Key features of the fx-CG50: an exam-ready recap
The Christmas and New Year period is always an interesting time in schools, not least for GCSE and A-level maths teachers preparing their students for mock examinations.
Calculators are a vital source of support and reassurance for students at exam time. With that in mind, we thought this would be a good opportunity to revisit some key skills, calculator modes and exam techniques with our resident mathematician and fx-CG50 expert, Simon May.
Equation mode is where A-level and GCSE maths students will spend a lot of time on the fx-CG50, our most advanced graphic calculator. They can rely on it for fundamentals like solving simultaneous equations, which can be approached numerically but also represented as a graph, giving students a simple way to check their answers visually by looking at where the lines of functions cross.
Investigation of polynomials and solving quadratics, cubics and quartics is also possible in Equation mode. The calculator has the advantage that it can represent the answer as a rationalised surd, which is a big benefit when students are required to give an exact answer to a question.
When working with equations, the fx-CG50 also provides the option to solve them numerically using the SolveN function, which Simon highlighted as another key feature that students should know how to use effectively before going into their exams.
SolveN can show answers as surds and fractions, and also works in tandem with the calculator’s graphing function, providing the option to solve equations using notations from graphs that have already been drawn.
Going a step further, Simon noted that students can store the values they’ve gained through SolveN via the calculator’s answer history function. They can then use these figures for other calculations and later steps in the question, without wasting time – and potentially making mistakes – writing them out by hand.
The ability to draw graphs is a standout feature of the fx-CG50, and it can be a big help in exams.
Simon illustrated this with the example of a modulus function such as y = |2x + 1|, where it’s only possible to have positive values of y and the resulting graph won’t go below the x axis.
Students could be asked where this function equals another function such as y = x + 1.
“You could approach this algebraically, and follow a very rigid structure to solve it,” Simon said. “If you approach it graphically, you can see there are two answers because there are two intersections, and the calculator easily finds them for you.”
Students could also get into difficulties with these sorts of exam questions if they assume there are two answers, because in some cases there may only be one – if the second function above is changed to y = 3x + 1, for example.
“If you make a mistake approaching this algebraically, you could get two answers,” Simon said. “A graph will clearly show there’s only one intersection, so there is only one valid answer.
“Modulus functions provide a really nice, simple demonstration of the fact that, if you graph something, you’re less likely to do erroneous work or get incorrect values.”
Another key aspect of the fx-CG50 that Simon was keen to highlight is the Distribution app. This really comes into its own for A-level maths students tackling probability distribution questions in exams.
It has some features relevant to all A-level students – namely binomial and normal distributions – as well as other functions specifically for Further Maths, such as Poisson and geometric distributions.
A valuable benefit of this app is its ability to draw distributions, giving students a simple visual representation where the heights of the displayed lines represent the range of probabilities.
In the example below, the image shows the distribution of probabilities for getting six or more heads when tossing an unbiased coin ten times.
Noticeably, the Distribution app has the capability to create right-hand probabilities. This removes the need to go through the more long-winded and error-prone process of performing a calculation with a left-hand probability, which could be a big advantage in an exam scenario.
Much like in Equation mode, students using the Distribution app can apply the answers they have already found later, again saving themselves valuable time and reducing the risk of mistakes.
“Students really need to know about the Distribution app, because it just makes their lives so much easier, especially in exams,” Simon said.
As teachers and students look ahead to mocks in January and their full exams later in the year, Simon offered some general pointers relating to calculator use at this crucial time.
Firstly, he emphasised the importance of students putting their calculators in exam mode and clearing the memory, seeing as mocks are treated in the same way as official exams and have the same restrictions.
They also need to be comfortable and familiar with their calculator settings, specifically when it comes to things like working in degrees and radians.
Being in the wrong setting could lead to some strange-looking graphs and wildly wrong answers, and sometimes it’s absolutely essential to work in a particular mode. Trigonometric integration, for example, has to be calculated in radians.
On a more general note, Simon pointed out that mocks can be a great opportunity for students to reassess how they’re working and look for chances to gain more marks, which could mean using their calculator more effectively.
The teacher has a key role to play in this process, of course. If you want to improve your knowledge of the fx-CG50 and its capabilities, you can find model-specific training videos and other support in our resources centre.
We also offer free introductory training sessions, led by experts with in-depth knowledge of the calculator. Book your place here.