Casio fx-9860GII User Manual

Using a graphic display calculator
© Oxford University Press 2012: this may be reproduced for class use solely for the purchaser’s institute
Casio fx-9860GII
Finding information about the graph
The GDC can give you a lot of information about the graph of a function,
such as the coordinates of points of interest and the gradient (slope).
1.2 Finding the gradient (slope) of a line
The correct mathematical notation for gradient (slope) is
d
d
y
x
. You will fi nd
out more about this in the chapter on differential calculus. Here we just need
to know this is the notation that will give us the gradient (slope) of the line.
Example 2
Find the gradient of y = 2x + 1.
First draw the graph of y = 2x + 1 as in Example 1.
Press
SHIF T
(SET UP).
Set Derivative to On.
Press
EXE
and
F6
DRAW to return to the graph.
Press
SHIF T
F1
Trace.
The calculator displays the coordinates of the point and the gradient.
Move the point along the line using the and
keys.
The gradient (slope) is shown by dy/dx and is 2 at every point along
the line.
1.3 Solving simultaneous equations graphically
To solve simultaneous equations graphically you draw the straight lines and then
fi nd their point of intersection. The coordinates of the point of intersection give
you the solutions x and y.
Note: The calculator will only draw the graphs of functions that are expressed
explicitly. By that we mean functions that begin with ‘y =’ and have a function that
involves only x to the right of the equals sign. If the equations are written in a different
form, you will need to rearrange them before using your calculator to solve them.
Example 3
Solve the simultaneous equations 2x + y = 10 and x − y = 2 graphically with your GDC.
First rearrange both equations in the form y =
2x − y = 10 x − y = 2
y = 10 − 2x −y = 2 − x
y = x − 2
Solving simultaneous
equations using a
non-graphical method is
covered in section 1.5.
{ Continued on next page
3

Casio fx-9860GII Specifications

General

Type	Graphing
Form factor	Desktop
Control type	Buttons
Product color	Silver
Housing material	Plastic
Built-in capability	Yes
Digits	- digits
Display type	LCD
Second display	No
Display tilting	-
Display resolution	64 x 128 pixels
Display character size	8 x 21 mm
Display number of lines	8 lines
Display number of characters	21
Flash memory	1.5 MB
RAM capacity	0.064 MB
Storage media type	Flash
Battery type	AAA
Power source	Battery
Number of batteries supported	4

Summary

Functions

1.1 Graphing linear functions

Plotting linear functions on the calculator screen.

1.2 Finding information about the graph

Using the GDC to find graph properties like gradient.

1.3 Solving simultaneous equations graphically

Finding the intersection of graphs to solve simultaneous equations.

1.4 Solving simultaneous linear equations in two unknowns

Using the calculator's equation solver for two linear equations.

1.5 Solving simultaneous linear equations in three unknowns

Solving systems of three linear equations using the GDC.

1.6 Drawing a quadratic graph

Plotting quadratic functions using the GDC's graphing mode.

1.7 Solving quadratic equations

Finding roots of quadratic equations using the calculator.

1.8 Finding a local minimum or maximum point

Finding extrema of functions using tables and built-in functions.

1.9 Operations with complex numbers

Performing arithmetic operations with complex numbers on the GDC.

1.10 Conjugate, modulus and argument

Calculating conjugate, modulus, and argument of complex numbers.

1.11 Solving equations with complex roots

Solving polynomial equations with complex roots using the calculator.

1.12 Polar form

Converting complex numbers between Cartesian and polar forms.

1.13 Drawing an exponential graph

Graphing exponential functions using the GDC.

1.14 Finding a horizontal asymptote

Identifying horizontal asymptotes by analyzing function behavior.

1.15 Evaluating logarithms

Calculating logarithms with different bases using the GDC.

1.16 Finding an inverse function

Finding and graphing inverse functions on the calculator.

1.17 Drawing a logarithmic graph

Plotting logarithmic functions and adjusting the view window.

1.18 Degrees and radians

Switching between degree and radian modes for trigonometric calculations.

1.19 Drawing trigonometric graphs

Graphing trigonometric functions with appropriate axis settings.

1.20 Solving a combined quadratic and exponential equation

Finding intersection points of quadratic and exponential functions.

1.21 Summation of a series

Calculating sums of arithmetic and geometric series.

1.22 Using sinusoidal regression

Fitting a sine curve to data using the GDC's regression function.

1.23 Drawing a piecewise function

Plotting functions defined by multiple conditions or intervals.

Differential calculus

2.1 Finding the gradient at a point

Calculating the instantaneous rate of change (gradient) of a function.

2.2 Drawing a tangent to a curve

Visualizing and finding the equation of a tangent line to a curve.

2.3 Finding maximum and minimum points

Identifying local extrema (maxima and minima) of functions.

2.4 Finding a numerical derivative

Evaluating the derivative of a function at a specific x-value numerically.

2.5 Graphing a numerical derivative

Plotting the gradient function (derivative) of a given function.

2.6 Using the second derivative

Applying the second derivative to determine the nature of stationary points.

Integral calculus

3.1 Finding the value of a definite integral

Calculating definite integrals to find areas or accumulated quantities.

3.2 Finding the area under a curve

Computing the area bounded by a curve and the x-axis using integration.

Vectors

4.1 Calculating a scalar product

Computing the dot product of two vectors using list operations.

4.2 Calculating the angle between two vectors

Finding the angle between two vectors using the dot product formula.

4.3 Calculating a vector product

Note on the GDC's inability to perform cross products of vectors.

Statistics and probability

5.1 Entering lists of data

Inputting numerical data into the calculator's list editor.

5.2 Entering data from a frequency table

Entering data using number-frequency pairs in lists.

5.3 Drawing a frequency histogram from a list

Creating histograms from raw data stored in a list.

5.4 Drawing a frequency histogram from a frequency table

Generating histograms from data entered as frequency tables.

5.5 Drawing a box and whisker diagram from a list

Visualizing data distribution using box plots from list data.

5.6 Drawing a box and whisker diagram from a frequency table

Creating box plots from data entered in a frequency table.

5.7 Calculating statistics from a list

Computing summary statistics (mean, median, etc.) for list data.

5.8 Calculating statistics from a frequency table

Calculating summary statistics for data from a frequency table.

5.9 Calculating the interquartile range

Determining the IQR (Q3 - Q1) from calculated statistics.

5.10 Using statistics

Accessing stored statistical values for further calculations.

5.11 The use of nCr

Calculating combinations (nCr) for probability problems.

5.12 Calculating binomial probabilities

Finding probabilities for binomial distributions using the GDC.

5.13 Calculating Poisson probabilities

Calculating probabilities for Poisson distributions (P.D. and C.D.).

5.14 Calculating normal probabilities from X-values

Finding probabilities for normal distributions given X-values and parameters.

5.15 Calculating X-values from normal probabilities

Finding X-values for normal distributions given probabilities and parameters.