Lacsap’s Fractions:
Lacsap is Pascal backwards and the way that Lacsap’s fractions are presented is fairly similar to Pascal’s triangle. Thus, various aspects of Pascal’s triangle can be applied in Lacsap’s fraction.

To determine the numerators:
To determine the numerator (n), consider it in relation to the number of the row (r) that it is a part of.

The relation between the numerator and the row number can be shown by the equation:
Where the numerator = n
And the row = r
0.5r2 + 0.5r = the numerator (n)

When r=1
0.5(12) + 0.5(1) = 1
When r=2
0.5(22) + 0.5(2) = 3
When r=3
0.5(32) + 0.5(3) =6
When r=4
0.5(42) + 0.5(4) = 10
When r=5
0.5(52) + 0.5(5) = 15

Therefore if you are attempting to find the 6th or 7th row numerators, you simply plug (n) into the equation:
When r=6
0.5(62) + 0.5(6) = 21
When r=7
0.5(72) + 0.5(7) = 28

Therefore the terms in the 6th row include:
1211621132112211321161

...tendency, variation and other descriptive statistics have been calculated for this variable are below:
|Descriptive Statistics: |
|Size |
|Mean |3.42 |
|Median |3 |
|Mode |2 |
|Standard Deviation |1.73898868 |
|Sample Variance |3.02408163 |
|Range |6 |
|Minimum |1 |
|Maximum |7 |
|Sum |171 |
|Count |50 |
|Frequency Distribution: |
|Size |Frequency |
|1 |5 |
|2 |15 |
|3 |8 |
|4 |9 |
|5 |5 |
|6 |5 |
|7 |3 |
[pic]
The mean size of house hold of the customers is handling as 3.42. The median of the data is 3 and the mode is 2. The standard deviation is given...

...using a mathematical formula that accounts for a person’s height and weight. BMI is equal to a person’s weight in kilograms (kg) divided by height in meters squared (BMI=).
Aim
The aim of this project work is to investigate the relationship between height, weight and BMI with students’ health condition. The purpose of this campaign is to create awareness among students about obesity or underweight related to health problems. We should select an appropriate balanced diet to avoid from being a victim to such illness. Nutritional guidelines play an important role in helping us to make informed choices about our nutrient intake. The foods that constitute a balanced diet should contain the major nutrients which include carbohydrates, proteins and lipids, as well as vitamins, minerals, water and dietary fibre. A balanced diet is essential for the healthy growth and development of the body.
The objectives of carrying out this project work are:
1 To collect data on the heights and weights of students.
2 To calculate BMI of each students.
3 To represent data using various methods.
4 To relate students’ knowledge with the data obtained.
5 To suggest ways to practice healthy lifestyle.
The methods of research are as follows:
1 To obtain the height, weight and BMI of 50 students in Form 1 and 50 students in Form 5.
2 To tabulate the data consisting the height, weight and BMI of this 100 students.
3...

...Jonghyun Choe
March 25 2011
MathIB SL
Internal Assessment – LASCAP’S Fraction
The goal of this task is to consider a set of fractions which are presented in a symmetrical, recurring sequence, and to find a general statement for the pattern.
The presented pattern is:
Row 111
Row 21 32 1
Row 3
1 64 64 1
Row 4
1 107 106 107 1
Row 5
1 1511 159 159 1511 1
Step 1: This pattern is known as Lascap’s Fractions. En(r) will be used to represent the values involved in the pattern. r represents the element number, starting at r=0, and n represents the row number starting at n=1. So for instance, E52=159, the second element on the fifth row. Additionally, N will represent the value of the numerator and D value of the denominator.
To begin with, it is clear that in order to obtain a...

...challenge in designing brake systems. For measurement, a tribometer is an instrument that measures friction on a surface and a profilograph is a device used to measure pavement surface roughness. Friction is also used to heat and ignite matchsticks.
Anybody that moves, in one way or another, experiences an opposing force either from air or from another body in contact. This force tends to retard the motion of the body. The presence of friction between contact surfaces generates sound, light, and heat energy. It is also referred to as the retarding force or even drag force in the form of air resistance.
Frictional force is found to be directly proportional to the normal force (N) which is mathematically expressed as:
f ∝N
f=kN (Equation 1)
The coefficient of friction (µ) takes the place of k which is the constant of proportionality. Thus:
f=µN (Equation 2)
26904953626485Figure 3. Angle of Repose
Figure 3. Angle of Repose
269061011472000If the body slides down the incline due to its own weight, the angle between the horizontal and the incline is called angle of repose 𝜽, as shown in Figure 3. In the previous experiment, if we are measuring along the y-axis, the formula will be
ΣFy=0, f=Wcosθand if we are measuring along the x-axis, the formula will be
ΣFx=0, f=Wsinθ.
The coefficient of friction is equal to the tangent of the angle of repose.
µ=fN=WsinθWcosθ, µ=tanθ(Equation 3)
In this experiment, we should be able to determine the coefficient of...

