• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month
Page
1. 1
1
2. 2
2
3. 3
3
4. 4
4
5. 5
5
6. 6
6
7. 7
7
8. 8
8
9. 9
9
10. 10
10
11. 11
11
12. 12
12
13. 13
13
14. 14
14

# Gold Medal heights IB IA- score 15

Extracts from this document...

Introduction

 International Baccalaureate Gold Medal Heights  SL Math IA- Type II Turner Fenton Secondary School

Completed by: Harsh Patel

Student Number: 643984

IB number:

Teacher: Mr. Persaud

Course Code: MHF4U7-C

Due Date: November 16th, 2012

Introduction

This report will investigate the winning heights of high jump gold medalists in the Olympics. The Olympics composed of several events evaluating physical strength of humans. Every Olympic game brings different numerical value for a height that a person can jump, allowing for different data collection. First of all, the data ranging from the years 1932 to 1980 will be portrayed on a graph for observation. From thorough investigation, the best curvature or line that fits the trend of the data will be selected to represent the relation. The function will be algebraically approached using the numerical values of the data points. Through the use of technology, the parameters will be plugged in to illustrate that function electronically. The function will be observed and any limitations with the model will be indicated. The function might need refinement according to any outliers/ anomalies, also to better represent the trend. The model function and a given function by the programme will be compared. Since the Olympics were not held during the years 1940 and 1944 due to WWII, this function will help determine the possible outcomes of the gold medal heights during those years. Also, a prediction of the years 1984 and futuristic year 2016 will be made according to the function created manually. Furthermore, the range of data will be extended to evaluate the effectiveness of the created function for extrapolated points. Analysis of the extrapolated points will be discussed with special reference of significant fluctuations. Lastly, the

...read more.

Middle

figure 1 and will be used in this investigation.

Creating an equation for the Sinusoidal Function

The general equation for the function is f (x) = a sin (bx – c) +d, where each variable impacts the appearance of the function in different way. The parameters of the sinusoidal function in the equation are a, b, c, and d. The a effects the amplitude also knows as vertical stretch/compression which is calculated by finding the midpoint between the max and min. The b value affects the horizontal stretch/compression which is calculated by two times pi all over k. The k represents the period which is the distance between two successive maximum points or minimum points. The c value affects the horizontal shift which is calculated after knowing all over variables then solving for c. Lastly, the d value represents the vertical shift, which can be calculated by finding the average point of heights.

Algebraicallyapproaching the function

Amplitude (a)

Period (k)

The year with lowest height is 1932, and highest height is 1980. Therefore, multiplying the difference by two will give the distance of one cycle (between two successive max and/or min).

Horizontal stretch/ compression (b)

Sub in value of k

This will not be converted to degree in order to maintain exact value.

Vertical shift (d)

Horizontal shift (c)

h = a sin [b (x-c)] +d

Sub in all known variables

h= 19.5 sin [

(x – c) ] + 216.5

Take a value of any point and plug it into the equation and solve for c, the decision was taking (1960, 216) since it’s in centre of the values gives.

216 = 19.5sin [

(1960-c)] + 216.5
-0.5 = 19.5 sin [

(1960-c)]
−0.0256410256410 ≈ sin(π/48(1960-c))
−0.0256438361401≈ (π/48(1960-c))        - sin inverse applied
−0.3918089550276≈1960-c            - note: calculator in radiant
−1960.391808955 ≈ -c
c≈1960.391808955
c≈1960.4                    - therefore c is approximately 1960

Model of the algebraic derived function

The general formula of sinusoidal function becomes h = 19.5 sin [

(t - 1960)] + 216.5

...read more.

Conclusion

Modifications can be made to the algebraic model function based on the first set to data to best fit the additional data as well. The amplitude needs to be increased to adjust with fluctuation in wide range of heights that are achieved by gold medalists. There also needs to be a significant change in the period because the maximum and minimums are located much further apart with the additional set of data, thus requiring a greater horizontal stretch. Afterwards, a horizontal shift will remain relatively the same as equal amount of Olympic Games have been added before and after the original set of data. The vertical shift will be reduced by a little because the previous set of data from 1932 is much less in heights than the increase in height after the year 1980. Therefore the average of the vertical height will drop allowing for a smaller vertical shift. Through these modifications the new function would represent the addition data much more accurately.

