# 50+ IB Maths AA IA Ideas

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This list contains a selection of curated IB Math AA IA ideas It includes 50+ specific ideas for IB Math IA Internal Assessment Examples and topics. The topics cover a wide range of mathematical concepts, including calculus, algebra, geometry, statistics, and probability, and are suitable for both SL and HL students and it also includes MATHS AA IA samples.

## 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 you’re a classical music geek, this one’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 China’s Income Distribution from a Mathematical Perspective using the Lorenz Curve and Gini Coefficient**

**Mathematics**:

Using various mathematical concepts like integration and functions.

China’s income distribution can be found using secondary methods or primary, depending on your geographical location.

**Procedure:**

Using the data, you can plot Lorenz’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 vehicle’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.

**6.) Using origami to design foldable furniture**

**Mathematics:**

There is plenty of math’s related to origami. Origami works on math principles and theorems. One can apply algebra, sequences and series, calculus and logical ability to design foldable furniture analogous to folding paper in origami.

**Procedure:**

You will have to pick a tessellation which you will use to design the piece of furniture and then decide the optimum number of folds (using calculus) for the size of furniture you’ve picked

**Analysis:**

Designing a foldable furniture is useful when there are small areas. For example, folding a dining table into a coffee table. Applying Origami and math to it would help to determine the most optimized way of doing the same.

**7.) Numerical model of the solar system**

**Mathematics:**

The planets orbit around the sun in elliptical paths, with sun at one of the foci. Using geometry and algebra you can find the equations of each planets and model the entire solar system.

**Procedure:**

Using data from the web you can find the equations using the concept of ellipses. As an extension you can find the areas that each planets covers as they revolve around the sun and compare their properties that are affected due to this revolution.

**Analysis:**

If you’re interested in space, this exploration will give you insights of planetary motion and how math is involved in understand the physical world.

**8.) Analysis of AC circuits by using complex numbers**

**Mathematics:**

If you’re a physics student and wish to dig deeper in math’s behind AC circuits, you can start by applying complex numbers to the previously leant concepts.

**Procedure:**

Complex numbers are utilized in calculations of current, voltage or resistance in AC circuits. One can make use of math to analyze AC circuits.

**Analysis:**

Math’s and Physics go hand in hand. Physics makes use of mathematical tools to justify and understand the theorems and concepts. This exploration will help understand the relation between math’s and physics.

**9.) Chess and Mathematics**

**Mathematics:**

Combinatory is the mathematics of counting and probabilities. You can explore chess and all the different ways a chess game can play out using statistics, probability and combinatory.

**Procedure:**

Math exists inherently in the game. Starting with the initial positions of the chess pieces, start to analyses all the possible moves and use mathematical tools to figure various ways in which the game can be played out. Instead of dealing with the whole game, you can also create situations on the board which a player might face and then using math calculate all the possible moves and find out the right one.

**Analysis:**

This exploration connects the game of chess with math. Although there will be numerous simulations of the game possible, one can still analyses the certain situations on the board using math’s and make conclusions.

**10.) Mathematics of solar panel**

**Mathematics:**

Solar energy has great importance in today’s world. There are various mathematical tools that can be used to design and install the most optimum solar panel. This exploration may involve vectors, trigonometry and calculus.

**Procedure:**

The various aspects which you can work on are-

- Optimum tilt of the solar panel
- Find the size of PV modules according to use
- Number of PV panels required

**Analysis:**

Solar panels are installed in many households and according to the power consumption, they must be customized. This exploration makes use of math to determine the most optimal way to make use of solar panels.

**11.) Relation of diversity of ecosystem and climate**

**Mathematics:**

Referring to previous techniques in mapping the relation and implementing them in sample data such as diversity indices and parameterization along with providing effective numbers

**Procedure**:

Obtain data of diversity and climatic conditions for a variety of regions with different properties and implement diversity indices and parameterization.

**Analysis**:

The data and mathematics will help determine the diversity of species that survive and require the variety of climatic conditions

**12.) Relationship between number of gear shifts and probability to win in a F1 race**

**Mathematics**:

Utilising previous statistics of F1 races and probability, we determine how drivers who have won shift the gears of their cars along with its frequency

**Procedure**:

Gather previous race statistics of different positioned racers in one or more series of races while noting the car model

**Analysis**:

F1 is an exhilarating sport and victories are determined not only by the car’s performance but also the decisiveness of the driver, which includes the number and pace of gear shifts throughout the track.

**13.) The Golden Chord Progression**

**Mathematics**:

Utilising the golden ratio to determine harmonious and discordant chords

**Procedure:**

The golden ratio can be applied to sample melodies and songs which can provide a progression series of chords.

**Analysis:**

The golden chord progression is a technique that enables music producers to determine chord progressions that fit a melody based on the melody’s properties.

**14.) Investigating the mathematics of cryptography**

**Mathematics**:

Cryptography involves the use of mathematical algorithms and techniques to secure information and protect it from unauthorised access.

**Procedure:**

One way to investigate the mathematics of cryptography is to examine different encryption and decryption methods, such as the RSA algorithm and the Diffie-Hellman key exchange protocol. This can involve analysing the mathematical properties of these methods and exploring how they are used in real-world applications.

**Analysis:**

By studying the mathematics of cryptography, one can gain a deeper understanding of how information is secured and how cryptographic techniques can be used to protect sensitive data. This can lead to new insights and discoveries in the field of cryptography, as well as in related areas such as computer science and cybersecurity.

**15.) Investigating the mathematics of chaos theory**

**Mathematics**:

Chaos theory is a branch of mathematics that studies the behaviour of dynamical systems that are highly sensitive to initial conditions.

**Procedure:**

One way to investigate the mathematics of chaos theory is to explore the properties of chaotic systems, such as the Lorenz system or the logistic map. This can involve analysing the bifurcation diagrams and phase portraits of these systems, as well as studying the Lyapunov exponents and other quantitative measures of chaos.

**Analysis:**

By studying the mathematics of chaos theory, one can gain a better understanding of the complex and often unpredictable behaviour of natural systems. This can lead to new insights and discoveries in fields such as physics, meteorology, and biology, as well as in the development of new mathematical models and computational techniques.