Lascap's Fraction Portfolio

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MATHEMATICS SL PORTFOLIO

DZHARIF ALIAH BT SABRI

M11P

INTRODUCTION

The given triangle shows number that is arranged symmetrically from one row to another. Besides that, a lot of patterns can be derived from the existing elements making it possible to explore the other sub-elements within this triangle like the numerator and denominator.

Keys :

  • n = row
  • r = column

  1. Finding the numerator of the sixth row

A triangle consisting of only the numerators is made.

1        1

1        3             1

                                 1        6        6        1

1              10              10              10               1

1        15        15        15        15        1

From the figure,

With the exception of the first and last columns which the value is fixed to ‘1’, a pattern can be observed from the other numerators. The difference between the value of the numerator from each row, n, to another row increases by 1.

The highlighted columns show that the difference of the numerator between the rows increases by 1. The table above also shows an attempt to find the numerator when n = 6 which follows the pattern from the previous rows. Since the value of the numerator from each row, n, shows the same value, the numerator of the sixth row can be calculated by adding 6 to the numerator in the fifth row; 15. The numerator of the sixth row is as follows:

1        21        21        21        21        21        1

  1. Using technology, plot the relation between row number, n, and the numerator of each row. Describe what you notice from your plot and write a general statement to represent this.

The technology used to find any general statement is by using Graphic Display Calculator, TI-84. The programme used is Quadratic Regression which is a programme that finds the equation of the parabola given a set of data. I denote y-axis as N (numerator) while x-axis as n (rows). The steps of using the TI-84 are as follows:

The screen pictures of the processes are shown below.

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Image 1

Caption: Image 1 shows the set of data. L1 represents number of row (n) while L2 represents the value of numerator (N)

Image 2

Caption: Image 2 shows the range set which is -2≤ n ≤ 6 for the x-axis while -2 ≤ y ≤ 20 for the y-axis

Image 3

Caption: Image 3 shows the general equation obtained by using Quadratic Regression. Based on image 3, the general equation to find numerator is N = 0.5n2 + 0.5n.

Image 4

Caption: Image 4 shows the general equation to find the numerator on ...

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