a point P is described by its distance from origin, O, and the amount of counterclockwise turn from a baseline OA to OP. Th us, the coordinates of P are (5, 340°).

A. Mark the points B (3, 30°) and C (4, 120°) on the graph above.

1 2 3 4 5

90º

270º

0º180º

350º

340º

20º

10º

30º

40º

50º

60º70º

80º

O 6

100º110º120º

130º

140º

150º

160º

170º

190º

200º

210º

220º

230º

240º250º

260º 280º290º

300º

310º

320º

330º

P

A

B. Draw the angle BOC. What is the measure of angle BOC?

Angle BOC = ___________°

Item Number: M042300Z

SCORINGNote:TwoscorepointswillbegivenifbothpartsAandBarecorrect.Onescorepointwillbegivenif only part A is correct. No credit is given if only part B is correct.

M042300ACorrect Response• Bothpointscorrectlymarked(picturedonright)

Incorrect Response• Onepointcorrectlymarked• Otherincorrect(includingcrossedout,erased,straymarks,illegible,orofftask)

M042300BCorrect Response• 90o

Incorrect Response• Correctvaluegivenforincorrectpoint(s)drawninA• Otherincorrect(includingcrossedout,erased,straymarks,illegible,orofftask)



Japan 73Chinese Taipei-CHN 71Korea, Rep. of 71Hong Kong-CHN 68Singapore 63Russian Federation 59Slovenia 46Italy 45Lithuania 45Australia 43Ukraine 42Kazakhstan 39Finland 39Lebanon 37England-GBR 37Hungary 36Israel 33New Zealand 32Romania 32United States 32International average 31Tunisia 29Malaysia 25Armenia 25Macedonia, Rep. of 23Norway 22Sweden 21United Arab Emirates 21Thailand 21Iran, Islamic Rep. of 21Turkey 20Jordan 20Qatar 17Georgia 17Bahrain 17Oman 14Palestinian Nat'l Auth. 13Syrian Arab Republic 11Indonesia 9Chile 9Morocco 9Saudi Arabia 7Ghana 3


Percentcorrect

Quebec-CAN 50Massachusetts-USA 49Ontario-CAN 46Minnesota-USA 45Florida-USA 41Indiana-USA 39Colorado-USA 38Alberta-CAN 38North Carolina-USA 32Dubai-UAE 31Connecticut-USA 31California-USA 27Alabama-USA 24Abu Dhabi-UAE 20




MarkthepointsBandCongraph(continued)M042300Z


1 2 3 4 5

90º

270º

0º180º

350º

340º

20º

10º

30º

40º

50º

60º70º

80º

O 6

100º110º120º

130º

140º

150º

160º

170º

190º

200º

210º

220º

230º

240º250º

260º 280º290º

300º

310º

320º

330º

P

A


Angle BOC = ___________°

Incorrect Response:

1 2 3 4 5

90º

270º

0º180º

350º

340º

20º

10º

30º

40º

50º

60º70º

80º

O 6

100º110º120º

130º

140º

150º

160º

170º

190º

200º

210º

220º

230º

240º250º

260º 280º290º

300º

310º

320º

330º

P

A


Angle BOC = ___________°



Content Domain

GEOMETRY

Main Topic


Cognitive Domain

Applying

Calculate the area of a square

Th e perimeter of a square is 36 cm.

What is the area of this square?

A. 81 cm2

B. 36 cm2

C. 24 cm2

D. 18 cm2


Correct Response: A



Singapore 89Chinese Taipei-CHN 83Hong Kong-CHN 82Italy 78Korea, Rep. of 78Japan 66Israel 66Russian Federation 62Sweden 62Slovenia 60Lithuania 57Hungary 55Australia 54United States 53England-GBR 51Armenia 50Finland 50Turkey 49Kazakhstan 48International average 47Ukraine 47Romania 47Georgia 46New Zealand 45Norway 45Tunisia 43Macedonia, Rep. of 41Malaysia 40Chile 39United Arab Emirates 39Iran, Islamic Rep. of 35Palestinian Nat’l Auth. 34Syrian Arab Republic 33Lebanon 31Qatar 30Bahrain 29Indonesia 29Saudi Arabia 27Jordan 26Oman 25Morocco 23Ghana 22Thailand 20


Percentcorrect

Quebec-CAN 77Massachusetts-USA 75Colorado-USA 67North Carolina-USA 66Ontario-CAN 65Indiana-USA 61Alberta-CAN 60Connecticut-USA 59Minnesota-USA 57Florida-USA 53California-USA 44Dubai-UAE 43Alabama-USA 42Abu Dhabi-UAE 37




Content Domain

GEOMETRY

Main Topic


Cognitive Domain

Reasoning

Numberofbookstofillthebox

Ryan is packing books into a rectangular box.

All the books are the same size.

What is the largest number of books that will fi t inside the box?