...
The case between Beauty and Stylish involves concept of a valid contract, pre-contractual statements, express term and misrepresentation.
A valid contract is established between Beauty and Stylish when an offer is accepted and there is intention for both parties to create legal relations. An offer refers to the expression of willingness of the offerer to be contractually bound by an agreement if his or her offer is properly accepted. It has to be clear and certain in terms. It must also be communicated to the offeree before it is being accepted. In addition, the acceptance has to be unqualified, unconditional and made by a positive act. In the case of Beauty and Stylish, a positive act refers to the signing of the contract. All terms of the offer must be accepted without any changes and cannot be subjected to any condition, taking effect only upon fulfillment of that condition. When Beauty and Stylish enter into the agreement, they must intend to bind and bound legally to each other by their agreement. This is the intention to create legal relations between two parties. In the meanwhile, this contract must possess consideration. A contract must therefore be a two-sided affair, with each side providing or promising to provide something of value in exchange for what the other is to provide.
Every contract, whether oral or written, contain terms. The terms of a contract set out the rights and duties of the parties. Terms are the promises and undertakings given by each...

...Introduction:
The task of this assessment is to consider and investigate geometric shapes that lead to stellar numbers. One of the simplest forms of this would be of square numbers, terms 1, 2, 3, 4, and 5 in terms of geometric shapes lead to the special numbers of 1, 4, 9, 16, and 25. To find these outcomes, simply all that is needed to be done is to square the nth term of the sequence. For example, 12=1, 22=4, 32=9, 42=16, and 52=25, therefore the resulting formula for square numbers would be n2=Tn where T=total amount of n. For this investigation though, the geometric shapes of equilateral triangles are studied. Triangular numbers are the amount of dots that evenly fit inside the triangle. After solving the sequence of the triangular numbers and finding a formula to solve for all equilateral triangles, the knowledge attained from triangular numbers will then be used to find and solve the correlation between triangular numbers and stellar (star) numbers.
Here is a sample of the first 5 terms in the triangular numbers sequence:
The row of numbers above the triangles is the number of each term or n.
The rows of numbers below the triangles are triangular numbers of each term or n.
` n1 n2 n3 n4 n5
Here is a sample of the first 4 stages of p-stellar shapes that are being investigated. P indicates the amount of vertices in the stellar shape. In this case the stellar shapes being investigated are 6-stellar, however...

...Lacsap’s Fractions
IBMath SL
Internal Assessment Paper 1
Lacsap’s Fractions
Lacsap is Pascal spelled backward. Therefore, Pascal’s Triangle can be used practically especially with this diagram.
(Diagram 1)
This diagram is of Pascal’s Triangle and shows the relationship of the row number, n, and the diagonal columns, r. This is evident in Lacsap’s Fractions as well, and can be used to help understand some of the following questions.
Solutions
Describe how to find the numerator of the sixth row.
There are multiple methods for finding the numerator of each consecutive row; one way is with the use of a formula, and another by using a diagonal method of counting illustrated by a diagram.
The following image can be used to demonstrate both techniques to finding the numerator:
(Diagram 2)
This formula uses “n” as the row number and the outcome is the numerator of the requested sixth row.
n2 + n
2
As indicated, inputting the number 6, as the requested sixth row, for n gives the solution of 21.
X = n2 + n
2
X = (6)2 + (6)
2
X = 36 + 6
2
X = 42
2
X = 21
Therefore, as shown, the numerator of the sixth row is 21, and this can be checked for validity by entering each number, 1 through 5, into the formula and making sure that the answer corresponds with the numerator in the above diagram.
Where n = 5: Where n = 4:...

...
Laurie Scott
SL Math Internal Assessment
Mr. Winningham
9/5/12
Instructions: In this task you will consider a set of numbers that are presented in a symmetrical pattern.
Pascal’s Triangle
|n=0 |1 |
|1 |0 |
|2 |3 |
|3 |6 |
|4 |10 |
|5 |15 |
|6 |21 |
Table 1: Relationship between Row Number and Numerator of Figure 2
[pic]
Figure 3: Graph of the relationship between Row Number and Numerator of Figure 2
In order to find the sixth and seventh rows, a pattern for determining the denominator must be found:
First it is helpful to determine a relationship between the numerator and denominator of the first term in each row:
|Row Number ( n ) |Difference of Numerator and |
| |Denominator (1st term) |
|1 |0 |
|2 |1 |
|3 |2 |
|4 |3 |
|5 |4 |
Table 2: Relationship between Row Number and the difference of the Numerator and Denominator of the 1st...