timss resource kit - national center for education … 2003 8th-grade mathematics concepts and...

8RELEASED

MATHEMATICS ITEMS

This book contains the released Trends in International Mathematics and Science Study (TIMSS) 2003 grade 8 mathematics assessment items. This is not a complete set of all TIMSS 2003 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.

18675.0206

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 2003, please use the following acknowledgement:

SOURCE: TIMSS 2003 Assessment. Copyright © 2005 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.

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Guide to the Content and Layout of This Book

This book contains the released items from TIMSS 2003. Due to slight revisions in terminology and released information between cycles, the format for the items in each cycle differs slightly. Each item appears on a single page and is accompanied by a number of descriptors.

2003 Content Domains:

• Algebra• Data• Geometry• Measurement• Number

2003 Cognitive Domains:

• Knowing facts and procedures• Using concepts• Solving routine problems• Reasoning

Looking at Value of -3x given value of x, the first item from TIMSS 2003, the content domain (algebra) and the cognitive domain (knowing facts and procedures) are also accompanied by the Main Topic (algebraic expressions).

International item numbers identify each item. This number appears just below the item box.

Correct answers are shown beneath each item. These correct answers take two forms:

• Letter code. This form is used for the correct response on multiple-choice items.

• Scoring guide. This form is used to assist in scoring write-in responses. In some cases, partial creditmay be awarded and these items will provide guidelines for fully correct, partially correct, and incorrectresponses.

Sample student responses are provided for some extended response items.

International benchmarks are provided in a table next to each item. These consist of statistics on the percentage of students in each country who answered the question correctly. The countries are ordered in terms of this percentage. The international average is included as well, and this display also indicates which countries scored significantly higher, significantly lower, and not significantly different from this international average.

Main TopicContent Domain

Correct Response: A

Cognitive Domain

TIMSS 2003 8th-Grade Mathematics Concepts and Mathematics Items

Overall Percent Correct

Country average vs. International average:

Higher pNotdifferent OLower q

AlgebRA AlgebraicExpressionsKnowingFactsandProcedures

Valueof-3xgivenvalueofx

Item Number: M012042

e

M012042

If x = −3, what is the value of −3x ?

a −9

b −6

c −1

d 1

e 9

Hong Kong, SAR 84 pKorea, Republic of 84 pChinese Taipei 83 pSingapore 80 pEstonia 77 pJapan 74 pRussian Federation 73 pHungary 69 pIsrael 67 pSerbia and Montenegro 65 pUnited States 65 pBelgium (Flemish) 63 pArmenia 62 pLatvia 61 pLithuania 60 pSlovak Republic 58 pBulgaria 57 pMoldova, Republic of 54 pNetherlands 54 pRomania 51 OSlovenia 51 OLebanon 49 OInternational average 48 OMalaysia 48 OMacedonia, Republic of 47 OIran, Islamic Republic of 44 OPhilippines 44 qIndonesia 43 qJordan 41 qBahrain 40 qCyprus 38 qAustralia 37 qEgypt 37 qEngland 37 qItaly 37 qNew Zealand 35 qBotswana 30 qSweden 28 qTunisia 26 qPalestinian Nat’l Auth. 25 qMorocco 24 qScotland 24 qSouth Africa 16 qChile 15 qSaudi Arabia 11 qNorway 9 q

3Copyright © 2005 International Association for the Evaluation of Educational Achievement (IEA).

Correct Response:

Main TopicContent Domain Cognitive Domain






e


Subtractfractionsinvolvingx

M022185

Subtract:

3

7 7

x x− =

a

2

7

b 3

c 2x

d

x

7

e

2

7

x

Korea, Republic of 86 pHong Kong, SAR 83 pSingapore 81 pJapan 76 pLatvia 76 pChinese Taipei 76 pHungary 74 pRussian Federation 67 pLebanon 67 pRomania 65 pIsrael 65 pEstonia 65 pSerbia and Montenegro 64 pSlovak Republic 63 pBulgaria 63 pMalaysia 61 pArmenia 60 pBelgium (Flemish) 60 pCyprus 58 pMoldova, Republic of 58 pLithuania 57 OInternational average 54 OJordan 54 OBahrain 49 qPhilippines 49 qUnited States 49 qItaly 48 qEgypt 48 qSlovenia 47 qTunisia 47 qBotswana 46 qIran, Islamic Republic of 46 qPalestinian Nat’l Auth. 44 qAustralia 44 qIndonesia 43 qMorocco 43 qNew Zealand 42 qScotland 41 qNorway 40 qSweden 39 qNetherlands 39 qSaudi Arabia 37 qMacedonia, Republic of 37 qEngland 36 qChile 27 qSouth Africa 27 q



Correct Response:

Cognitive Domain






Whichequals2xminus3yplus7xplus5y


C

M03

2036

Which of these is equal to 2x − 3y + 7x + 5y?

a 5x + 2y

b 5x + 8y

c 9x + 2y

d 9x + 8y

Korea, Republic of 82 pJapan 82 pChinese Taipei 79 pSingapore 79 pSlovak Republic 76 pHong Kong, SAR 74 pHungary 74 pEstonia 72 pBelgium (Flemish) 67 pLatvia 66 pIsrael 65 pSerbia and Montenegro 62 pRussian Federation 62 pBulgaria 58 pRomania 58 pLebanon 55 OSlovenia 55 ONetherlands 54 OLithuania 53 OItaly 53 OIran, Islamic Republic of 52 OMalaysia 51 OInternational average 49 OScotland 48 OUnited States 47 OMoldova, Republic of 46 OSweden 45 OEgypt 45 OAustralia 45 OMacedonia, Republic of 41 qNorway 41 qArmenia 41 qJordan 38 qPhilippines 36 qCyprus 35 qPalestinian Nat’l Auth. 33 qEngland 33 qNew Zealand 33 qMorocco 32 qBahrain 27 qChile 25 qBotswana 25 qTunisia 24 qSouth Africa 23 qSaudi Arabia 23 qIndonesia 22 q







AlgebRA AlgebraicExpressions Reasoning

Thevalueofa+2times(bplusc)


SCORINgCorrect Response

• 11

Incorrect Response

• 8

• Otherincorrect(includingcrossedout/erased,straymarks,illegibleorofftask).

M032557

If a + 2b = 5 and c = 3, what is the value of a + 2(b + c)?

Answer: _______________

Korea, Republic of 64 pSingapore 58 pChinese Taipei 57 pHong Kong, SAR 56 pRussian Federation 53 pRomania 40 pHungary 38 pIsrael 38 pJapan 37 pEstonia 35 pLatvia 34 pSerbia and Montenegro 34 pArmenia 33 pMoldova, Republic of 31 pBulgaria 30 pSlovak Republic 28 pBelgium (Flemish) 28 pLithuania 26 pLebanon 25 OInternational average 22 OMalaysia 20 OAustralia 20 OUnited States 20 OCyprus 20 OMacedonia, Republic of 18 qScotland 18 OItaly 16 qNetherlands 16 qEngland 15 qNew Zealand 14 qSlovenia 13 qSweden 10 qEgypt 10 qJordan 9 qIndonesia 8 qTunisia 5 qPalestinian Nat’l Auth. 5 qPhilippines 5 qMorocco 4 qIran, Islamic Republic of 3 qChile 3 qNorway 3 qSouth Africa 3 qBotswana 2 qBahrain 2 qSaudi Arabia 0 q


Student Responses


Thevalueofa+2times(bplusc)(continued)Item Number: M032557

Correct Response:

Incorrect Response:


Correct Response: A







Threeconsecutiveevennumbers

AlgebRA AlgebraicExpressions SolvingRoutineProblems

M022002

Sam wanted to find three consecutive even numbers that add up to 84.He wrote the equation k + (k + 2) + (k + 4) = 84.What does the letter k represent?

a The least of the three even numbers

b The middle even number

c The greatest of the three even numbers

d The average of the three even numbers

Hong Kong, SAR 57 pChinese Taipei 50 pSingapore 48 pKorea, Republic of 46 pRomania 42 pEstonia 37 pRussian Federation 36 pMoldova, Republic of 34 pJapan 34 pBulgaria 34 pSerbia and Montenegro 33 pLatvia 33 pHungary 31 pIsrael 31 pArmenia 30 pBelgium (Flemish) 30 pSlovak Republic 27 ONetherlands 27 OPhilippines 25 OBahrain 25 OInternational average 24 OUnited States 23 OMacedonia, Republic of 22 OItaly 21 OAustralia 20 OBotswana 20 qSouth Africa 19 qSaudi Arabia 19 qLithuania 19 qCyprus 19 qEgypt 18 qJordan 18 qIndonesia 16 qEngland 16 qPalestinian Nat’l Auth. 16 qNew Zealand 16 qIran, Islamic Republic of 15 qSweden 15 qMorocco 15 qSlovenia 12 qLebanon 12 qChile 11 qScotland 11 qNorway 11 qMalaysia 11 qTunisia 6 q



Correct Response:

Cognitive Domain





AlgebRA AlgebraicExpressions UsingConcepts

Totalnumberofbooksthreeboyshave


C

M022251

Graham has twice as many books as Bob. Chan has six more books thanBob. If Bob has x books, which of the following represents the total numberof books the three boys have?

a 3x + 6

b 3x + 8

c 4x + 6

d 5x + 6

e 8x + 2

Singapore 66 pChinese Taipei 59 pKorea, Republic of 55 pHong Kong, SAR 53 pIsrael 41 pHungary 41 pSlovak Republic 38 pRussian Federation 36 pJapan 35 pRomania 35 pNetherlands 35 pEstonia 34 pCyprus 34 pBelgium (Flemish) 33 pItaly 33 OLatvia 32 OLithuania 32 ONew Zealand 31 OSerbia and Montenegro 31 OSlovenia 31 OInternational average 29 OMoldova, Republic of 29 OAustralia 28 OBulgaria 28 OSweden 28 OArmenia 26 OUnited States 26 qEngland 25 qMalaysia 25 qScotland 25 qTunisia 24 qNorway 23 qIran, Islamic Republic of 23 qMorocco 22 qMacedonia, Republic of 22 qEgypt 21 qJordan 20 qLebanon 20 qPalestinian Nat’l Auth. 20 qPhilippines 19 qBahrain 18 qChile 18 qIndonesia 18 qSaudi Arabia 15 qBotswana 13 qSouth Africa 12 q


Correct Response:






AlgebRA AlgebraicExpressions UsingConcepts

Carlapaidxzedsfor3cartonsofjuice


A

M032044

Carla paid x zeds for 3 cartons of juice. What is the price in zeds of1 carton of juice?

a 3x

b x

3

c 3 + x

d 3x

Singapore 85 pHong Kong, SAR 81 pChinese Taipei 74 pBelgium (Flemish) 67 pNetherlands 62 pMalaysia 59 pRussian Federation 58 pEngland 55 pHungary 55 pKorea, Republic of 53 pEstonia 53 pIsrael 53 pSlovak Republic 52 pSweden 52 pJapan 51 pLithuania 51 pScotland 49 pAustralia 49 OUnited States 48 pArmenia 48 OLebanon 48 OLatvia 46 OItaly 45 OInternational average 45 ONew Zealand 43 OSerbia and Montenegro 42 ORomania 42 OBulgaria 42 OMoldova, Republic of 41 OPhilippines 40 qNorway 40 qSlovenia 40 qMacedonia, Republic of 39 qIndonesia 39 qTunisia 36 qCyprus 36 qEgypt 35 qJordan 34 qChile 31 qBahrain 30 qPalestinian Nat’l Auth. 30 qBotswana 29 qMorocco 28 qGhana 28 qSouth Africa 23 qSaudi Arabia 22 qIran, Islamic Republic of 21 q



Correct Response:

Cognitive Domain






b

Findnfromproportionalityequation

AlgebRA EquationsandFormulasKnowingFactsandProcedures

M012040

If

12n

=

3621

, then n equals

a 3

b 7

c 36

d 63

Singapore 93 pKorea, Republic of 89 pHong Kong, SAR 88 pBelgium (Flemish) 86 pNetherlands 85 pChinese Taipei 83 pMalaysia 83 pUnited States 80 pHungary 79 pJapan 79 pScotland 79 pAustralia 76 pEngland 74 pSlovak Republic 74 pIsrael 72 pSlovenia 72 pEstonia 71 pLebanon 71 pRussian Federation 71 pLatvia 70 pNew Zealand 68 OIran, Islamic Republic of 66 OSweden 66 OCyprus 65 OItaly 65 OInternational average 64 OLithuania 64 OTunisia 64 OSerbia and Montenegro 63 OMoldova, Republic of 61 ORomania 61 OBulgaria 59 qNorway 59 qEgypt 58 qIndonesia 58 qArmenia 54 qMorocco 54 qJordan 53 qPalestinian Nat’l Auth. 52 qPhilippines 52 qMacedonia, Republic of 50 qBahrain 44 qChile 44 qBotswana 41 qSaudi Arabia 30 qGhana 28 qSouth Africa 26 q


Correct Response: A







TrueexpressionforvaluesofL,K,M


M022196

If L = 4 when K = 6 and M = 24, which of the following is true?

a L =

M

K

b L =

K

M

c L = KM

d L = K + M

e L = M − K

Singapore 88 pKorea, Republic of 86 pHong Kong, SAR 84 pChinese Taipei 82 pEstonia 81 pRussian Federation 79 pHungary 79 pJapan 77 pBelgium (Flemish) 76 pSlovak Republic 75 pLatvia 75 pSerbia and Montenegro 73 pLithuania 73 pSweden 70 pLebanon 69 pRomania 67 pArmenia 66 pSlovenia 66 pIsrael 64 pMoldova, Republic of 63 pBulgaria 63 OTunisia 63 pUnited States 62 pMacedonia, Republic of 60 ONetherlands 59 OInternational average 58 OMorocco 57 OItaly 57 OEngland 54 OMalaysia 54 OIndonesia 54 OCyprus 52 qAustralia 49 qScotland 49 qNew Zealand 49 qJordan 44 qNorway 40 qEgypt 38 qIran, Islamic Republic of 38 qPalestinian Nat’l Auth. 35 qBahrain 35 qBotswana 28 qPhilippines 25 qSaudi Arabia 22 qChile 21 qSouth Africa 14 q








• 15

Incorrect Response

• 25[100÷4]

• 60[80–(4x5)]

• 71[80–4–5]

• Anyexpressionorequation,otherthanx=15,containingx.

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


Solveequationforx


M022253

If 4(x + 5) = 80, then x =

Answer: _______________

Hong Kong, SAR 90 pSingapore 82 pKorea, Republic of 82 pJapan 80 pChinese Taipei 80 pEstonia 72 pHungary 70 pRussian Federation 66 pSlovak Republic 65 pBelgium (Flemish) 64 pLatvia 64 pSlovenia 64 pArmenia 61 pSerbia and Montenegro 61 pRomania 60 pBulgaria 59 pUnited States 57 pIsrael 57 pCyprus 54 pMoldova, Republic of 53 pLithuania 51 pAustralia 50 pMalaysia 46 ONetherlands 44 OInternational average 44 OEngland 44 ONew Zealand 44 OMacedonia, Republic of 37 qItaly 37 qScotland 37 qLebanon 31 qSweden 28 qTunisia 26 qJordan 25 qIndonesia 25 qEgypt 23 qPhilippines 22 qBahrain 19 qIran, Islamic Republic of 18 qPalestinian Nat’l Auth. 17 qMorocco 16 qNorway 11 qChile 9 qSaudi Arabia 6 qSouth Africa 5 qBotswana 5 q


Student Responses


Solveequationforx(continued)Item Number: M022253

Correct Response:

Incorrect Response:



Correct Response: A

Cognitive Domain






Ifxplus3yequals11and2xplus3yequals13


M032728

If x + 3y = 11 and 2x + 3y = 13, then y =

a 3

b 2

c −2

d −3

Korea, Republic of 76 pSingapore 70 pChinese Taipei 69 pJapan 61 pHong Kong, SAR 59 pScotland 55 pBelgium (Flemish) 53 pLatvia 51 pEstonia 50 pUnited States 49 pSerbia and Montenegro 49 pEngland 49 ORomania 48 OHungary 47 OSlovak Republic 46 ONew Zealand 45 OMoldova, Republic of 45 OBulgaria 45 ORussian Federation 44 OAustralia 44 OIsrael 44 ONetherlands 43 OMalaysia 43 OInternational average 42 OLebanon 40 OBotswana 38 OLithuania 37 OJordan 37 qTunisia 36 qSlovenia 36 OMacedonia, Republic of 36 qSweden 35 qPhilippines 35 qCyprus 34 qEgypt 34 qIran, Islamic Republic of 34 qIndonesia 33 qChile 31 qPalestinian Nat’l Auth. 31 qSouth Africa 31 qNorway 30 qSaudi Arabia 29 qArmenia 29 qItaly 28 qBahrain 27 qMorocco 23 q


Correct Response:






AlgebRA EquationsandFormulas SolvingRoutineProblems

Ifxminusyequals5andx/2equals3


b

M032208

If x − y = 5 and

x

2 = 3, what is the value of y?

a 6

b 1

c −1

d −7

Singapore 82 pKorea, Republic of 79 pHong Kong, SAR 78 pChinese Taipei 77 pAustralia 69 pBelgium (Flemish) 69 pNew Zealand 67 pHungary 67 pEngland 66 pUnited States 63 pScotland 61 pJapan 61 pMalaysia 58 pIsrael 58 pEstonia 58 pSerbia and Montenegro 58 pRomania 57 pLatvia 56 pSlovenia 55 OCyprus 55 pNorway 55 OSweden 53 ONetherlands 53 OLithuania 53 ORussian Federation 52 OInternational average 51 OLebanon 48 OSlovak Republic 47 OMoldova, Republic of 47 OItaly 46 qMacedonia, Republic of 45 qBulgaria 44 qPalestinian Nat’l Auth. 43 qArmenia 43 qBotswana 39 qIndonesia 38 qBahrain 38 qJordan 38 qChile 37 qEgypt 36 qPhilippines 33 qTunisia 31 qMorocco 31 qSouth Africa 30 qIran, Islamic Republic of 26 qSaudi Arabia 24 q



Correct Response: A

Cognitive Domain





Ifa/bequals70



M032210

If

a

b = 70, then

a

b2 =

a 35

b 68

c 72

d 140

Chinese Taipei 70 pSingapore 69 pKorea, Republic of 69 pHong Kong, SAR 68 pEstonia 61 pRussian Federation 60 pHungary 58 pSerbia and Montenegro 57 pJapan 55 pRomania 53 pLatvia 53 pBelgium (Flemish) 52 pLithuania 51 pSlovak Republic 47 pBulgaria 46 pIsrael 44 pItaly 44 OMacedonia, Republic of 42 OMoldova, Republic of 41 OIndonesia 41 OArmenia 41 OInternational average 40 ONetherlands 40 OSweden 38 OUnited States 38 OEngland 38 OLebanon 37 OSlovenia 37 OAustralia 37 OMalaysia 36 ONew Zealand 32 qScotland 30 qCyprus 30 qTunisia 30 qPhilippines 27 qIran, Islamic Republic of 27 qEgypt 26 qBotswana 25 qMorocco 24 qJordan 23 qNorway 22 qChile 22 qPalestinian Nat’l Auth. 21 qSouth Africa 17 qSaudi Arabia 15 qBahrain 15 q








7orangesand4lemonscost43zeds



• 7x+4y=43(orequivalent)and11x+12y=79(orequivalent).