Answer: ________________

6 cm

20 cm15 cm

20 cm

36 cm30 cmBook

Box






Chinese Taipei-CHN 66Hong Kong-CHN 65Korea, Rep. of 62Singapore 60Japan 58Russian Federation 36Israel 34Kazakhstan 33Lithuania 30Australia 29Finland 29Malaysia 28Slovenia 28New Zealand 27England-GBR 26United States 26Armenia 25International average 25Ukraine 23Norway 22Italy 22Romania 22Hungary 21Sweden 20United Arab Emirates 20Turkey 20Thailand 16Chile 16Macedonia, Rep. of 16Georgia 15Palestinian Nat’l Auth. 14Bahrain 14Iran, Islamic Rep. of 14Qatar 13Tunisia 12Saudi Arabia 12Indonesia 11Oman 11Lebanon 11Jordan 9Syrian Arab Republic 9Morocco 8Ghana 4


Percentcorrect

Massachusetts-USA 49North Carolina-USA 46Indiana-USA 45Ontario-CAN 39Alberta-CAN 39Minnesota-USA 36Quebec-CAN 34Connecticut-USA 33Colorado-USA 32Florida-USA 32Dubai-UAE 26California-USA 22Abu Dhabi-UAE 19Alabama-USA 18




Content Domain

GEOMETRY

Main Topic

Geometric Shapes

Cognitive Domain

Reasoning

What is the size of angle B

In this triangle:

AC = BC

AB is twice as long as CX.

What is the size of angle B?

Answer: ______________ °

A

C

BX






Korea, Rep. of 89Japan 85Singapore 83Hong Kong-CHN 72Chinese Taipei-CHN 72Lebanon 57England-GBR 52Russian Federation 52Italy 52Hungary 51Finland 48Australia 48Israel 46Slovenia 43Kazakhstan 43International average 41Lithuania 41Norway 40Ukraine 40New Zealand 40Romania 39United States 39Thailand 39Iran, Islamic Rep. of 37Macedonia, Rep. of 37Sweden 36Armenia 35Tunisia 34Syrian Arab Republic 33Georgia 33Turkey 33Palestinian Nat’l Auth. 30Malaysia 28Jordan 27Morocco 27United Arab Emirates 25Qatar 24Bahrain 19Indonesia 18Oman 17Chile 17Ghana 13Saudi Arabia 12


Percentcorrect

Massachusetts-USA 63Minnesota-USA 56Quebec-CAN 56Florida-USA 53Ontario-CAN 52North Carolina-USA 46Connecticut-USA 45Indiana-USA 44Colorado-USA 43Alberta-CAN 35Dubai-UAE 34California-USA 27Alabama-USA 24Abu Dhabi-UAE 23




Content Domain

GEOMETRY

Main Topic

Geometric Shapes

Cognitive Domain

Reasoning

Valueofangleb

Lines m and n are parallel.

What is the value of b?

Answer: ______________

m

b°

n

60°

70°






Japan 86Korea, Rep. of 85Singapore 80Hong Kong-CHN 75Chinese Taipei-CHN 49Russian Federation 48Kazakhstan 44Israel 41Turkey 39Finland 36Ukraine 35Lebanon 34Slovenia 33International average 33Armenia 32Malaysia 32Italy 32England-GBR 30Iran, Islamic Rep. of 29Thailand 29Australia 28Tunisia 28Lithuania 28Hungary 27New Zealand 25Romania 25United States 24Jordan 23Macedonia, Rep. of 23United Arab Emirates 22Sweden 22Syrian Arab Republic 22Palestinian Nat’l Auth. 21Norway 20Chile 20Indonesia 20Ghana 19Saudi Arabia 18Bahrain 18Georgia 18Qatar 17Morocco 17Oman 12


Percentcorrect

Massachusetts-USA 39Minnesota-USA 36Quebec-CAN 35Ontario-CAN 34Florida-USA 30Colorado-USA 29Dubai-UAE 27Indiana-USA 25North Carolina-USA 25Alberta-CAN 23Alabama-USA 21Connecticut-USA 21Abu Dhabi-UAE 21California-USA 20




Content Domain

DATA AND CHANCE

Main Topic

Chance

Cognitive Domain

Knowing

Howlikelytogetpinkcandy

A machine has 100 candies and dispenses a candy when a lever is turned. Th e machine has the same number of blue, pink, yellow, and green candies all mixed together. Megan turned the lever and obtained a pink candy. Peter turned the lever next.

How likely is it that Peter will get a pink candy?

A. It is certain that his candy will be pink.

B. It is more likely than it was for Megan.

C. It is exactly as likely as it was for Megan.

D. It is less likely than it was for Megan.


Correct Response: D



Korea, Rep. of 84Hong Kong-CHN 71Singapore 71Chinese Taipei-CHN 68Slovenia 67Australia 65Israel 65Japan 64United States 63Italy 61Lithuania 60Norway 60Finland 59New Zealand 59England-GBR 58Hungary 58Sweden 55Turkey 54Romania 54Russian Federation 52Thailand 52Ukraine 50Chile 48International average 48United Arab Emirates 44Saudi Arabia 42Georgia 42Macedonia, Rep. of 40Iran, Islamic Rep. of 40Kazakhstan 40Jordan 37Tunisia 37Qatar 37Armenia 34Bahrain 31Syrian Arab Republic 29Indonesia 26Oman 26Malaysia 25Palestinian Nat’l Auth. 24Morocco 24Lebanon 21Ghana 11


Percentcorrect

Massachusetts-USA 74North Carolina-USA 68Minnesota-USA 68Quebec-CAN 64California-USA 64Indiana-USA 61Ontario-CAN 60Alberta-CAN 59Connecticut-USA 58Colorado-USA 58Florida-USA 56Alabama-USA 54Dubai-UAE 47Abu Dhabi-UAE 44




Content Domain

DATA AND CHANCE

Main Topic

Chance

Cognitive Domain

Applying

Numberoftimesspinnerinredarea

Th e spinner is for Steve’s new game. Out of 600 spins, approximately how many times should he expect the arrow to land on the red sector?

