Casio fx-CG50 Manual

Introduction

Your calculator can complete a huge variety of operations. This guide will help you to get started with Graphs, Calculations, Statistics and Equations.
It is especially aimed at A-level Mathematics.

Choosing your mode

From the main menu you can select various options which will take you to screens where you can

• perform calculations
• work with statistics
• plot graphs
• solve equations

and much more. The most useful menus to start learning the calculator for Maths are

	Use this mode for arithmetic calculations, function calculations, binary, octal, decimal, and hexadecimal calculations, matrix and vector calculations.
	Use this mode to perform single-variable and paired-variable statistical calculations, to perform tests, to analyse data and to draw statistical graphs.
	Use this mode to store graph functions, plot and analyse the functions.
	Use this mode to solve linear equations with two to six unknowns, and polynomials from 2nd to 6th degree.

Some important keys NOT found on your scientific calculator

Many of the general features are very similar to your scientific calculator. So for most things, just try looking for the key you would usually use.

One basic difference is that the "=" key is replaced with an "EXE" key. This stands for "execute", and is what you press to actually complete most actions on the calculator.

Allows you to change between screens. For example to go from plotting a graph to solving an equation or just completing a calculation, you would go via the main menu.

This is like your "back" button. If you want to go back to where you were previously, this will take you there.

Allows you to access a whole range of different options. If you can't find something, this is often a good place to start looking!

Always keep an eye on the bottom of the screen as there will often be a list of things that you can do there. You can choose these options by pressing one of keys to , which lines up below the choice you want to make.

Some advice

We strongly recommend that you reset the calculator before learning about it. Please see "Resetting the calculator" for more information.

You can't break the calculator! At least, not by using it. If you get stuck, try a different menu or the key.

Graphs [Option 5]

Plotting graphs – basics

Type the equations of the graphs that you would like to plot...

Hint: you can change between types of graphs by pressing on this screen, and this will allow you to plot parametric curves if you need to.

...then press to see the drawing of the graphs

View window

If the scale on your graph is just far too big or small for you to see what you need, then you can change the view window manually.

• V-Window – press and this will take you to a screen where you can change what you can see your graph. You can alter the range of x and y values that you can see on the screen, the scale, and the grid. From the graph screen, will reset the view window to the original settings.
  

If the grid isn't showing, then you will need to adjust either or both of the following

• the scale is too fine (too many marks on the axis) or too coarse (no marks show on the axis)
• the grid is not set to LINE ( (SETUP) and scroll to GRID).

You can also move around your graph. You can try

• Zoom – press or when you are looking at your graph, and this will zoom in or out, based on the scale settings ( (ZOOM),then ). will "auto" zoom so will often give a sensible scale.
• Move – press or when you are looking at your graph, and this will move the view left or right.
• Pan – if you need to move a long way it is quicker to use pan. Press to get into the pan mode. Then use the four-way arrow button to scroll to where you want to pan from. Press to select that position, scroll again to move the graph around, and when you have the position you want, press again and then to get out of pan mode.
• Trace –you can move along a graph by pressing . Move along a graph by using the cursor .
  Move between graphs using the cursor . Move to a specific coordinate by entering an x-value.

Once you have the plot of your graph(s) there are a number of useful features that you can take advantage of...

Feature

Useful for...
If you need to sketch an inverse function, or find the range or domain of the inverse function.
Hint: Check the domain is valid for the inverse, and that the inverse is not one-many or many-many.

Steps / key presses
Press to get the function, then choose again for INVERSE. If you have more than one graph plotted, choose the one you want by using the keys, then

Screen
Here is the inverse of the blue graph, plotted in green...

Feature

Useful for...
Checking the roots/solutions of an equation.

Steps / key presses
Press to get the function, and then choose for ROOT.
Select which curve you want the roots of, then use and to switch between roots if there are more than one.

Screen

Feature

Useful for...
Checking the coordinates of maximum and minimum points of a curve.

Steps / key presses
Press to get the function, and then choose for MAX or for MIN.
Select which curve you want the max or min of, then use and to switch between stationary points if there is more than one.

Screen

Feature

Useful for...
Checking the coordinates of points of intersection between two curves.

Steps / key presses
Press to get the function, and then choose for INTERSECT.
Use and to switch between points of intersection if there is more than one, and press if you want to see the coordinate point labelled on the graph.

Screen

Feature

Useful for...
Checking the corresponding y or x value when finding coordinates of points that are on the curve.

Steps / key presses
Press to get the function, and then choose to go to the next page. Then choose for Y-CAL and choose for X-CAL.
Select which curve you want a value from, then type in the value you want.

Screen

This was to find the y-value when x was equal to 2.25

Feature

Useful for...
Checking the area under a curve, or the area between a curve and a line

Steps / key presses
Press to get the function, and then choose to go to the next page. Then choose for the integral. Within this you can choose

• which gives the area under a curve between any limits that you choose yourself
• which gives the area under the curve between the roots of the function
• which gives the area between a line and a curve

Screen

Area under a curve between two limits:

Area under a curve between two roots of the equation:

Area between a line and a curve:

Feature

Useful for...
Draw a tangent to a curve.
Hint: to show the value of the derivative (the gradient), use SETUP (w) and scroll to DERIVATIVE, then choose ON.

