Using Numerical Methods on the FX-CG50
Numerical methods help students solve equations that have no obvious algebraic solution. They’re one of the most challenging topics in GCSE, A-level and IB Mathematics. The FX-CG50 graphing calculator makes them much easier to teach and learn.
Resource Keypoints
- Learn how to apply numerical methods to solve equations without an obvious algebraic solution
- Use the Table function to apply the decimal search method
- Explore fixed point iteration and see how it develops through spiral graph visualisation.
Decimal Search & Change of Sign
Decimal search and change of sign
Our most advanced graphic calculator offers various ways to explore the decimal search method of equation solving.
A good place to start is Table mode. Here, you can experiment with entering a y = function and inputting a range of x values to approximate the point at which the corresponding y values change from negative to positive.
This helps you identify the range in which y equals zero, and therefore where the solution lies, to a required number of decimal places.
We can put this into context with the example of a quadratic equation such as y = x2 – 2x – 2.
When you enter Table mode, you can input your function in the table relation list, then press F5 to open the settings menu. Here you can add your chosen start and end values for x, as well as the increments by which you want values to increase within this range.
For example, with x2 – 2x – 2 as the saved function, you could enter your start and end points for x as -0.73 and -0.74, respectively, and choose to go up in one thousandths by inputting 0.001 in the Step field.
When you press F6 in the table relation list screen to view your table, you’ll see that the change of sign in the y column occurs when the x value is within the range of -0.732 to -0.733.
Depending on the level of accuracy you need, you could then go through the same process again to narrow down the range of values even further, using -0.732 and -0.733 as your start and end points.
The FX-CG50 also gives you the option to visualize what’s happening by graphing the data in your table.
Fixed Point Iteration
Fixed point iteration
Recursion can come into play when exploring numerical method: fixed point iteration.
If a student is presented with an equation in terms of y =, once they’ve rearranged it in terms of x =, they can enter the data into Recursion mode to create a sequence of values.
A key benefit of doing this in Recursion mode on the FX-CG50 is that they can then use the values to plot a spiral, or cobweb, graph.
Frequently Asked Questions
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Using Numerical Methods on the FX-CG50
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