# How can a graphic calculator aid the transition to A-level maths?

The transition from GCSE to A-level maths can be a challenge for students, as they find themselves faced with significantly more advanced topics to get to grips with, and less time in which to do it.

At A-level, calculators play a pivotal role in the classroom as students require a deeper understanding of how specific functions can help to solve complex problems, and must be confident enough to apply this knowledge during exams. Having access to the most effective tools to aid learning and understanding can make all the difference at this time, not only for students but for teachers as well.

One such tool is the Casio fx-CG50, our most advanced graphic calculator. The extensive functionality available on this handset can help GCSE and A-level maths students of all abilities, including those who struggle with the increase in difficulty levels in year 12.

In this blog post, we share some practical examples of how the calculator can help with navigating this transition, with insights from our mathematician and fx-CG50 expert, Simon May.

## Using Modify for function transformations

One topic that A-level maths students are likely to come across fairly early in year 12 is transformations of functions. This provides a good example of how visualising concepts on a graphic calculator can foster deeper understanding and empower students to do their own investigations.

Using the graphing functionality on the fx-CG50, it’s possible to graph a quadratic function such as f(x) = x^{2} – x – 2, which produces the typical parabola-shaped quadratic curve.

You can then encourage students to explore other possibilities using the calculator’s Modify tool, which allows them to change variables within the function and see what effect this has on the resulting graph.

By taking the above function and subtracting the variable ‘A’, students will see that the graph moves to the right when A>0 , and to the left when A<0.

As soon as students get the hang of modifying functions and analysing the visual results, they can start to experiment with all sorts of changes and investigate the results.

“Using the Modify function can be really useful quite early on in A-level maths,” Simon said. “It helps give students the confidence to do their own investigations and use the calculator to get a clearer idea of what’s happening.”

## Solving equations with SolveN

Another powerful feature of the fx-CG50 that can be especially helpful for students navigating the transition to A-level maths is SolveN. This tool – which is only available on our most advanced graphing calculator – solves equations numerically and can show the solutions as exact values, including surds and fractions.

Continuing with the quadratic function example above, using SolveN can quickly show that the roots of this function are -1 and 2.

Furthermore, if the function has already been graphed and saved as graph Y1, for example, all the student has to do is input SolveN (by pressing OPTN, F4 [CALC], F5 [SolveN]), followed by (Y1 = 0) to find the roots.

They can explore and indulge their curiosity further by inputting something like SolveN (Y1 (x – 1) = 0) to see how this affects the roots of the function. This can lead to further conversations and exploration of areas such as factorisation and the rectangular form of the quadratic.

“SolveN isn’t on any other calculator and it’s a really powerful feature that’s worth using very early on in year 12,” Simon said.

“Less able students may benefit from it even more than the more able students, because it gives them the answers straight away and they will feel more confident when it comes to solving equations and interpreting what’s happening.”

## Accessing resources to ease the transition

Managing the transition to A-level maths is also a challenge for teachers, as you focus on introducing new topics, engaging with your students and teaching much more advanced mathematics.

So it’s understandable if you have questions about how to stay on top of these fundamentals while your students are also getting used to a new calculator.

Simon’s advice where the fx-CG50 is concerned is to get them using the calculator as early as possible – possibly at GCSE for those who are certain they will continue to A-level – and start with the basics.

“Introducing students to the handset very early on and encouraging them to use the simple stuff – like SolveN and Equation mode – can really help them out and give them confidence that they can cope with the higher demands of A-level,” he said.

Casio can also help, with various free resources available to support students at this demanding stage in their education. We’ll be hosting three fx-CG50 webinars in September and October, giving an introduction to how A-level maths students can use the graphic calculator efficiently.

Full details and sign-up forms are available on our webinar page.

You can also access a deep library of dedicated fx-CG50 resources on our website, including a ‘Getting Started’ collection specifically for people who are new to the calculator.

Here, you’ll find videos and leaflets covering operations such as plotting graphs of functions, creating basic statistical charts, accessing the main menu and a lot more.