Math Portfolio SL TYPE I
LACSAP’S FRACTIONS
Introduction
This assignment requires us to solve patterns in numerators and denominators in LACSAP’S FRACTIONS, and the first five rows look like:
Figure 1: Lacsap’s Fractions
1 1st row
1 3/2 1 2nd row
1 6/4 6/4 1 3rd row
1 10/7 10/6 10/7 1 4th row
1 15/11 15/9 15/9 15/11 1 5th row Then, let’s look at each part of the question.
Part 1: Numerator of the Sixth Row
Describe how to find the numerator of the sixth row.
For the first part of the question, we need to describe how to find the numerator of the sixth row. To begin with, let’s make all the numerators look the same in a row:
Figure 2: Lacsap’s Fractions
1/1 1/1 1st row
3/3 3/2 3/3 2nd row
6/6 6/4 6/4 6/6 3rd row
10/10 10/7 10/6 10/7 10/10 4th row
15/15 15/11 15/9 15/9 15/11 15/15 5th row Then, we can take out the denominator and go down by the row and just look at the numerator for this part of question, which will look like:
t1=1; t2=3; t3=6; t4=10; t5=15
We can investigate that the numerator starts with 1 in the first row, and the numerators are the same in one row. Each numerator after 1 is the sum of 1+2+…+n (n=row number) which forms an arithmetic series. For example:
When n=3, the numerator will be t3=1+2+3=6.
Table 1: Row Number and Numerator
Row NumberNumeratorInvestigation
11t1=1
23t2=1+2
36t3=1+2+3
410t4=1+2+3+4
515t5=1+2+3+4+5
Therefore, according to this arithmetic series tn=1+2+3+…+n, (n=row number), we can find out the numerator of the sixth row is t6=1+2+3+4+5+6=21
Part 2: General Statement for Numerator and Row Number
Using technology, plot the relation between the row number, n, and the numerator in each...
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...axis is considered to scale the time. We can get new data table as follows:
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0.01  2  4.61  35 
0.03  1.52  3.51  28 
0.1  1  2.3  20 
0.3  0.52  1.2  15 
1  0  0  11 
3  0.478  1.1  9 
10  1  2.3  6 
30  1.478  3.4  4.5 
Then we plot the graph of Log Time and Ln Time as follows:
From the graph, it can be seen that the shape of...
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The Founding Father, the Propagandist, and a Wife
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Part B: Cubic Polynomials 12
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Math SL PortfolioLacsap’s Fractions 
Type1: Investigation Portfolio
Greenwood High (An International School) 




Table of Contents:
Introduction……………………………………………………………………………………………………..……..…...Page 2
Patterns in Numerator………………………………………………………………………………….………………Page 2 and Page 3
Plotting Graph of Row Number and Numerator……………………………………………………………Page 4 to Page 7
Finding...
...
IB Math: Studies Statistics
Portfolio:
What is the relationship between the numbers of goals the top sixteen players of the FIFA world cup 2014 score with the height of the players?
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School Name: Franklin Delano Roosevelt
Course: IB Math Studies
Name: Valerie Philco
What is the relationship between football player’s height that is participating...
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Page 1 of 1
Solutionbank C1
Edexcel Modular Mathematics for AS and ALevel
Algebraic fractions
Exercise A, Question 1
Question:
Factorise completely
(a) 2x3 − 13x2 − 7x
(b) 9x2 − 16
(c) x4 + 7x2 − 8
Solution:
(a)
2x3 − 13x2 − 7x
x is a common factor
= x ( 2x2 − 13x − 7 )
So take x outside the bracket.
= x ( 2x2 + x − 14x − 7 )
For the quadratic, ac = − 14 and
1...
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48 Pages
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