Steps / key presses
Press to enter the function, and then choose .
Use the scroll cursor to move the tangent, or enter a x-value for a specific coordinate.
Hint: Press to see the equation of the tangent.

Screen

Run-Matrix (Calculations) [Option 1]

Changing the mode for calculations

Once you have reset your calculator most things will be automatically set up how you need them.
If you are doing a calculation and you do need to change between degrees and radians mode, for example, you can do this by pressing which takes you to the SETUP screen. Scroll down to find the ANGLE option and you can choose degrees or radians here.

Feature

Useful for...
Typing in logarithms which are not base 10.

Steps / key presses
Go to the menu by pressing , and then press

Screen

Feature

Useful for...
Typing in modulus functions.

Steps / key presses
Go to the menu by pressing , and then press

Screen

Feature

Useful for...
Checking answers if you have to find "the value of when x =..."

Steps / key presses
Go to the menu by pressing , and then press again

Screen

Feature

Useful for...
Checking answers if you have to find "the value of when x =..."

Steps / key presses
Go to the menu by pressing , and then press

Screen

Feature

Useful for...
Checking answers for definite integration (with limits).

Steps / key presses
Go to the menu by pressing , and then press to go to the next page of options, the select the integral function by pressing

Screen

Feature

Useful for...
Checking answers if you are working out the sum to n terms of a series.

Steps / key presses
Go to the menu by pressing , and then press to go to the next page of options, the select the "sum" function by pressing

Screen

Feature

Useful for...
Checking solutions to quadratics, cubics, trig equations, exponential and logarithmic equations, modulus equations, etc.
Hint: if you want an exact value when solving a quadratic or cubic, you will be much better using the "Polynomial" function in the "Equation" menu, as this will give you your solutions in both decimal and surd form.

Steps / key presses
Press to get into the menu. From here press to get into mode.
From here you can type in the equation you want to solve, using to get an = symbol when you need it.
For trig equations you can specify your interval. After typing your equation, type minimum value maximum value before pressing to get your solutions. Make sure you are in the correct mode (radians or degrees).

Screen
Solving a quadratic example

Solving a trig equation example:
"Solve , "
Type in the equation to be solved and the region...

and press for the solutions...

Feature
True/False

Useful for...
Checking work on algebraic fractions (simplifying, adding, writing as partial fractions, changing improper to mixed). Checking that you have simplified a logarithmic or exponential equation correctly.
Checking that you have simplified using trig identities correctly, or just checking that you memorised a trig identity correctly.

Steps / key presses
Type what you started with on the LHS, an "=" in the middle (by typing . to get the "=" remember!) and what you finished with on the RHS.
When you press the calculator will give a value of... 1 if what you typed is TRUE 0 if what you typed is FALSE.

Hint: BEFORE USING THIS, make sure that you define x as an appropriate value. For example, if x is set to equal 0, it will tell you that 2x=3x is TRUE (clearly not true for all real values of x)!
Make sure you choose an appropriate value for x for the identity or equation that you are checking. To do this, type the value you want to use for x, then press . This will assign that value to x.

Screen
Confirming that these are simplified correctly...

Confirming that this identity is NOT correct...

Statistics [Option 2]

Data are stored in lists. From these, you can calculate statistics such as mean and standard deviation.

Feature

Useful for...
Typing in the data. Enter the data line by line, pressing after each item.
Hint: you can type a label for the data in the cell below the List number.

Steps / key presses
Enter the data line by line, pressing after each item.

Screen

Feature

Useful for...
Telling the calculator which list(s) to use for calculations.
For 1-variable statistics set 1-Var lists.
For 2-variable statistics (regression), set 2-Var lists.

Steps / key presses
Press to enter mode, then and scroll to the 1-Var or 2-Var lists.
XLIST is the list of values. Press to change the List number.
YLIST is the 2^nd list of values for 2-variable data.
FREQ is the frequency of each data item. This is either 1 or a list of frequencies. Press to specify frequencies in a list.

Screen

Feature

Useful for...
Calculating statistics of a single variable, for example mean or standard deviation.
Hint: BEFORE USING THIS make sure that you have told the calculator which list to use (see )

Steps / key presses
Press to enter mode, then
Hint: use to scroll down for more statistics such as quartiles

Screen

Feature

Useful for...
Calculate regression statistics (equation of the regression line and the correlation coefficient)

Steps / key presses
Press to enter the statistics calculation menu, then ().
This will give you a choice of regression types.
Choose () for linear regression and then () for the equation type.

Screen

You can draw graphs from the lists of data using ()

Feature

Useful for...
Telling the calculator what type of graph and which list(s) to use.
The settings depend on the type of graph – see examples below.
Hint: you can set 3 graphs

Steps / key presses
From the statistics menu press () then ().
Choose which graph number you wish to set ().
Press to return to the graph screen.

