• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

# IB math project

Extracts from this document...

Introduction

 1  My conjecture, for the function bounded by between ‘a’ and ‘b’, is, the ratio of area A to area B is equivalent to the ratio of n to 1.

## Test

1. n Ζ+
2. Fraction
3. Negatives
4. Irrational Numbers

1) n Ζ+

n=3

n=5  2) Fractions  3) Negatives For all values of n in , no values exist in the region bounded by 0 and 1; therefore no conjecture can be inferred.

4) Irrational Numbers  2 ## Bounds 0 to 2 ## Bounds 1 to 2 ## TEST

Bounds 0 to 2 Bounds 0 to 3 Bounds 2 to 4 My conjecture is valid for all functions of Middle

and , then my conjecture, of n to 1, holds true for all ratios between areas A and B.

For Negative Bounds:

## Bounds –1 to 0 The conjecture of n:1 is the exact opposite for conjecture of the negatively bounded regions in quadrant III. (1:n)

If a set of positive bounds were to be changed to negative, then the ratio between A and B in the positive bounds would be equivalent to that of B and A in the negative bounds. (see diagram explanation below)   3

As mentioned in question 2, my conjecture, of n to 1, holds true for all ratios between areas A and B, if a<b; as long the function in question is .

Proof:

With the function in question being Conclusion 4b.   My conjecture, for the function revolved around the y-axis, bounded by between ‘0’ and ‘1’, is, the ratio of area A to area B is equivalent to the ratio of 1 to 2n. In correlation to the ratio of the function revolved around the x-axis, the ratio between area A and area B is the exact opposite.

## Test

1. n=3, n=5
2. Fraction

Different Bounds

n=2

n=5  2) Fractions  3) Bounds

Bounds 0 to 2

Bounds 1 to 2  Proof:

With the function in question being rotated around the x-axis, I was able to calculate area A by finding the intregal using the shells method, and by using simple international methods I was able to determine area B. The ratio between area A and area B is 2n to 1 (refer to diagram on the right) 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. ## Extended Essay- Math