Incorrect Response

• Oneequationcorrectandoneincorrect/missing.


M032545

At a market, 7 oranges and 4 lemons cost 43 zeds, and 11 oranges and12 lemons cost 79 zeds. Using x to represent the cost of an orange and y torepresent the cost of a lemon, write two equations that could be used to findthe values of x and y.

Equation 1:__________________________________________________________

Equation 2:__________________________________________________________

Hong Kong, SAR 72 pJapan 67 pChinese Taipei 62 pArmenia 61 pSingapore 60 pKorea, Republic of 57 pEstonia 46 pSerbia and Montenegro 43 pIsrael 41 pRussian Federation 39 pRomania 38 pJordan 37 pHungary 34 pBulgaria 33 pMoldova, Republic of 27 OEgypt 27 OSlovak Republic 25 OMacedonia, Republic of 24 OInternational average 24 OBelgium (Flemish) 22 OIran, Islamic Republic of 20 OUnited States 20 qLatvia 20 qScotland 20 qLithuania 19 qEngland 18 qBahrain 16 qIndonesia 16 qMalaysia 15 qSweden 15 qAustralia 15 qItaly 14 qNew Zealand 12 qCyprus 11 qSlovenia 9 qMorocco 9 qNetherlands 9 qPhilippines 7 qPalestinian Nat’l Auth. 6 qLebanon 6 qBotswana 5 qSaudi Arabia 4 qNorway 3 qChile 3 qGhana 2 qSouth Africa 2 qTunisia 1 q


Student Responses


Correct Response:

Incorrect Response:

7orangesand4lemonscost43zeds(continued)Item Number: M032545


Correct Response:






C


Objectsbalancedonscale

AlgebRA EquationsandFormulas UsingConcepts

M012002

The objects on the scale make it balance exactly. On the left pan there is a1 kg weight (mass) and half a brick. On the right pan there is one brick.

What is the weight (mass) of one brick?

a 0.5 kg

b 1 kg

c 2 kg

d 3 kg

1 kg

Estonia 86 pRussian Federation 85 pNetherlands 83 pJapan 82 pSingapore 82 pHong Kong, SAR 81 pItaly 79 pBelgium (Flemish) 78 pKorea, Republic of 78 pSlovak Republic 78 pSweden 78 pLatvia 77 pAustralia 76 pChinese Taipei 76 pEngland 76 pLithuania 76 pHungary 75 pNew Zealand 75 pMalaysia 74 pScotland 74 pUnited States 74 pBulgaria 73 pSlovenia 73 pMoldova, Republic of 68 pIsrael 67 pNorway 66 ORomania 66 OSerbia and Montenegro 65 OCyprus 64 OInternational average 63 OIran, Islamic Republic of 63 OMacedonia, Republic of 63 OJordan 52 qArmenia 51 qTunisia 51 qChile 50 qMorocco 49 qPalestinian Nat’l Auth. 45 qBahrain 42 qEgypt 42 qIndonesia 41 qLebanon 41 qBotswana 36 qPhilippines 34 qSaudi Arabia 31 qSouth Africa 28 qGhana 26 q



Correct Response: A

Cognitive Domain





M032046

If 23 += xy , which of these expresses x in terms of y?

a 32−

=y

x

b 32+

=y

x

c x =

y

3 − 2

d x =

y

3 + 2

AlgebRA EquationsandFormulas UsingConcepts

Ifyequals3xplus2


Singapore 61 pHong Kong, SAR 60 pKorea, Republic of 52 pChinese Taipei 48 pJapan 46 pArmenia 45 pRussian Federation 44 pRomania 44 pSerbia and Montenegro 43 pMoldova, Republic of 34 pBulgaria 34 pMalaysia 31 pBelgium (Flemish) 31 pIndonesia 30 pMacedonia, Republic of 30 pEstonia 27 OUnited States 26 OInternational average 25 OLebanon 24 OIsrael 24 OJordan 23 OPhilippines 22 qEgypt 21 qLithuania 21 qHungary 21 qLatvia 21 qCyprus 20 qItaly 20 qEngland 20 qSlovak Republic 19 qAustralia 18 qNetherlands 17 qTunisia 17 qIran, Islamic Republic of 16 qPalestinian Nat’l Auth. 15 qBahrain 15 qSlovenia 15 qNew Zealand 14 qScotland 12 qMorocco 12 qSaudi Arabia 12 qSweden 11 qBotswana 10 qSouth Africa 10 qChile 9 qNorway 6 q


Correct Response:






AlgebRA Patterns Reasoning

Numberofmatchstickscontinuingpattern


b

M012017

Matchsticks are arranged as shown in the figures.

If the pattern is continued, how many matchsticks would be used to makeFigure 10?

a 30

b 33

c 36

d 39

e 42

Figure 1 Figure 3Figure 2

Korea, Republic of 78 pSingapore 73 pChinese Taipei 71 pJapan 67 pHong Kong, SAR 66 pBelgium (Flemish) 64 pNew Zealand 63 pAustralia 62 pScotland 61 pHungary 61 pSlovak Republic 60 pNetherlands 59 pRussian Federation 59 pSweden 59 pEstonia 58 pIsrael 58 pMalaysia 57 pUnited States 56 pSlovenia 56 pLithuania 56 pMoldova, Republic of 55 pItaly 54 pBulgaria 53 OEngland 52 ORomania 51 OSerbia and Montenegro 51 OMacedonia, Republic of 50 OLatvia 49 OCyprus 49 OInternational average 48 OArmenia 47 ONorway 46 OChile 43 qPhilippines 41 qBahrain 37 qIran, Islamic Republic of 34 qJordan 33 qLebanon 32 qEgypt 30 qTunisia 29 qIndonesia 29 qPalestinian Nat’l Auth. 29 qBotswana 27 qMorocco 26 qSouth Africa 24 qSaudi Arabia 16 qGhana 16 q







SCORINgCorrect

• 55

Incorrect Response

• 27AND46[23+4and37+9]

• Either27OR46



Numbersinsequenceincreasingby4

AlgebRA Patterns Reasoning

M022008

The numbers in the sequence 7, 11, 15, 19, 23, … increase by four. Thenumbers in the sequence 1, 10, 19, 28, 37, … increase by nine. The number19 is in both sequences. If the two sequences are continued, what is the nextnumber that is in BOTH the first and the second sequences?

Answer: _______________

Armenia 63 pKorea, Republic of 51 pSingapore 50 pHungary 49 pJapan 46 pUnited States 45 pItaly 45 pBelgium (Flemish) 43 pSlovenia 41 pAustralia 39 pHong Kong, SAR 39 pSlovak Republic 39 pChinese Taipei 39 pBulgaria 38 pEstonia 38 pNetherlands 38 pScotland 37 pSweden 35 pMalaysia 35 pEngland 34 OTunisia 34 ONew Zealand 33 OLithuania 33 ORussian Federation 32 ORomania 32 OIsrael 31 OCyprus 31 OLatvia 31 OInternational average 31 OMoldova, Republic of 30 OIran, Islamic Republic of 25 qMacedonia, Republic of 24 qChile 24 qIndonesia 23 qSerbia and Montenegro 23 qBahrain 22 qMorocco 20 qNorway 20 qPalestinian Nat’l Auth. 19 qBotswana 18 qLebanon 17 qJordan 16 qEgypt 14 qPhilippines 14 qSaudi Arabia 8 qSouth Africa 6 qGhana 4 q


Student Responses


Numbersinsequenceincreasingby4(continued)Item Number: M022008

Correct Response:

Incorrect Response:



Item Number: M022261A


• 18AND32

Incorrect Response

• 18andanynumberotherthan32.

• 18andnonumericalresponseforthe4thfigure.


Sequenceoffigureswithtriangles:filltable

M022261

The three figures below are divided into small congruent triangles.

A. Complete the table below. First, fill in how many small triangles makeup Figure 3. Then, find the number of small triangles that would beneeded for the 4th figure if the sequence of figures is extended.

Number ofFigure Small Triangles

1 2

2 8

3

4

B. The sequence of figures is extended to the 7th figure. How many smalltriangles would be needed for Figure 7?

Answer: _______________

C. The sequence of figures is extended to the 50th figure. Explain a way tofind the number of small triangles in the 50th figure that does notinvolve drawing it and counting the number of triangles.

Figure 1 Figure 2 Figure 3

1

2

12

34

5

6

7

8




Korea, Republic of 78 p

Singapore 74 p

Japan 74 p

Hong Kong, SAR 72 p

Chinese Taipei 69 p

Netherlands 59 p

Australia 57 p

England 57 p

New Zealand 55 p

Armenia 53 p

Scotland 53 p

Belgium (Flemish) 51 p

Hungary 50 p

United States 50 p

Estonia 50 p

Sweden 49 p

Slovenia 42 p

Malaysia 42 p

Israel 42 p

Russian Federation 41 p

Slovak Republic 40 O

Latvia 38 O

Lithuania 38 O

International average 36 O

Italy 35 O

Norway 34 O

Romania 31 O

Moldova, Republic of 31 q

Serbia and Montenegro 31 q

Cyprus 30 q

Bulgaria 30 q

Macedonia, Republic of 25 q

Chile 23 q

Jordan 21 q

Indonesia 20 q

Palestinian Nat’l Auth. 17 q

Philippines 17 q

Morocco 16 q

Bahrain 16 q

Iran, Islamic Republic of 15 q

Egypt 15 q

Lebanon 12 q

Botswana 11 q

South Africa 6 q

Tunisia 5 q

Saudi Arabia 4 q

Ghana 3 q

Main Topic

A. AlgebRAB.ALgEBRAC.ALgEBRA

PatternsPatternsPatterns

Solving Routine ProblemsSolvingRoutineProblems

Reasoning

Content Domain Cognitive Domain


Student Responses


Sequenceoffigureswithtriangles:filltable(continued)Item Number: M022261A

Correct Response:

Incorrect Response:


Item Number: M022261B


• 98

Incorrect Response

• 49[Multiplies7x7]

• 58[Seriesis2,8,18,28,38…7thtermis58]


Sequenceoffigureswithtriangles:7thfigure

M022261




1 2

2 8

3

4


Answer: _______________



1

2

12

34

5

6

7

8





Singapore 56 p

Chinese Taipei 56 p

Hong Kong, SAR 56 p

Japan 55 p

Armenia 42 p

Netherlands 40 p

Australia 33 p

Scotland 31 p

Hungary 30 p

United States 30 p

New Zealand 29 p


Sweden 26 p

England 25 O

Malaysia 24 O

Estonia 24 O

Italy 24 O

Russian Federation 23 O

Slovenia 22 O



Moldova, Republic of 20 O

Israel 20 O

Lithuania 19 O

Romania 19 O

Latvia 19 O

Serbia and Montenegro 19 O

Cyprus 17 q

Bulgaria 16 q

Indonesia 15 q

Norway 14 q

Jordan 12 q

Philippines 11 q



Chile 9 q

Egypt 9 q

Bahrain 8 q


Morocco 7 q

Lebanon 6 q

Botswana 5 q

South Africa 4 q

Tunisia 2 q

Ghana 2 q

Saudi Arabia 0 q


Main Topic

A.ALgEBRAb. AlgebRAC.ALgEBRA


SolvingRoutineProblemsSolving Routine Problems

Reasoning



Student Responses


Sequenceoffigureswithtriangles:7thfigure(continued)Item Number: M022261B

Correct Response:

Incorrect Response:



Item Number: M022261C

SCORINgCorrect Response• Correctgeneral(i.e.,literal)expression,e.g.,2n2,orequivalentexpressedinwords.

• 2x502OR2x50x50OR100x50OR(50+50)x50ORequivalentexpressedinwords(disregarderrorsincomputation).

Partial Response• Derivesanswer(5000)withoutshowingwork.

• Otherpartiallycorrect.

Incorrect Response• 50x2OR100

• 50x50OR2,500


Sequenceoffigureswithtriangles:50thfigure

M022261




1 2

2 8

3

4


Answer: _______________



1

2

12

34

5

6

7

8




Chinese Taipei 49 p


Hong Kong, SAR 45 p

Singapore 44 p

Japan 44 p

Netherlands 36 p

Australia 26 p

Hungary 24 p

Scotland 22 p


England 20 p

United States 19 p

Sweden 17 p

New Zealand 16 O

Estonia 15 O



Italy 14 O

Latvia 13 O

Slovenia 13 O

Serbia and Montenegro 11 q

Lithuania 11 q

Romania 11 O

Malaysia 10 q

Israel 10 q

Cyprus 10 q

Norway 9 q

Russian Federation 9 q

Armenia 8 q

Indonesia 7 q

Chile 6 q

Jordan 5 q

Egypt 5 q



Philippines 4 q

Bulgaria 4 q

Bahrain 4 q


Morocco 2 q

Botswana 2 q

South Africa 1 q

Tunisia 1 q

Lebanon 1 q

Ghana 1 q

Saudi Arabia 0 q

Moldova, Republic of 0 q

Main Topic

A.ALgEBRAB.ALgEBRAC. AlgebRA


SolvingRoutineProblemsSolvingRoutineProblems

Reasoning



Student Responses


Sequenceoffigureswithtriangles/50thfigure(continued)Item Number: M022261C

Correct Response:

Partial Response:



Sequenceoffigureswithtriangles/50thfigure(continued)Item Number: M022261C

Student Responses (continued)

Incorrect Response:






TIMSS 2003 8th-Grade Mathematics Concepts and Mathematics ItemsM

032744

If the pattern on the grid below was continued, what letter would identifythe orientation of the tile in the cell labeled X?

Answer: _______________________

Questions for Geometry Tiling continue.

X


• D(includingdrawingoftileD).

Incorrect Response

• A,B,orC(includingdrawings).



Geometrytiling:identifycellwithletter

AlgebRA Patterns UsingConcepts

Japan 73 pKorea, Republic of 66 pSingapore 62 pSweden 57 pHong Kong, SAR 57 pNetherlands 55 pChinese Taipei 55 pEstonia 55 pHungary 54 pScotland 54 pAustralia 53 pNew Zealand 51 pBelgium (Flemish) 50 pUnited States 48 pEngland 47 pSlovak Republic 46 pLatvia 45 pMalaysia 44 pSlovenia 43 pRussian Federation 39 pNorway 36 OItaly 34 OIsrael 34 OInternational average 32 OBulgaria 30 ORomania 29 OLithuania 27 OCyprus 24 qChile 23 qBahrain 22 qSerbia and Montenegro 20 qJordan 16 qMoldova, Republic of 15 qPhilippines 14 qIran, Islamic Republic of 13 qMacedonia, Republic of 13 qIndonesia 11 qLebanon 10 qSouth Africa 8 qSaudi Arabia 8 qMorocco 7 qEgypt 7 qBotswana 7 qArmenia 6 qPalestinian Nat’l Auth. 3 qTunisia 2 q


Student Responses


Geometrytiling:identifycellwithletter(continued)Item Number: M032744

Correct Response:



Geometrytiling:identifycellwithletter(continued)Item Number: M032744

Incorrect Response:




Correct Response:

Cognitive Domain





M012029

(3, 6) , (6, 15) , (8, 21)

Which of these describes how to get the second number from the firstnumber in every ordered pair above?

a Add 3

b Subtract 3

c Multiply by 2

d Multiply by 2 and then add 3

e Multiply by 3 and then subtract 3

AlgebRA Relationships Reasoning


e

Setsoforderedpairsofnumbers

Korea, Republic of 85 pJapan 76 pHungary 75 pEstonia 74 pChinese Taipei 71 pSingapore 71 pHong Kong, SAR 71 pLatvia 71 pAustralia 70 pRussian Federation 69 pScotland 69 pUnited States 68 pNetherlands 68 pNew Zealand 67 pEngland 64 pLithuania 64 pBelgium (Flemish) 62 pSerbia and Montenegro 58 pIsrael 57 pSlovak Republic 56 pBulgaria 54 OSlovenia 53 OItaly 51 OMalaysia 51 OInternational average 50 OJordan 46 qSweden 45 qMacedonia, Republic of 42 qRomania 42 qNorway 40 qMoldova, Republic of 39 qBahrain 38 qBotswana 36 qIran, Islamic Republic of 35 qArmenia 34 qEgypt 33 qIndonesia 33 qPalestinian Nat’l Auth. 33 qPhilippines 31 qSaudi Arabia 26 qCyprus 25 qChile 24 qGhana 23 qLebanon 23 qSouth Africa 21 q


Correct Response:






012025

The graph represents the distance and time of a hike taken by Joshua and Liam.

If they both started from the same place and walked in the same direction,at what time did they meet?

a 8:00

b 8:30

c 9:00

d 10:00

e 11:00

8:00 8:30 9:00 9:30 10:00 10:30 11:00 11:30 12:00 12:30

Time

Dis

tance

(ki

lom

eter

s)

JoshuaLiam

5.5

5.0

4.5

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0

AlgebRA Relationships SolvingRoutineProblems

Intersectionpointofdistance/timegraphs


D

Japan 96 pHong Kong, SAR 90 pKorea, Republic of 89 pEstonia 88 pSingapore 87 pHungary 84 pLithuania 84 pSweden 84 pRussian Federation 81 pNetherlands 81 pChinese Taipei 81 pEngland 81 pUnited States 80 pSlovenia 79 pLatvia 78 pItaly 75 pAustralia 75 pBelgium (Flemish) 73 pScotland 73 pNew Zealand 72 pIsrael 72 pSlovak Republic 70 pSerbia and Montenegro 68 pBulgaria 67 pNorway 64 OInternational average 62 OCyprus 58 ORomania 58 OMacedonia, Republic of 53 qMalaysia 53 qJordan 52 qArmenia 52 qChile 51 qBahrain 50 qEgypt 47 qMoldova, Republic of 47 qIndonesia 46 qLebanon 42 qBotswana 41 qPalestinian Nat’l Auth. 39 qSaudi Arabia 37 qPhilippines 31 qIran, Islamic Republic of 26 qGhana 21 qSouth Africa 19 qTunisia 14 q



Correct Response:

Cognitive Domain





b


Testscorefrequencytable

DATA DataInterpretation Reasoning

/

///

///// /

//

////

///

/

M01

2037

The table shows scores for a class on a 10-point test.

Test Score Tally Frequency

4

5

6

7

8

9

10 1

3

4

2

6

3

1

How many in the class had a score greater than 7 ?

a 2

b 8

c 10

d 12

e 20

Korea, Republic of 85 pNetherlands 77 pSlovenia 68 pBelgium (Flemish) 67 pSweden 65 pUnited States 65 pScotland 64 pSingapore 63 pLithuania 61 pIsrael 59 pNew Zealand 59 pEngland 58 pEstonia 58 pAustralia 56 pHungary 56 pSerbia and Montenegro 56 pNorway 55 pIndonesia 53 pLatvia 53 pRussian Federation 52 OBahrain 51 OChinese Taipei 51 OMacedonia, Republic of 51 OSlovak Republic 49 OHong Kong, SAR 48 OInternational average 48 OMalaysia 47 ORomania 47 OJordan 46 OItaly 45 OJapan 44 qCyprus 42 qEgypt 42 qIran, Islamic Republic of 42 qArmenia 39 qPhilippines 39 qPalestinian Nat’l Auth. 36 qTunisia 35 qBulgaria 34 qBotswana 33 qChile 33 qLebanon 31 qMoldova, Republic of 31 qGhana 27 qSaudi Arabia 26 qSouth Africa 22 qMorocco 21 q


Correct Response:






DATA Datainterpretation Reasoning

Howmanypencilssoldfrombargraph


C

M022189

The graph shows the number of pens, pencils, rulers, and erasers sold by astore in one week.

The names of the items are missing from the graph. Pens were the itemmost often sold, and fewer erasers than any other item were sold.More pencils than rulers were sold. How many pencils were sold?

a 40

b 80

c 120

d 140

Items Sold by Store

Num

ber

of

Item

s

0

20

40

60

80

100

120

140

160

Belgium (Flemish) 90 pChinese Taipei 89 pJapan 88 pHong Kong, SAR 88 pKorea, Republic of 87 pMalaysia 87 pEstonia 87 pSlovenia 86 pUnited States 86 pSweden 86 pNetherlands 85 pHungary 85 pScotland 84 pSingapore 83 pLatvia 82 pSlovak Republic 80 pRussian Federation 80 pItaly 80 pNorway 78 pEngland 78 pNew Zealand 78 pLithuania 77 pCyprus 76 pAustralia 76 pIsrael 70 OInternational average 67 OBulgaria 67 OBahrain 66 OSerbia and Montenegro 63 qMoldova, Republic of 62 qIran, Islamic Republic of 61 qMacedonia, Republic of 59 qRomania 59 qJordan 59 qMorocco 53 qArmenia 51 qChile 50 qEgypt 49 qIndonesia 49 qPalestinian Nat’l Auth. 48 qSaudi Arabia 45 qLebanon 42 qTunisia 40 qBotswana 37 qPhilippines 32 qSouth Africa 28 qGhana 24 q







032762

Betty talks for less than 2 hours per month. Which plan would be lessexpensive for her?

Less expensive plan ______________

Explain your answer in terms of both the monthly fee and free minutes.

Questions for Phone Plans continue.


• PlanBwithexplanationthatincludesfreeminutesusedandexplicitreferencetolowermonthlyfeeforPlanB.

Partial Response

• PlanBwithexplicitreferencetolowermonthlyfeeandnoreferencetofreeminutes.

Incorrect Response

• PlanBwithinadequate(onlyfreeminutes)ornoexplanation.

• PlanAwithorwithoutexplanation.



Phoneplans:leastexpensiveplanforBetty

DATA Datainterpretation Reasoning

Japan 49 pEngland 45 pAustralia 44 pEstonia 44 pKorea, Republic of 40 pSingapore 40 pHungary 39 pBelgium (Flemish) 38 pLithuania 37 pUnited States 37 pScotland 36 pIsrael 33 pNew Zealand 30 pNetherlands 28 pHong Kong, SAR 28 pSlovenia 27 pSweden 27 pMalaysia 27 pChinese Taipei 27 pSlovak Republic 26 pItaly 23 OLatvia 22 OInternational average 21 OJordan 20 OBahrain 18 ONorway 18 qRomania 16 qRussian Federation 15 qEgypt 14 qCyprus 13 qIndonesia 12 qSerbia and Montenegro 12 qChile 12 qBulgaria 12 qLebanon 11 qPhilippines 11 qMacedonia, Republic of 10 qSaudi Arabia 8 qMorocco 7 qSouth Africa 6 qPalestinian Nat’l Auth. 5 qIran, Islamic Republic of 4 qTunisia 4 qGhana 3 qBotswana 2 qArmenia 2 qMoldova, Republic of 1 q


Student Responses


Correct Response:

Partial Response:

Incorrect Response:

Phoneplans:leastexpensiveplanforBetty(continued)Item Number: M032762



Correct Response:

Cognitive Domain





A


graphofcoolingwater

DATA Datainterpretation SolvingRoutineProblems

M022135

A beaker of water which has reached boiling point is allowed to cool.The temperature of the water is recorded at five minute intervals, and atemperature-time graph is drawn.

Cooling Curve

About how many minutes did it take for the water to cool the first20 degrees?

a 3

b 8

c 37

d 50

100

80

60

40

20Tem

per

ature

(°C

)

Time (minutes)

0 5 10 15 20 25 30 35 40 45 50

Belgium (Flemish) 70 pSweden 62 pAustralia 59 pEstonia 57 pHungary 56 pScotland 55 pEngland 55 pNorway 54 pSingapore 54 pNetherlands 53 pUnited States 52 pNew Zealand 49 pLithuania 49 pLatvia 47 pChinese Taipei 45 pLebanon 40 pItaly 40 pSlovenia 39 pJapan 39 pRussian Federation 38 pIsrael 36 OIndonesia 35 OArmenia 35 OSlovak Republic 34 OMalaysia 33 OInternational average 33 OSerbia and Montenegro 33 OBulgaria 32 ORomania 30 OMoldova, Republic of 28 qHong Kong, SAR 26 qChile 25 qCyprus 21 qJordan 18 qIran, Islamic Republic of 18 qMacedonia, Republic of 17 qSouth Africa 14 qPalestinian Nat’l Auth. 14 qGhana 13 qBotswana 12 qKorea, Republic of 11 qBahrain 11 qMorocco 10 qPhilippines 10 qSaudi Arabia 9 qEgypt 8 qTunisia 4 q








• PlanA=140zedsandPlanB=375zeds,withworkshown.

Partial Response

• 140zedsand375zedswithnoworkshown.

• PlanAorplanBcorrectwithworkshownbutnotboth.

Incorrect Response

• Incorrect(includingcrossedout/erased,straymarks,illegible,orofftask).


Phoneplans:costofplansforFrank


M032763

Frank talks for 5 hours per month at the night rate. What would each plancost him per month? Show your work.

Cost Per Month for Plan A: _______________ zeds

Cost Per Month for Plan B: _______________ zeds

Questions for Phone Plans continue.

Singapore 27 pJapan 19 pChinese Taipei 18 pHong Kong, SAR 15 pKorea, Republic of 15 pNetherlands 14 pSweden 12 pLithuania 11 pBelgium (Flemish) 11 pEstonia 10 pHungary 10 pEngland 8 OUnited States 8 pNew Zealand 7 OScotland 7 OSlovak Republic 7 OAustralia 7 OIsrael 6 OMalaysia 6 OInternational average 6 OLatvia 6 OSlovenia 5 ORussian Federation 5 ORomania 5 ONorway 5 OBulgaria 4 OSerbia and Montenegro 3 qItaly 3 qMoldova, Republic of 2 qJordan 1 qCyprus 1 qMacedonia, Republic of 1 qIndonesia 1 qSouth Africa 1 qArmenia 1 qPalestinian Nat’l Auth. 1 qPhilippines 1 qChile 0 qIran, Islamic Republic of 0 qEgypt 0 qLebanon 0 qBahrain 0 qGhana 0 qTunisia 0 qMorocco 0 qBotswana 0 qSaudi Arabia 0 q


Student Responses


Correct Response:

Inorrect Response:

Phoneplans:costofplansforFrank(continued)Item Number: M032763








• 150withworkshown.

Partial Response

• 150withnoworkshown.

• Correctmethodbutwithcalculationerror.

• 1230withcalculationsleadingto30.

Incorrect Response



Phoneplans:minutestalkbyDarlene


Singapore 28 pKorea, Republic of 22 pHong Kong, SAR 21 pChinese Taipei 20 pJapan 19 pNetherlands 17 pBelgium (Flemish) 13 pSweden 12 pEstonia 11 pEngland 11 pHungary 9 pLithuania 9 pAustralia 8 OUnited States 8 pSlovak Republic 8 ONew Zealand 7 OInternational average 6 OLatvia 6 OScotland 6 OSlovenia 5 OIsrael 5 ORomania 5 ONorway 5 ORussian Federation 4 qMalaysia 4 qGhana 3 qBulgaria 3 qItaly 3 qMoldova, Republic of 2 qJordan 2 qCyprus 2 qSerbia and Montenegro 2 qMacedonia, Republic of 1 qIndonesia 1 qSouth Africa 1 qBahrain 1 qLebanon 0 qTunisia 0 qIran, Islamic Republic of 0 qChile 0 qPhilippines 0 qArmenia 0 qPalestinian Nat’l Auth. 0 qMorocco 0 qBotswana 0 qEgypt 0 qSaudi Arabia 0 q

M032764

Darlene signed up for the Plan B, and the cost of one month of service was75 zeds. How many minutes did she talk that month? Show your work.

Minutes talked ______________

End of Phone Plans section.


Student Responses


Phoneplans:minutestalkbyDarlene(continued)Item Number: M032764

Correct Response:

Partial Response:

Incorrect Response:


Correct Response:






C


Comparisonoftwoaveragescores

DATA DataInterpretation UsingConcepts

Chinese Taipei 90 pKorea, Republic of 90 pSingapore 88 pHong Kong, SAR 87 pMalaysia 84 pJapan 81 pSlovak Republic 78 pLithuania 76 pNetherlands 76 pLatvia 75 pTunisia 75 pSlovenia 74 pUnited States 74 pBulgaria 73 pIsrael 73 pScotland 73 pEstonia 72 pHungary 72 pMoldova, Republic of 72 ORomania 72 pSerbia and Montenegro 72 pRussian Federation 70 OAustralia 69 OBelgium (Flemish) 69 OItaly 69 OInternational average 68 OMacedonia, Republic of 68 OSweden 66 OArmenia 65 OCyprus 65 OIran, Islamic Republic of 64 OMorocco 64 OChile 62 qNorway 61 qPhilippines 61 qEgypt 60 qEngland 60 qNew Zealand 60 qBahrain 58 qIndonesia 56 qBotswana 53 qJordan 52 qPalestinian Nat’l Auth. 51 qGhana 43 qSouth Africa 43 qSaudi Arabia 38 q

M012006

Joe had three test scores of 78, 76, and 74, while Mary had scores of 72, 82,and 74. How did Joe’s average (mean) score compare with Mary’s average(mean) score?

a Joe’s was 1 point higher.

b Joe’s was 1 point lower.

c Both averages were the same.

d Joe’s was 2 points higher.

e Joe’s was 2 points lower.



Correct Response:

Cognitive Domain





DATA DataInterpretation UsingConcepts

Piegraphofcropdistribution


D

Korea, Republic of 93 pJapan 92 pNetherlands 88 pAustralia 86 pBelgium (Flemish) 86 pSweden 85 pHong Kong, SAR 85 pChinese Taipei 84 pLatvia 84 pSingapore 83 pSlovak Republic 82 pEngland 82 pEstonia 82 pSlovenia 82 pLithuania 82 pHungary 81 pNew Zealand 81 pUnited States 81 pScotland 81 pIsrael 79 pNorway 78 pRussian Federation 78 pCyprus 76 pItaly 74 ORomania 72 OInternational average 71 OTunisia 71 OBulgaria 70 OEgypt 69 OMoldova, Republic of 67 OMorocco 67 OJordan 66 qMacedonia, Republic of 65 qSerbia and Montenegro 65 qIran, Islamic Republic of 64 qMalaysia 63 qBahrain 63 qPalestinian Nat’l Auth. 61 qArmenia 60 qChile 57 qSaudi Arabia 52 qBotswana 51 qPhilippines 50 qLebanon 49 qIndonesia 45 qGhana 41 qSouth Africa 33 q

M012014

The graph shows the distribution of crops grown in a certain country.

According to the information in the graph, which of these statements is true?

a More oats are grown than wheat.

b Corn is more than one-half of the country’s crop.

c Oats are more than one-third of the country’s crop.

d The total crop of oats and wheat is greater than the corn crop.

Wheat Corn

OatsOther


Correct Response:






b


Mostlikelysectoronspinner

DATA UncertaintyandProbability Reasoning

Hong Kong, SAR 87 pChinese Taipei 85 pNetherlands 85 pJapan 82 pSweden 81 pBelgium (Flemish) 81 pEngland 79 pSingapore 79 pKorea, Republic of 79 pUnited States 78 pAustralia 78 pHungary 76 pScotland 76 pIsrael 74 pSlovenia 74 pNorway 73 pEstonia 73 pLatvia 71 pNew Zealand 71 pSlovak Republic 69 pCyprus 69 pLithuania 67 pSerbia and Montenegro 66 pMalaysia 65 pBulgaria 60 ORussian Federation 60 OInternational average 60 OItaly 58 ORomania 57 OMacedonia, Republic of 54 qArmenia 47 qMoldova, Republic of 46 qJordan 46 qPhilippines 43 qIran, Islamic Republic of 43 qEgypt 43 qLebanon 42 qPalestinian Nat’l Auth. 41 qBahrain 40 qMorocco 39 qChile 38 qIndonesia 37 qBotswana 34 qSaudi Arabia 34 qGhana 34 qSouth Africa 34 qTunisia 31 q

M022252

The figure below shows a spinner with 24 sectors. When someone spins thearrow, it is equally likely to stop on any sector.

1

8 of the sectors are blue,

1

24 are purple,

1

2 are orange, and

1

3 are red. If a

person spins the arrow, on which color sector is the spinner LEAST likely tostop?

a blue

b purple

c orange

d red



Correct Response:

Cognitive Domain





Hong Kong, SAR 81 pSingapore 80 pNetherlands 78 pChinese Taipei 77 pKorea, Republic of 75 pBelgium (Flemish) 71 pJapan 66 pEstonia 61 pSweden 61 pUnited States 60 pHungary 56 pAustralia 56 pNew Zealand 55 pLithuania 55 pItaly 55 pScotland 53 pRussian Federation 52 pLatvia 50 OMalaysia 49 OEngland 49 OIsrael 47 OInternational average 47 ONorway 46 OSlovak Republic 45 OSerbia and Montenegro 44 OMoldova, Republic of 44 OSlovenia 44 OBulgaria 43 OCyprus 43 qLebanon 41 qArmenia 39 qTunisia 39 qJordan 39 qRomania 38 qEgypt 38 qMacedonia, Republic of 36 qIran, Islamic Republic of 35 qIndonesia 34 qChile 32 qPalestinian Nat’l Auth. 32 qPhilippines 31 qMorocco 28 qBotswana 28 qSaudi Arabia 26 qBahrain 23 qSouth Africa 23 qGhana 23 q

DATA UncertaintyandProbability Reasoning

Inaschooltherewere1200students


C

M03

2271

In a school there were 1,200 students (boys and girls). A sample of 100

students was selected at random, and 45 boys were found in the sample.

Which of these is most likely to be the number of boys in the school?

a 450

b 500

c 540

d 600


Correct Response:






DATA UncertaintyandProbability SolvingRoutineProblems

Numberofstudentsfromprobability


e

Korea, Republic of 89 pSingapore 87 pChinese Taipei 86 pJapan 86 pHong Kong, SAR 84 pNetherlands 82 pBelgium (Flemish) 79 pSweden 71 pMalaysia 69 pScotland 66 pEngland 63 pArmenia 62 pAustralia 60 pLatvia 59 pUnited States 58 pEstonia 57 pItaly 56 pHungary 55 pIsrael 54 pNew Zealand 54 OCyprus 53 OSlovenia 53 OLithuania 52 ORussian Federation 51 ONorway 50 OBulgaria 50 OInternational average 50 OSlovak Republic 50 OSerbia and Montenegro 46 OIndonesia 42 qRomania 39 qIran, Islamic Republic of 37 qJordan 33 qEgypt 33 qBotswana 32 qMacedonia, Republic of 32 qPhilippines 32 qMoldova, Republic of 31 qPalestinian Nat’l Auth. 28 qLebanon 28 qGhana 28 qSouth Africa 26 qBahrain 24 qChile 23 qTunisia 22 qSaudi Arabia 18 qMorocco 18 q

M022146

In an eighth-grade class of 30 students, the probability that a student

chosen at random will be less than 13 years old is

1

5. How many students in

the class are less than 13 years old?

a Two

b Three

c Four

d Five

e Six








• LinedrawnfromAto(approximate)midpointofBC.

Incorrect Response

• LinedrawnfromCorB.



DrawalinetodividetriangleABC

geOMeTRy CongruenceandSimilarityKnowingFactsandProcedures

Singapore 88 pJapan 86 pKorea, Republic of 84 pHong Kong, SAR 79 pArmenia 77 pRussian Federation 73 pBelgium (Flemish) 72 pChinese Taipei 71 pLatvia 71 pLithuania 70 pEstonia 69 pIsrael 66 pBahrain 65 pRomania 62 pBulgaria 61 pSlovak Republic 60 pNetherlands 59 pMoldova, Republic of 56 OLebanon 55 OAustralia 55 OUnited States 54 OSlovenia 53 OTunisia 53 OHungary 53 OMalaysia 52 OInternational average 52 OCyprus 51 OEngland 48 ONew Zealand 48 OJordan 47 qScotland 47 OItaly 45 qIran, Islamic Republic of 43 qNorway 42 qMorocco 41 qSerbia and Montenegro 40 qEgypt 40 qSaudi Arabia 39 qPalestinian Nat’l Auth. 36 qMacedonia, Republic of 35 qIndonesia 26 qSweden 20 qChile 19 qBotswana 14 qPhilippines 11 qSouth Africa 7 q

M032403

The triangle ABC has AB = AC.

Draw a line to divide triangle ABC into two congruent triangles.

A

C

B


Student Responses


DrawalinetodividetriangleABC(continued)Item Number: M032403

Correct:

Incorrect:



Correct Response:

Cognitive Domain





geOMeTRy CongruenceandSimilarity Reasoning

Propertyofcongruenttrapezoids


A

Korea, Republic of 86 pEstonia 84 pJapan 83 pHong Kong, SAR 81 pSingapore 81 pChinese Taipei 79 pLatvia 77 pRussian Federation 77 pLithuania 74 pBelgium (Flemish) 73 pSlovak Republic 73 pNetherlands 69 pUnited States 69 pHungary 69 pSlovenia 68 pRomania 68 pItaly 67 pBulgaria 67 pAustralia 66 pIsrael 66 pScotland 64 OMalaysia 64 OMoldova, Republic of 63 OSweden 62 OMorocco 62 OTunisia 62 ONew Zealand 61 OCyprus 61 OInternational average 60 OMacedonia, Republic of 60 OArmenia 59 ONorway 58 OEngland 57 OIndonesia 56 OSerbia and Montenegro 56 qLebanon 55 qBahrain 54 qJordan 48 qIran, Islamic Republic of 45 qSaudi Arabia 39 qChile 39 qPalestinian Nat’l Auth. 37 qEgypt 35 qBotswana 34 qPhilippines 30 qGhana 25 qSouth Africa 24 q

M012015

ABCD is a trapezoid.

Another trapezoid, GHIJ (not shown), is congruent (the same size and shape)to ABCD. Angles G and J each measure 70°. Which of these could be true?

a GH = AB

b Angle H is a right angle.

c All sides of GHIJ are the same length.

d The perimeter of GHIJ is 3 times the perimeter of ABCD.

e The area of GHIJ is less than the area of ABCD.

B

A

70˚

C

D

70˚


Correct Response:






geOMeTRy CongruenceandSimilarity UsingConcepts

Falsestatementofcongruenttriangles


b

Korea, Republic of 86 pJapan 85 pChinese Taipei 82 pEstonia 82 pHong Kong, SAR 79 pLatvia 78 pBulgaria 74 pRussian Federation 74 pLithuania 73 pNetherlands 72 pSingapore 72 pCyprus 69 pBelgium (Flemish) 68 pSlovak Republic 68 pRomania 64 pArmenia 62 pIsrael 62 pSweden 62 pSlovenia 61 pItaly 58 OMorocco 58 OBahrain 57 OInternational average 56 OMoldova, Republic of 56 OIndonesia 55 OUnited States 55 OJordan 54 OIran, Islamic Republic of 53 OMalaysia 50 qTunisia 49 qEgypt 46 qNorway 46 qHungary 45 qLebanon 45 qMacedonia, Republic of 45 qPalestinian Nat’l Auth. 44 qScotland 44 qAustralia 43 qNew Zealand 42 qSerbia and Montenegro 41 qPhilippines 39 qEngland 35 qSaudi Arabia 35 qChile 28 qSouth Africa 26 qBotswana 25 q

M012005

In square EFGH, which of these is FALSE?

a ∆EIF and ∆EIH are congruent.

b ∆GHI and ∆GHF are congruent.

c ∆EFH and ∆EGH are congruent.

d ∆EIF and ∆GIH are congruent.

I

H G

FE



Correct Response:

Cognitive Domain





geOMeTRy CongruenceandSimilarity UsingConcepts

Identifysimilartriangles


D

Korea, Republic of 83 pHong Kong, SAR 76 pSingapore 75 pJapan 70 pChinese Taipei 68 pRussian Federation 61 pNetherlands 60 pBelgium (Flemish) 59 pIran, Islamic Republic of 54 pHungary 51 pMalaysia 51 pLithuania 50 pLatvia 49 pEstonia 46 pUnited States 46 pLebanon 46 OItaly 44 OEngland 43 OInternational average 42 OJordan 41 OPhilippines 41 OSweden 41 OAustralia 40 ORomania 39 OSerbia and Montenegro 38 OPalestinian Nat’l Auth. 38 qMoldova, Republic of 38 ONew Zealand 37 qSlovak Republic 37 qArmenia 36 qIsrael 36 qMacedonia, Republic of 36 qCyprus 34 qNorway 34 qEgypt 34 qIndonesia 33 qBulgaria 31 qSlovenia 30 qScotland 29 qBahrain 27 qChile 25 qGhana 23 qBotswana 23 qSouth Africa 21 qMorocco 21 qTunisia 16 qSaudi Arabia 12 q

M032261

Which of the following triangles is similar to the triangle shown above?

a b

c d

8 cm 10 cm

12 cm

10 cm

12 cm

15 cm 10 cm

14 cm

12 cm

12 cm8 cm

6 cm

24 cm

16 cm

20 cm


Correct Response:






b


Sumofanglesequalto180degrees

geOMeTRy LinesandAnglesKnowingFactsandProcedures

Japan 83 pKorea, Republic of 81 pHong Kong, SAR 79 pSingapore 72 pChinese Taipei 67 pEstonia 63 pBelgium (Flemish) 62 pLatvia 56 pRussian Federation 54 pAustralia 49 pLithuania 49 pEngland 48 OIsrael 47 OBulgaria 47 OMoldova, Republic of 47 OHungary 47 OSlovak Republic 46 OBahrain 46 ONetherlands 45 ONew Zealand 45 OSerbia and Montenegro 43 OInternational average 43 OArmenia 43 OCyprus 42 OScotland 41 OSlovenia 41 ORomania 41 OMalaysia 41 OLebanon 38 qEgypt 37 qUnited States 37 qItaly 36 qMacedonia, Republic of 35 qPalestinian Nat’l Auth. 34 qNorway 34 qSweden 32 qIndonesia 31 qJordan 29 qTunisia 28 qMorocco 28 qPhilippines 26 qIran, Islamic Republic of 25 qChile 25 qSouth Africa 23 qGhana 22 qSaudi Arabia 22 qBotswana 19 q

M022142

In this figure, PQ and RS are parallel.

Of the following, which pair of angles has the sum of 180°?

a ∠ 5 and ∠ 7

b ∠ 3 and ∠ 6

c ∠ 1 and ∠ 5

d ∠ 1 and ∠ 7

e ∠ 2 and ∠ 8

P

R

Q

S

1 2

4 3

5 68 7








• 60

Incorrect Response

• 30OR50[140°–110°or140°–90°]

• 55[110÷2]



Measureofangleinadjacentangles

geOMeTRy LinesandAngles Reasoning

Korea, Republic of 63 pJapan 60 pSingapore 58 pHong Kong, SAR 57 pChinese Taipei 49 pHungary 44 pNorway 41 pRussian Federation 40 pArmenia 39 pLatvia 37 pBelgium (Flemish) 36 pSlovak Republic 36 pEstonia 36 pSerbia and Montenegro 35 pRomania 34 pBulgaria 34 pIsrael 32 pMoldova, Republic of 32 OMalaysia 32 pNetherlands 28 ONew Zealand 28 OInternational average 28 OLithuania 27 OMacedonia, Republic of 26 OAustralia 26 OLebanon 26 OItaly 25 OSlovenia 25 OEngland 23 qUnited States 22 qCyprus 21 qSweden 20 qTunisia 18 qScotland 17 qPalestinian Nat’l Auth. 16 qIndonesia 16 qBahrain 16 qEgypt 15 qJordan 13 qMorocco 11 qPhilippines 11 qIran, Islamic Republic of 11 qChile 10 qBotswana 9 qSaudi Arabia 6 qSouth Africa 4 q

M022202

In the figure, the measure of ∠POR is 110°, the measure of ∠QOS is 90°,and the measure of ∠POS is 140°.

What is the measure of ∠QOR?

Answer: _______________

S

R

Q

PO


Student Responses


Correct Response:

Incorrect Response:

Measureofangleinadjacentangles(continued)Item Number: M022202



Correct Response:

Cognitive Domain





geOMeTRy LinesandAngles SolvingRoutineProblems

Sumofanglesfromintersectinglines


C

Korea, Republic of 84 pSingapore 84 pHong Kong, SAR 83 pChinese Taipei 82 pJapan 78 pMalaysia 69 pEstonia 67 pLatvia 66 pRussian Federation 64 pBelgium (Flemish) 59 pSerbia and Montenegro 59 pIsrael 58 pRomania 58 pSlovenia 58 pBulgaria 57 pNetherlands 57 pLebanon 55 pLithuania 54 OAustralia 52 OMoldova, Republic of 52 OSlovak Republic 52 OEngland 50 OInternational average 50 OItaly 50 OHungary 48 OIran, Islamic Republic of 48 OUnited States 47 OCyprus 46 qNew Zealand 46 OMacedonia, Republic of 45 qArmenia 44 qEgypt 43 qSweden 43 qScotland 41 qTunisia 41 qJordan 40 qPalestinian Nat’l Auth. 40 qIndonesia 38 qNorway 34 qBahrain 33 qMorocco 33 qChile 32 qPhilippines 27 qBotswana 26 qSaudi Arabia 26 qGhana 21 qSouth Africa 16 q

M012039

In the figure, PQ and RS are intersecting straight lines.

What is the value of x + y ?

a 15

b 30

c 60

d 180

e 300

S

QR

x˚ y˚

P

150˚


Correct Response:






geOMeTRyLocations

andSpatialRelationshipsKnowingFactsandProcedures

Pointonalinedefinedbytwopoints


D

Netherlands 66 pEngland 62 pScotland 56 pKorea, Republic of 56 pSingapore 56 pChinese Taipei 54 pSweden 53 pAustralia 51 pUnited States 51 pJapan 50 pNorway 49 pHong Kong, SAR 47 pHungary 46 pLithuania 44 pNew Zealand 44 pBelgium (Flemish) 43 pRussian Federation 42 pEstonia 40 pMalaysia 38 OLatvia 37 OCyprus 36 OInternational average 35 OSlovenia 35 OIsrael 34 OSerbia and Montenegro 31 OIndonesia 31 qSlovak Republic 30 qChile 29 qEgypt 28 qMorocco 28 qRomania 28 qMacedonia, Republic of 27 qItaly 26 qJordan 26 qMoldova, Republic of 25 qBulgaria 24 qArmenia 23 qLebanon 23 qBotswana 22 qPhilippines 22 qPalestinian Nat’l Auth. 21 qBahrain 21 qIran, Islamic Republic of 20 qGhana 19 qSaudi Arabia 19 qSouth Africa 19 qTunisia 8 q

M022016

A straight line passes through the points (2,3) and (4,7). Which of thesepoints is also on the line?

a (0,2)

b (1,2)

c (2,4)

d (3,5)

e (4,5)



Correct Response:

Cognitive Domain





geOMeTRyLocations

andSpatialRelationshipsKnowingFactsandProcedures

Whichpointcouldhavecoordinates(2,-4)


C

Chinese Taipei 87 pJapan 86 pKorea, Republic of 83 pEstonia 81 pRussian Federation 79 pSingapore 77 pNetherlands 75 pHong Kong, SAR 74 pHungary 74 pLithuania 73 pLatvia 72 pUnited States 72 pMalaysia 71 pIran, Islamic Republic of 69 pBelgium (Flemish) 68 pEngland 67 pLebanon 66 pScotland 65 pIsrael 62 pSerbia and Montenegro 61 pBulgaria 60 ORomania 59 OSlovenia 58 OMacedonia, Republic of 58 ONew Zealand 58 OAustralia 58 OItaly 57 OInternational average 56 OJordan 55 OArmenia 53 OMoldova, Republic of 53 OIndonesia 53 OEgypt 47 qSweden 45 qSlovak Republic 43 qNorway 43 qPhilippines 41 qBahrain 38 qPalestinian Nat’l Auth. 34 qSaudi Arabia 32 qMorocco 31 qCyprus 30 qTunisia 28 qSouth Africa 28 qBotswana 26 qChile 25 qGhana 19 q

M032588

In the coordinate plane above, which point could havecoordinates (2,−4)?

a P

b Q

c R

d S

y

x

P Q

S R

O


Correct Response:






geOMeTRyLocations

andSpatialRelationshipsUsingConcepts

Whichcouldbefoldedtomakea3-Dfigure


D

Japan 97 pChinese Taipei 96 pKorea, Republic of 94 pHong Kong, SAR 94 pSingapore 94 pNetherlands 89 pMalaysia 89 pNew Zealand 88 pEstonia 87 pBelgium (Flemish) 87 pAustralia 86 pEngland 86 pScotland 86 pHungary 85 pLithuania 83 pSlovak Republic 81 pSerbia and Montenegro 77 pUnited States 76 pSweden 76 pSlovenia 75 pItaly 73 pLatvia 72 ONorway 71 OBulgaria 70 ORussian Federation 69 OIndonesia 68 OInternational average 68 ORomania 68 OChile 67 OCyprus 63 qMacedonia, Republic of 63 qIsrael 62 qMorocco 61 qLebanon 59 qTunisia 58 qIran, Islamic Republic of 55 qJordan 52 qPalestinian Nat’l Auth. 51 qMoldova, Republic of 49 qBahrain 46 qPhilippines 46 qBotswana 43 qSaudi Arabia 40 qArmenia 40 qEgypt 31 qSouth Africa 28 qGhana 24 q

M032489

Which of these could be folded to make a shape like the 3-D figure above?

a

b

c

d



Correct Response:

Cognitive Domain





geOMeTRySymmetry

andTransformationsReasoning

Centerpointofrotationofrectangle

Japan 79 pChinese Taipei 76 pKorea, Republic of 75 pHong Kong, SAR 73 pSlovenia 71 pEstonia 71 pNetherlands 65 pSingapore 64 pHungary 63 pEngland 63 pBelgium (Flemish) 62 pLatvia 61 pSweden 60 pNew Zealand 59 pLithuania 58 pItaly 58 pSlovak Republic 54 pAustralia 54 pIsrael 54 pMalaysia 54 pRussian Federation 52 pSerbia and Montenegro 50 ONorway 49 OUnited States 49 OInternational average 47 OBulgaria 47 OMoldova, Republic of 46 ORomania 46 OScotland 45 OJordan 44 OArmenia 40 qCyprus 39 qIran, Islamic Republic of 37 qPalestinian Nat’l Auth. 34 qBahrain 34 qLebanon 32 qEgypt 31 qIndonesia 29 qTunisia 29 qMacedonia, Republic of 28 qMorocco 28 qChile 28 qPhilippines 25 qBotswana 23 qSaudi Arabia 18 qSouth Africa 18 qGhana 13 q


C

M022154

Rectangle PQRS can be rotated (turned) onto rectangle UVST.

What point is the center of rotation?

a P

b R

c S

d T

e V

P

VU

T S R

Q








• Allcellsarecorrectwithsymmetricalgeometricpatternaboutbothaxes,PQandRS(lettersordrawings).

Partial Response

• Withrespecttoatleastoneoftheoriginaltilestheotherthreetilesarecorrect.

Incorrect Response

• LettersplacedsymmetricallywithrespecttobothPQandRS.



Geometrytiling:produceapatternusingletters

geOMeTRySymmetry

andTransformationsReasoning

Lithuania 16 pJapan 14 pKorea, Republic of 12 pSingapore 11 pHong Kong, SAR 10 pScotland 9 pEngland 9 pChinese Taipei 9 pNetherlands 8 pSlovenia 8 pEstonia 7 pAustralia 7 ONew Zealand 7 OBelgium (Flemish) 7 pUnited States 6 OMorocco 5 ORussian Federation 5 OMalaysia 5 OInternational average 4 OHungary 4 OSlovak Republic 3 OLatvia 3 ONorway 3 OMoldova, Republic of 3 OSweden 3 OIndonesia 2 qRomania 2 qIsrael 2 qBulgaria 2 qItaly 1 qArmenia 1 qLebanon 1 qMacedonia, Republic of 1 qSouth Africa 1 qEgypt 1 qChile 1 qPhilippines 1 qIran, Islamic Republic of 1 qBotswana 1 qJordan 1 qBahrain 1 qCyprus 0 qSerbia and Montenegro 0 qTunisia 0 qPalestinian Nat’l Auth. 0 q

M032745

Continue to identify the tiles as shown above. On the grid below, write theletters A, B, C, or D to make a symmetrical pattern where PQ and RSwould be lines of symmetry. Arrange the tiles to make a pattern.

End of Geometry Tiling section.

CA DB

P

S

Q

R

D

C

B

A


Student Responses


Correct Response:

Geometrytiling:produceapatternusingletters(continued)Item Number: M032745



Partial Response:


Student Responses (Continued)



Incorrect Response:

Student Responses (Continued)









• Bothquadrantscorrectlyshaded(patternshadedordemarcatedinsomewaymakingsymmetricalpatternaboutbothaxes,ABandCD).

Incorrect Response

• Oneofthetwoquadrantscorrectlyshaded.



Geometrytiling:makesasymmetricalpattern

geOMeTRySymmetry

andTransformationsUsingConcepts

Scotland 85 pNetherlands 82 pKorea, Republic of 82 pNew Zealand 80 pEngland 80 pSingapore 77 pAustralia 76 pHong Kong, SAR 75 pHungary 69 pJapan 68 pChinese Taipei 68 pUnited States 67 pBelgium (Flemish) 65 pLithuania 63 pSlovenia 60 pLatvia 60 pJordan 59 pMalaysia 56 pSlovak Republic 54 ORussian Federation 53 OCyprus 51 OEstonia 50 OItaly 50 OInternational average 49 OBulgaria 48 ONorway 46 OSweden 46 ORomania 44 OBahrain 43 qIsrael 42 qSerbia and Montenegro 41 qPalestinian Nat’l Auth. 41 qIndonesia 39 qMorocco 38 qIran, Islamic Republic of 34 qSaudi Arabia 34 qPhilippines 34 qEgypt 31 qTunisia 25 qMacedonia, Republic of 25 qBotswana 20 qLebanon 18 qSouth Africa 17 qArmenia 13 qChile 13 qMoldova, Republic of 1 q

M032743

There are several ways of arranging the tiles so that they form patterns.The grid below has been shaded to show how tiles can be placed on some ofthe squares. The pattern can be continued so that AB and CD are lines ofsymmetry.

Shade in all the remaining squares on the grid so that the resulting patternis symmetrical about line AB, and also is symmetrical about line CD.

Questions for Geometry Tiling continue.

A

B

C D


Student Responses


Geometrytiling:makesasymmetricalpattern(continued)Item Number: M032743

Correct Response:



Incorrect Response:


Geometrytiling:makesasymmetricalpattern(continued)Item Number: M032743



Correct Response:

Cognitive Domain





GeOMeTRyTwo-andThree-

DimensionalShapesSolvingRoutineProblems

Angleinoverlappingcongruenttriangles


D

Korea, Republic of 84 pHong Kong, SAR 81 pJapan 80 pSingapore 79 pChinese Taipei 73 pEstonia 67 pBelgium (Flemish) 66 pLatvia 63 pBulgaria 60 pIsrael 57 pRussian Federation 55 pLebanon 55 pScotland 54 pSlovak Republic 54 pLithuania 51 pHungary 50 OAustralia 47 OEngland 47 OEgypt 47 OMalaysia 47 OInternational average 45 OArmenia 45 OMoldova, Republic of 45 OCyprus 44 ONetherlands 44 OSerbia and Montenegro 43 ONew Zealand 42 OJordan 42 OItaly 42 OTunisia 41 qBahrain 41 qSweden 40 qPalestinian Nat’l Auth. 39 qIran, Islamic Republic of 37 qSlovenia 37 qUnited States 36 qMacedonia, Republic of 33 qNorway 32 qIndonesia 31 qMorocco 31 qChile 30 qSaudi Arabia 26 qSouth Africa 21 qGhana 20 qBotswana 20 qRomania 18 qPhilippines 15 q

M01

2026

In this figure, triangles ABC and DEF are congruent with BC = EF .

What is the measure of angle EGC ?

a 20°

b 40°

c 60°

d 80°

e 100°

B E C F

G

40˚ 60˚

A D







SCORINGCorrect Response

• 60degrees

Incorrect Response

• 120degrees



Theanglebyaregularhexagon


DimensionalShapesSolvingRoutineProblems

Japan 73 pChinese Taipei 70 pKorea, Republic of 68 pHong Kong, SAR 64 pSingapore 62 pHungary 59 pSlovenia 52 pNorway 50 pSerbia and Montenegro 46 pRomania 45 pBelgium (Flemish) 45 pSlovak Republic 43 pArmenia 42 pRussian Federation 42 pNetherlands 40 pMacedonia, Republic of 39 pMoldova, Republic of 39 pEstonia 37 OLatvia 33 OMalaysia 33 OInternational average 33 OItaly 32 OBulgaria 32 OLithuania 31 OEngland 30 OTunisia 29 qLebanon 28 qNew Zealand 27 qAustralia 27 qIsrael 26 qSweden 24 qIran, Islamic Republic of 24 qJordan 23 qPalestinian Nat’l Auth. 23 qEgypt 23 qScotland 23 qBahrain 22 qSaudi Arabia 21 qUnited States 20 qCyprus 19 qIndonesia 17 qGhana 16 qBotswana 14 qChile 9 qMorocco 9 qPhilippines 6 qSouth Africa 5 q

M032693

The figure above is a regular hexagon. What is the value of x?

Answer: _______________

x˚


Student Responses


Correct Response:

Incorrect Response:

Theanglebyaregularhexagon(continued)Item Number: M032693


Correct Response:






C


ThesizeofanglePRQ


DimensionalShapesUsingConcepts

Korea, Republic of 70 pChinese Taipei 70 pHungary 69 pTunisia 66 pJapan 64 pMalaysia 62 pHong Kong, SAR 59 pNorway 58 pSlovak Republic 58 pLebanon 58 pSerbia and Montenegro 58 pEstonia 56 pBelgium (Flemish) 54 pSlovenia 52 pRussian Federation 51 ORomania 51 OMacedonia, Republic of 50 OSingapore 49 pBulgaria 48 OLatvia 46 OInternational average 46 ONew Zealand 45 OMoldova, Republic of 44 ONetherlands 44 OSaudi Arabia 43 OLithuania 43 OPalestinian Nat’l Auth. 42 OEngland 42 OItaly 41 qMorocco 40 qJordan 39 qGhana 38 qEgypt 38 qChile 37 qAustralia 37 qArmenia 36 qIran, Islamic Republic of 36 qScotland 35 qSweden 35 qBahrain 35 qIsrael 34 qUnited States 34 qBotswana 34 qCyprus 34 qIndonesia 32 qSouth Africa 29 qPhilippines 25 q

M032689

In the figure above, an arc of a circle with center P has been drawn to cutthe line at Q. Then an arc with the same radius and center Q was drawn tocut the first arc at R. What would be the size of angle PRQ ?

a 30º

b 45º

c 60º

d 75º

P Q

R



Correct Response:

Cognitive Domain





MeaSuReMeNT AttributesandUnitsKnowingFactsandProcedures

250 ml bottles filled by 400 liters


C

Singapore 68 pNetherlands 59 pBelgium (Flemish) 55 pSweden 54 pMalaysia 53 pLatvia 51 pEstonia 50 pAustralia 49 pLithuania 49 pRomania 48 pHungary 48 pHong Kong, SAR 47 pRussian Federation 46 pSlovak Republic 44 pJapan 44 pMoldova, Republic of 43 OItaly 42 ONorway 42 OEngland 42 OArmenia 42 ONew Zealand 41 OSlovenia 41 OKorea, Republic of 41 OChinese Taipei 41 OCyprus 41 OScotland 40 OBulgaria 39 OInternational average 39 OSerbia and Montenegro 38 OIsrael 38 OUnited States 33 qPhilippines 32 qIndonesia 32 qSouth Africa 31 qPalestinian Nat’l Auth. 30 qLebanon 30 qChile 29 qJordan 29 qMacedonia, Republic of 29 qEgypt 29 qIran, Islamic Republic of 28 qTunisia 27 qBahrain 27 qBotswana 25 qSaudi Arabia 25 qMorocco 22 qGhana 20 q

M02

2005

The number of 250 milliliter bottles that can be filled from 400 liters of

water is

a 16

b 160

c 1,600

d 16,000


Correct Response:






Whichisleastamountoftime


Chinese Taipei 66 pKorea, Republic of 63 pHungary 63 pSingapore 60 pBelgium (Flemish) 59 pJapan 54 pHong Kong, SAR 54 pSlovenia 54 pSlovak Republic 52 pNetherlands 52 pLatvia 51 pArmenia 50 pSerbia and Montenegro 49 pEstonia 48 pMacedonia, Republic of 48 pRussian Federation 47 pUnited States 47 pMalaysia 47 OMoldova, Republic of 45 OItaly 45 OBulgaria 44 OSweden 44 OInternational average 43 ORomania 43 OLithuania 42 OIsrael 41 OTunisia 41 OAustralia 41 OLebanon 40 OCyprus 39 qEngland 39 ONorway 39 qJordan 38 qScotland 38 qPalestinian Nat’l Auth. 37 qNew Zealand 36 qEgypt 36 qChile 35 qSaudi Arabia 35 qPhilippines 35 qIran, Islamic Republic of 35 qSouth Africa 32 qBahrain 32 qMorocco 32 qGhana 27 qIndonesia 26 qBotswana 26 q


B

M02

2188

Which of these is the LEAST amount of time?

a 1 day

b 20 hours

c 1,800 minutes

d 90,000 seconds



Correct Response:

Cognitive Domain






The unit used for a soccer field

Estonia 90 pSweden 89 pNew Zealand 89 pItaly 88 pSingapore 88 pHungary 88 pAustralia 87 pSlovak Republic 87 pChile 87 pBelgium (Flemish) 86 pNetherlands 86 pLatvia 86 pRomania 86 pLithuania 84 pSerbia and Montenegro 84 pBulgaria 84 pRussian Federation 83 pHong Kong, SAR 82 pChinese Taipei 82 pJapan 82 pEngland 82 pMoldova, Republic of 82 pScotland 81 pNorway 80 pMalaysia 77 OUnited States 76 OMacedonia, Republic of 76 OInternational average 75 OKorea, Republic of 74 OSlovenia 74 OIsrael 73 OArmenia 71 qCyprus 69 qTunisia 68 qIndonesia 66 qBahrain 66 qMorocco 64 qJordan 64 qEgypt 62 qBotswana 61 qPhilippines 60 qPalestinian Nat’l Auth. 58 qLebanon 56 qSaudi Arabia 55 qIran, Islamic Republic of 52 qSouth Africa 52 qGhana 35 q


C

M032699

Which of these units would usually be used for an area the size of a soccerfield?

a square centimeters

b cubic centimeters

c square meters

d cubic meters


Correct Response:







Measureoftheareaofatriangle

Japan 84 pSingapore 81 pEstonia 78 pChinese Taipei 76 pBelgium (Flemish) 75 pRussian Federation 75 pHong Kong, SAR 73 pSlovenia 71 pSweden 70 pNetherlands 70 pLithuania 70 pKorea, Republic of 69 pHungary 68 pSlovak Republic 67 pSerbia and Montenegro 67 pItaly 67 pMalaysia 64 pRomania 62 pLatvia 61 pNew Zealand 57 OMoldova, Republic of 56 OInternational average 55 OLebanon 55 ONorway 54 OBulgaria 52 OMacedonia, Republic of 52 OAustralia 52 OCyprus 52 OEngland 51 OScotland 48 qBotswana 48 qUnited States 47 qEgypt 46 qJordan 45 qIndonesia 44 qArmenia 44 qIsrael 43 qTunisia 43 qPalestinian Nat’l Auth. 42 qBahrain 37 qChile 36 qGhana 34 qSouth Africa 34 qSaudi Arabia 32 qMorocco 30 qPhilippines 27 qIran, Islamic Republic of 22 q


C

M032732

Which of these could be the measure of the area of a triangle?

a 2 cm

b 3 m

c 5 cm2

d 8 m3



Correct Response:

Cognitive Domain





MeaSuReMeNTTools,Techniques,

andFormulasKnowingFactsandProcedures

Actuallengthofboxfromroundedmeasure

Korea, Republic of 90 pHungary 89 pNetherlands 88 pHong Kong, SAR 87 pSingapore 87 pBelgium (Flemish) 82 pSlovak Republic 81 pChinese Taipei 80 pSweden 80 pScotland 76 pEngland 75 pAustralia 73 pRussian Federation 73 pLatvia 70 pEstonia 67 pUnited States 67 pNew Zealand 65 pIsrael 64 pJapan 64 pMalaysia 62 pNorway 61 pRomania 58 pSerbia and Montenegro 55 pSlovenia 53 OItaly 52 OInternational average 50 OArmenia 45 qMacedonia, Republic of 42 qMoldova, Republic of 42 qJordan 39 qChile 38 qCyprus 37 qBahrain 33 qPalestinian Nat’l Auth. 33 qEgypt 30 qIndonesia 30 qBulgaria 28 qLebanon 23 qPhilippines 23 qLithuania 21 qBotswana 20 qIran, Islamic Republic of 15 qSaudi Arabia 13 qSouth Africa 13 qGhana 8 qMorocco 8 qTunisia 7 q


D

M012003

The length of a box is 9 cm to the nearest centimeter. Which of these couldbe the actual length of the box?

a 10 cm

b 9.9 cm

c 9.6 cm

d 8.6 cm


Correct Response:








Lengthofpipefrommeterscale

Singapore 95 pHong Kong, SAR 94 pJapan 93 pEstonia 91 pChinese Taipei 90 pKorea, Republic of 89 pNetherlands 89 pBelgium (Flemish) 87 pHungary 86 pMalaysia 86 pSweden 86 pLatvia 83 pRussian Federation 82 pLithuania 81 pScotland 81 pEngland 80 pNew Zealand 79 pSlovak Republic 79 pSlovenia 79 pAustralia 78 pItaly 74 pNorway 74 pUnited States 73 pBulgaria 72 pIsrael 72 pSerbia and Montenegro 72 pMacedonia, Republic of 70 OInternational average 67 OLebanon 64 OMoldova, Republic of 64 ORomania 64 OBotswana 61 qCyprus 61 qChile 58 qArmenia 54 qIndonesia 54 qMorocco 50 qTunisia 49 qIran, Islamic Republic of 48 qPhilippines 42 qSouth Africa 40 qGhana 39 qJordan 38 qPalestinian Nat’l Auth. 34 qBahrain 32 qEgypt 31 qSaudi Arabia 27 q


C

M012038

Meters (m)

What is the length of the pipe being measured?

a 0.085 m

b 0.805 m

c 0.85 m

d 8.5 m

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0



Correct Response:

Cognitive Domain







Areaofpavedwalkwayaroundpool

Singapore 86 pHong Kong, SAR 82 pKorea, Republic of 77 pChinese Taipei 77 pJapan 76 pMalaysia 60 pNetherlands 57 pEstonia 53 pBelgium (Flemish) 51 pSlovak Republic 50 pSweden 48 pAustralia 46 pItaly 45 pNew Zealand 44 OLithuania 43 pHungary 43 pEngland 40 OSlovenia 40 OUnited States 40 OCyprus 39 OScotland 39 OInternational average 38 OSerbia and Montenegro 38 OLatvia 38 OBulgaria 38 ORussian Federation 38 OIsrael 37 OEgypt 33 qMoldova, Republic of 33 qNorway 32 qRomania 30 qIran, Islamic Republic of 28 qArmenia 28 qJordan 26 qIndonesia 25 qBahrain 23 qPalestinian Nat’l Auth. 22 qMacedonia, Republic of 20 qLebanon 19 qChile 19 qTunisia 18 qMorocco 18 qSaudi Arabia 17 qBotswana 16 qPhilippines 16 qSouth Africa 16 qGhana 13 q


C

M02

2021

A rectangular shaped swimming pool has a paved walkway around it as

shown.

What is the area of the paved walkway?

a 100 m2

b 161 m2

c 710 m2

d 1,610 m2

70 m

23 m

50 m

18 mPool

Walkway


Correct Response:







andFormulasReasoning

Orangesarepackedinboxes

Japan 62 pNetherlands 61 pSweden 57 pSingapore 57 pBelgium (Flemish) 56 pAustralia 56 pEngland 55 pKorea, Republic of 55 pChinese Taipei 55 pHungary 55 pLatvia 54 pScotland 53 pRussian Federation 53 pEstonia 53 pHong Kong, SAR 51 pSlovenia 51 pSlovak Republic 51 pNew Zealand 51 pLithuania 50 pUnited States 50 pNorway 48 pBulgaria 46 OItaly 45 OInternational average 44Serbia and Montenegro 43 OCyprus 42 OMoldova, Republic of 42 OMacedonia, Republic of 41 OChile 40 qIsrael 39 qBotswana 37 qMalaysia 37 qRomania 36 qMorocco 35 qPhilippines 35 qLebanon 34 qBahrain 32 qEgypt 32 qTunisia 31 qIndonesia 31 qIran, Islamic Republic of 31 qSouth Africa 31 qArmenia 31 qJordan 29 qGhana 29 qPalestinian Nat’l Auth. 28 qSaudi Arabia 28 q


B

M03

2647

Oranges are packed in boxes. The average diameter of the oranges is 6 cm,

and the boxes are 60 cm long, 36 cm wide, and 24 cm deep.

Which of these is the BEST approximation of the number of oranges that

can be packed in a box?

a 30

b 240

c 360

d 1,920



Correct Response:

Cognitive Domain





B


Singapore 81 pJapan 65 pChinese Taipei 62 pHong Kong, SAR 62 pKorea, Republic of 62 pNetherlands 56 pBelgium (Flemish) 56 pSweden 54 pEstonia 53 pLatvia 52 pAustralia 50 pRussian Federation 47 pEngland 46 pSlovak Republic 45 pSerbia and Montenegro 45 pNew Zealand 45 pIsrael 44 pBulgaria 43 pRomania 43 pItaly 42 pMalaysia 41 ONorway 40 OMoldova, Republic of 39 OUnited States 39 OLithuania 38 OInternational average 37 OScotland 37 OHungary 37 OCyprus 36 OSlovenia 33 qArmenia 31 qIran, Islamic Republic of 28 qMacedonia, Republic of 27 qChile 27 qTunisia 26 qLebanon 23 qJordan 22 qPalestinian Nat’l Auth. 19 qEgypt 18 qBahrain 18 qBotswana 17 qSouth Africa 16 qSaudi Arabia 14 qMorocco 14 qPhilippines 14 qIndonesia 13 qGhana 13 q

Lengthofrectanglefromwidth/perimeter


andFormulasSolvingRoutineProblems

M012030

A thin wire 20 centimeters long is formed into a rectangle. If the width ofthis rectangle is 4 centimeters, what is its length?

a 5 centimeters

b 6 centimeters

c 12 centimeters

d 16 centimeters








• 7:25

• Otherresponseequivalentto7:25.

Incorrect Response

• 7:20

• 7:30

• 6:25



Netherlands 91 pBelgium (Flemish) 85 pHungary 84 pEngland 80 pSweden 78 pSingapore 78 pScotland 76 pAustralia 72 pNorway 71 pNew Zealand 68 pHong Kong, SAR 67 pSlovenia 67 pItaly 65 pRomania 63 pJapan 63 pIsrael 63 pSlovak Republic 59 pChinese Taipei 59 pEstonia 58 pCyprus 58 pKorea, Republic of 57 pUnited States 55 pMalaysia 51 pLatvia 46 OInternational average 45 OLebanon 45 OMoldova, Republic of 42 ORussian Federation 41 OSerbia and Montenegro 36 qBulgaria 36 qArmenia 35 qLithuania 34 qChile 29 qTunisia 20 qEgypt 20 qJordan 19 qMacedonia, Republic of 18 qIndonesia 18 qPalestinian Nat’l Auth. 16 qMorocco 15 qIran, Islamic Republic of 15 qBahrain 14 qBotswana 11 qSaudi Arabia 9 qSouth Africa 8 qPhilippines 8 qGhana 4 q



Time when finish homework

M022148

Kris begins her homework at 6:40. If it takes Kris three-quarters of an hourto do her homework, at what time will she finish?

Answer: _______________


Student Responses


Correct Response:

Incorrect Response:

Time when finish homework (continued)Item Number: M022148








• 49

Incorrect Response

• 1



5squares:areaofonesquare



Singapore 89 pHong Kong, SAR 88 pKorea, Republic of 87 pJapan 86 pArmenia 84 pChinese Taipei 83 pEstonia 69 pNetherlands 69 pRussian Federation 68 pBelgium (Flemish) 67 pSlovenia 66 pScotland 63 pUnited States 60 pMalaysia 60 pHungary 60 pBulgaria 59 pRomania 58 pTunisia 57 pMoldova, Republic of 57 pItaly 57 pSlovak Republic 57 pLithuania 57 pAustralia 56 OInternational average 51 OLebanon 49 OSweden 48 OEngland 47 OSerbia and Montenegro 47 qIsrael 47 qEgypt 46 qNew Zealand 45 qJordan 45 qCyprus 43 qMacedonia, Republic of 41 qIran, Islamic Republic of 38 qBahrain 37 qIndonesia 33 qPhilippines 32 qNorway 32 qMorocco 31 qPalestinian Nat’l Auth. 30 qBotswana 28 qChile 24 qSaudi Arabia 15 qGhana 10 qSouth Africa 8 qLatvia

M022227

The figure consists of 5 squares of equal area. The area of the whole figureis 245 cm2.

A. Find the area of one square.

Answer: _______________ cm2

B. Find the length of one side of one square.

Answer: _______________ cm

C. Find the perimeter of the whole figure in centimeters.

Answer: _______________ cm


Student Responses


Correct Response:

Incorrect Response:

5squares:areaofonesquare(continued)Item Number: M022227A








• 7 (or 49)

• Correctsquarerootofincorrectanswertoparta.

Incorrect Response

• 1–onlyiftheanswertopartAisnot1.

• Indication of division of area of one square (as obtained in part a) by 4 (e.g., 12.25, 49/4, etc.).

• 24.5 or other indication of division by 2.



5squares:lengthofoneside



Singapore 80 pHong Kong, SAR 78 pKorea, Republic of 70 pChinese Taipei 65 pArmenia 62 pRomania 45 pRussian Federation 43 pItaly 43 pJapan 42 pEstonia 39 pNetherlands 38 pBelgium (Flemish) 37 pSerbia and Montenegro 36 pMoldova, Republic of 35 pHungary 35 pMalaysia 34 pLithuania 33 pBulgaria 32 OUnited States 29 OSlovak Republic 29 OSlovenia 29 OInternational average 28 OScotland 27 OAustralia 26 OEngland 23 OSweden 23 qNew Zealand 23 qCyprus 21 qIsrael 20 qMacedonia, Republic of 20 qEgypt 20 qLebanon 18 qLatvia 17 qJordan 16 qPalestinian Nat’l Auth. 16 qIndonesia 15 qBahrain 14 qNorway 11 qIran, Islamic Republic of 11 qPhilippines 10 qTunisia 9 qMorocco 8 qSaudi Arabia 8 qChile 6 qBotswana 4 qSouth Africa 3 qGhana 2 q

M022227



Answer: _______________ cm2


Answer: _______________ cm


Answer: _______________ cm


Student Responses


Correct Response:

Incorrect Response:

5squares:lengthofoneside(continued)Item Number: M022227B








• 84

• 12,oncondition1wastheresponseforpartb.