Screen

Feature
Scatter

Useful for...
Draw a SCATTER GRAPH.
Use above and the following settings:
GRAPH TYPE: Scatter ()
XLIST: List number with your 1^st set of values YLIST: List number with your 2^nd set of values FREQUENCY: 1 or List of frequencies
The other settings allow you to set colours and mark type.

Steps / key presses
From the graph screen press the key for your graph in SET
You can draw the regression line (line of best fit). From the graph plot, press for a linear regression.

Screen

Feature
MedBox

Useful for...
Draw a BOX PLOT
Use above and the following settings:
Graph Type: MedBox ()
XList: List number with your values
Frequency: 1 or List of frequencies
Outliers: Off (default) or On"
The other settings allow you to set colours.

Steps / key presses
From the graph screen press the key for your graph created in SET.
Hint: You can find the values of each quartile by pressing (TRACE) and using the cursor

Screen

Feature
Hist

Useful for...
Draw a HISTOGRAM. Use above and the following settings:
GRAPH TYPE: Hist ()
XLIST: List number with your values
FREQUENCY: 1 or List of frequencies
The other settings allow you to set colours.

Steps / key presses
From the graph screen press the key for your graph created in SET.
Enter the START value (the lowest value for the graph to start) and the WIDTH of each interval. Then press

Screen

Equations [Option A]

Simultaneous linear equations

The equation has to be entered in the form ax+by = c (2 unknowns) or ax+by+cz = d (3 unknowns), and similarly for more unknowns. Don't forget to rearrange your equation if it is not in this form.

Feature

Useful for...
Find the solutions of the equations.
Hint: If the lines (2 unknowns) or planes (3 unknowns) are parallel, the calculator will show 'No Solution'. If the lines or planes are coincident (lie on each other) it will show 'Infinite Solutions').

Steps / key presses
From the EQUATION menu, press to choose the menu, then choose the number of unknowns. Press

Screen

Notice that the exact value is given on the bottom right

Polynomial equations

The equations must be in the form ax²+bx=0 for quadratics and ax³+bx²⁺cx+d=0 for cubics.
Remember to rearrange your equation if necessary.

Feature

Useful for...
Find the solutions of the equations.
Hint 1: If the equation does not have one of the terms, enter 0 for the coefficient e.g. for x³-2x-4=0 enter

Hint 2: If the display shows 'No Real Solutions' or a solution such 3+2i, see below.

Steps / key presses
From the EQUATION menu press to choose the menu then the degree (e.g. 2 for quadratics, 3 for cubics).
Enter the coefficients of your equations.
Press

Screen

Notice that the exact value is given on the bottom right

If the quadratic equation has no real solutions, or a cubic has only 1 real solution, then the calculator will show the result depending on how it is set up.

Type
Quadratic

Screen

Explanation
The graph lies entirely above the x-axis.

How to change
To show complex roots, press .
Enter SETUP by pressing and scroll to Complex Mode, then choose the appropriate notation ( or ).

Type
Quadratic

Screen

Explanation
The graph lies entirely above the x-axis. Complex roots are shown.

How to change
To show real roots only, press . Enter SETUP by pressing . Scroll to Complex Mode, then press .

Type
Cubic

Screen

Explanation
The function has complex roots.

How to change
To show real roots only, press . Enter SETUP by pressing . Scroll to Complex Mode, then press .

Type
Cubic

Screen

Explanation
The graph only crosses the x-axis once.

How to change
To show complex roots, press . Enter SETUP by pressing and scroll to Complex Mode, then choose the appropriate notation ( or ).

Resetting the calculator

From the main menu, choose System (Option G)

Choose RESET (), then MAIN (). You will be asked to confirm. Press .

Return to the main menu.

Taking it further

This guide has introduced you to some of the common uses of the fx-CG50 in Maths A-level. There are many other things you can do.

Follow the on-screen menus to explore. Some menus have more options indicated by

• a black background (for example )
• an arrow

More menus can usually be found by pressing the key.

You can access stored values of variables from statistics, graphs and probability distributions by pressing the key.

The calculator can undertake a huge variety of maths. Now you have tried the basic functions, take a look at these

	Use this mode to calculate probabilities from many distributions, and graph the normal distribution.
	Use this mode to store functions, to generate a table of values, and to draw graphs.
	Use this mode to store recursion formulas, to generate a table of values, and to draw graphs.
	Use this mode to draw graphs of conic sections.
	Use this mode to plot and analyse 3-dimensional graphs.

You can explore much more sophisticated maths and ways of using the calculator in the manual.

Casio have many videos, lesson resources and skills sheets. Take a look at our dedicated education website https://education.casio.co.uk/

Casio gratefully thanks Kim Ogden for substantial contributions to this guide. We hope that you enjoy using the calculator.

Documents / Resources

References

• Casio Calculators

Download manual

Here you can download full pdf version of manual, it may contain additional safety instructions, warranty information, FCC rules, etc.

Download Casio fx-CG50 Manual

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