A-Level Graphical Calculator Guide

Casio fx-CG100

Essential Administration on CG100

Exam Mode

HOME → Exam Mode → Enter Exam Mode → United Kingdom

(exam mode lasts 12 hours)

Reset the Calculator

HOME → System → Reset → Initialize All

(or pick another option)

Set Your Name (Ownership Identification)

HOME → System → User Name

to store your credentials. Helpful for reclaiming misplaced units!

Speed Tip

Speed Tip: Use the numbers on menus to jump straight to items without having to scroll down and press OK.

New Essential Graphical Calculator Skills

Calculating P(X ≤ r) for Binomial Distribution: X ~ B(n, p)

OPTION A:

HOME → Calculate

use CATALOG → Distribution → Binomial Cumulative Dist to populate BinomialCD(r, n, p) directly on screen.

OPTION B:

HOME → Distribution → Binomial

Set Tail to (X≤) (safest)
Set Data to Variable.
Input target value for x (the value r), Numtrial (n), and p (probability p).
Scroll down to Execute and press OK or EXE.

Calculating P(X ≤ r) for Normal Distribution: X ~ N(μ, σ²)

OPTION A:

HOME → Calculate

use CATALOG → Distribution → Normal Cumulative Dist to populate NormCD(-999, (r-μ)/σ) directly on screen.

OPTION B:

HOME → Distribution → Normal

Set Tail to (≤X≤) (safest)
Set Data to Variable.
Set Lower to a large negative bound (e.g. -99999).
Set Upper to your boundary value r.
Input mean (μ) and standard deviation (σ). Note the order!
Scroll to Execute and press OK.

IMPORTANT ADVICE: Always write the correct notation on your exam scripts: Φ((r-μ)/σ)

Calculating P(X ≤ r) for Poisson Distribution: X ~ Poisson(λ)Further Maths

OPTION A:

HOME → Calculate

use CATALOG → Distribution → Poisson Cumulative Dist to call PoissonCD(r, λ).

OPTION B:

HOME → Distribution → Poisson

Set Tail to (X≤)
Set Data to Variable.
Input target value x (r) and parameter λ.
Scroll to Execute and press OK.

Inverse Binomial: Find min r such that P(X ≤ r) > x

HOME → Calculate

use CATALOG → Distribution → Inverse Binomial Cumulative to call InvBinomialCD(x,n,p)

IMPORTANT ADVICE: You MUST check your answer using the non-inverse function to obtain upper and lower bounds. You must write these down.

Inverse Normal: For X ~ N(μ, σ²) Solve to find z=(r-μ)/σ if P(X ≤ r)=p

HOME → Calculate

use CATALOG → Distribution → Inverse Normal Cumul Dist to call InvNormCD(p)

IMPORTANT ADVICE: You MUST write Φ^-1(p) =... on your exam paper to show correct notation.

Inverse Poisson: for X ~ Poisson(λ)Further Maths

HOME → Calculate

use CATALOG → Distribution → Inverse Poisson Cumul Dist to call InvPoissonCD(p,λ)

IMPORTANT ADVICE: You MUST check your answer using the non-inverse function to obtain upper and lower bounds. You must write these down.

Matrix Determinants and Inverses and PowersFurther Maths

HOME → Calculate

To Enter Matrix: Press TOOLS → m×n enter rows x cols (mxn) and fill in matrix
Inverse: [enter matrix]^-1 (use power -1), (or CATALOG → Matrix → Inverse Matrix)
Determinant: CATALOG → Matrix → Determinant to call Det([enter matrix])
Power: Like inverse, but use power other than -1. Power must be a positive integer.

Matrix MultiplicationFurther Maths

HOME → Calculate

To Enter Matrix: Press TOOLS → m×n enter rows x cols (mxn) and fill in matrix
Use the regular multiplication (×) button to multiply two matrices entered as above.

Using Matrix AnswerFurther Maths

HOME → Calculate

To use previous Matrix Answer: Press VARIABLE → Matrix → Mat Ans:

Complex numbersFurther Maths

HOME → Calculate

Use the green i button (green SHIFT and i is on the 9 button).
Then just enter your calculation using i as needed. eg √(4i)
For Complex Conjugate, Argument etc. Use the CATALOG → Complex Number menu.

Vector Calculations (Dot and Cross Product and Magnitude)Further Maths

HOME → Calculate

Right tab to Vectors.
EXE to enter a Vector
Left tab back to Calculation
Use CATALOG → Vector → Dot Product (for Dot product) etc.
Insert vector using VARIABLE → Vector and select your vector.
For Magnitude use CATALOG → Vector → Vector Norm

Other Essential Skills

Calculating Combination (nCr), Permutations (nPr), and Factorials (!)

