Grade 9
Maths
Class 16
Class 17
Class 18
Class 19
Class 20
11 May 2020
12 May 2020
13 May 2020
14 May 2020
15 May 2020
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Patterns
Patterns
Patterns
Pythagoras
Pythagoras
1
GRADE 9
GREY COLLEGE
MATHS
BASIC PATTERNS
Pattern
Patterns included those with a constant difference between consecutive
terms, a constant ratio between consecutive terms and other patterns
which did not have a constant difference or ratio.
2
NUMBER PATTERNS WITH A CONSTANT DIFFERENCE
With these patterns, there is a constant difference between consecutive terms.
Consider the sequence: 5 ; 7 ; 9 ;11; ...................
There is a constant difference of 2 between consecutive terms. We call this constant
difference d.
The sequence is generated by adding d to each term. In this example ,d = 2 .
How to determine the general rule
Consider the following: 5 ; 7 ; 9 ;11; ...................
Tn 2n 3
The general rule using the letter n is Tn = 2n + 3 where 2 represents the constant difference
and n the position of the term in the sequence. It is important to note that the value of n is
always a natural number. We say that the nth term of the sequence is Tn = 2n + 3. This
general rule can now be used to determine any term of the sequence.
3
EXAMPLE
4
EXAMPLE
5
GRADE 9
GREY COLLEGE
MATHS
Class 16
EXERCISE 1
2020
11 MAY 2020
Do the following in Book 1 (or on paper)
1.
6
NUMBER PATTERNS WITH A CONSTANT RATIO BETWEEN TERMS
The general rule in words for the sequence is therefore:
Multiply the first term 2 by the constant ratio 3 which has been raised to the exponent
which is the position of the term minus 1.
EXAMPLE
7
OTHER TYPES OF NUMBER PATTERNS
These number patterns don’t have a constant difference or constant ratio.
EXAMPLE
8
GRADE 9
GREY COLLEGE
MATHS
Class 17
EXERCISE 2
2020
12 MAY 2020
Do the following in Book 1 (or on paper)
1.
2.
9
GEOMETRIC PATTERNS
Geometric patterns are number patterns represented diagrammatically.
EXAMPLE
10
GRADE 9
MATHS
EXERCISE 3
GREY COLLEGE
Class 18
2020
13 MAY 2020
Do the following in Book 1 (or on paper)
1.
2.
11
THE THEOREM OF PYTHAGORAS
12
13
14
GRADE 9
GREY COLLEGE
MATHS
EXERCISE 1
Class 19
2020
14 MAY 2020
Do the following in Book 2 (or on paper)
1. Calculate the length of the unknown side in each of the following triangles. (The
triangles are not drawn to scale).
a)
d)
b)
e)
c)
f)
15
EXAMPLE
16
GRADE 9
MATHS
EXERCISE 2
GREY COLLEGE
Class 20
2020
15 MAY 2020
Do the following in Book 2 (or on paper)
1.
2.
3.
4.
17