2 number+patterns+and+sequences

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Collection of TIMSS released items based onKBSM Mathematics Curriculum

[Form 1]Number Patterns and Sequences

1

1. The numbers in the sequence 2, 7, 12, 17, 22, increase by fives. The

numbers in the sequence 3, 10, 17, 24, 31, increase by sevens. The

number 17 occurs in both sequences. If the two sequences are continued,

what is the next number that will be seen in both sequences?

Answer: _____________________________________

Answer Cognitive Domain

52 Solving Problems

Source:http://timss.bc.edu/timss1995i/items.html
http://timss.bc.edu/timss1995i/items.htmlhttp://timss.bc.edu/timss1995i/items.htmlhttp://timss.bc.edu/timss1995i/items.htmlhttp://timss.bc.edu/timss1995i/items.html


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2

2. The table represents a relation betweenx andy.

What is the missing number in the table?

A. 2

B. 3

C. 4

D. 5

E. 6


B Applying/Analysing


x y

1 1

2 ?

4 7

7 13


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3

3. These shapes are arranged in a pattern.

Which set of shapes is arranged in the same pattern?

A.

B.

C.

D.


C Knowing



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4

4. Here is a sequence of three similar triangles. All of the small triangles are

congruent.

a. Complete the chart by finding how many small triangles make up eachfigure.

FigureNumber of

small triangles

1 1

2

3

b. The sequence of similar triangles is extended to the 8th Figure.

How many small triangles would be needed for Figure 8?

2

3

Figure 1 Figure 2 Figure 3


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Answer(for Question a) Cognitive Domain

4 AND 9 Solving problems

Answer(for Question b) Cognitive Domain

64 Solving problems



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5. The figures show four sets consisting of circles.

Figure 1 Figure 2 Figure 3 Figure 4

a) Complete the table below. First, fill in how many circles make up Figure

4. Then, find the number of circles that would be needed for the 5th

figure if the sequence of figures is extended.

Figure Number of circles

1 1

2 3

3 6

4

5

b) The sequence of figures is extended to the 7th figure. How many

circles would be needed for Figure 7?

Answer: __________________

c) The 50th figure in the sequence contains 1275 circles. Determine the

number of circles in the 51st figure. Without drawing the 51st figure,

explain or show how you arrived at your answer.


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Answer(for Question a) Cognitive Domain

10 AND 15 Analysing/Solving problems

Answer(for Question b) Cognitive Domain

28 Analysing/Solving problems

Answer(for Question c) Cognitive Domain

Correct response:

i. 1326. Correct general expression

2

1)( nn

,2

51(52), or equivalent

ii. 1326 [Adds 1275 + 51]

iii. Other fully correct, including[(figure number)2 number of circles in

previous figure]

Partial response:

i. 1326 without showing how obtained

ii. Correct method but does not write 1326as answer

iii. Other partially correct

Analysing/Reasoning

Source:http://timss.bc.edu/timss1999i/study.html
http://timss.bc.edu/timss1999i/study.htmlhttp://timss.bc.edu/timss1999i/study.htmlhttp://timss.bc.edu/timss1999i/study.htmlhttp://timss.bc.edu/timss1999i/study.html


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8

6. Matchsticks are arranged as shown in the figures.


If the pattern is continued, how many matchsticks would be used to make

Figure 10?

A. 30

B. 33

C. 36

D. 39

E. 42


B Analysing and Reasoning

Source:http://timss.bc.edu/timss2003i/released.html
http://timss.bc.edu/timss2003i/released.htmlhttp://timss.bc.edu/timss2003i/released.htmlhttp://timss.bc.edu/timss2003i/released.htmlhttp://timss.bc.edu/timss2003i/released.html


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7. (3, 6), (6, 15), (8, 21)

Which of these describes how to get the second number from the first number

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


E Reasoning



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10

8. The numbers in the sequence 7, 11, 15, 19, 23, increase by four. The

numbers in the sequence 1, 10, 19, 28, 37, increase by nine. The number

19 is in both sequences. If the two sequences are continued, what is the next

number that is in BOTH the first and the second sequences?

Answer: ____________________________


55 Analysing /Reasoning



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9. The three figures below are divided into small congruent triangles.


A. Complete the table below. First, fill in how many small triangles make

up Figure 3. Then, find the number of small triangles that would be

needed for the 4th figure if the sequence of figures is extended.

FigureNumber of

Small Triangles

1 2

2 8

3

4

B. The sequence of figures is extended to the 7th figure. How many small

triangles would be needed for Figure 7?

Answer: ___________________________

C. The sequence of figures is extended to the 50th figure. Explain a way

to find the number of small triangles in the 50th figure that does not

involve drawing it and counting the number of triangles.


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Answer(for Question A) Cognitive Domain

18 AND 32 Analysing/Solving problems

Answer(for Question B) Cognitive Domain

98 Analysing/Solving problems

Answer(for Question C) Cognitive Domain

Correct response:i. Correct general (i.e., literal) expression,

e.g., 2n2, or equivalent expressed in

words

ii. 2 502 OR 2 50 50 OR 100 50OR (50 + 50) 50 OR equivalentexpressed in words (disregard errors incomputation)

Partial response:

i. Derives answer (5000) without showingwork

ii. Other partially correct

Analysing/Reasoning



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10. Which of these shows 1080 as the product of prime factors?

A. 1080 = 8 27 5

B. 1080 = 2 4 3 9 5

C. 1080 = 2 2 2 3 3 3 5

D. 1080 = 22 32 6 5


C Knowing

Source:http://timss.bc.edu/timss2007/items.html
http://timss.bc.edu/timss2007/items.htmlhttp://timss.bc.edu/timss2007/items.htmlhttp://timss.bc.edu/timss2007/items.htmlhttp://timss.bc.edu/timss2007/items.html


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11. 2, 5, 11, 23,

Starting the pattern at 2, which of these rules would give each of the terms in

the number pattern above?

A. Add 1 to the previous term and then multiply by 2.

B. Multiply the previous term by 2 then add 1.

C. Multiply the previous term by 3 then subtract 1.

D. Subtract 1 from the previous term and then multiply by 3.


B Applying

Source:http://timss.bc.edu/timss2007/items.html
http://timss.bc.edu/timss2007/items.htmlhttp://timss.bc.edu/timss2007/items.htmlhttp://timss.bc.edu/timss2007/items.htmlhttp://timss.bc.edu/timss2007/items.html

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