A. 30

B. 40

C. 50

D. 60

Purple

Orange

Green

Blue

Red


Correct Response: C



Singapore 70Korea, Rep. of 68Japan 60Hong Kong-CHN 55Chinese Taipei-CHN 55England-GBR 50Australia 45United States 40Israel 40Finland 39New Zealand 38Sweden 37Norway 32Russian Federation 32International average 31Hungary 31Slovenia 31Italy 31Malaysia 29Turkey 29Lithuania 28Ukraine 26Chile 26Qatar 25Saudi Arabia 24Kazakhstan 24Iran, Islamic Rep. of 24Tunisia 24Bahrain 23United Arab Emirates 23Palestinian Nat’l Auth. 23Lebanon 23Romania 23Macedonia, Rep. of 23Oman 22Thailand 22Syrian Arab Republic 21Georgia 20Morocco 20Jordan 20Armenia 16Indonesia 14Ghana 13


Percentcorrect

Minnesota-USA 56Massachusetts-USA 53Quebec-CAN 49Connecticut-USA 46Alberta-CAN 45North Carolina-USA 44Colorado-USA 43Ontario-CAN 42Indiana-USA 38Florida-USA 35California-USA 30Alabama-USA 28Dubai-UAE 25Abu Dhabi-UAE 24




Content Domain

DATA AND CHANCE

Main Topic

DataOrganizationand Representation

Cognitive Domain

Knowing

Carproductiongraph/timecarsmade

Th e solid line ( ) on the graph shows car production by the NU Car Motor Company during a particular day.

Th e dotted line (-----) shows what the total number of cars produced would be if the rate of production were constant.

A. By what time had a total of 150 cars been produced?

Answer: _______________

8 am 9 am 10 am 11 am 12 noon 1 pm 2 pm 3 pm 4 pm

400

350

300

250

200

150

100

50

0

Tota

l Num

ber o

f Car

s Pro

duce

d

Time

Car Production


SCORINGCorrect Response• 10a.m.

Incorrect Response• 11a.m.• Otherincorrect(includingcrossedout,erased,straymarks,illegible,orofftask)



Korea, Rep. of 87Japan 85Finland 83Singapore 82Hungary 81Chinese Taipei-CHN 80Hong Kong-CHN 80Russian Federation 76Italy 75Australia 73Slovenia 72Lithuania 71Sweden 71England-GBR 70Israel 70Ukraine 70United States 70Thailand 68New Zealand 66Tunisia 65Malaysia 61International average 60Norway 59Turkey 59Indonesia 57United Arab Emirates 57Romania 55Chile 54Palestinian Nat’l Auth. 52Lebanon 52Kazakhstan 51Saudi Arabia 49Jordan 48Bahrain 45Iran, Islamic Rep. of 44Qatar 44Oman 41Macedonia, Rep. of 40Morocco 36Georgia 35Ghana 29Armenia 27Syrian Arab Republic 26


Percentcorrect

Massachusetts-USA 78Minnesota-USA 77Quebec-CAN 77Indiana-USA 75Alberta-CAN 73Connecticut-USA 72North Carolina-USA 72Colorado-USA 72Ontario-CAN 68Florida-USA 67California-USA 66Alabama-USA 66Dubai-UAE 65Abu Dhabi-UAE 53




Carproductiongraph/timecarsmade(continued)M032681A



Answer: _______________

Incorrect Response:


Answer: _______________



Content Domain

DATA AND CHANCE

Main Topic

Data Interpretation

Cognitive Domain

Applying

Carproductiongraph/avgbyhour



B. What was the average number of cars produced per hour on this day?

Answer: _______________


400

350

300

250

200

150

100

50

0

Tota

l Num

ber o

f Car

s Pro

duce

d

Time

Car Production






Chinese Taipei-CHN 65Japan 57Hong Kong-CHN 56Finland 55England-GBR 52New Zealand 50Singapore 49United States 48Australia 47Korea, Rep. of 46Turkey 42Slovenia 40Hungary 37Sweden 36Thailand 36Israel 34Romania 32Tunisia 31Kazakhstan 30International average 29Chile 29Italy 29Norway 27Russian Federation 26Iran, Islamic Rep. of 23United Arab Emirates 23Malaysia 23Lithuania 22Qatar 19Macedonia, Rep. of 19Indonesia 19Bahrain 18Ukraine 17Lebanon 16Armenia 13Ghana 13Georgia 11Jordan 10Oman 8Syrian Arab Republic 8Palestinian Nat’l Auth. 7Morocco 7Saudi Arabia 6


Percentcorrect

Massachusetts-USA 55Minnesota-USA 53California-USA 52Florida-USA 51Alberta-CAN 49Indiana-USA 46North Carolina-USA 45Colorado-USA 44Alabama-USA 43Connecticut-USA 43Ontario-CAN 40Dubai-UAE 37Quebec-CAN 33Abu Dhabi-UAE 18




Carproductiongraph/avgbyhour(continued)M032681B





Answer: _______________


400

350

300

250

200

150

100

50

0

Tota

l Num

ber o

f Car

s Pro

duce

d

Time

Car Production

Incorrect Response:




Answer: _______________


400

350

300

250

200

150

100

50

0

Tota

l Num

ber o

f Car

s Pro

duce

d

Time

Car Production



Content Domain

DATA AND CHANCE

Main Topic

Data Interpretation

Cognitive Domain

Applying

Carproductiongraph/identifytime



C. During which hour were the most cars produced?

Between _______________ and _______________


400

350

300

250

200

150

100

50

0

Tota

l Num

ber o

f Car

s Pro

duce

d

Time

Car Production


SCORINGCorrect Response• 1p.m.and2p.m.




Japan 82Korea, Rep. of 78Finland 77Hong Kong-CHN 73England-GBR 70Chinese Taipei-CHN 69Singapore 67Sweden 64Australia 63New Zealand 61United States 59Slovenia 55Norway 53Hungary 50Russian Federation 47Israel 45Lithuania 35Ukraine 35Turkey 34International average 34Italy 28Thailand 28Kazakhstan 25Chile 20Malaysia 20United Arab Emirates 20Qatar 17Bahrain 16Lebanon 16Tunisia 13Armenia 13Romania 13Macedonia, Rep. of 13Iran, Islamic Rep. of 12Georgia 9Indonesia 8Saudi Arabia 6Jordan 6Oman 5Morocco 4Palestinian Nat’l Auth. 3Ghana 3Syrian Arab Republic 2


Percentcorrect

Massachusetts-USA 72Minnesota-USA 70Indiana-USA 67Connecticut-USA 64Alberta-CAN 63Colorado-USA 63Quebec-CAN 62North Carolina-USA 59Ontario-CAN 54California-USA 51Florida-USA 49Alabama-USA 40Dubai-UAE 34Abu Dhabi-UAE 17




Carproductiongraph/identifytime(continued)M032681C





Between _______________ and _______________


400

350

300

250

200

150

100

50

0

Tota

l Num

ber o

f Car

s Pro

duce

d

Time

Car Production

Incorrect Response:




Between _______________ and _______________


400

350

300

250

200

150

100

50

0

Tota

l Num

ber o

f Car

s Pro

duce

d

Time

Car Production



Content Domain

DATA AND CHANCE

Main Topic


Cognitive Domain

Applying

Makeapiechartwithlabels

Of the 400 students in a school, 50 plan to go to university, 100 to a polytechnic school, 150 to a business college, and the remainder plan to enterworkforce.

Use the circle below to make a pie chart showing the proportions of students planning to do each of these. Put labels on your chart.


SCORINGCorrect Response• Piechartcorrectlydividedandlabeled(1section–university;2sections–polytechnic;2sections–workforce;3sections–business

college)

Partially Correct Response• Foursectionswithatleasttwo,butnotall,ofcorrectsizeandcorrectlylabeled• Foursectionsofcorrectsizebutnolabels,orlabels50,100,150,100

Incorrect Response• Foursectionswithoneornoneofcorrectsize• Otherincorrect(includingcrossedout,erased,straymarks,illegible,orofftask)



Singapore 84Chinese Taipei-CHN 80Japan 77Korea, Rep. of 77Hong Kong-CHN 74Finland 70Russian Federation 67Australia 65Slovenia 64Hungary 63England-GBR 61New Zealand 60Lithuania 58Norway 57Israel 55Sweden 54Italy 53United States 53International average 45Malaysia 45Ukraine 44Turkey 43Thailand 43Chile 43United Arab Emirates 35Romania 35Kazakhstan 34Iran, Islamic Rep. of 33Macedonia, Rep. of 30Jordan 29Bahrain 29Tunisia 28Oman 27Indonesia 26Palestinian Nat’l Auth. 25Qatar 25Armenia 25Georgia 23Saudi Arabia 23Lebanon 20Syrian Arab Republic 19Morocco 13Ghana 10


Percentcorrect

Massachusetts-USA 70Quebec-CAN 69Ontario-CAN 63Minnesota-USA 61North Carolina-USA 61Connecticut-USA 60Colorado-USA 60Alberta-CAN 58Indiana-USA 58California-USA 47Florida-USA 43Dubai-UAE 39Alabama-USA 39Abu Dhabi-UAE 36




Makeapiechartwithlabels(continued)M032695









Makeapiechartwithlabels(continued)M032695

Student ResponsesIncorrect Response:



Content Domain

DATA AND CHANCE

Main Topic

Data Interpretation

Cognitive Domain

Reasoning

Salesoftwotypesofsoftdrinks

Th e graph shows the sales of two types of soft drink over 4 years. If the sales trends continue for the next 10 years, determine the year in which the sales of Cherry Cola will be the same as the sales of Lemon Cola.

A. 2003

B. 2004

C. 2005

D. 2006

Soft Drink Sales

1998 1999 2000 20010

10

20

30

40

50

60 Cherry ColaLemon Cola

Num

ber o

f can

s (m

illio

ns)

Year


Correct Response: B



Korea, Rep. of 68Singapore 60Chinese Taipei-CHN 58Japan 57Australia 48Finland 48Hong Kong-CHN 48Israel 46England-GBR 46Hungary 45Italy 45Sweden 44Turkey 43Slovenia 43Russian Federation 42New Zealand 42Norway 40International average 40Lithuania 39Ukraine 38United Arab Emirates 38United States 38Chile 37Qatar 36Thailand 35Macedonia, Rep. of 35Malaysia 35Tunisia 35Kazakhstan 34Oman 34Morocco 34Georgia 33Lebanon 33Bahrain 33Indonesia 33Syrian Arab Republic 32Saudi Arabia 32Palestinian Nat’l Auth. 32Iran, Islamic Rep. of 32Ghana 30Romania 29Jordan 29Armenia 24


Percentcorrect

Massachusetts-USA 55Quebec-CAN 51North Carolina-USA 50Florida-USA 47Ontario-CAN 45Minnesota-USA 44Alberta-CAN 43Dubai-UAE 42Indiana-USA 39Colorado-USA 38Connecticut-USA 38California-USA 35Abu Dhabi-UAE 33Alabama-USA 33




Content Domain

DATA AND CHANCE

Main Topic

Data Interpretation

Cognitive Domain

Knowing

Meannumberofstaffmembers

Th e Real Burger Company owns 5 restaurants. Th e numbers of staff members employed in its 5 restaurants are: 12, 18, 19, 21, and 30 people.

A. What is the mean number of staff members in the 5 restaurants?

Answer: ________________






Hong Kong-CHN 85Japan 83Singapore 81Korea, Rep. of 81Chinese Taipei-CHN 76Lithuania 73Finland 72Israel 67United States 64Norway 64Hungary 63Italy 61Russian Federation 61Sweden 56England-GBR 56Ukraine 52Slovenia 49Turkey 48Australia 46International average 43Iran, Islamic Rep. of 41New Zealand 38Armenia 38Kazakhstan 36Palestinian Nat’l Auth. 36United Arab Emirates 34Saudi Arabia 33Macedonia, Rep. of 31Georgia 31Syrian Arab Republic 30Romania 28Bahrain 26Oman 23Qatar 20Malaysia 19Indonesia 19Thailand 15Lebanon 15Jordan 14Chile 12Ghana 10Tunisia 9Morocco 2


Percentcorrect

Florida-USA 79Massachusetts-USA 79Indiana-USA 75Minnesota-USA 75North Carolina-USA 72Quebec-CAN 69Connecticut-USA 66Colorado-USA 64Ontario-CAN 56California-USA 50Alabama-USA 46Alberta-CAN 37Abu Dhabi-UAE 37Dubai-UAE 33




Meannumberofstaffmembers(continued)M042169A




Answer: ________________

Incorrect Response:



Answer: ________________



Content Domain

DATA AND CHANCE

Main Topic

Data Interpretation

Cognitive Domain

Knowing

Mediannumberofstaffmembers


B. What is the median number of staff members in the 5 restaurants?

Answer: ________________






United States 81England-GBR 63Norway 61Turkey 58Saudi Arabia 58Singapore 56New Zealand 56United Arab Emirates 54Australia 48Israel 47Bahrain 45Ghana 42Chinese Taipei-CHN 40Sweden 40Japan 38Syrian Arab Republic 35Armenia 32Qatar 30International average 29Jordan 29Oman 26Italy 26Palestinian Nat’l Auth. 26Lithuania 25Russian Federation 24Hong Kong-CHN 23Chile 21Kazakhstan 19Macedonia, Rep. of 16Hungary 14Lebanon 13Korea, Rep. of 12Tunisia 12Georgia 11Romania 10Thailand 8Ukraine 7Iran, Islamic Rep. of 7Malaysia 6Finland 6Morocco 6Indonesia 3Slovenia 2


Percentcorrect

Florida-USA 90North Carolina-USA 89Indiana-USA 88Massachusetts-USA 87Colorado-USA 86Minnesota-USA 83Connecticut-USA 80Alabama-USA 75California-USA 70Ontario-CAN 68Abu Dhabi-UAE 60Dubai-UAE 46Alberta-CAN 45Quebec-CAN 9




Mediannumberofstaffmembers(continued)M042169B




Answer: ________________

Incorrect Response:



Answer: ________________



Content Domain

DATA AND CHANCE

Main Topic

Data Interpretation

Cognitive Domain

Applying

Change in mean and median


C. If the restaurant with 30 staff members increased its number of staff members to 50, how would this aff ect the median and the mean?


SCORINGCorrect Response• Themeanwouldincrease/change,themedianwouldnotchange.Ifstudentgivesanewvalueforthemean,itshouldbebetween21and29.Ifavalueisgivenforthemedian,itmustbecorrect(i.e.,19ortheanswergivenforPartBifincorrect)

Incorrect Response• Bothwouldincrease• Incorrect(includingcrossedout,erased,straymarks,illegible,orofftask)



Singapore 46United States 43England-GBR 37Norway 35Israel 31Sweden 27Turkey 25Australia 25New Zealand 24Chinese Taipei-CHN 22United Arab Emirates 17Bahrain 17Lithuania 15Italy 15Japan 14Saudi Arabia 14International average 13Russian Federation 13Hong Kong-CHN 12Hungary 11Qatar 9Palestinian Nat’l Auth. 9Oman 9Macedonia, Rep. of 8Georgia 7Kazakhstan 7Armenia 7Finland 6Korea, Rep. of 6Jordan 6Chile 6Syrian Arab Republic 5Romania 5Ukraine 4Indonesia 4Ghana 2Malaysia 2Tunisia 2Iran, Islamic Rep. of 2Lebanon 1Thailand 1Slovenia #Morocco #


Percentcorrect

Massachusetts-USA 61North Carolina-USA 60Minnesota-USA 56Florida-USA 53Indiana-USA 51Colorado-USA 48Connecticut-USA 45Ontario-CAN 41California-USA 29Alabama-USA 29Alberta-CAN 27Abu Dhabi-UAE 18Dubai-UAE 16Quebec-CAN 7


# Rounds to zero



Change in mean and median (continued)M042169C


Incorrect Response:



Content Domain

DATA AND CHANCE

Main Topic

Chance

Cognitive Domain

Applying

Numberofregularsizebottles

Over recent weeks, a shop’s average sales of bottles of soda have been 50% in the regular size, 40% in the small size, and 10% in the large size. Next week, the shopkeeper will order 1,200 bottles of soda. How many of these bottles should he order in the regular size?