ï¿½984ï¿½\$ï¿½ï¿½Fï¿½i5ï¿½m\B ï¿½-Qï¿½WIï¿½ï¿½P|ï¿½hï¿½#ï¿½ï¿½hyï¿½Yï¿½ï¿½ï¿½ï¿½zyO*ï¿½ï¿½:o%Zï¿½ï¿½oï¿½~ï¿½Ö­8ï¿½E[ï¿½Jï¿½ï¿½ï¿½ï¿½ï¿½Uï¿½@ï¿½]"vï¿½ï¿½'ï¿½ï¿½'ï¿½(r)@ï¿½ÐXZZï¿½Fï¿½7ï¿½xï¿½ï¿½ï¿½-<xï¿½_ï¿½ï¿½""]{;Ô´ï¿½ï¿½Z9T'KENÕª0jï¿½+ï¿½;ï¿½ï¿½ï¿½κï¿½ï¿½[=vï¿½ï¿½ï¿½ï¿½×¯ß1c&Mï¿½dï¿½...ï¿½7ï¿½[O"ï¿½(ï¿½@ï¿½ 6oï¿½,)&ï¿½-ï¿½ 4kÖï¿½ï¿½'>ï¿½+(r)ï¿½ï¿½X Sï¿½Nï¿½3gN}}ï¿½ Aï¿½ï¿½ï¿½Hï¿½Ø1ï¿½ï¿½ï¿½S"ï¿½ï¿½ï¿½c*\ï¿½ï¿½@ï¿½ï¿½ï¿½ RMï¿½49pï¿½[o1/2ï¿½oï¿½3/4ï¿½ bï¿½H<xï¿½eï¿½lï¿½ï¿½ ï¿½ï¿½9Rï¿½@ï¿½Yï¿½o)ï¿½ï¿½Uï¿½q 5ï¿½Ñ3ï¿½ zï¿½'(r)\ï¿½ï¿½yï¿½ï¿½^bï¿½--ï¿½jï¿½ï¿½NÅ¯ï¿½ï¿½ï¿½#}Xï¿½hNLYï¿½ï¿½ij'Gï¿½ ï¿½ï¿½ï¿½SOÍ5kï¿½ï¿½(tm)Mï¿½^bï¿½zï¿½ï¿½ï¿½eLJï¿½ï¿½"ï¿½2ï¿½ÖZLzï¿½ aï¿½ï¿½ï¿½ ï¿½:`ï¿½ï¿½Lï¿½<yï¿½ï¿½ï¿½ï¿½wÈºwï¿½3/4cï¿½ ï¿½Ý¶mï¿½zï¿½ï¿½ï¿½]cÔ°qÞ dk'ï¿½_9zZï¿½ï¿½...a(tm)wï¿½Aï¿½CXï¿½ï¿½qï¿½'ï¿½Fï¿½ï¿½wï¿½5jï¿½ï¿½ï¿½ï¿½1/2(tm)5p3ï¿½Fï¿½Bï¿½s=oï¿½1/4^1/2zï¿½(r)ï¿½Bï¿½uï¿½J!"SØ"ï¿½Z"<m+ï¿½ï¿½O>>ï¿½?Fï¿½ï¿½cï¿½ï¿½(c)ï¿½ï¿½:eï¿½ï¿½×`ï¿½8ï¿½ï¿½4lcZ"<ï¿½ï¿½ï¿½Ñ£ï¿½rTBQï¿½ï¿½Q+J&ï¿½(r)ï¿½ï¿½ï¿½ï¿½~ï¿½]1/45ï¿½BM0ï¿½ï¿½8ï¿½0Ý"'#GNï¿½0ï¿½oï¿½3/4I ï¿½:ï¿½ï¿½Xï¿½ï¿½ï¿½ï¿½ï¿½uï¿½CUï¿½\ï¿½lï¿½ï¿½ï¿½Æ-ï¿½hï¿½^q(ï¿½ (c)ï¿½bï¿½#P9Kï¿½Jï¿½`ï¿½(r)5ï¿½ï¿½ï¿½(r)ï¿½ï¿½B<ï¿½\ï¿½]Q-ï¿½gï¿½B":ï¿½È¨Yï¿½Yï¿½{Ø¡ï¿½ï¿½ï¿½Xï¿½"%'ï¿½bï¿½B...ï¿½" ï¿½fï¿½|ï¿½ziï¿½Y'NDï¿½Sï¿½ï¿½ï¿½ï¿½È¨Yï¿½z]"vï¿½Nï¿½t ï¿½" ï¿½ftï¿½Tï¿½ï¿½ï¿½ï¿½ï¿½È¨Yï¿½Vï¿½sï¿½ï¿½ï¿½Vï¿½ï¿½Ò§6vï¿½ï¿½ï¿½Hï¿½2jFï¿½-"Tï¿½"ï¿½ï¿½3ï¿½uï¿½d(c)ï¿½pZT'ï¿½ï¿½Eï¿½@Dï¿½(c)%ï¿½"ï¿½d(c)dP'\ï¿½ï¿½Zï¿½+TÇï¿½9l-}Vï¿½ï¿½cï¿½Ô¢ hc2jvi...mï¿½:A*ï¿½ï¿½ï¿½Csjï¿½ Nï¿½ï¿½"ï¿½Wï¿½nÅï¿½[!"-GAï¿½[ï¿½Iï¿½IQprï¿½ 5"tï¿½>ï¿½Evï¿½"^iï¿½<1/2ï¿½ï¿½hï¿½dï¿½ï¿½R|Zï¿½\ï¿½ï¿½ï¿½aiï¿½ï¿½ï¿½ï¿½wï¿½?%dï¿½,R\$ï¿½H#ï¿½ï¿½ï¿½Tï¿½ï¿½ï¿½P'Y'ï¿½Z'ï¿½+Ô¥ï¿½Eï¿½ï¿½á§¶ï¿½E ï¿½|y2jï¿½uï¿½"ï¿½ï¿½"ï¿½ï¿½ï¿½ï¿½"n^ï¿½H9Kï¿½ï¿½9ï¿½ï¿½eï¿½^(r):ï¿½ï¿½ï¿½g9@Q?ï¿½Yï¿½"1/2Qï¿½e"<cdÔï¿½/ï¿½ï¿½ï¿½.ï¿½b-ï¿½k #PVï¿½ï¿½pï¿½...Ë¨%ï¿½1/4dï¿½ï¿½ï¿½hï¿½mI:ï¿½<ï¿½_A<\M-*ï¿½f'~~ï¿½ï¿½(tm)ï¿½ï¿½(c)ï¿½3Iï¿½Ð7&P'ï¿½Hï¿½ï¿½ï¿½Zbï¿½+Tï¿½ HÝ´ ï¿½bx s-ï¿½ï¿½ï¿½d'2j&ï¿½ï¿½ï¿½Í¯ï¿½qï¿½)ï¿½Nï¿½ï¿½RLezï¿½ï¿½ï¿½S ï¿½QKr *ï¿½lÓ¦M ï¿½ï¿½ï¿½ï¿½?ï¿½m4Z+ï¿½ï¿½ï¿½ï¿½'dï¿½ï¿½ï¿½"ï¿½;oï¿½iï¿½\$ ï¿½[ï¿½nï¿½Rï¿½Sï¿½V5[Lgï¿½Cï¿½l'&Krï¿½ï¿½ï¿½gï¿½ï¿½ï¿½Yjqï¿½ï¿½*ï¿½f...ï¿½9Aï¿½iÓ¦ ...ï¿½ï¿½&cBï¿½V@"ï¿½5:ï¿½ÍQï¿½B" ï¿½aP ï¿½ï¿½iï¿½ï¿½G^ï¿½ï¿½Zï¿½Hï¿½ï¿½ ï¿½0ï¿½"zï¿½95V?5ï¿½Nï¿½ï¿½È¨(tm)ï¿½ï¿½(c)ï¿½> j"&Pï¿½ï¿½ï¿½ï¿½ZF-Zï¿½!Kcï¿½)_ï¿½ï¿½ï¿½xï¿½]:ï¿½ ï¿½V"!ï¿½f...*-wï¿½ï¿½ï¿½Ñ£ ï¿½ ï¿½#\$ ï¿½!ÌEï¿½G`ï¿½SoCï¿½ï¿½5zjï¿½ï¿½H+ÊQ3ï¿½ï¿½0(r)ï¿½ï¿½K-,1.ï¿½ï¿½"ï¿½ï¿½Z\$k*DQ1/4kï¿½ï¿½ï¿½xï¿½ï¿½ï¿½ï¿½ï¿½`i3/4 5ï¿½:X"vm"vï¿½ï¿½ï¿½'m ï¿½ï¿½-ï¿½ï¿½dï¿½ï¿½ï¿½Q"ï¿½upï¿½QÚkï¿½"'AF-ï¿½5ï¿½(ï¿½5ï¿½ï¿½eï¿½ (r)^1/2:ï¿½ï¿½Tï¿½I2j&ï¿½S7Kï¿½ï¿½{ï¿½iXï¿½ï¿½WO4mUKï¿½W ï¿½fXï¿½ï¿½4ï¿½ï¿½ï¿½ï¿½cï¿½Uï¿½0 ï¿½ï¿½-Q3ï¿½?~'ï¿½ï¿½1,"ï¿½?ï¿½(:ï¿½t(tm)ï¿½,ï¿½ï¿½oAFÍ°×¯_/ï¿½Oï¿½:8\=]4= ï¿½ï¿½eï¿½ +ï¿½ 7l'2,"ï¿½ï¿½gDÈ¯ ßï¿½ï¿½a%ï¿½1/4ï¿½ ï¿½"ï¿½Ý"Kï¿½KÐ¥"dï¿½Lï¿½ï¿½ 5ï¿½sï¿½hï¿½¤ï¿½ï¿½0ï¿½ï¿½ï¿½<|ï¿½ï¿½]% ï¿½fRslaWp " 8ï¿½n@(tm)