HOME → Calculate and use CATALOG → Probability

For nCr or nPr: Type the value n first, then use Combination (C) or Permutation (P) from CATALOG → Probability, then type r, and press EXE.
For Factorial: Type your value, then select Factorial (!) from the Probability catalog.

Calculate Mean, Variance and Standard Deviation of a Data Set

Enter data:

HOME → Statistics

Input your sample values down List 1.
Optionally put frequencies in List 2:
Tab-Right ( ->| ) to Setup
Set top option to Calculate Summary Statistics
Set 2nd option to 1-Variable
Set 1Var Freq to be 1 (default) or List2 (for frequency data)

View summary statistics:

Scroll down to Execute and press OK to see summary statistics. Note sx is the sample standard deviation (dividing by (n-1))

Use summary data in calculations:

HOME → Calculate use CATALOG → Statistics

Mean: CATALOG → Statistics → Mean to use Mean() then VARIABLE → List → List 1 (Only works for non-frequency data).
Standard Deviation: CATALOG → Statistics → Sample Standard Deviation to use StdDev() then VARIABLE → List → List 1 (Only works for non-frequency data).
Variance: Square the Standard Deviation obtained from above.

Setting Degrees or Radians

SETTINGS → Angle

(Use SETTINGS button again to exit SETTINGS mode)

Converting Answers Between Fractions and Decimals

Direct Key → FORMAT (button at bottom right of calculator)

Press the primary physical FORMAT key once to toggle intermediate calculation answers instantly between fractional/radical forms and rounded decimal values.
Press SHIFT → FORMAT for a comprehensive menu of representations.
Go to SETTINGS → FORMAT Key to change the behaviour of the FORMAT button.

Hyperbolic Trig FunctionsFurther Maths

HOME → Calculate use CATALOG → Hyperbolic Calc

Select the required hyperbolic function (sinh, cosh, tanh) or their unique inverses directly from the catalog listing.

Important Skills to Aid Efficiency etc

Variable Storage

Needs right green arrow (green SHIFT and button below shift) and letter (orange ALPHA button and pick a letter).
Eg type: “Ans → A” to store the previous answer as variable A.

The Table Function (eg to Search for Polynomial Root)

HOME → Graph&Table

Scroll up to the top option (Type | Viewing Setup) and press OK
Change Type as necessary (usually to y=)
Use TOOLS → Delete to delete existing formulae if necessary
Use x button (immediately under green shift button) to start typing formula. Press ‘EXE’ to save it
Tab left (|<-) to get to the Table view (or use arrow buttons and OK to select ‘table’).
When viewing a Table use TOOLS → Set Table Domain → Range to set the domain values as a range (start, end, step).
Notice that you can use a ‘List’ instead for your domain values.
(Enter a ‘List’ at HOME → Statistics)

Drawing Cartesian x-y Graphs

HOME → Graph&Table (Same as above for tables)

then enter a formula, and tab to (or select) graph.
TOOLS → View Window lets you change the axes. (Tip: The Pre-set Windows are good)
You then have to press back (curly back arrow under Home button at top left) then Tab right to the graph again and press OK on the Draw option.
To zoom in and out, use the addition (+) and subtraction (-) buttons on your calculator. To move around, use the arrow buttons.
When viewing a graph, press the back button to return to the formulae.

Finding Roots of Graphs

HOME → Graph&Table (when viewing a graph)

TOOLS → Graph Solve → Root
Use up/down arrow buttons to choose a graph, then press the OK button select it.
Use left/right arrow buttons to select a root.
Press the OK button to mark the selected root on the graph with its coordinates.
Read the value of the selected root at the bottom of the screen
Press the Back button to exit ‘Root viewing mode’

Finding Intersections of Graphs

HOME → Graph&Table (when viewing a graph)

TOOLS → Graph Solve → Intersection
Use left/right arrow buttons to select an intersection.
Press the OK button to mark the selected intersection on the graph with its coordinates.
Read the accurate coordinates of the selected intersection at the bottom of the screen
Press the Back button to exit ‘Intersection viewing mode’.