A. 120

B. 480

C. 600

D. 720


Correct Response: C



Korea, Rep. of 83Singapore 82Hong Kong-CHN 80Japan 80Finland 79Norway 77Chinese Taipei-CHN 77Hungary 75Slovenia 71Italy 71England-GBR 68Lithuania 68Australia 66Russian Federation 64Israel 64New Zealand 63United States 63Sweden 61Turkey 57Ukraine 56Chile 55International average 54Thailand 52Romania 49Malaysia 49United Arab Emirates 49Georgia 45Armenia 44Bahrain 43Kazakhstan 41Iran, Islamic Rep. of 41Macedonia, Rep. of 41Qatar 41Lebanon 40Tunisia 37Palestinian Nat’l Auth. 37Saudi Arabia 35Jordan 34Syrian Arab Republic 34Morocco 32Indonesia 30Oman 30Ghana 20


Percentcorrect

Quebec-CAN 74Minnesota-USA 72Massachusetts-USA 72Colorado-USA 70Alberta-CAN 69North Carolina-USA 69Ontario-CAN 68Connecticut-USA 66Indiana-USA 64Florida-USA 59California-USA 58Alabama-USA 55Dubai-UAE 52Abu Dhabi-UAE 47




Content Domain

DATA AND CHANCE

Main Topic

Chance

Cognitive Domain

Applying

Chanceofgettingabutton

Th ere are 10 red, 8 blue, and 4 white buttons in a bag. What is the chance of taking out either a blue button or a white button?

A.

B.

C.

D.


Correct Response: D



Korea, Rep. of 92Singapore 85Japan 83United States 80Australia 77England-GBR 77Israel 75Italy 69Chinese Taipei-CHN 68Finland 68Sweden 67New Zealand 66Hong Kong-CHN 65Turkey 63Norway 62Slovenia 57United Arab Emirates 55Hungary 55International average 54Lithuania 53Russian Federation 53Palestinian Nat’l Auth. 52Oman 48Bahrain 47Qatar 45Ukraine 45Saudi Arabia 45Thailand 44Chile 43Romania 43Georgia 43Jordan 42Kazakhstan 41Iran, Islamic Rep. of 40Macedonia, Rep. of 37Armenia 37Syrian Arab Republic 37Lebanon 35Tunisia 35Ghana 35Indonesia 34Malaysia 33Morocco 29


Percentcorrect

Minnesota-USA 90Massachusetts-USA 86Colorado-USA 85Indiana-USA 84Alberta-CAN 82North Carolina-USA 82Ontario-CAN 79Connecticut-USA 78Florida-USA 78Quebec-CAN 78Alabama-USA 75California-USA 69Dubai-UAE 58Abu Dhabi-UAE 55




Content Domain

DATA AND CHANCE

Main Topic


Cognitive Domain

Applying

Completeandlabelthispiechart

480 students were asked to name their favorite sport. Th e results are shown in this table.

Sport Number of StudentsHockey 60Football 180Tennis 120Basketball 120

Use the information in the table to complete and label this pie chart.

Popularity of Sports


SCORINGCorrect Response• Hockey1/8,Football3/8,Tennis,Basketballboth1/4,andlabelsallcorrect

Partially Correct Response• Allsectorscorrectsizebutlabelingincompleteormissing




Singapore 85Korea, Rep. of 85Chinese Taipei-CHN 80Hong Kong-CHN 76Japan 75Finland 70Slovenia 67Australia 67England-GBR 65Israel 63Russian Federation 63United States 62Lithuania 62Hungary 62Norway 61New Zealand 59Sweden 58Italy 54Malaysia 50Ukraine 48Turkey 48International average 47Thailand 45Chile 44United Arab Emirates 41Kazakhstan 40Jordan 34Qatar 33Bahrain 33Oman 30Palestinian Nat’l Auth. 30Georgia 30Romania 29Indonesia 28Tunisia 27Armenia 25Macedonia, Rep. of 24Iran, Islamic Rep. of 23Syrian Arab Republic 23Saudi Arabia 19Morocco 18Lebanon 17Ghana 11


Percentcorrect

Massachusetts-USA 74Quebec-CAN 72Minnesota-USA 71Connecticut-USA 70Indiana-USA 69Colorado-USA 69North Carolina-USA 67Ontario-CAN 67Alberta-CAN 66Florida-USA 65California-USA 58Alabama-USA 55Dubai-UAE 48Abu Dhabi-UAE 40




Completeandlabelthispiechart(continued)M042207





Completeandlabelthispiechart(continued)M042207

Student ResponsesIncorrect Response:



Content Domain

DATA AND CHANCE

Main Topic

Chance

Cognitive Domain

Knowing

HowlikelystudentvotedforPat

Pat and Chris were candidates for school president.

Here are the election results:

Pat 80%

Chris 20%

How likely would it be for a student asked at random to have voted for Pat?

A. It is certain that the student voted for Pat.

B. It is likely that the student voted for Pat.

C. It is unlikely that the student voted for Pat.

D. It is certain that the student did not vote for Pat.


Correct Response: B



Korea, Rep. of 95Chinese Taipei-CHN 89Finland 89Japan 88Hong Kong-CHN 87England-GBR 87Australia 84Lithuania 84Italy 82New Zealand 80Norway 77Slovenia 77Israel 77Singapore 77Turkey 77United States 76Hungary 74Ukraine 70Sweden 70Romania 67Chile 65Russian Federation 65International average 64Bahrain 59United Arab Emirates 55Jordan 53Iran, Islamic Rep. of 53Thailand 52Georgia 52Kazakhstan 52Saudi Arabia 51Qatar 48Armenia 47Oman 46Palestinian Nat’l Auth. 46Ghana 46Macedonia, Rep. of 45Lebanon 45Syrian Arab Republic 44Malaysia 37Tunisia 36Indonesia 35Morocco 28


Percentcorrect

Quebec-CAN 87Ontario-CAN 85Massachusetts-USA 84Alberta-CAN 84Minnesota-USA 84Connecticut-USA 82Indiana-USA 80North Carolina-USA 79Colorado-USA 78Alabama-USA 76Florida-USA 76California-USA 70Dubai-UAE 66Abu Dhabi-UAE 53




Content Domain

DATA AND CHANCE

Main Topic

Data Interpretation

Cognitive Domain

Reasoning

Long jump competition

Th e results of a long jump competition were reported as follows:

Average Length

Team A 3.6 m

Team B 4.8 m

Th ere were the same number of students in each team. Which statement about the competition MUST be true?

A. Each student in team B jumped farther than any student in team A.

B. Aft er every student in team A jumped, there was a student in team B who jumped farther.

C. As a group, team B jumped farther than team A.

D. Some students in team A jumped farther than some students in team B.


Correct Response: C



Hong Kong-CHN 87Korea, Rep. of 83Chinese Taipei-CHN 82Japan 77Finland 75Australia 73Singapore 73Slovenia 73Italy 72England-GBR 71New Zealand 69Norway 68Sweden 67United States 67Israel 66Iran, Islamic Rep. of 65Romania 65Hungary 65Turkey 63Malaysia 61Russian Federation 60Chile 59International average 58Ukraine 55Georgia 53Macedonia, Rep. of 52Jordan 51Lebanon 50United Arab Emirates 50Kazakhstan 47Morocco 46Qatar 45Bahrain 45Palestinian Nat’l Auth. 45Tunisia 44Syrian Arab Republic 44Saudi Arabia 44Armenia 44Ghana 40Thailand 40Lithuania 38Oman 38Indonesia 29


Percentcorrect

Minnesota-USA 80North Carolina-USA 79Massachusetts-USA 76Indiana-USA 76Connecticut-USA 74Alberta-CAN 73Quebec-CAN 69Ontario-CAN 66Colorado-USA 65California-USA 63Alabama-USA 62Florida-USA 62Dubai-UAE 54Abu Dhabi-UAE 49




Content Domain

DATA AND CHANCE

Main Topic

Chance

Cognitive Domain

Reasoning

Probabilitythatthemarbleisred

Th ere are 10 marbles in a bag: 5 red, and 5 blue.

Sue draws a marble from the bag at random. Th e marble is red.

She puts the marble back into the bag.

What is the probability that the next marble she draws at random is red?

A. 12

B. 4

10

C.15

D.1

10


Correct Response: A



Singapore 78Korea, Rep. of 76Australia 75England-GBR 72Japan 70Chinese Taipei-CHN 70New Zealand 68Slovenia 67United States 66Finland 66Sweden 65Norway 64Hong Kong-CHN 64Israel 59Hungary 51Lithuania 51Russian Federation 47International average 45Turkey 44Italy 42Macedonia, Rep. of 41Romania 39Armenia 39Palestinian Nat’l Auth 38Ukraine 38Kazakhstan 38Thailand 37United Arab Emirates 36Indonesia 35Iran, Islamic Rep. of 35Saudi Arabia 35Qatar 34Georgia 33Chile 31Ghana 28Malaysia 28Jordan 26Bahrain 24Oman 23Lebanon 21Tunisia 20Syrian Arab Republic 18Morocco 16


Percentcorrect

Massachusetts-USA 79Minnesota-USA 78Connecticut-USA 78Colorado-USA 76Indiana-USA 76North Carolina-USA 74Alberta-CAN 73Ontario-CAN 73Quebec-CAN 72Florida-USA 60California-USA 60Alabama-USA 52Dubai-UAE 45Abu Dhabi-UAE 34




Content Domain

DATA AND CHANCE

Main Topic

Data Interpretation

Cognitive Domain

Reasoning

Age structures of country X and Y

Comparison of Age Structure Between Country X and Country Y

Th e graphs for Country X and Country Y show the age structure of each country’s population. Th e population is divided into three age groups from youngest to oldest. Th e graphs enable predictions about population growth.