2. ## Statistics project. Comparing and analyzing the correlation of the number of novels read per ...

the number of books read can be accounted for by the variation in the modal mark. In other words, approximately 70% of the variation is attributed to other factors. GIRLS No of books(x) Modal mark(y) (xy) (x�) (y�) 2 70 140 4 4900 3 70 210 9 4900 2 70

1. ## Maths Project. Statistical Analysis of GCSE results at my secondary school summer 2010 ...

8 34 m 34 78 McC 9 40 m 40 77 McG 10 34 m 34 76 McG 9 46 m 46 75 McM 9 34 m 34 74 McMi 9 46 f 46 73 Mi 10 46 f 46 72 Mi 11 40 m 40 71 Mi 10 34

2. ## Artificial Intelligence &amp;amp; Math

Either the possible threat is dismissed or acted upon defensively by police, leading to a decrease in successful cyber crimes. IT concepts well described and some developments; not enough detail, particularly of developments for explanation, and certainly no analysis. The Impact of the Issue The legislature will increase the number

1. ## Investigating ratio of areas and volumes

and values for Area A and Area B were rounded to 3 d.p.) From the above data the following conjecture can be made: For the graph of y = xn in between the points x = 0 and x = 1 the ratio area A: area B is: n: 1.

2. ## SL Math IA: Fishing Rods

Therefore it was no surprise that this function acts as the best fit for this data. The other cause for this septic function having the best correlation to the original data is due to the septic function being established by creating a system of equations using all of the data points.

1. ## Gold Medal heights IB IA- score 15

point at the height points of data point and the minimum point at the lowest data point. The regression model is limited because the stretch only represents majority of the average data and not the overall image of the correlation.

2. ## Lacsap's fractions - IB portfolio

using the fourth formula: k6= 0.5×62+0.5×6=18+3=21 k7= 0.5×72+0.5×7=24.5+3.5=28 All four formulae had the same results, thus it can be concluded that they are valid. GENERAL STATEMENT FOR THE DENOMINATOR Graph 2: It shows the relation between n (the row number) • Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to 