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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