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

Maths Portfolio Infinite Surds

Extracts from this document...

Introduction

Maths Portfolio

SL Type 1

Infinite Surds

In this mathematics portfolio we are instructed to investigate different expression of infinite surds in square root form and then find the exact value and statement for these surds.

INFINITE SURDS

The following expression is an example of an infinite surd.

image05.png

The first ten terms of the surd can be expressed in the sequence:

image06.png

From the tem terms of the sequence we can observe that the formula for the sequence is displayed as:


image16.png

The results had to be plotted in a graph as shown below:

image27.png

The graph above shows us the relationship between n andimage10.png. We can observe that as n increases, image10.png also increases but each time less than before, suggesting that at a large certain point of n it stops increasing and just follows in a straight line.

...read more.

Middle

From the tem terms of the sequence we can observe that the formula for the sequence is displayed as:


image08.pngimage09.png

The results had to be plotted in a graph as shown below:

The graph above also shows us the relationship between n andimage10.png. We can observe that as n increases, image10.png also increases but each time less than before, suggesting that at a large certain point of n it stops increasing and just follows in a straight line.

To find the exact infinite value for this sequence we would use the equation and rearrange in the correct way to find the value.

Finding the exact value for the surd

image00.pngimage11.png

image03.pngimage04.png

image12.png

image13.png

The exact value for the surd is 2 as the second answer does not fit in the problem

The general infinite surd in terms of k

image14.png

...read more.

Conclusion

image30.pngimage29.png

The results show us that the limitations found in the general statement are those that didn’t give an integer as a final answer. Therefore k has to be an integer, however not a decimal or a fraction as results wouldn’t be a whole number. It also isn’t possible to obtain an integer if k is a negative number because there is no square root for a negative number. For a pleasing result, 1+4k , needs to give a number that possesses a perfect square root, an integer.

I arrived at this general statement by subtracting the n term from the k, and like that finding out that the product of this subtraction is the n term to the power of 2. Like that I found the equationimage31.png. By rearranging the formula to make k the subject I came to the conclusion that image32.png, the general statement.

...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

See related essaysSee related essays

Related International Baccalaureate Maths essays

  1. IB Mathematics Portfolio - Modeling the amount of a drug in the bloodstream

    I just assume the line would reach to the amount when it can't be measured and call it the zero mark. (b) Doses continue to be taken every 6 hours. If dose continues, then the graph would continue. The left over amount of drug in the body would continue get higher and higher.

  2. Mathematics Portfolio. In this portfolio project, the task at hand is to investigate the ...

    in respect to the time, as the line representing the function is displayed under the function found with technology. In the hand calculated function the g-force also decreases more after the same amount of time (35 minutes). After solely looking at horizontal g-force, vertical g-force must also be considered.

  1. Math Portfolio: trigonometry investigation (circle trig)

    Likewise, when the value of x is divided by the value of r, a negative number is divided by a positive number resulting to a negative number. The value of y and the value of x equal to a negative number respectively in quadrant 3.

  2. Math Portfolio Type II

    Therefore, the equation for the linear growth factor in terms of un will be: - rn = (-2 x 10-5)un + 2.2 Now, to find the recursive logistic function, we shall substitute the value of rn calculated above in the following form un+1= rn.un un+1 = [(-2 x 10-5)un +

  1. Infinite Surds. The aim of this folio is to explore the nature of ...

    The next integer value would be equal to 3. It can be worked out using the value for the General Infinite Surd. Find when is equal to 3. The value for where the value of the infinite surd is equal to 1 can also be worked out.

  2. Gold Medal Heights Maths Portfolio.

    3. 4. Subtract equation 1 from 2 5. Subtract equation 3 from 4 6. Subtract equation 5 multiplied by 10 and equation 6 multiplied by 18 7. Substitute equation 7 into 1 8. Substitute equation 7 into 2 9.

  1. Lascap's Fraction Portfolio

    while x-axis as n (rows). The steps of using the TI-84 are as follows: The screen pictures of the processes are shown below. Image 1 Caption: Image 1 shows the set of data. L1 represents number of row (n) while L2 represents the value of numerator (N)

  2. Infinite Surds investigation with teacher's comments.

    The value of an approaches approximately 1.618 (i.e. an?1.618) but never reach it. In other words, as n gets larger, the difference with the successive term (also shown in the figures in the ?an+1 - an? column of the table)

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