A. Why could the age structure of Country X lead to more rapid population growth than the age structure of Country Y?

89847974696459544944393429241914

940

89847974696459544944393429241914

940

1 2 3 4 5 6 7 801234567 2 3 4 5 6 7 8012345678

Ages Ages

Percent of Population Percent of Population

Ages 0–19 Going to have children

Ages 20–44 Having children

Ages 45–89 Finished having children

Males Females Males Females

Country X Age DistributionRapid Growth

Country Y Age DistributionSlow Growth

18


SCORINGCorrect Response• WithinCountryXthereisalargerpercentageofpeopleinthe“havingchildren”or“goingtohavechildren”categoriesthaninCountryY.

Note:ThereferencetocountryXneedstobeclear.ThecomparisonwithCountryYdoesnotneedtobestated.

Also,accept“morepeople”as“proportionatelymore”and“youngoryounger”inplaceof“havingchildren”or“goingtohavechildren”

Examples:CountryXhasmorepeopleabouttohavechildrenorhavingchildrenthancountryYThere are more people going to have children in country XMore young people in country X

Incorrect Response• Incorrect(includingcrossedout,erased,straymarks,illegible,orofftask)Examples:Therearemore“goingtohavechildren”

Country X has more population compared to country Y



Korea, Rep. of 79Russian Federation 41Singapore 40Ukraine 39Hong Kong-CHN 34Romania 34Kazakhstan 32Japan 29Turkey 28Israel 28Finland 25Tunisia 25Bahrain 23Chinese Taipei-CHN 22International average 21Indonesia 21Australia 21Lithuania 20Norway 20United States 18Syrian Arab Republic 18Hungary 18Oman 18England-GBR 17New Zealand 17United Arab Emirates 17Armenia 16Macedonia, Rep. of 15Georgia 15Sweden 15Thailand 15Iran, Islamic Rep. of 14Slovenia 14Jordan 13Malaysia 13Italy 11Qatar 11Palestinian Nat’l Auth. 10Chile 9Lebanon 9Morocco 8Saudi Arabia 5Ghana 4


Percentcorrect

Massachusetts-USA 30Connecticut-USA 26Minnesota-USA 26Ontario-CAN 25Dubai-UAE 23Florida-USA 21Indiana-USA 20Colorado-USA 19Quebec-CAN 19Abu Dhabi-UAE 18Alberta-CAN 16California-USA 16North Carolina-USA 15Alabama-USA 15




Age structures of country X and Y (continued)M052503A


Incorrect Response:



Content Domain

DATA AND CHANCE

Main Topic

Data Interpretation

Cognitive Domain

Reasoning

Problemoftakingcareofelderly

Comparison of Age Structure Between Country X and Country Y

Th e graphs for Country X and Country Y show the age structure of each country’s population. Th e population is divided into three age groups from youngest to oldest. Th e graphs enable predictions about population growth.

B. Why could Country Y expect to have a bigger problem taking care of its elderly population than Country X?

89847974696459544944393429241914

940

89847974696459544944393429241914

940

1 2 3 4 5 6 7 8012345678 1 2 3 4 5 6 7 8012345678

Ages Ages

Percent of Population Percent of Population

Ages 0–19 Going to have children

Ages 20–44 Having children

Ages 45–89 Finished having children

Males Females Males Females

Country X Age DistributionRapid Growth

Country Y Age DistributionSlow Growth


SCORINGCorrect Response• WithinCountryY,thereisarelativelylargerpopulationofelderlypeople(“finishedhavingchildren”)

compared with younger populations.Note:Thecomparisonbetweenolderandyoungerpeoplemustbemadeorimplied.CountryXandCountryYdonothavetobementioned.Examples: More older people than younger people

NotenoughyoungpeopletotakecareoftheelderlyLessnumberofpeople“havingchildren”tokeepupthepopulationAgingpopulation,lessyoungsters,lesserworkforce

Incorrect Response•Incorrect(includingcrossedout,erased,straymarks,illegible,orofftask)Examples: There are many more elders in Y than X

Country Y has a wider range of not having children than country X



Singapore 39Japan 37Korea, Rep. of 36Chinese Taipei-CHN 32Bahrain 30Kazakhstan 29Finland 27Romania 26Tunisia 25Russian Federation 24Hungary 24Ukraine 23Australia 20Israel 20Turkey 19United States 18England-GBR 18Indonesia 18Hong Kong-CHN 18International average 17New Zealand 17Italy 17Oman 17Slovenia 17Jordan 16Lithuania 14Sweden 13Macedonia, Rep. of 13Syrian Arab Republic 13Norway 12Malaysia 11United Arab Emirates 10Palestinian Nat’l Auth. 10Armenia 9Thailand 8Georgia 8Morocco 7Lebanon 7Qatar 7Iran, Islamic Rep. of 6Chile 5Saudi Arabia 3Ghana 2


Percentcorrect

Ontario-CAN 24Massachusetts-USA 23Minnesota-USA 21Connecticut-USA 20Alberta-CAN 20Quebec-CAN 20Colorado-USA 19North Carolina-USA 19Florida-USA 17Indiana-USA 16Alabama-USA 15Abu Dhabi-UAE 12California-USA 11Dubai-UAE 11




Problemoftakingcareofelderly(continued)M052503B


Incorrect Response:

timss2011 g8 math

Documents

items classification

versions of items

items content domain

mathematics assessment

set of released items

international mathematics

science study timss

timss andpirls assessments