Finding Min/Max of Graph

HOME → Graph&Table (when viewing a graph)

TOOLS → Graph Solve → Maximum Value
Use up/down arrow buttons to choose a graph, then press the OK button select it.
Use left/right arrow buttons to select a maximum.
Press the OK button to mark the selected maximum on the graph with its coordinates.
Read the accurate coordinates of the selected maximum at the bottom of the screen
Press the Back button to exit ‘Maximum viewing mode’.
Minimums work in the same way. Just use TOOLS → Graph Solve → Minimum Value instead

Drawing Graphs of Modulus Functions

HOME → Graph&Table

use CATALOG → Numeric Calc → Absolute Value

Drawing Parametric Graphs

HOME → Graph&Table (when on the formula view)

Scroll up to the top option (Type | Viewing Setup) and press OK
Change Type to Param

Drawing Scatter Graphs, Getting the Line of Best Fit and Other Stats

HOME → Statistics

(and press the Back button if necessary to return to the List view)
Use TOOLS → Delete → All lists to clear the table
Enter your data
Tab right to Setup view
Press OK on the top option and select Draw Statistics Graph.
Press OK on Graph1 then press OK again to change it to Scatter Plot
Tab right to actually draw the graph.
Tab right again and select Linear Regression(ax+b) for equation and r value
Tab right again to see line of best fit (Regression line) drawn on the graph

Drawing Polar (r,θ) GraphsFurther Maths

HOME → Graph&Table (when on the formula view)

Scroll up to the top option (Type | Viewing Setup) and press OK
Change Type to r=
If your graph looks odd, check TOOLS → View Window → T,θ Pitch is small enough.

Solving Quadratic Equations

HOME → Equation → Polynomial

Scroll to the top (quadratic) option and press the OK button.
Enter the coefficients
Tab right to see the roots
Use the back button to solve a different equation.

Solving Simultaneous Equations

HOME → Equation → Simultaneous

Scroll to the number of unknowns required and press the OK button.
Enter the equations
Tab right to see the roots
Use the back button to solve a different set of equations.

Solving Any Equation Numerically (To Find All Roots)

HOME → Calculate

use CATALOG → Function Analysis → Solve Equation (SolveN)
Type your equation using the x key and the = key (Green shift on left bracket)
eg SolveN(5x-2=1)
eg SolveN(sin(2x)=0.5,x,0,360)

This is VERY useful for checking answers, but the examiners know you have this, so you MUST show your method in an exam. It isn’t guaranteed that it will work, and you may need to specify the range to search for roots (as in the 2nd example)

Solving Quadratic Inequalities

HOME → Num Ineq

Scroll to the top (quadratic) option and press the OK button.
Choose the desired inequality directional logic (> 0, ≤ 0, etc.).
Enter the equation coefficients.
Tab right to see the results

Calculating Definite Integrals (With Limits), to Check Work

HOME → Calculate

use CATALOG → Function Analysis → Integration (∫)
Fill in the boxes and press EXE

Calculating Gradients at a Specific Point

HOME → Calculate

use CATALOG → Function Analysis → 1st Derivative (d/dx)
Input the function using the x button (under the shift button)
Input the x coordinate of the point you wish to calculate the gradient
Press the EXE button

Interesting Features for Exploration When Learning

Defining Functions, for Composite and Recursive Expressions: f(Ans)

Define your functions at HOME → Graph&Table at y1 and y2 etc.
Use your functions at HOME → Calculate using VARIABLE → Function
Eg try: y1(y2(5)) or y1(Ans) EXE EXE EXE…

Visualising Graphs of Statistical Distributions

HOME → Distribution

For details see OPTION B of the Distribution Calculations near the top of this page.

Calculating and Drawing Tangents and Normals at a Specific Point

HOME → Graph&Table (when viewing a graph)

press TOOLS → Sketch → Tangent Line or Normal Line
Use up/down arrow buttons to choose a graph.
Use left/right arrow buttons to move position of tangent/normal.
Type an x coordinate value directly with the keypad and press EXE.

Probability Simulation

HOME → Prob Sim

Select built-in experiment animations (Coin Flip, Dice Roll, Card Draw, or Random Numbers).
Simulate multiple experiments very quickly and see visual results.

Recursion (Number-Crunch Up to 300 Terms of an Inductive Sequence)

HOME → Recursion

Use CATALOG → Recursion → u_n to enter recursive formula
Use navigation arrows to change top Viewing Setup options, including Set Table Domain

Other Features

Draw Box-Plots and Histograms

HOME → Statistics

Very similar to drawing scatter graphs (see above)

3D Graphs

HOME → 3D Graph

A bit fiddly, so not really recommended

Constructions (Geometry)

HOME → Geometry

A bit fiddly, so not really recommended

Designed for A-Level Maths students. Written by mrbutler with formatting help from Gemini AI

Exam observation: These Calculator abilities are not a secret 'cheat' for exams. The exam boards know about all this and explicitly encourage/require use of these calculators. You can certainly use your calculator to check an answer, but to get the marks in an exam you will often have to show how you do it with full method on paper.
An example phrase from the front of an A-level paper: