Content Domain Main Topic DATA Data Interpretation Reasoning Test score...

Main TopicContent Domain

Correct Response:

Cognitive Domain

119

TIMSS 2003 8th-Grade Mathematics Concepts and Mathematics Items

Overall Percent Correct

Country average vs. International average:

Higher pNotdifferent OLower q

b

Item Number: M012037

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:

120

Main TopicContent Domain Cognitive Domain





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

121





TIMSS 2003 8th-Grade Mathematics Concepts and Mathematics ItemsM

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.

SCORINgCorrect Response

• PlanBwithexplanationthatincludesfreeminutesusedandexplicitreferencetolowermonthlyfeeforPlanB.

Partial Response

• PlanBwithexplicitreferencetolowermonthlyfeeandnoreferencetofreeminutes.

Incorrect Response

• PlanBwithinadequate(onlyfreeminutes)ornoexplanation.

• PlanAwithorwithoutexplanation.

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


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

122

Student Responses


Correct Response:

Partial Response:

Incorrect Response:

Phoneplans:leastexpensiveplanforBetty(continued)Item Number: M032762


Correct Response:

Cognitive Domain

123





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

124







• 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

125

Student Responses


Correct Response:

Inorrect Response:

Phoneplans:costofplansforFrank(continued)Item Number: M032763

126







• 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.

127

Student Responses


Phoneplans:minutestalkbyDarlene(continued)Item Number: M032764

Correct Response:

Partial Response:

Incorrect Response:

Correct Response:

128






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

129





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:

130






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

131





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:

132






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

133







• LinedrawnfromAto(approximate)midpointofBC.

Incorrect Response

• LinedrawnfromCorB.

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


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

134

Student Responses


DrawalinetodividetriangleABC(continued)Item Number: M032403

Correct:

Incorrect:


Correct Response:

Cognitive Domain

135





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:

136






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

137





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:

138






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

139







• 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

140

Student Responses


Correct Response:

Incorrect Response:

Measureofangleinadjacentangles(continued)Item Number: M022202


Correct Response:

Cognitive Domain

141





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:

142






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

143





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:

144






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

145





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

146







• 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

147

Student Responses


Correct Response:

Geometrytiling:produceapatternusingletters(continued)Item Number: M032745

148


Partial Response:


Student Responses (Continued)

149


Incorrect Response:

Student Responses (Continued)


150







• 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

151

Student Responses


Geometrytiling:makesasymmetricalpattern(continued)Item Number: M032743

Correct Response:

152


Incorrect Response:

Student Responses (continued)

Geometrytiling:makesasymmetricalpattern(continued)Item Number: M032743


Correct Response:

Cognitive Domain

153





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



154




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˚

155

Student Responses


Correct Response:

Incorrect Response:

Theanglebyaregularhexagon(continued)Item Number: M032693

Correct Response:

156






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

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