# 50+ IB Maths AA IA Ideas

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## IB Math AA HL IA Ideas

**1.) The Math of Infectious Disease: Understanding and Interpreting Models in Epidemiology.**

**Mathematics:**

Using mathematical concepts like **exponential functions** and **calculus** to derive **differential equations** from various epidemiological models like SARS, etc.

**Procedure**:

In order to proceed with this topic, you must derive differential equations based on the model and find the solution using various methods like the homogenous method, linear method, etc.

**Analysis**:

The derivation of such differential equations for epidemiological models are of great importance when it comes to analyzing trends and forecasting data. The information gathered can then be used to control the spread of the disease and prevent future outbreaks.

**2.) Investigating the mathematical harmony of Beethoven.**

**Mathematics**:

If youâ€™re a classical music geek, this oneâ€™s for you. There are various mathematical properties that surround music such as trigonometry.

**Procedure**:

In the case of Beethoven, you can graph the notes and chords with sine waves. The simplest model of a musical sound is a sine wave, in which the domain (x-axis) is time and the range (y-axis) is pressure.

**Analysis**:

Using such mathematical concepts helps strengthen knowledge in music as counting, rhythm, scales, intervals, patterns, symbols, harmonies, time signatures, tone and pitch are determined by using math.

**3.) Understanding Chinaâ€™s Income Distribution from a Mathematical Perspective using the Lorenz Curve and Gini Coefficient.**

**Mathematics**:

Using various mathematical concepts like integration and functions.

Chinaâ€™s income distribution can be found using secondary methods or primary, depending on your geographical location.

**Procedure:**

Using the data, you can plot Lorenzâ€™s curve using Gini Coefficient to show the ideal income inequality in an economy as well as the reality. The areas below the graph using integration and the difference between the two will depict the gap between the rich and the poor.

**Analysis:**

Such models are of great importance when it comes to analysing trends and forecasting data. The Lorenz curve is important because it helps in understanding economic inequality. When the lorenz curve keeps moving away from the baseline it indicates that the level of unequal distribution keeps increasing.

**4.) Investigating the safe operating speed for ground vehicles on a given road segment.**

**Mathematics:**

Using mathematical concepts such as integration when calculating area under the graph and finding optimum speed. When driving a car, it is often necessary to slow down during a curve. This optimum speed can be found using mathematics.

**Procedure:**

An observer is placed at each end of the survey segment recording each vehicleâ€™s passing time and license plate, in order to calculate the time spent traversing the segment. This data can be used to derive the formula for speed and differentiate it in order to find maximum and minimum points.

**Analysis:**

The optimum speed when travelling in a curve is found for various reasons, the most important one being safety. Determining the optimum speed to operate at a turning is absolutely crucial when it comes to safety.

**5.) Calculating orbital flight paths/intercept trajectories in space for rockets.**

**Mathematics:**

Using mathematical concepts such as differentiation and integration to calculate the orbital flight path.

**Procedure:**

You will have to graph the pathway in which the rocket will move as well as model the rocket to determine the optimum speed and path.

**Analysis:**

Such analysis is crucial in order to reduce the fuel efficiency of rockets in space using gravity assist.

## IB Math AA SL IA Ideas

**1.) Surface Area of Hyperbolic Paraboloid – Integration by substitution.**

**Mathematics:**

**Differentiation** and **integration** are the most dominant mathematical concepts when it comes to calculating the surface area of a hyperbolic paraboloid.

**Procedure:**

Pick an object with a hyperbolic paraboloid and then plot it on a graph. Then you must split it into different parts. Derive the equation. Calculate the surface area using integration.

**Analysis:**

This analysis is most important when it comes to a businessâ€™s point of view. For instance, when manufacturing products of a hyperbolic paraboloid, one must optimise space to ensure consumer satisfaction.

**2.)Modelling the shape of an egg.**

**Mathematics**:

The are various mathematical concepts when modelling the shape of an egg, one of the most important ones being **integration**.

**Procedure**:

Firstly, you would have to draw the egg and then plot it on a graph. Then you must derive the equation. Calculate volume and surface area using integration.

**Analysis:**

The geometrical properties of eggs â€“ such as **volume and surface area** â€“ have uses ranging from ecological, physiological and morphological studies in birds, to predictions of conditions in the poultry industry.

**3.) The correlation between fertiliser concentration and plant growth.**

**Mathematics:**

Using mathematical concepts like **Pearsonâ€™s correlation**. This is a statistical tool that tests the strength of a linear correlation.

**Procedure:**

If you are a biology student, then this topic would be apt for you. Firstly, you must take at least 5 different pots with soil and a seed sown into it. Next, add varied concentration of fertilizer to each pot, as well as a control experiment. Measure plant growth over the span of 15 days (depending on the seed). Collect this data and use Pearsonâ€™s correlation to determine how strongly correlated the two variables are.

**Analysis:**

This research is especially important in finding out if the fertilizer has a significant impact on plant growth, as well as to find the optimum concentration

**4.) Modelling the pharmacokinetic profile of erythromycin.**

**Mathematics:**

Using mathematical concepts such as **exponential functions** and integration. The pharmacokinetic profile is the way and the amount of time in which a drug moves and gets absorbed by your body.

**Procedure:**

In this case, you would have to collect secondary data. Using the data points, the half-life of erythromycin can be calculated. Depending on the result, you can figure out at which stage is the drug most active.

**Analysis:**

It is highly important to know at which stage the drug is most active from the consumerâ€™s and producerâ€™s perspectives in order to determine at what time to consume the medicine and how long its effects will last.

**5.) Modeling a cooling cup of tea.**

**Mathematics:**

This IA is about finding the time it takes for a cup of tea to cool down using exponential functions.

**Procedure:**

To gather the data I needed to produce the graph a cup of tea cooling down needs to be measured. Using a temperature sensor and piece of graphing software a set of readings that measured the temperature of the tea can be produced. 3 exponential equations are derived with graphs and separate sets of data.

**Analysis:**

By comparing the average error difference of all 3 equations, one equation will be narrowed down. Using this equation, the time for the tea to cool down is calculated.

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