• Other responses consistent with answer to part b, using multiplication by 12 (e.g., 147, 294, etc.).

Incorrect Response

• An answer that is 4 times the response to part b.

• Indicationofmultiplicationby12butmultiplicationisincorrect.

• 245 [Confusion between area and perimeter].


Item Number: M022227C

5 squares: perimeter whole figure



Singapore 72 pHong Kong, SAR 58 pKorea, Republic of 53 pChinese Taipei 51 pJapan 47 pArmenia 42 pMalaysia 38 pNetherlands 38 pAustralia 30 pScotland 27 pEngland 27 pEstonia 26 pBelgium (Flemish) 25 pHungary 24 pSlovenia 24 pSlovak Republic 24 pNew Zealand 23 ORussian Federation 23 OUnited States 23 OItaly 22 OLithuania 22 OSweden 21 OInternational average 20 OSerbia and Montenegro 18 OLatvia 17 OCyprus 17 ONorway 16 OMoldova, Republic of 16 ORomania 16 qBulgaria 14 qIsrael 12 qMacedonia, Republic of 8 qTunisia 7 qIndonesia 5 qChile 5 qEgypt 5 qJordan 5 qBahrain 4 qPalestinian Nat’l Auth. 4 qBotswana 3 qLebanon 3 qMorocco 2 qIran, Islamic Republic of 2 qSouth Africa 2 qPhilippines 2 qSaudi Arabia 2 qGhana 1 q

M022227



Answer: _______________ cm2


Answer: _______________ cm


Answer: _______________ cm


Student Responses


Correct Response:

Incorrect Response:

5 squares: perimeter whole figure (continued)Item Number: M022227C








• 64 kph or 64 or equivalent.

Incorrect Response

• Incorrect(includingcrossedout/erased,straymarks,illegibleorofftask).


Carrally:averagespeed

a. MeaSuReMeNTB.MeASUReMeNT

Tools, Techniques, and Formulas

Tools,Techniques,andFormulas

Solving Routine Problems

Reasoning

Singapore 78 pHong Kong, SAR 76 pNetherlands 70 pRussian Federation 67 pArmenia 65 pEstonia 64 pChinese Taipei 59 pJapan 59 pHungary 59 pLithuania 56 pUnited States 55 pBelgium (Flemish) 54 pLatvia 50 pSlovak Republic 49 pSweden 45 pKorea, Republic of 43 pScotland 43 pItaly 42 pMoldova, Republic of 38 OEngland 37 ONorway 37 OAustralia 36 OIsrael 36 ONew Zealand 35 OInternational average 35 OSerbia and Montenegro 34 OSlovenia 33 OMalaysia 29 qRomania 29 qBulgaria 28 qTunisia 27 qMacedonia, Republic of 26 qJordan 24 qIndonesia 22 qBotswana 21 qPalestinian Nat’l Auth. 18 qCyprus 16 qLebanon 15 qChile 15 qPhilippines 14 qBahrain 12 qIran, Islamic Republic of 8 qEgypt 7 qSouth Africa 7 qMorocco 6 qSaudi Arabia 2 qGhana 2 q

M032649

In a car rally two checkpoints are 160 km apart. Drivers must travel fromone checkpoint to the other in exactly 2.5 hours to earn maximum points.

A. What must the average speed be to travel the 160 km in this time?

Answer: _______________

B. A driver took 1 hour to travel through a 40 km hilly section at thebeginning of the course.

What must the average speed, in kilometers per hour, be for theremaining 120 km if the total time between checkpoints is to be2.5 hours?

Answer: _______________


Student Responses


Correct Response:

Incorrect Response:

Carrally:averagespeed(continued)Item Number: M032649A








• 80kphor80

Incorrect Response

• 5, 2, 120 or 48 shown.



Carrally:averagespeedforonesection

A.MeASUReMeNTB. MeaSuReMeNT

Tools,Techniques,andFormulas

Tools, Techniques, and Formulas

SolvingRoutineProblems

Reasoning

Armenia 54 pSingapore 52 pNetherlands 50 pHong Kong, SAR 47 pChinese Taipei 39 pEstonia 35 pRussian Federation 34 pHungary 33 pJapan 33 pBelgium (Flemish) 30 pSweden 28 pLithuania 27 pKorea, Republic of 27 pLatvia 24 pUnited States 24 pScotland 23 pEngland 22 OAustralia 22 OSlovak Republic 21 ONew Zealand 19 ONorway 19 OInternational average 18 OIsrael 17 OMoldova, Republic of 17 OBulgaria 17 OSlovenia 16 OItaly 15 ORomania 13 qSerbia and Montenegro 10 qMacedonia, Republic of 8 qMalaysia 7 qCyprus 6 qJordan 6 qIran, Islamic Republic of 5 qTunisia 5 qChile 5 qEgypt 4 qBotswana 4 qBahrain 4 qIndonesia 4 qPalestinian Nat’l Auth. 4 qSouth Africa 3 qLebanon 2 qPhilippines 2 qSaudi Arabia 2 qGhana 1 qMorocco 1 q

M032649

In a car rally two checkpoints are 160 km apart. Drivers must travel fromone checkpoint to the other in exactly 2.5 hours to earn maximum points.

A. What must the average speed be to travel the 160 km in this time?

Answer: _______________

B. A driver took 1 hour to travel through a 40 km hilly section at thebeginning of the course.

What must the average speed, in kilometers per hour, be for theremaining 120 km if the total time between checkpoints is to be2.5 hours?

Answer: _______________


Student Responses


Correct Response:

Incorrect Response:

Carrally:averagespeedforonesection(continued)Item Number: M032649B


Correct Response:







andFormulasUsingConcepts

Volumesofstacksofblocks

Korea, Republic of 88 pSingapore 86 pHong Kong, SAR 83 pJapan 81 pChinese Taipei 81 pNetherlands 78 pAustralia 73 pEstonia 69 pSlovak Republic 68 pBelgium (Flemish) 67 pScotland 67 pLithuania 66 pLatvia 64 pMalaysia 62 pSlovenia 62 pNew Zealand 60 pHungary 58 pEngland 58 pRussian Federation 57 pNorway 56 pItaly 55 pUnited States 50 OInternational average 50 OSweden 50 OIsrael 49 OBulgaria 48 OMoldova, Republic of 48 ORomania 46 OSerbia and Montenegro 45 qArmenia 42 qCyprus 42 qBahrain 41 qPhilippines 35 qLebanon 34 qMacedonia, Republic of 33 qSaudi Arabia 32 qIndonesia 32 qPalestinian Nat’l Auth. 30 qJordan 29 qChile 27 qMorocco 26 qBotswana 26 qTunisia 26 qIran, Islamic Republic of 26 qEgypt 24 qSouth Africa 22 qGhana 20 q


a

M012013

All the small blocks are the same size. Which stack of blocks has a differentvolume from the others?

a b

c d



Correct Response:

Cognitive Domain





D


Singapore 82 pHong Kong, SAR 82 pKorea, Republic of 75 pChinese Taipei 74 pJapan 73 pNetherlands 65 pBelgium (Flemish) 61 pEstonia 53 pRussian Federation 51 pItaly 51 pSlovak Republic 51 pHungary 48 pMalaysia 48 pLatvia 46 pLithuania 45 pSweden 45 pScotland 44 pEngland 43 OSerbia and Montenegro 43 OAustralia 42 ONew Zealand 41 OSlovenia 41 ORomania 39 OInternational average 39 OUnited States 39 OBulgaria 38 OCyprus 37 OArmenia 36 OLebanon 35 ONorway 35 qIsrael 34 qMoldova, Republic of 33 qTunisia 30 qMacedonia, Republic of 30 qIran, Islamic Republic of 27 qJordan 25 qIndonesia 24 qEgypt 21 qBahrain 20 qMorocco 19 qPalestinian Nat’l Auth. 18 qChile 18 qBotswana 16 qPhilippines 15 qGhana 10 qSouth Africa 10 qSaudi Arabia 10 q


andFormulasUsingConcepts

TheareaoftherectangleABCD

M032678

In the figure above, ABCD is a rectangle, and circles P and Q each have aradius of 5 cm. What is the area of the rectangle?

a 50 cm2

b 60 cm2

c 100 cm2

d 200 cm2

5 cm

P Q

A

D

B

C


Correct Response:






NuMBeR FractionsandDecimalsKnowingFactsandProcedures

Pairofnumbersbracketing2.25


B

Korea, Republic of 77 pSingapore 71 pBelgium (Flemish) 63 pLithuania 61 pHong Kong, SAR 61 pChinese Taipei 60 pRussian Federation 58 pHungary 58 pEstonia 57 pIsrael 57 pSlovak Republic 55 pJapan 55 pSweden 55 OUnited States 54 pSerbia and Montenegro 54 OSlovenia 53 ORomania 52 OItaly 52 OAustralia 52 OLatvia 52 OPhilippines 52 ONetherlands 51 OScotland 51 ONorway 51 OCyprus 51 OInternational average 50 OBulgaria 50 OMalaysia 50 OEngland 50 OMoldova, Republic of 48 ONew Zealand 47 OBotswana 46 qArmenia 46 OSaudi Arabia 46 qLebanon 45 qGhana 44 qMacedonia, Republic of 44 qTunisia 43 qMorocco 41 qEgypt 40 qBahrain 40 qSouth Africa 39 qChile 39 qPalestinian Nat’l Auth. 39 qJordan 38 qIran, Islamic Republic of 38 q

M012016

In which of these pairs of numbers is 2.25 larger than the first number butsmaller than the second number?

a 1 and 2

b 2 and

52

c

52

and

114

d

114

and 3








• 30

Incorrect Response

• 30 kg [incorrect unit]

• 6/5 [6 x 1/5]

• 4 [4/5 more needed to complete 1 kg]

• 5 [5 scoops = 1 kg flour]

• 6 [from stem]



Scoops of flour needed to fill bag


Singapore 79 pHong Kong, SAR 76 pChinese Taipei 75 pNetherlands 74 pKorea, Republic of 68 pJapan 62 pBelgium (Flemish) 62 pSweden 60 pAustralia 53 pUnited States 52 pScotland 51 pEstonia 51 pLatvia 51 pHungary 51 pEngland 50 pRussian Federation 49 pIsrael 48 pMalaysia 47 pNew Zealand 46 pSlovenia 46 pArmenia 45 pLithuania 43 pSlovak Republic 43 pNorway 39 ORomania 39 OSerbia and Montenegro 38 OBulgaria 38 OInternational average 38 OCyprus 37 OMoldova, Republic of 37 OItaly 34 OIndonesia 26 qMacedonia, Republic of 22 qIran, Islamic Republic of 20 qTunisia 18 qEgypt 17 qJordan 16 qLebanon 15 qChile 13 qPhilippines 13 qBahrain 11 qBotswana 11 qPalestinian Nat’l Auth. 10 qMorocco 8 qSouth Africa 7 qSaudi Arabia 7 qGhana 6 q

M022156

A scoop holds

1

5 kg of flour. How many scoops of flour are needed to fill a

bag with 6 kg of flour?

Answer: _______________


Student Responses


Correct Response:

Incorrect Response:

Scoops of flour needed to fill bag (continued)Item Number: M022156



Correct Response:

Cognitive Domain






Addition/multiplicationwithfractions

Chinese Taipei 82 pKorea, Republic of 80 pJapan 75 pSingapore 72 pHong Kong, SAR 69 pEgypt 58 pRomania 54 pItaly 53 pBelgium (Flemish) 53 pSlovenia 51 pSlovak Republic 51 pHungary 50 pEstonia 50 pMalaysia 48 pBulgaria 48 pRussian Federation 48 pLatvia 46 pSerbia and Montenegro 45 pLithuania 44 pArmenia 42 OInternational average 40 OLebanon 40 OIsrael 40 ONetherlands 40 OMoldova, Republic of 39 OCyprus 36 qUnited States 36 qJordan 35 qIran, Islamic Republic of 34 qBahrain 29 qAustralia 28 qIndonesia 28 qEngland 28 qNew Zealand 28 qPalestinian Nat’l Auth. 27 qMacedonia, Republic of 27 qTunisia 26 qScotland 26 qMorocco 25 qBotswana 24 qSweden 22 qPhilippines 22 qChile 21 qNorway 21 qSouth Africa 18 qSaudi Arabia 16 q


e

M022199

3

5

3

10

4

15+ × =( )

a

3

51

b

1

6

c

6

25

d

11

25

e

17

25


Correct Response:






NuMBeR FractionsandDecimals Reasoning

Numberofmen/womenatmeeting

Korea, Republic of 89 pJapan 87 pNetherlands 86 pBelgium (Flemish) 83 pSingapore 81 pSweden 79 pNorway 77 pChinese Taipei 77 pMalaysia 74 pHong Kong, SAR 73 pHungary 71 pItaly 70 pSlovenia 68 pSlovak Republic 68 pEstonia 67 pScotland 67 pEngland 67 pBulgaria 67 pAustralia 66 pIsrael 65 pCyprus 64 pSerbia and Montenegro 63 pNew Zealand 63 OLatvia 62 OLithuania 60 OInternational average 59 ORussian Federation 57 OMoldova, Republic of 56 OIran, Islamic Republic of 56 OUnited States 52 qChile 51 qJordan 51 qIndonesia 50 qRomania 48 qBahrain 46 qPalestinian Nat’l Auth. 46 qMorocco 46 qEgypt 46 qMacedonia, Republic of 45 qBotswana 42 qTunisia 40 qArmenia 40 qSaudi Arabia 37 qGhana 31 qPhilippines 27 qLebanon 24 qSouth Africa 23 q


a

M022191

Two-thirds of the people present at the beginning of a meeting are men.Nobody leaves but 10 more men and 10 more women arrive at the meeting.Which of the following statements is true?

a There would then be more men than women at the meeting.

b There would then be the same number of men as there are women atthe meeting.

c There would then be more women than men at the meeting.

d From the information given, you cannot tell whether there would bemore women or men.



Correct Response:

Cognitive Domain





NuMBeR FractionsandDecimals SolvingRoutineProblems

Fractionofhourbetweentwotimepoints

Singapore 85 pHong Kong, SAR 80 pKorea, Republic of 77 pChinese Taipei 77 pSweden 73 pEngland 68 pNetherlands 67 pJapan 67 pBelgium (Flemish) 66 pHungary 66 pAustralia 65 pSlovak Republic 64 pScotland 63 pUnited States 62 pLatvia 62 pIsrael 61 pMalaysia 61 pNew Zealand 60 pSlovenia 58 pNorway 57 pBulgaria 56 pCyprus 56 pEstonia 55 ORussian Federation 53 OInternational average 52 OMoldova, Republic of 52 OArmenia 50 OLithuania 50 OSerbia and Montenegro 48 OJordan 46 qRomania 43 qPalestinian Nat’l Auth. 43 qEgypt 43 qItaly 41 qLebanon 40 qPhilippines 40 qMacedonia, Republic of 40 qBahrain 40 qIran, Islamic Republic of 38 qIndonesia 38 qSaudi Arabia 30 qBotswana 29 qChile 28 qSouth Africa 27 qMorocco 26 qGhana 24 qTunisia 20 q


B

M012027

What fraction of an hour has passed between 1:10 a.m. and 1:30 a.m.?

a

15

b

13

c

12

d

23

e

34


Correct Response:







Fraction birthdays in first half of year

Korea, Republic of 90 pSingapore 90 pHong Kong, SAR 86 pNetherlands 82 pChinese Taipei 79 pBelgium (Flemish) 76 pSweden 76 pEngland 75 pMalaysia 75 pIsrael 74 pUnited States 72 pNorway 71 pAustralia 69 pNew Zealand 69 pScotland 69 pJapan 68 pEstonia 62 pSlovenia 60 pCyprus 59 pHungary 58 pItaly 57 pLatvia 57 pLithuania 57 ORussian Federation 55 OSlovak Republic 54 OInternational average 52 OIran, Islamic Republic of 46 qBulgaria 43 qRomania 41 qBotswana 40 qMoldova, Republic of 38 qJordan 37 qChile 36 qIndonesia 36 qEgypt 35 qLebanon 33 qMacedonia, Republic of 31 qPalestinian Nat’l Auth. 31 qSerbia and Montenegro 31 qTunisia 31 qBahrain 30 qPhilippines 28 qArmenia 27 qMorocco 21 qSouth Africa 21 qGhana 20 qSaudi Arabia 15 q


D

M012041

In a group of children, 16 have birthdays during the first half of the year,and 14 have birthdays during the second half of the year. What fraction ofthe group have birthdays during the first half of the year?

a

1430

b

1416

c

1614

d

1630

e

3016



Correct Response:

Cognitive Domain






4/5 of books more than 2/3

Singapore 85 pKorea, Republic of 80 pHong Kong, SAR 78 pChinese Taipei 78 pMalaysia 69 pNetherlands 68 pJapan 66 pSweden 65 pBelgium (Flemish) 63 pScotland 61 pHungary 60 pEngland 57 pLatvia 57 pSlovenia 57 pItaly 56 pEstonia 54 pRomania 53 pAustralia 53 pSlovak Republic 52 OIsrael 52 OCyprus 51 OLithuania 50 ONew Zealand 50 OUnited States 50 OBulgaria 49 OSerbia and Montenegro 48 OInternational average 48 ORussian Federation 45 OMoldova, Republic of 44 ONorway 43 qMacedonia, Republic of 38 qArmenia 38 qIran, Islamic Republic of 38 qEgypt 37 qPhilippines 35 qIndonesia 35 qPalestinian Nat’l Auth. 34 qBotswana 33 qJordan 33 qChile 33 qLebanon 28 qBahrain 27 qSouth Africa 27 qGhana 25 qTunisia 25 qMorocco 24 qSaudi Arabia 24 q


C

M022004

A teacher and a doctor each have 45 books. If

4

5 of the teacher’s books and

2

3 of the doctor’s books are novels, how many more novels does the teacher

have than the doctor?

a 2

b 3

c 6

d 30

e 36


Correct Response:







TimeforBettytorunrace

Singapore 88 pKorea, Republic of 87 pMalaysia 81 pNetherlands 81 pHungary 80 pChinese Taipei 80 pJapan 78 pRussian Federation 76 pHong Kong, SAR 75 pSlovak Republic 74 pUnited States 74 pSlovenia 73 pEstonia 72 pBelgium (Flemish) 71 pScotland 71 pMoldova, Republic of 69 pSerbia and Montenegro 68 pLatvia 67 pBulgaria 66 pLithuania 65 pRomania 64 OTunisia 63 OAustralia 63 OSweden 63 OItaly 62 OBotswana 61 OLebanon 61 OInternational average 61 OArmenia 60 OMacedonia, Republic of 59 OCyprus 59 OEgypt 58 OIsrael 58 OIndonesia 55 qEngland 54 qNew Zealand 53 qJordan 46 qNorway 46 qPhilippines 45 qMorocco 45 qBahrain 45 qIran, Islamic Republic of 44 qChile 42 qPalestinian Nat’l Auth. 37 qGhana 32 qSouth Africa 29 qSaudi Arabia 19 q


a

M022010

Alice ran a race in 49.86 seconds. Betty ran the same race in 52.30 seconds.How much longer did it take Betty to run the race than Alice?

