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

IB Coursework Maths SL BMI

Extracts from this document...


                Lydia Smith

Body Mass Index

Body mass index (BMI) is a measure of one’s body fat. It is calculated by taking one’s weight (kg) and dividing by the square of one’s height (m).


In this assessment, I will be modelling the data provided in the table below, which represents the median BMI for females of different ages in the US in the year 2000. I will focus particularly on the different functions which could be matched to this data, as well as comparing this data to similar data showing women of another country.

The table below shows the aforementioned data. Age is found in the ‘X’ column because this is the independent, constant variable. The BMI values are found in the ‘Y’ column because this information is the dependent variable.

Age (years)








































The graph below is a representation of the previous table. The graph was plotted using Autograph.


The independent variable for the above graph is the age in years, and this is shown on the x-axis.

The dependent variable is the BMI, and this is shown on the y-axis.

The highest BMI is 21.

...read more.


20.85 = 289a + 17b + c

I can use simultaneous equations to find the values of a, b and c. First, I will substitute the first equation I found (line of symmetry equation) into the second equation.

15.7 = 9a + 3(-10a) + c

15.7 = -21a + c

Next I will substitute the first equation into the third equation.

20.85 = 289a + 17(-10a) + c

20.85 = 289a – 170a + c

20.85 = 119a + c

To use simultaneous equations:

20.85 = 119a + c


15.7 = -21a + c


5.15 = 140a

In order to find a:

a= image07.png = 0.0368 (to 3 s.f.)

If we substitute this equation into the first equation:

b = -10a = -10(0.0368) = 0.368

Therefore, if we substitute this to the full equation:

20.85 = 119(0.0368) + c

c = 16.47

Therefore, the quadratic equation is:

y = 0.368x2 – 0.368x + 16.47

Using information from the equation y= 0.368x2 – 0.368x + 16.47, I put all the new y values in a table (shown below). To compare the

...read more.



While I did manage to find some functions that resembled the original equation, they were all deeply flawed. As previously mentioned, in the polynomial quadratic function equation, the shape of the plotted points are close to accurate, but the trend for the rest of the line does not fit at all. This makes using this function to predict future results impossible. In the cubic polynomial function equation, the shape of the plotted points are even closer to accurate than the polynomial quadratic function equation, and the trend for the rest of the line is much closer to that of the original equation, but still the line does not fit. The quartic function modelled the behaviour of the graph best, but it is only accurate and therefore reasonable up to the age of 20. We see  that after reaching 20 on the x-axes, the graph descends to the point where the BMI would be completely impossible for that age group.

I tried many other functions, but could find none that were closer and therefore none that solved this problem.

...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. Math IB SL BMI Portfolio

    Assuming that the point 21.65 is the maximum of the sinusoidal curve and using 15.20 as the minimum, one can find the value for d using the formula: d = 18.425 d = 18.4 The line of symmetry in a sinusoidal function is equal to its vertical displacement (d) value.

  2. Mathematics (EE): Alhazen's Problem

    They emphasize the fact that for any given ellipse, if a ball is placed in each focus then any point on the rim would be a solution (such is the nature of the foci points).

  1. Virus Modelling

    20 72 =(160/100*B19)-(50000*4) 21 76 =(160/100*B20)-(50000*4) 22 80 =(160/100*B21)-(50000*4) 23 84 =(160/100*B22)-(50000*4) 24 88 =(160/100*B23)-(50000*4) 25 92 =(160/100*B24)-(50000*4) 26 96 =(160/100*B25)-(50000*4) 27 100 =(160/100*B26)-(50000*4) 28 104 =(160/100*B27)-(50000*4) 29 108 =(160/100*B28)-(50000*4) 30 112 =(160/100*B29)-(50000*4) 31 116 =(160/100*B30)-(50000*4) 32 120 =(160/100*B31)-(50000*4) 33 124 =(160/100*B32)-(50000*4) Hours No. Particles 0 1000000 4 1400000 8 2040000 12 3064000 16 4702400 20 7323840 24 11518144

  2. Analysis of Functions. The factors of decreasing and decreasing intervals (in the y ...

    Because there are not turning points the relative max and min don't exist in this type of function. As we can see in the graphs above, there is a discontinuity when the exponent of the function is negative; the type of discontinuity that is present is the asymptote.

  1. Mathematic SL IA -Circles (scored 17 out of 20)

    It is not possible to draw three circles required. Through the 4 different types of test, we can notice that the general statement is valid on first three tests, but not for the last one. The only characteristic I found out was that the length of OP is shorter 2 units than the length of r.

  2. Gold Medal heights IB IA- score 15

    In order to make this function more accurate a few adjustments need to be made. The restrictions on the function as established in the beginning remains the same. Domain of the function in Figure 6 is {tϵâ |1932 ≤ x ≤ 1980} and the range for this function is {hϵâ |197 ≤ y ≤ 236}.

  1. MATH IB SL INT ASS1 - Pascal's Triangle

    The formula would be: Yn(2) = Yn-1(2) + (n-2) If we do the same with d3 we will get a series of 6; 7; 9; 12; 15; ? . The formula would be: Yn(3) = Yn-1(3) + (n-3) The question why the last two series start with 3(6)

  2. Mathematic SL IA -Gold medal height (scored 16 out of 20)

    The other one is that the time of Olympic Games holding cannot be before than 1896. This is because the year 1896 is the first time the Olympic was composed. There are many types of mathematical function we have studied.

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