Introduction: In this task I will consider a set of numbers that are presented in a symmetrical pattern and try to find a general equation to find the elements in the [pic]row. Consider the five rows of number shown below.

Figure 1 Lacsap’s Fractions

The aim of this task is to find the numerator of the sixth row and to find the general statement for [pic]. Let [pic] be the [pic]element in the [pic]row, starting with r=0.

First, I will make a table of the numerator and the row number to show the relationship between the numerator and the row number.

Table 1 A table showing the relationship of rows and numerator The difference between the numerator of row 1 and row 2 is 2, then the difference between the numerator of row 2 and row 3 is 3. The second difference for each row is 1 and it shows that this is a geometric sequence. So, I will start by finding the equation using the quadratic formula, [pic], in which x is the row number and y is the numerator. First, I will plug in the numbers in the second row, which is 2 for x and 3 for y to try finding the quadratic equation of the Lacsap’s sequence. Then, I will plug in the numbers in the third row and it forms a simultaneous equation. I will use substitution method to solve the equation as there are two unknowns in the equation. First, I will solve for ‘a’ by substituting the answer ‘b’ from the first equation, which is row 2, to the second equation, which is row 3. The workings are shown below. The answer of ‘a’ and ‘b’ are both 0.5. So, we found out the equation for the numerator is [pic], where n is row number. [pic][pic]

The aim of this task is to find out the numerator of the sixth row. So, I plugged in row number in the equation to find the numerator of the sixth row. [pic]
From this method, we found out the numerator of the sixth row should be 21. In order to test the...

...Santoro, A. (2004). “Manipulatives: A Hands-On Approach to Math.” Principal, 84 (2), (28-28).
This article speaks about the importance and significance of the use of manipulatives in the classroom, specifically in the subject of math. Manipulatives have proven to be valuable when used in a math class and are even more valuable to the children when they are young, and are learning new math concepts. Students are able to physically...

...EUROPEAN SCHOOL
Mathematics Higher Level
Portfolio
Type 1
SHADOW FUNCTIONS
Candidate Name: Emil Abrahamyan
Candidate Number: 006343-021
Supervisor: Avtandil Gagnidze
Session Year: 2013 May
Candidate Name: Emil Abrahamyan
Candidate Number: 006343-021
Mathematics Higher Level
Type 1: Shadow Functions
SHADOW FUNCTIONS
The Aim of the Investigation:
The overall aim of this investigation is to investigate different polynomials with different powers
and create shadow...

...Name: Linh Nguyen
IB MathIA
02/06/12
Part A
Consider this 2× 2 system of linear equations: x + 2y = 3
2x - y = -4
We can see patterns in the constants of both equations. In the first equation, the constants are 1, 2, and 3. The common difference between the constants is 1:
3 – 2 = 1
2 – 1 = 1
Based on this, we can set up a general formula for the constant of this equation:
Un = U1 + (n - 1)d Where:
n: The number of the series
d: the...

...IB Math Studies Internal Assessment:
Is the distance a tennis ball travels horizontally dependent on the angle of which it is dropped at?
Exam Session: May 2014
School Name:
Teacher:
Course: IB Math Studies
Word Count: 654
Name:
Is the distance a tennis ball travels horizontally dependent on the angle of which it is dropped at?
Introduction
In tennis, players hit the tennis ball in certain ways so the ball goes the way they want it to...

...• What were the most revolutionary social and economic developments of the last quarter of the nineteenth century?
• How did different groups of Americans respond to those changes and how effective were their responses?
• What role did government play in these developments?
In the late 1900s some of the most social and economic developments were railroads, steel oil, the type writer cash register, light bulb and agriculture. The development of the railroad made it easier for immigrant to...

...
ANALYSIS
Physics has a lot of topics to cover. In the previous experiments, we discussed Forces, Kinematics, and Motions. In this experiment, the focus is all about Friction. Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction like fluid friction which describes the friction between layers of a viscous fluid that are moving relative to each other; dry friction which...

...
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...

...Practice MathIA
• Each set of steps above is composed of 1x1 squares
• Show what 4 steps and 5 steps look like
• ‘n’ represents the number of steps
• Find the area for n= 1,2,3,4,5
Step 1: Step 2: Step 3: Step 4: Step 5:
12 = 1 12 x 3 = 3 1 2 x6 = 6 1 2x10 = 10 12x...