a 2.44 seconds

b 2.54 seconds

c 3.56 seconds

d 3.76 seconds



Correct Response:

Cognitive Domain






Fuelremainingintankatendoftrip

Singapore 56 pChinese Taipei 50 pHong Kong, SAR 43 pKorea, Republic of 43 pJapan 38 pNetherlands 38 pMalaysia 34 pMoldova, Republic of 33 pLithuania 32 pHungary 32 pEstonia 31 pRomania 30 OBelgium (Flemish) 30 pRussian Federation 29 OAustralia 28 OArmenia 27 OLatvia 26 OInternational average 26 OSlovenia 26 OMacedonia, Republic of 25 OUnited States 25 OSlovak Republic 24 ONew Zealand 24 OIndonesia 23 OSweden 23 OJordan 23 OBulgaria 23 OCyprus 22 qSaudi Arabia 22 OIsrael 22 qSerbia and Montenegro 22 qItaly 21 qEgypt 21 qBotswana 20 qChile 20 qGhana 20 qEngland 20 qScotland 19 qMorocco 19 qTunisia 19 qSouth Africa 18 qIran, Islamic Republic of 18 qPalestinian Nat’l Auth. 17 qPhilippines 17 qBahrain 16 qNorway 16 qLebanon 12 q


a

M022127

A car has a fuel tank that holds 45 L of fuel. The car consumes 8.5 L of fuelfor each 100 km driven. A trip of 350 km was started with a full tank of fuel.How much remained in the tank at the end of the trip?

a 15.25 L

b 16.25 L

c 24.75 L

d 29.75 L


Correct Response:







JohnandCathytodivideanumberby100

Singapore 58 pBelgium (Flemish) 58 pEstonia 56 pJapan 56 pHong Kong, SAR 56 pKorea, Republic of 52 pRussian Federation 51 pHungary 51 pNetherlands 51 pChinese Taipei 46 pSlovak Republic 45 pLithuania 43 pIsrael 41 pSweden 41 pLatvia 37 ONew Zealand 36 OAustralia 35 OScotland 35 OInternational average 34 OItaly 34 OEngland 34 OCyprus 33 OSlovenia 32 OUnited States 32 OMoldova, Republic of 32 OSerbia and Montenegro 32 ONorway 31 ORomania 29 qArmenia 28 qEgypt 27 qMalaysia 27 qSaudi Arabia 26 qLebanon 26 qMacedonia, Republic of 23 qBahrain 23 qPhilippines 23 qMorocco 23 qChile 23 qIran, Islamic Republic of 22 qGhana 22 qBulgaria 22 qIndonesia 21 qPalestinian Nat’l Auth. 21 qSouth Africa 20 qTunisia 18 qBotswana 16 q


B

M032079

John and Cathy were told to divide a number by 100. By mistake Johnmultiplied the number by 100 and obtained an answer of 450.Cathy correctly divided the number by 100. What was her answer?

a 0.0045

b 0.045

c 0.45

d 4.5



Correct Response:

Cognitive Domain





NuMBeR FractionsandDecimals UsingConcepts

Numberofsquaresinshadedfraction

Singapore 88 pHong Kong, SAR 87 pBelgium (Flemish) 84 pKorea, Republic of 82 pNetherlands 80 pJapan 79 pChinese Taipei 78 pSweden 71 pMalaysia 67 pIsrael 67 pHungary 66 pAustralia 66 pScotland 63 pNorway 62 pEngland 62 pUnited States 61 pNew Zealand 60 pSlovenia 59 pEstonia 59 pCyprus 56 pLatvia 56 pRussian Federation 52 OSlovak Republic 52 OMoldova, Republic of 50 OItaly 50 OInternational average 49 OLithuania 47 OBulgaria 46 ORomania 45 OArmenia 42 qSerbia and Montenegro 42 qIran, Islamic Republic of 41 qMacedonia, Republic of 37 qJordan 32 qEgypt 30 qPalestinian Nat’l Auth. 29 qTunisia 26 qBahrain 25 qPhilippines 23 qLebanon 22 qMorocco 22 qChile 21 qIndonesia 21 qSaudi Arabia 19 qSouth Africa 16 qBotswana 16 qGhana 8 q


a

M012001

In the figure, how many MORE small squares need to be shaded so that

45

of

the small squares are shaded?

a 5

b 4

c 3

d 2

e 1








• A fraction with numerator smaller than 4 and denominator equal to 9, includes 3/9 = 1/3 OR 1/3.

• A fraction with numerator equal to 4 and denominator greater than 9, includes 4/10 = 2/5 OR 2/5.

• 3/8

• Othercorrectfraction

Incorrect Response

• 5/9

• 2/3

• Any fraction equivalent to 4/9.



Singapore 84 pKorea, Republic of 81 pJapan 81 pHong Kong, SAR 79 pChinese Taipei 77 pIsrael 74 pHungary 72 pArmenia 72 pAustralia 71 pSweden 70 pUnited States 69 pNetherlands 69 pEngland 68 pSlovak Republic 66 pNew Zealand 64 pNorway 64 pSlovenia 64 pEstonia 63 pBelgium (Flemish) 62 pRussian Federation 62 pScotland 60 pCyprus 60 pInternational average 54 ORomania 54 OBulgaria 54 OSerbia and Montenegro 52 OEgypt 52 OLatvia 52 OLithuania 50 OPalestinian Nat’l Auth. 50 qBotswana 49 qItaly 48 qJordan 48 qTunisia 47 qIran, Islamic Republic of 47 qMalaysia 43 qBahrain 41 qMoldova, Republic of 40 qSaudi Arabia 39 qChile 36 qMacedonia, Republic of 35 qSouth Africa 30 qLebanon 28 qIndonesia 26 qPhilippines 25 qMorocco 24 qGhana 21 q

Fraction less than 4/9


M022012

Write a fraction that is less than

4

9.

Answer: ______________________________


Student Responses


Fraction less than 4/9 (continued)Item Number: M022012

Correct Response:

Incorrect Response:


Correct Response:







Decimalroundedtonearesthundredth

Korea, Republic of 88 pSerbia and Montenegro 74 pRussian Federation 73 pLithuania 72 pHungary 72 pSlovak Republic 71 pBelgium (Flemish) 66 pUnited States 66 pEstonia 62 pMoldova, Republic of 55 pSweden 55 pSingapore 54 pItaly 54 pJapan 54 pLatvia 54 pNetherlands 54 pChinese Taipei 49 OSlovenia 49 OInternational average 47 OAustralia 47 OCyprus 46 OLebanon 45 OMalaysia 45 OPalestinian Nat’l Auth. 44 OIsrael 43 ONew Zealand 41 qEgypt 41 qScotland 41 qJordan 40 qEngland 40 qIndonesia 39 qPhilippines 38 qBulgaria 38 qIran, Islamic Republic of 37 qMorocco 37 qSaudi Arabia 36 qRomania 35 qNorway 33 qBahrain 32 qMacedonia, Republic of 32 qChile 30 qArmenia 29 qGhana 29 qHong Kong, SAR 29 qBotswana 28 qSouth Africa 22 q


D

M022144

Which of the following is 78.2437 rounded to the nearest hundredth?

a 100

b 80

c 78.2

d 78.24

e 78.244



Correct Response:

Cognitive Domain






Decimalsorderedgreatesttoleast


D

Singapore 79 pBelgium (Flemish) 74 pHong Kong, SAR 72 pNetherlands 66 pChinese Taipei 63 pEstonia 62 pMalaysia 62 pKorea, Republic of 59 pSweden 59 pLatvia 58 pJapan 53 pAustralia 53 pSlovak Republic 52 pLithuania 49 pRussian Federation 49 pScotland 48 OUnited States 48 pSlovenia 48 OItaly 47 OHungary 47 OBulgaria 47 OEgypt 46 ORomania 46 OMoldova, Republic of 44 OEngland 44 OInternational average 44 OArmenia 42 OLebanon 42 ONew Zealand 42 OCyprus 39 OIsrael 38 qMorocco 38 qChile 35 qNorway 35 qJordan 35 qSerbia and Montenegro 34 qTunisia 33 qMacedonia, Republic of 32 qIndonesia 29 qPalestinian Nat’l Auth. 29 qBahrain 27 qPhilippines 25 qSaudi Arabia 23 qGhana 20 qIran, Islamic Republic of 18 qBotswana 18 qSouth Africa 16 q

M022198

In which list are the numbers ordered from greatest to least?

a 0.233, 0.3, 0.32, 0.332

b 0.3, 0.32, 0.332, 0.233

c 0.32, 0.233, 0.332, 0.3

d 0.332, 0.32, 0.3, 0.233


Correct Response:







Thenumberclosestto10

Netherlands 97 pSweden 96 pEstonia 96 pSingapore 95 pLithuania 95 pBelgium (Flemish) 94 pKorea, Republic of 94 pMalaysia 93 pJapan 92 pSerbia and Montenegro 91 pNorway 91 pRussian Federation 91 pLatvia 90 pSlovak Republic 90 pItaly 90 pHong Kong, SAR 89 pScotland 89 pChinese Taipei 89 pCyprus 88 pHungary 88 pAustralia 88 pUnited States 87 pSlovenia 87 pNew Zealand 86 pBulgaria 85 pEngland 82 pMoldova, Republic of 82 pIsrael 81 pRomania 79 OMacedonia, Republic of 78 OInternational average 76 OTunisia 76 OMorocco 75 OIndonesia 74 OIran, Islamic Republic of 69 qChile 67 qLebanon 67 qArmenia 66 qJordan 55 qPalestinian Nat’l Auth. 50 qBahrain 49 qEgypt 48 qPhilippines 42 qBotswana 40 qSaudi Arabia 35 qSouth Africa 30 qGhana 24 q


B

M03

2760

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

B. Pat made a shape that used 49 black tiles.

How many red tiles did Pat use in that shape?

Answer: ____________ red tiles

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



Correct Response:

Cognitive Domain





NuMBeR IntegersKnowingFactsandProcedures

Thevalueof1minus5times-2


a

Japan 74 pSingapore 70 pHong Kong, SAR 67 pChinese Taipei 66 pNetherlands 61 pBelgium (Flemish) 55 pKorea, Republic of 54 pSlovak Republic 52 pEstonia 52 pIsrael 52 pRomania 49 pNew Zealand 48 pRussian Federation 46 pBulgaria 46 pAustralia 45 pArmenia 44 pLatvia 42 pHungary 42 pLebanon 42 pMalaysia 39 OBotswana 39 OLithuania 38 OUnited States 38 OItaly 37 OEgypt 37 OSlovenia 36 OInternational average 35 OSerbia and Montenegro 33 OMoldova, Republic of 33 OMacedonia, Republic of 32 OEngland 25 qTunisia 24 qCyprus 23 qPhilippines 21 qJordan 19 qPalestinian Nat’l Auth. 19 qScotland 18 qSouth Africa 17 qBahrain 15 qIndonesia 12 qSaudi Arabia 12 qSweden 10 qChile 10 qIran, Islamic Republic of 10 qMorocco 6 qNorway 5 q

M032612

What is the value of 1 − 5 × (−2)?

a 11

b 8

c −8

d −9


Correct Response:






NuMBeR Integers UsingConcepts

Ifnisanegativeinteger

Korea, Republic of 78 pChinese Taipei 74 pRussian Federation 69 pJapan 68 pHong Kong, SAR 67 pSingapore 58 pHungary 53 pEstonia 51 pLatvia 49 pBelgium (Flemish) 48 pUnited States 48 pIsrael 48 pArmenia 47 pSlovak Republic 46 pSerbia and Montenegro 46 pNetherlands 44 OBulgaria 42 ORomania 41 OLebanon 41 OLithuania 40 OMalaysia 40 OInternational average 40 OMoldova, Republic of 39 OSlovenia 38 OEgypt 37 OAustralia 36 OCyprus 34 qItaly 32 qIran, Islamic Republic of 32 qPhilippines 32 qMacedonia, Republic of 32 qNew Zealand 31 qJordan 29 qPalestinian Nat’l Auth. 29 qSweden 28 qScotland 28 qIndonesia 27 qEngland 26 qSouth Africa 26 qNorway 25 qMorocco 25 qSaudi Arabia 25 qBahrain 22 qTunisia 22 qBotswana 22 qChile 18 q


C

M032643

If n is a negative integer, which of these is the largest number?

a 3 + n

b 3 × n

c 3 − n

d 3 ÷ n



Correct Response:

Cognitive Domain





NuMBeRRatio,Proportions,

andPercentKnowingFactsandProcedures

Percentdecreaseintraveltime


C

Singapore 70 pNetherlands 62 pHong Kong, SAR 61 pMalaysia 48 pSweden 47 pAustralia 46 pKorea, Republic of 45 pScotland 42 pEngland 42 pHungary 40 pChinese Taipei 40 pNew Zealand 40 pJapan 39 pSlovak Republic 38 pIsrael 38 pSlovenia 38 pBelgium (Flemish) 38 pEstonia 37 pLatvia 37 pUnited States 35 pLithuania 34 OCyprus 34 ONorway 34 ORussian Federation 32 OSerbia and Montenegro 32 OInternational average 31 OMoldova, Republic of 29 OBulgaria 28 ORomania 27 qJordan 22 qSouth Africa 21 qChile 21 qArmenia 20 qItaly 20 qMacedonia, Republic of 19 qBahrain 19 qIndonesia 19 qPalestinian Nat’l Auth. 18 qIran, Islamic Republic of 18 qBotswana 18 qLebanon 17 qEgypt 17 qPhilippines 17 qSaudi Arabia 17 qMorocco 15 qGhana 15 qTunisia 12 q

M022139

When a new highway is built, the average time it takes a bus to travel fromone town to another is reduced from 25 minutes to 20 minutes. What is thepercent decrease in time taken to travel between the two towns?

a 4%

b 5%

c 20%

d 25%


Correct Response:







andPercentKnowingFactsandProcedures

Theratiooftheshadedareatotheunshaded

Singapore 87 pChinese Taipei 81 pKorea, Republic of 80 pHong Kong, SAR 74 pMalaysia 72 pJapan 71 pSlovak Republic 56 pAustralia 55 pScotland 54 pLatvia 52 pEngland 52 pHungary 52 pNetherlands 51 pUnited States 50 pLithuania 50 pSlovenia 48 pSerbia and Montenegro 48 pRussian Federation 47 pIndonesia 45 OBulgaria 44 OBelgium (Flemish) 43 OEstonia 42 OInternational average 41 ONew Zealand 39 OIsrael 38 OCyprus 37 ORomania 37 OPhilippines 37 OMoldova, Republic of 37 OItaly 35 qMacedonia, Republic of 35 qSweden 31 qArmenia 28 qPalestinian Nat’l Auth. 27 qIran, Islamic Republic of 26 qEgypt 26 qSaudi Arabia 26 qNorway 23 qJordan 21 qChile 20 qBahrain 19 qBotswana 17 qSouth Africa 16 qMorocco 16 qLebanon 16 qTunisia 14 q


a

M032447

In the figure above, each of the smaller triangles has the same area. Whatis the ratio of the shaded area to the unshaded area?

a 5:3

b 8:5

c 5:8

d 3:5







A computer club had 40 members


• 48% with calculations shown.

Partial Response

• 24 girls

• Correctmethodbutcomputationalerror.

• 48% with no calculations shown.

Incorrect Response

• 50%




andPercentReasoning

M03

2233

A computer club had 40 members, and 60% of the members were girls.

Later, 10 boys joined the club. What percent of the members now are girls?

Show the calculations that led to your answer.

Answer: _______________

Singapore 64 pKorea, Republic of 44 pChinese Taipei 41 pHong Kong, SAR 29 pHungary 28 pMalaysia 23 pBelgium (Flemish) 21 pSweden 21 pSlovak Republic 19 pEstonia 19 pNetherlands 18 pLithuania 18 pJapan 16 pEngland 16 OScotland 14 OUnited States 14 OAustralia 13 OSlovenia 13 OIsrael 13 ONew Zealand 12 OInternational average 12 OLatvia 9 OSerbia and Montenegro 9 OArmenia 8 ORomania 7 qRussian Federation 6 qItaly 6 qBulgaria 6 qCyprus 4 qNorway 3 qChile 3 qIndonesia 3 qLebanon 3 qPhilippines 2 qSouth Africa 2 qIran, Islamic Republic of 2 qJordan 2 qPalestinian Nat’l Auth. 2 qEgypt 2 qMorocco 1 qBotswana 1 qTunisia 1 qMoldova, Republic of 1 qMacedonia, Republic of 1 qBahrain 0 qGhana 0 q


Student Responses


A computer club had 40 members (continued)Item Number: M032233

Correct Response:

Partial Response:

Incorrect Response:



Correct Response:

Cognitive Domain






andPercentSolvingRoutineProblems

LapsrunbyCarolandAlicefromratio


D

Singapore 75 pBelgium (Flemish) 69 pJapan 68 pChinese Taipei 66 pNetherlands 66 pSweden 62 pHong Kong, SAR 61 pSlovak Republic 59 pLatvia 55 pLithuania 55 pRussian Federation 54 pIsrael 53 pAustralia 52 ONorway 52 pEstonia 51 pKorea, Republic of 51 pIran, Islamic Republic of 48 OUnited States 48 OGhana 47 OInternational average 47 OSerbia and Montenegro 47 OSouth Africa 47 OCyprus 46 OLebanon 46 ONew Zealand 46 OSlovenia 46 OEngland 45 OScotland 45 OHungary 43 qMalaysia 43 OPalestinian Nat’l Auth. 43 qArmenia 42 qPhilippines 42 qTunisia 42 qJordan 41 qEgypt 40 qMoldova, Republic of 40 qBotswana 39 qRomania 37 qBulgaria 36 qMacedonia, Republic of 36 qItaly 35 qSaudi Arabia 35 qIndonesia 34 qMorocco 33 qChile 32 qBahrain 29 q

M012004

Alice can run 4 laps around a track in the same time that Carol can run3 laps. When Carol has run 12 laps, how many laps has Alice run?

a 9

b 11

c 13

d 16


Correct Response:






