Download MA101D Assignment 2012

Date Issued:
13/2/12
Due Date:
2/3/12
Student Name _______________________
Class Teacher Code _______________
MA101D Investigation # 1
‘FACTORS’
Criteria
Rating
Understanding
/15
Reasoning and Problem Solving
/10
Communication
A
B
C
D
E
*This front page is to be stapled to your assignment which is to be completed on A4 paper.
Use the investigation format below.
Factors
The number 15 has four factors- 1, 3, 5 and 15. It has an even number of factors. Fifteen is said to be
“deficient” since the sum of its factors (don’t include the number itself) is less than the number itself.
[15 is deficient since 1 + 3 + 5 = 9 and 9 is less than 15]
A number is said to be “abundant” if the sum of its factors (don’t include the number itself) is greater
than the number itself. For example; 18 has factors 1, 2, 3, 6 and 9 which total 21; therefore 18 is
abundant (21 is greater than 18)
A perfect number has factors which add to the number itself. The first perfect number 6, has factors 1,
2 and 3 (not including the number itself) which total 6. [6 = 1 + 2 + 3]
Part A (15 marks)
Q1.
List all of the factors of 12 in ascending order.
(1 mark)
Q2.
Show that 12 is an abundant number.
(1 mark)
Q3.
Show that 10 is a deficient number.
(1 mark)
Q4.
What is the largest one digit deficient number?
(1 mark)
Q5.
Show that 36 is an abundant number.
(1 mark)
Q6.
Express 36 as a product of prime factors.
(1 mark)
Q7.
Show that 28 is a perfect number.
(1 mark)
D:\565348572.doc
Q8.
Complete the table below for the first 20 whole numbers. Make sure your table is accurate so
that you can answer Part B with confidence.
(8 marks)
Numbe Factors in
Total number
Sum of factors (not
Deficient Prime
r
ascending
of factors,
including the number
Abundant Factorisation
order
including the
itself)
Perfect
number itself
1
1
1
0
deficient
No prime
factorisation
2
3
1, 3
2
1
deficient
3=3
4
1, 2, 4
3
1+2=3
deficient
22 = 4
5
6
1, 2, 3,6
4
1+2+3=6
perfect
2×3=6
7
8
9
10
deficient
11
12
abundant
13
14
15
1, 3, 5,15
4
1+3+5=9
deficient
3 x 5 = 15
16
17.
18
19
20
Part B (10 marks)
Investigate the sequence of numbers below:
2, 4, 8, 16, 32, …………..





D:\565348572.doc
Add another 5 terms so there are at least 10 terms in the sequence
Include the prime factorisation for each term
Determine if each of the terms are abundant or deficient
Describe how the sum of the factors for each term relates to the number. (In other
words how can you determine the sum of the factors without actually listing them?)
Give an example of a number in the sequence which would be greater than 2000 and
determine the sum of its factors.
Reasoning & Problem Solving (/10)
Communication (A-E)
The following table to help you write up your Assignment. To get full marks, each one of the dot
points must be used in your write-up. DO NOT put the four headings on your assignment.
Sequence
1. CLARIFY the problem
(Communication)
2. CHOOSE an approach
Write-up
Tell the reader what the task is about and what you are asked to do.
(Two-three sentences)
Do:

tell the reader what the task is about.

give an example that illustrates the situation to the reader (if possible).
Don’t:
 rewrite the task situation word-for-word
 comment on what you will do to solve the challenge
 solve the challenge here
Describe the approach you will use to solve the challenge.
(One or more sentences)
Do:

describe the strategy or strategies that you used to find the complete solution.
Don’t:
 show any working here
 solve the challenge here
(Communication)
3. USE the approach
(10 marks)
(Reasoning & Problem
Solving)
4. INTERPRET
the results
(Communication)
Mathematical
Communication
7-8
A
5-6
B
4
C
2-3
D
0-1
E
(Communication)
D:\565348572.doc
Show the reader how you have solved the challenge and explain/show how you did it as mathematically
as you can.
(One or more pages)
Do:

show all important working.

be systematic/ logical in your explanation or working.

show all essential diagrams, tables and formulae.

be accurate with your explanation or working.

make sure that you solve all the problem.

check that your findings make sense.
Don’t
 just use guess and check
 work randomly
 rewrite the question here
Review your attempt for the reader outlining what you have accomplished, mentioning any interesting
features. (One paragraph)
Do:

describe your findings.

explain how your results have solved the problem.
Don’t:
 repeat the solution/problem
 describe unrelated information
A
B
C
D
E
Write up your assignment in a legible and logical manner.
Do:

follow the format above.

use appropriate mathematical terms and symbols throughout the assignment.

use correct spelling of mathematical terms throughout your assignment.
H:\8 MA\MA101D Assignment 2012.docDon’t:
 repeat the solution
 describe unrelated information