This investigation has contributed in further understanding the detailed curvature of various functions and using it to model data. The functions have several parameters which affect it in various ways, either horizontally or vertically. I have learned how to algebraically approach in creating a function to model specific set of data. Upon deriving an algebraic function, I compared it to a regression model using computer software which helped me learn the similarities and differences of different methods in approaching a best fit model. I learned how to interpolate and extrapolate using a derived function and was able to evaluate its accuracy by making connecting with the trend of the data. Lastly, I learned that a model function my not adjust with addition data. This occurs because the derived function was solely based on the first set of data and new parameters would need to be set for additional data. Overall, many previous concepts were revived and new ideas were learned from conducting this investigation.

...read more.

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

## Found what you're looking for?

• Start learning 29% faster today
• 150,000+ documents available
• Just £6.99 a month

Not the one? Search for your essay title...
• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

# Related International Baccalaureate Maths essays

1. ## Math Studies I.A

Malaysia 15,300 72.76 1113228 234090000 5294.0176 Mali 1,200 54.5 65400 1440000 2970.25 Marshall Islands 2,500 70.61 176525 6250000 4985.7721 Mauritius 12,100 72.88 881848 146410000 5311.4944 Mexico 14,200 76.2 1082040 201640000 5806.44 Moldova 2,500 70.2 175500 6250000 4928.04 Mongolia 3,200 66.99 214368 10240000 4487.6601 Montserrat 3,400 72.6 246840 11560000 5270.76 Mozambique

2. ## Math IA - Logan's Logo

changing the variable c will affect the horizontal shift of the sine curve, so thatare translations to the right, whileare translations to the left. The original sine curve starts (meaning it crosses the center line of its curve) at point (0,0), and using this point as a reference, I can determine how many units leftwards my curve has shifted.

1. ## Tide Modeling

Difference 0.725 0.637 0.31 0 0.14 0.087 0.325 0.412 0.29 0 0.26 0.438 ??=5.675,sin-,,??-6.,??...+6.475 and ??=5.675,cos-,,??-6.,??-3...+ 6.475 Only one color is shown because graphs overlap each other since they are the same. 4. Use the regression feature of your graphing calculator to develop a best-fit function for this data.

2. ## A logistic model

(?3.0 ? 10?5 )(u 2 ) ? 2.8u ?5 2 un?1 ? (?3.0 ?10 )(un ) ? 2.8un {9} 7 IB Mathematics HL Type II Portfolio: Creating a logistic model International School of Helsingborg - Christian Jorgensen The findings for a, b and c enables one to calculate the magnitude of the population for three studies with different growth factor.

1. ## Maths IA Type 2 Modelling a Functional Building. The independent variable in ...

with maximum volume under the curve, we find the area of the face of the cuboid: Let {sub in value} Differentiate to find maximum area at , {these values are the roots} Find the second derivative to prove that this is a maximum curve: ?

2. ## MATH IA- Filling up the petrol tank ARWA and BAO

Let?s investigate the effects of changing p1, p2 and d. Before we do that Let?s find the range of d, p1 and p2. If you get cheaper fuel on your way then why would you take expensive fuel ? Range of values of d are 0< d? 100km In this world we get nothing for free.

1. ## Math IA Type 1 Circles. The aim of this task is to investigate ...

In this case when r = 1, OP ? . The value OP= will only work if r < 1. Therefore, the general statement OP?= , is only valid for { OP, r R I OP ?, }. To further test the validity of the general statement, we will keep

2. ## IB Math Methods SL: Internal Assessment on Gold Medal Heights

on, let?s simplify it so that the t-axis shows how many years have elapsed since 1932, which will simplify our equations without sacrificing accuracy. Hence, we arrive at Graph 2, shown below. Graph 2: Height achieved by gold medalists in various Olympic Games Domain: 0 t 60 Range: 190 t

• Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to
improve your own work