PORT SHEPSTONE ISLAMIC SCHOOL
MATHEMATICS
INVESTIGATION
GRADE 8
TERM 2 2022
EXAMINER: B GUNDANI
MODERATOR: I ATCHA
TIME: 1 Hour
TOTAL: 50
NAME :……………………………………………………..
CLASS:………………
NSTRUCTIONS AND INFORMATION
1.
This investigation consists of 7 questions.
2.
Answer ALL the questions.
3.
Number the answers correctly according to the numbering
system used in this question paper.
4.
Write neatly and legibly.
Question Mark
1
2
3
4
5
6
7
TOTAL
This investigation consists of 6 pages.
Investigation: Exponents, Numeric and Geometric Patterns
[Turn over
2
QUESTION 1
1.1
Write the following in exponential form, state your answer as a single
exponent.( e.g 2a or 5b)
1.1.1 2 × 2 × 2
(1)
1.1.2 2 × 2 × 2 × 2 × 2
(1)
1.1.3 (2 × 2 × 2) × (2 × 2 × 2 × 2 × 2)
(1)
1.1.4 5 × 5 × 5 × 5
(1)
1.1.5 5 × 5 × 5 × 5× 5 × 5
(1)
1.1.6 (5 × 5 × 5 × 5) × (5 × 5 × 5 × 5× 5 × 5)
(1)
1.2
Use your answer to 1.1.3 to write down the answer in exponential form
of : 23 × 25
(1)
1.3
Use your answer to 1.1.6 to write down the answer in exponential form
of : 54 × 56
(1)
1.4
From your observation in 1.1.3 and your answer to 1.2, complete the
box below with the correct operation ( + , × , –, ÷ )
23 × 25 = 23 5
_
1.5
(1)
From your observation in 1.1.6 and your answer to 1.3, complete the
box below with the correct operation ( + , × , –, ÷ )
54 × 56 = 54 6
(1)
1.6
In terms of m and n : am × an =
(1)
[11]
3
QUESTION 2
2.1
Write the expression
2 2 2 2 2
2a
in exponential form b
2 2
2
(1)
2.2
Simplify, write your answer in exponential form :
2 2 2 2 2
2 2
(1)
2.3
Write the expression
5 5 5 5 5 5 5
5 5 5
5a
in exponential form
5b
(1)
2.4
Simplify, write your answer in exponential form
5 5 5 5 5 5 5
5 5 5
(1)
2.5
From your observation in 2.1 and your answer to 2.2, complete the box
below with the correct operation ( + , × , –, ÷ )
25 ÷ 22 = 25 2
(1)
2.6
From your observation in 2.3 and your answer to 2.4, complete the box
below with the correct operation ( + , × , –, ÷ )
57 ÷ 53 = 57 3
(1)
2.7
In terms of m and n : am ÷ an =
(1)
[7]
QUESTION 3
Study the following two examples:
Example 1 : a 2  a2 a2 a 2 
3
= (a × a) × (a × a) × (a × a)
= a6
Example 2 : 54  = 5 4  5 4 
2

= ( 5 × 5 × 5 × 5 ) × ( 5 × 5 × 5 × 5)
= 58
4
3.1
Use the same method in Examples 1 and 2 above to simplify :
3 
3 4
×
=
×
)×(
=(
(1)
×
)×(
)×(
)
=
3.2
(1)
(1)
From your observation in Example 1, 2 and 3.1 above, complete the
box below with the correct operation ( + , × , –, ÷ )
a  = a2 3
2 3

(1)
3.3
In terms of m and n : a m  =
n
(1)
[5]
QUESTION 4
2 2 2 2 2
4.1
Write the expression
2 2 2 2 2 in exponential form
2a
2b
(1)
4.2
Simplify the expression :
2 2 2 2 2
2 2 2 2 2
(1)
4.3
Using the law you discovered in 2.7, simplify the expression in the
form 2a
(1)
4.4
From your observation : x0 =
(1)
[4]
QUESTION 5
APPLICATION OF EXPONENTIAL LAWS
Using the exponential laws you discovered above, simplify the following, state
the answer in exponential form:
5.1
34 × 39
(1)
5.2
5x2 × 4x5
(1)
5
5.3
912 ÷ 95
(1)
5.4
64x7 ÷ 8x4
(1)
5.5
a 
5 4
(1)
5.6
3a 
2 2
(1)
5.7
110
(1)
[7]
QUESTION 6
Given the sequence:
6.1
7 ; 11 ; 15 ; 19 ; . . .
Write down the next two terms in the sequence.
(2)
6.2
Describe the relationship between the terms.
(2)
6.3
Write a formula in terms of n to describe the relationship between the
position of a term in the sequence and term itself.
(2)
6.4
Use your formula in 6.3 to find the 20th term.
(2)
[8]
6
QUESTION 7
A factory makes window frames. Type 1 has one window pane, type 2 has four
window panes, type 3 has nine window panes, and so on
Type 5
7.1
In the space above draw type 5 window frame.
7.2
How many window panes will there be in type:
(2)
7.2.1 5?
(1)
7.2.2 6?
(1)
7.3
Copy and complete the table below:
Frame type
1
2
3
4
Number of window panes
1
4
9
16
5
6
15
20
(2)
7.4
How many window panes will be in type n?
(2)
[8]
GRAND TOTAL : 50