CHAPTER 6 - NUMERIC AND GEOMETRIC PATTERNS

CHAPTER 6 - NUMERIC AND GEOMETRIC PATTERNS

INPUT VALUE OUTPUT VALUE RULE ALGEBRAIC LANGUAGE FLOW DIAGRAM

WORDS

Examples: 1.1. Complete the table below:

Input Output

1

2

3

4

5

6

7 ...... 10 100

7 11 15 19

1.2. Explain the relationship between and in words.

1.3. Write the algebraic formula. 1.4. Make a flow diagram.

2.1. Complete the table below:

Input

x

1

2

3

4

5

6

7 ...... 10 100

Output y - 3 - 6 - 9 - 12

2.2. Explain the relationship between and in words.

2.3. Write the algebraic formula. 2.4. Make a flow diagram.

Page 1 of 6

3.1 Complete the table below according to the rule given:

Input Output

-2 -1 0

1

2

3

4 ...... 10 100

HOMEWORK PG. 84 Ex.5.1 #1 a ? l , 5 and 6 Parent sign:

Describing patterns

To describe terms in a pattern we use the following notation:

o T1 is the 1 term of a sequence. o T4 is the 4 term of a sequence. o Tn is the general term and is often expressed as the n term of a sequence.

A sequence does not have to follow a pattern but when it does, we can write an equation for the general term. The general term can be used to calculate any term in the sequence.

For example, consider the following linear sequence: 1;4;7;10;13;...

The term is given by the equation Tn = 3 -2. You can check this by substituting values for n:

If we find the relationship between the position of a term and its value, we can describe the pattern and find any term in the sequence.

Eg.1. Given: 4; 8; 12; 16; ...; ...; ...

Eg.2. Given: 2; 7; 12; 17; ...; ...; ...

1.1. Write down the next three terms. 1.2. Calculate the general (Tn) term.

2.1. Write down the next three terms. 2.2. Calculate the general (Tn) term.

1.3. Calculate the 100th term (T100)

2.3. Calculate the 100th term (T100)

1.4. Which term is equal to 2000?

2.4. Which term is equal to 297?

Page 2 of 6

Eg.3. Given: 2; 4; 8; 16; ....; ....; .... 3.1. Write down the next three terms. 3.2. Calculate the general (Tn) term.

3.3. Hence, calculate the 10th term (T10)

3.4. Which term is equal to 32768?

Eg.4. Write down the next three terms of the pattern: 1 ; 1 ; 2 ; 3 ; 5 ; .....; ....; .... What is this kind of pattern called?

Eg.5. The pattern below shows the number of matches needed to make certain pattern.

5.1. Draw the next pattern

5.2. Complete the following table:

Number of triangles

1

2

3

4

10

n

Number of matches

5.3. If a pattern had 35 triangles, how many matches would be needed?

5.4. If a pattern had 101 matches, how many triangles are there?

Page 3 of 6

Eg.6 The pattern below shows the number of matches needed to make certain pattern.

6.1. Draw the next pattern

6.2. Complete the following table:

Number of house(s)

1

2

3

4

10

n

Number of matches

6.3. If a pattern had 35 houses, how many matches would be needed?

6.4. If a pattern had 251 matches, how many houses are there?

Eg.7 The pattern for the number of chairs and tables needed at a restaurant is shown below:

7.1 Complete the table below

Number of tables

1

2

3

4

5

50

n

Number of chairs

Page 4 of 6

7.2 If the restaurant had 31 tables, how many chairs would be needed?

7.3 If the restaurant had 204 chairs, how many tables would be needed?

EXAM TYPE QUESTIONS

1.1 Write down the next two terms in the given sequence: -1; 1; 3; .... ; .... (1)

1.2 Write down the general term of the given sequence in the form Tn = ... (2)

1.3 What is the value of the 50th term?

(2)

1.4 Which term in the sequence is equal to 37?

(2)

2. Match sticks are arranged to form the following patterns:

FI G 1

FI G 2

FI G 3

2.1. Determine the number of matches in the fourth pattern.

(2)

2.2. Write down the general term in the form of Tn = .............

(2)

2.3. How many matches will be in the 25th term?

(2)

2.4. Which term will have 306 matches?

(3)

3.1. Given: 6; 10; 14; ....

3.1.1. Extend the sequence by 2 terms.

(2)

3.1.2. Find a rule that describes the number pattern. (Tn = ......)

(2)

3.1.3. Hence, determine the 10th term.

(2)

3.2. Given: 2; 4; 8; 16; ....

3.2.1. Extend the sequence by 2 terms.

(2)

3.2.2. Find a rule that describes the number pattern. (Tn = .....)

(2)

3.2.3. Hence, determine the 10th term.

(2)

3.3. Given: 1; 4: 9; 16; 25; ....

3.3.1. Extend the sequence by 2 terms.

(2)

3.3.2. Find a rule that describes the number pattern. (Tn = ......)

(2)

3.3.3. Hence, determine the 10th term.

(2)

Page 5 of 6

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download