Math
MATHEMATICS SL INTERNAL ASSESSMENT TYPE 1
LACSAP’S FRACTIONS
10/11/2012
Tracy Braganza IB2T
In mathematics, Lacsap’s fractions are based upon Pascal's triangle. In this portfolio, the aim that was given was to consider a set of numbers that are presented in a symmetrical pattern, deduce a general statement and also to determine the limitations of the general statement that have been found. The answers in this portfolio will be attained with the help of a GDC calculator (GDC – TI84 Plus Silver Edition).
Investigation:
Considering the five rows of numbers shown below 1 1 1 32 1 1 64 64 1 1 107 106 107 1
1 1511 159 159 1511 1
In order to find the numerator of the sixth row we have been given the numerators of the five rows shown above. Excluding the first and last numerators of each row, thus we will consider the numerators 1, 3,6,10, and 15.
Figure 1:
This figure will portray the relationship between the first row and second row, second row and third row, third row and fourth row, and fourth row and fifth row. Through the figures obtained we will be able to justify the relationship between the fifth row and sixth row.
Row | Numerator | 1st differences | 2nd differences | 1 | 1 | 2 | 1 | 2 | 3 | | | | | 3 | | 3 | 6 | | 1 | | | 4 | | 4 | 10 | | 1 | | | 5 | | 5 | 15 | | |
Thus with the help of the figure above it is evident to say that the difference between the numerator in row 1 and row 2 is 2, row 2 and row 3 is 3, row 3 and 4 is 4 and row 4 and 5 is 5. The second difference for each row number is 1 showing that the equation for the numerator is a quadratic sequence. In order to acquire the numerator of the sixth row I will find the equation of the sequence by using the general form of a quadratic equation formula, y = ax2 + bx
LACSAP’S FRACTIONS
10/11/2012
Tracy Braganza IB2T
In mathematics, Lacsap’s fractions are based upon Pascal's triangle. In this portfolio, the aim that was given was to consider a set of numbers that are presented in a symmetrical pattern, deduce a general statement and also to determine the limitations of the general statement that have been found. The answers in this portfolio will be attained with the help of a GDC calculator (GDC – TI84 Plus Silver Edition).
Investigation:
Considering the five rows of numbers shown below 1 1 1 32 1 1 64 64 1 1 107 106 107 1
1 1511 159 159 1511 1
In order to find the numerator of the sixth row we have been given the numerators of the five rows shown above. Excluding the first and last numerators of each row, thus we will consider the numerators 1, 3,6,10, and 15.
Figure 1:
This figure will portray the relationship between the first row and second row, second row and third row, third row and fourth row, and fourth row and fifth row. Through the figures obtained we will be able to justify the relationship between the fifth row and sixth row.
Row | Numerator | 1st differences | 2nd differences | 1 | 1 | 2 | 1 | 2 | 3 | | | | | 3 | | 3 | 6 | | 1 | | | 4 | | 4 | 10 | | 1 | | | 5 | | 5 | 15 | | |
Thus with the help of the figure above it is evident to say that the difference between the numerator in row 1 and row 2 is 2, row 2 and row 3 is 3, row 3 and 4 is 4 and row 4 and 5 is 5. The second difference for each row number is 1 showing that the equation for the numerator is a quadratic sequence. In order to acquire the numerator of the sixth row I will find the equation of the sequence by using the general form of a quadratic equation formula, y = ax2 + bx