Unlock Your CAS Calculator’s Potential: A Guide To UDFs in VCE Maths

⏱ 4-5 min

Struggling to remember complex formulas or tired of repeatedly typing long calculations into your CAS calculator during VCE Maths? What if there was a way to streamline these processes, save precious time, and enhance your confidence? The answer lies in harnessing the power of User Defined Functions (UDFs).

Your CAS should be your most powerful ally in VCE Maths. It’s packed with built-in functions you use to tackle a wide range of mathematical problems, e.g. ‘solve()‘. However, these still require some legwork from you when combining functions to solve multi-step problems. UDFs are a game-changer, allowing you to create new tailored functions that automate formulas and calculations you frequently encounter.

Hear our lead Methods tutor on leveraging UDFs for success

 

Work smarter, not harder: Why Use UDFs?

Imagine facing a challenging Methods SAC. One step of a question requires you to find the distance between two points (x1, x2) and (y1, y2). Normally, you’d have to recall the distance formula:

Then, you’d meticulously input the values for each coordinate. While your trusty CAS can handle this, doing it multiple times can be time-consuming and prone to typing errors, especially under test pressure.

But picture this: you’ve defined the UDF dist(x1,y1,x2,y2) and set it equal to the distance formula above. Now, instead of typing the entire rule each time, you simply input dist(x1,y1,x2,y2) – plugging in the coordinates. The CAS instantly performs the calculation, giving you the result for distance.

This simple example highlights the core advantages of using UDFs:

1. Significant Time Savings

In high-stakes exams where every second counts, UDFs shave valuable minutes off your calculation time. As a result, you get more time to deeply understand the questions and check answers.

2. Reduced Risk of Errors

By defining a formula once and then simply calling the function with different inputs, you minimise the chances of making typos that lead to mistakes.

3. Save Yourself The Stress

Complex or frequently used formulas become easily automated, streamlining your problem-solving process. This can lead to a smoother and less stressful assessment.

4. Enhanced Understanding

The act of defining a UDF can actually deepen your understanding of the underlying formula and the variables involved.

 

UDFs go beyond the limits of built-in functions

The beauty of UDFs lies in their versatility. They aren’t limited to just the distance formula. Think about other concepts you encounter in VCE Maths Methods and Specialist Maths:

Find Average Value of a Function

Instead of manually typing in the above formula each time, defining it as a UDF like avg(f(x),a,b) can automate this.

Calculate Area Between Two Curves

Define a UDF such as ar2curves(f(x),g(x),a,b) to quickly find the integral from a to b of f(x)-g(x). Then when you do questions, you won’t need to type out the integral ever again – simply call ar2curves() and fill the brackets with the right inputs.

Transformations of Functions 

You could even create UDFs (even easier, get them from us at Vanguard!) to apply translations, dilations, and reflections to functions effortlessly.

Statistical Calculations

For subjects like Further Maths, UDFs are incredibly useful for rapid calculations of means, standard deviations, and probabilities for different distributions.

The possibilities are virtually limitless, constrained only by the capabilities of your specific CAS calculator model and your creativity. 

 

Get started with UDFs today

The exact steps for defining a UDF will vary slightly depending on the model of your calculator (e.g., TI-Nspire, Casio ClassPad). However, the general process is the same.

1. Define a new function

Look for an option like ‘Define,”’ or a similar command within your calculator’s menu system. Consult your calculator’s manual if you’re unsure.

2. Name Your UDF

Choose a short and self-explanatory  name for your function (e.g., dist for distance between 2 points). Something you’ll remember easily and type out fast.

3. Define the Arguments

In brackets after the UDF name, specify the input variables/parameters that your function will take (e.g., x1, y1, x2, y2 for the distance formula).

4. Enter the Formula or Expression

Add an equal sign, the type in the mathematical formula or expression that your function will evaluate, using the defined arguments.

5. Save Your Function

Once defined, ensure you save your function so it’s available for use in your calculations.

 

Unsure how or not a fan of coding? We’ve got you 

Tutoring VCE maths at Vanguard means you’ll get our comprehensive set of pre-defined UDFs designed to optimise your performance in SACs and exams. Think of it as having a library of shortcuts at your fingertips!

By mastering UDFs, you’re not just learning to use your calculator more efficiently – you’re developing a deeper understanding of the mathematical concepts behind common calculations, and gaining a significant advantage in your VCE journey.

Ready to unlock the full potential of your CAS? Book your FREE trial with Vanguard today where you can ask all about our UDF resources – and see how we can help you excel!