C


A shop increased its prices by 20%



Singapore 87 pHong Kong, SAR 86 pNetherlands 79 pChinese Taipei 74 pKorea, Republic of 74 pSlovak Republic 73 pHungary 72 pBelgium (Flemish) 72 pSweden 70 pEstonia 65 pJapan 63 pScotland 62 pMalaysia 62 pRussian Federation 61 pLithuania 58 pIsrael 58 pUnited States 57 pAustralia 55 pSlovenia 55 pRomania 54 OLatvia 54 OEngland 52 OSerbia and Montenegro 51 OInternational average 49 ONew Zealand 49 OItaly 49 ONorway 48 OBulgaria 47 OArmenia 45 qCyprus 45 qMoldova, Republic of 44 qChile 41 qTunisia 40 qMacedonia, Republic of 39 qIndonesia 34 qBotswana 32 qPhilippines 31 qLebanon 31 qMorocco 30 qEgypt 29 qBahrain 27 qPalestinian Nat’l Auth. 26 qJordan 25 qIran, Islamic Republic of 24 qSaudi Arabia 22 qSouth Africa 19 qGhana 16 q

M03

2228

A shop increased its prices by 20%. What is the new price of an item which

previously sold for 800 zeds?

a 640 zeds

b 900 zeds

c 960 zeds

d 1,000 zeds



Correct Response:

Cognitive Domain







A machine uses 2.4 liters of gasoline


B

Singapore 89 pNetherlands 78 pHong Kong, SAR 77 pKorea, Republic of 75 pBelgium (Flemish) 74 pChinese Taipei 71 pMalaysia 68 pJapan 66 pEstonia 65 pLithuania 64 pSlovak Republic 63 pHungary 63 pSweden 60 pLebanon 55 pUnited States 55 pRussian Federation 54 pIsrael 53 pEngland 50 OScotland 50 OLatvia 50 OSlovenia 50 OAustralia 49 ORomania 48 OInternational average 47 OSerbia and Montenegro 45 OItaly 44 ONorway 44 OMoldova, Republic of 44 OCyprus 44 OBulgaria 43 ONew Zealand 42 OArmenia 41 qJordan 40 qMacedonia, Republic of 38 qEgypt 34 qIran, Islamic Republic of 31 qIndonesia 31 qPalestinian Nat’l Auth. 31 qTunisia 30 qChile 29 qPhilippines 27 qMorocco 27 qBotswana 23 qBahrain 23 qSaudi Arabia 22 qSouth Africa 17 qGhana 17 q

M032533

A machine uses 2.4 liters of gasoline for every 30 hours of operation.How many liters of gasoline will the machine use in 100 hours?

a 7.2

b 8.0

c 8.4

d 9.6


Correct Response:






D


Three brothers receive 45,000 zeds



Singapore 85 pHong Kong, SAR 73 pKorea, Republic of 71 pChinese Taipei 68 pSweden 67 pHungary 67 pEstonia 67 pNetherlands 66 pSlovak Republic 65 pBelgium (Flemish) 63 pJapan 60 pMalaysia 57 pEngland 55 pAustralia 55 pRomania 53 pIsrael 52 pRussian Federation 52 pNew Zealand 50 OLithuania 49 OItaly 48 OScotland 48 OSerbia and Montenegro 48 OUnited States 45 ONorway 45 OSlovenia 45 OInternational average 45 OCyprus 42 OChile 41 OMoldova, Republic of 40 OLatvia 37 qBulgaria 37 qMacedonia, Republic of 36 qIran, Islamic Republic of 35 qSouth Africa 32 qGhana 32 qPhilippines 29 qJordan 29 qArmenia 28 qPalestinian Nat’l Auth. 28 qIndonesia 27 qLebanon 26 qTunisia 24 qMorocco 22 qBotswana 21 qBahrain 21 qEgypt 20 qSaudi Arabia 18 q

M03

2727

Three brothers, Bob, Dan, and Mark, receive a gift of 45,000 zeds from their

father. The money is shared between the brothers in proportion to the

number of children each one has. Bob has 2 children, Dan has 3 children,

and Mark has 4 children.

How many zeds does Mark get?

a 5,000

b 10,000

c 15,000

d 20,000



Correct Response:

Cognitive Domain






andPercentUsingConcepts

3/25ofthepeopleintheaudiencewerechildren


a

Singapore 96 pHong Kong, SAR 90 pBelgium (Flemish) 87 pMalaysia 84 pNetherlands 79 pChinese Taipei 77 pKorea, Republic of 76 pEngland 71 pUnited States 70 pBotswana 70 pNew Zealand 67 pAustralia 67 pLatvia 65 pCyprus 64 pScotland 63 pIsrael 63 pSlovenia 61 pSweden 61 pJapan 60 pLithuania 59 OEstonia 57 OSlovak Republic 56 OHungary 55 OInternational average 55 ORussian Federation 52 OIndonesia 51 OBulgaria 50 ONorway 50 qRomania 49 qItaly 47 qSerbia and Montenegro 45 qEgypt 44 qArmenia 42 qMacedonia, Republic of 42 qPhilippines 42 qMoldova, Republic of 42 qGhana 41 qIran, Islamic Republic of 39 qPalestinian Nat’l Auth. 39 qJordan 39 qChile 39 qBahrain 36 qLebanon 34 qSouth Africa 33 qTunisia 30 qMorocco 29 qSaudi Arabia 25 q

M032570

At a play,

325

of the people in the audience were children.

What percent of the audience was this?

a 12%

b 3%

c 0.3%

d 0.12%


Correct Response:






D


The closest to 11 squared plus 9 squared

NuMBeR WholeNumbersKnowingFactsandProcedures

Hong Kong, SAR 88 pLatvia 88 pHungary 85 pRussian Federation 84 pUnited States 82 pSlovak Republic 82 pEstonia 81 pSlovenia 81 pLebanon 80 pBelgium (Flemish) 80 pKorea, Republic of 80 pMalaysia 80 pChinese Taipei 80 pRomania 80 pSingapore 80 pSerbia and Montenegro 79 pItaly 79 pLithuania 77 pCyprus 74 pAustralia 73 pNetherlands 69 pMacedonia, Republic of 68 pBulgaria 67 pIndonesia 65 OEngland 64 OArmenia 64 OIsrael 63 OInternational average 61 OScotland 59 ONew Zealand 56 OTunisia 53 qJapan 50 qJordan 49 qPalestinian Nat’l Auth. 48 qMorocco 47 qPhilippines 45 qEgypt 44 qIran, Islamic Republic of 44 qChile 41 qBahrain 37 qSweden 36 qGhana 28 qBotswana 26 qSaudi Arabia 22 qSouth Africa 20 qMoldova, Republic of 18 qNorway 13 q

M032609

Which of these is closest to 11 92 2+ ?

a 20 + 20

b 20 + 80

c 120 + 20

d 120 + 80



Correct Response:

Cognitive Domain





NuMBeR WholeNumbersKnowingFactsandProcedures

Which equals 370 times 998 plus 370 times 2


a

Singapore 70 pHong Kong, SAR 69 pChinese Taipei 68 pHungary 61 pNetherlands 59 pEstonia 57 pLebanon 53 pIsrael 52 pEgypt 52 pBelgium (Flemish) 50 pRussian Federation 49 pAustralia 49 pUnited States 48 pLithuania 47 pMalaysia 47 pNew Zealand 46 pKorea, Republic of 43 ORomania 43 OBotswana 41 OScotland 40 OInternational average 39 OArmenia 38 OLatvia 38 OSlovak Republic 38 OJapan 37 OBulgaria 37 OMoldova, Republic of 37 OSlovenia 36 OItaly 35 OMacedonia, Republic of 34 OEngland 34 OPalestinian Nat’l Auth. 33 qTunisia 31 qPhilippines 30 qBahrain 28 qCyprus 24 qSweden 23 qSerbia and Montenegro 23 qNorway 22 qSaudi Arabia 22 qMorocco 21 qSouth Africa 21 qChile 18 qIndonesia 18 qJordan 17 qIran, Islamic Republic of 14 q

M03

2690

Which of these is equal to 370 × 998 + 370 × 2?

a 370 × 1,000

b 372 × 998

c 740 × 998

d 370 × 998 × 2


Correct Response:






C


Arrangements of 4-digit whole numbers

NuMBeR WholeNumbers SolvingRoutineProblems

Korea, Republic of 92 pSingapore 88 pChinese Taipei 87 pHong Kong, SAR 86 pJapan 85 pMalaysia 79 pLatvia 77 pSlovenia 75 pBelgium (Flemish) 75 pSweden 72 pBulgaria 71 pItaly 71 pRussian Federation 70 pRomania 70 pUnited States 70 pSerbia and Montenegro 70 pSlovak Republic 69 pEstonia 68 pAustralia 68 pMoldova, Republic of 67 pScotland 66 pIsrael 66 pHungary 65 pLithuania 65 pMacedonia, Republic of 64 pNetherlands 61 OEngland 60 OInternational average 59 OArmenia 57 ONew Zealand 56 OIran, Islamic Republic of 56 OCyprus 55 qEgypt 53 qTunisia 52 qJordan 50 qChile 50 qNorway 45 qPalestinian Nat’l Auth. 41 qLebanon 41 qBahrain 41 qIndonesia 40 qPhilippines 35 qBotswana 32 qMorocco 30 qGhana 22 qSouth Africa 21 qSaudi Arabia 21 q

M01

2028

The four digits above are to be arranged from largest to smallest to form a

four-digit number. The same four digits are then to be arranged from

smallest to largest to form another four-digit number. What is the

difference between the two resulting four-digit numbers?

a 3,726

b 4,726

c 8,082

d 8,182

e 8,192

9 1 4 5



Correct Response:

Cognitive Domain






Approximatenumberofmagazinessold


D

Korea, Republic of 74 pSingapore 74 pChinese Taipei 71 pNetherlands 69 pBelgium (Flemish) 69 pHong Kong, SAR 68 pAustralia 67 pHungary 66 pJapan 66 pSweden 63 pNew Zealand 62 pEstonia 62 pEngland 61 pSlovenia 60 pSlovak Republic 59 pUnited States 58 pMalaysia 58 pRussian Federation 58 pScotland 58 pNorway 58 pLithuania 57 pLatvia 57 pBulgaria 56 pIsrael 54 pItaly 53 pSerbia and Montenegro 50 OInternational average 49 ORomania 47 OCyprus 47 OMoldova, Republic of 44 OMacedonia, Republic of 42 qArmenia 39 qIndonesia 38 qTunisia 37 qPhilippines 36 qLebanon 36 qChile 36 qMorocco 33 qBahrain 31 qIran, Islamic Republic of 29 qJordan 28 qEgypt 23 qSaudi Arabia 23 qPalestinian Nat’l Auth. 21 qSouth Africa 20 qBotswana 19 qGhana 18 q

M02

2194

About 7,000 copies of a magazine are sold each week. Approximately how

many magazines are sold each year?

a 8,400

b 35,000

c 84,000

d 350,000

e 3,500,000








• 15

Incorrect Response

• 14 or 14.88



Theteachersplantosend6newslettersperyear


Armenia 60 pNetherlands 57 pSingapore 57 pHong Kong, SAR 53 pBelgium (Flemish) 46 pJapan 44 pChinese Taipei 44 pKorea, Republic of 43 pUnited States 36 pHungary 35 pSlovak Republic 33 pScotland 32 pEstonia 32 pSweden 30 pNew Zealand 29 pRussian Federation 29 pLithuania 29 pAustralia 28 pEngland 27 OSlovenia 24 OLatvia 22 OInternational average 21 OItaly 21 OBulgaria 20 OIsrael 20 ONorway 20 OCyprus 18 qRomania 14 qSerbia and Montenegro 13 qMacedonia, Republic of 11 qMoldova, Republic of 10 qMalaysia 8 qChile 8 qTunisia 8 qJordan 4 qLebanon 4 qPhilippines 3 qIndonesia 3 qSouth Africa 3 qIran, Islamic Republic of 3 qBahrain 3 qEgypt 3 qPalestinian Nat’l Auth. 2 qMorocco 1 qBotswana 0 qGhana 0 qSaudi Arabia 0 q

M032652

The teachers at Parkway School plan to send 6 newsletters per year toeach of the 620 families with children at the school. The newsletters eachneed 2 sheets of paper. The paper is sold in packs of 500 sheets.

What is the least number of packs of paper needed to print the schoolnewsletter for the year?

Answer: _______________


Student Responses


Theteachersplantosend6newslettersperyear(continued)Item Number: M032652

Correct Response:

Incorrect Response:








• 400 or equivalent.

Incorrect Response



Singapore 91 pNetherlands 88 pHong Kong, SAR 87 pBelgium (Flemish) 86 pKorea, Republic of 85 pEstonia 85 pChinese Taipei 83 pSweden 82 pMalaysia 81 pUnited States 78 pLatvia 78 pRussian Federation 78 pNew Zealand 77 pAustralia 76 pEngland 75 pHungary 72 pIsrael 72 pLithuania 72 pScotland 71 pItaly 71 pSlovenia 67 pMoldova, Republic of 66 pCyprus 66 pRomania 65 pBulgaria 63 OSlovak Republic 63 OJapan 61 OChile 61 OSerbia and Montenegro 61 OInternational average 61 ONorway 60 OMacedonia, Republic of 56 qIndonesia 49 qTunisia 48 qArmenia 47 qIran, Islamic Republic of 44 qLebanon 43 qJordan 43 qBahrain 41 qMorocco 39 qEgypt 36 qPhilippines 35 qPalestinian Nat’l Auth. 33 qBotswana 28 qSaudi Arabia 23 qSouth Africa 18 qGhana 11 q

Garden with 14 rows of 20 plants each

M032671

A garden has 14 rows. Each row has 20 plants. The gardener thenplants 6 more rows with 20 plants in each row.

How many plants are now there altogether?

Answer: _______________



Student Responses


Correct Response:

Incorrect Response:

Garden with 14 rows of 20 plants each (continued)Item Number: M032671


Content Domain Page

Algebra

M012042 Valueof-3xgivenvalueofx 3

M022185 Subtractfractionsinvolvingx 4

M032036 Whichequals2xminus3 plus7xplus5y 5

M032557 Thevalueofa+2times(bplusc) 6

M022002 Threeconsecutiveevennumbers 8

M022251 Totalnumberofbooksthreeboyshave 9

M032044 Carlapaidxzedsfor3cartonsofjuice 10

M012040 Findnfromproportionalityequation 11

M022196 TrueexpressionforvaluesofL,K,M 12

M022253 Solveequationforx 13

M032728 Ifxplus3y equals11and2xplus3yequals13 15

M032208 Ifxminusyequals5andx/2equals3 16

M032210 Ifa/bequals70 17

M032545 7orangesand4lemonscost43zeds 18

M012002 Objectsbalancedonscale 20

M032046 Ifyequals3xplus2 21

M012017 Numberofmatchstickscontinuingpattern 22

M022008 Numbersinsequenceincreasingby4 23

M022261A Sequenceoffigureswithtriangles:filltable 25

M022261B Sequenceoffigureswithtriangles:7thfigure 27

M022261C Sequenceoffigureswithtriangles:50thfigure 29

M032744 Geometrytiling:identifycellwithletter 32

M012029 Setsoforderedpairsofnumbers 35

M012025 Intersectionpointofdistance/timegraphs 36

Data

M012037 Testscorefrequencytable 37

M022189 Howmanypencilssoldfrombargraph 38

M032762 Phoneplans:leastexpensiveplanforBetty 39

M022135 Graphofcoolingwater 41

M032763 Phoneplans:costofplansforFrank 42

M032764 Phoneplans:minutestalkbyDarlene 44

M012006 Comparisonoftwoaveragescores 46

M012014 Piegraphofcropdistribution 47

M022252 Mostlikelysectoronspinner 48

M032271 Inaschooltherewere1200students 49

M022146 Numberofstudentsfromprobability 50

Content Domain Page

Geometry

M032403 DrawalinetodividetriangleABC 51

M012015 Propertyofcongruenttrapezoids 53

M012005 Falsestatementofcongruenttriangles 54

M032261 Identifysimilartriangles 55

M022142 Sumofanglesequalto180degrees 56

M022202 Measureofangleinadjacentangles 57

M012039 Sumofanglesfromintersectinglines 59

M022016 Pointonalinedefinedbytwopoints 60

M032588 Whichpointcouldhavecoordinates(2,-4) 61

M032489 Whichcouldbefoldedtomakea3-Dfigure 62

M022154 Centerpointofrotationofrectangle 63

M032745 Geometrytiling:produceapatternusingletters 64

M032743 Geometrytiling:makesasymmetricalpattern 68

M012026 Angleinoverlappingcongruenttriangles 71

M032693 Theanglebyaregularhexagon 72

M032689 ThesizeofanglePRQ 74

Measurement

M022005 250mlbottlesfilledby400liters 75

M022188 Whichisleastamountoftime 76

M032699 Theunitusedforasoccerfield 77

M032732 Measureoftheareaofatriangle 78

M012003 Actuallengthofboxfromroundedmeasure 79

M012038 Lengthofpipefrommeterscale 80

M022021 Areaofpavedwalkwayaroundpool 81

M032647 Orangesarepackedinboxes 82

M012030 Lengthofrectanglefromwidth/perimeter 83

M022148 Timewhenfinishhomework 84

M022227A 5squares:areaofonesquare 86

M022227B 5squares:lengthofoneside 88

M022227C 5squares:perimeterwholefigure 90

M032649A Carrally:averagespeed 92

M032649B Carrally:averagespeedforonesection 94

M012013 Volumesofstacksofblocks 96

M032678 TheareaoftherectangleABCD 97

Continued

Item Index 2003

y

Content Domain Page

Number

M012016 Pairofnumbersbracketing2.25 98

M022156 Scoopsofflourneededtofillbag 99

M022199 Addition/multiplicationwithfractions 101

M022191 Numberofmen/womenatmeeting 102

M012027 Fractionofhourbetweentwotimepoints 103

M012041 Fractionbirthdaysinfirsthalfofyear 104

M022004 4/5ofbooksmorethan2/3 105

M022010 TimeforBettytorunrace 106

M022127 Fuelremainingintankatendoftrip 107

M032079 JohnandCathytodivideanumberby100 108

M012001 Numberofsquaresinshadedfraction 109

M022012 Fractionlessthan4/9 110

M022144 Decimalroundedtonearesthundredth 112

M022198 Decimalsorderedgreatesttoleast 113

M032670 Thenumberclosestto10 114

M032612 Thevalueof1minus5times-2 115

M032643 Ifnisanegativeinteger 116

M022139 Percentdecreaseintraveltime 117

M032447 Theratiooftheshadedareatotheunshaded 118

M032233 Acomputerclubhad40members 119

M012004 LapsrunbyCarolandAlicefromratio 121

M032228 Ashopincreaseditspricesby20% 122

M032533 Amachineuses2.4litersofgasoline 123

M032727 Threebrothersreceive45,000zeds 124

M032570 3/25ofthepeopleintheaudiencewerechildren 125

M032609 Theclosestto11squaredplus9squared 126

M032690 Whichequals370times998plus370times2 127

M012028 Arrangementsof4-digitwholenumbers 128

M022194 Approximatenumberofmagazinessold 129

M032652 Theteachersplantosend6newslettersperyear 130

M032671 Gardenwith14rowsof20plantseach 132

Item Index 2003

timss resource kit - national center for education … 2003 8th-grade mathematics concepts and...

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