How to use sliders in graph and table to explore function transformations.
Use one of the 2D templates to solve systems of equations with 2 or more variables.
Two methods to restrict the range of solutions returned when solving trig equations in Main.
Solve simultaneously the equations 2x – 3y = -1 and x + y = 7 using a traditional step by step elimination method in Main.
Find the inverse of a function algebraically using invert and also view the inverse graphically.
Solve simultaneously the equations 3y – 2x = 5 and x + 2y – 8 = 0 graphically using both Main and Graph windows.
Draw a line segment between two points A and B and construct its midpoint.
Create and use a function with many variables. Also edit a user defined function in the program editor.
Managing your own user defined functions such as those created in the previous topic.
Create your own user functions.
Examples (i) f(x)=1/x or (ii) Ckh2ms to convert speeds from km/h to m/s
Eliminate one variable from an equation using another equation.
Example: If x=8-2t and y=6t-1 find an expression for y in terms of x.
Use the sequence function in Main to find the defining rule for various sequences
Factorisation of numbers and expressions (eg quadratics)
Collect like terms and expand and simplify expressions such as 3(4-2x)^2.
How to download programs, eActivities, csv files, pictures and so on into your handheld ClassPad from a Mac or Windows computer.
How to update the operating system of your hand-held ClassPad using a Windows PC.
How to create a small program on your hand held Classpad.
Five examples of small utility programs freely available from the internet are shown.
A brief overview of using the Casio Picture Conversion Engine software to creating a picture for use on ClassPad II for modeling functions in Picture Plot or as an ending screen.
How to set a picture as the ending screen – the picture that briefly flashes onto the screen when you turn your ClassPad off.
Modify the functions assigned to the shift key and save time when using your favourite commands on your Classpad.
A brief overview of picture plot, including the use of sliders to modify function parameters.
A brief tour of the InterActive DiffCalc app and how it can be used to explore concepts of differential calculus.
A brief look at the Conics app and how it can be used to determine the centre and radius of a circle.
Using the program repayII to solve reducible interest problems. repayII is freely available from www.charliewatson.com/classpad/.
Smooth time series data in the statistics app with the program mavII. Also fit a regression line and predict future values. mavII is freely available from www.charliewatson.com/classpad/.
Use the Verify tool in Main to check steps when manually simplifying expressions.
Solve loan repayment problems in Financial, including payments, time periods and loan amounts.
Solve compound interest problems in Financial, including finding future values, interest rates and time required.
Calculate simple interest and future values in the Financial application.
Use the built-in probability simulation tool in Main (or eActivity) to simulate throwing one or two dice or selecting items at random from a container.
Learn some tips on working efficiently in NumSolve.
An introduction to using NumSolve from the Main menu in the context of the simple interest formula I=PRT/100.
Determine the explicit formula for a sequence from a recursive definition using Sequence RUN and the rSolve() function.
Use sequence to examine the balance of a reducible interest loan, determine total interest paid and find individual monthly interest figures.
Examine the growth of money over 10 years using compound interest and also use the difference tool to find individual amounts of interest for any year.
Create the Fibonacci Sequence, graph the first 10 terms and find the ratio of conscutive terms.
Create an arithmetic sequence, then a geometric sequence, also finding the sums of the GP.
Create the sequence of Triangle Numbers using an explicit definition, and graph the first 12 terms.
Basic settings in the Sequence application.
Examine sum of opposite pairs of angles using the Expression tool.
Examine the angle in the semi-circle using the Animation tool.
Examine the angle in the semi-circle using a slider.
Fast track your animation skills by animating a tangent line around a circle.
Use an object and its transformed image in Geometry to determine the equivalent transformation matrix in Main.
Create a triangle in Geometry, apply a matrix transformation to the vertices in Main and view the image back in Geometry.
How to change the labels of any Geometry object using the annotation tool – eg change triangle ABC to triangle PQR.
Find the equation of the line through (2, -1) perpendicular to the line 5x – 2y +6 = 0.
How to use sliders in geometry to change lengths and angles.
Construct angles on the circumference and at the centre from a common chord and examine.
Examine the angle between a tangent to a circle and a radius.
Construct 2 tangents to a circle from an external point and examine their lengths.
Construct a cyclic quadrilateral and examine sum of opposite pairs of angles.
Construct 2 angles on the circumference from a common chord and examine.
Construct a tangent to a circle and then examine angles in the alternate segment.
Construct a diameter in a circle and then examine the angle in the semi-circle.
Draw a circle and construct a diameter.
Construct and solve triangle ABC given all three sides.
Construct and solve triangle ABC given two sides and a non-included angle.
Construct and solve triangle ABC given two sides and the included angle.
Construct a right triangle and measure angles, sides, area and perimeter.
Draw a simple triangle and learn how to measure angles, sides, area and perimeter.
Draw a line segment between two points A and B and determine its length.
Draw a line segment, measure its properties of length, gradient, equation.
Setting up the geometry window, including scales, displaying axes, integer grid and saving.
A Geometry Link in an eActivity is used to investigate translations applied to a parabola. Other possibilities are also hinted at.
Create and save an eActivity to calculate ANY of the parameters (eg mean, sd, etc) involved in a normal probability question.
Create and save an eActivity to calculate the average rate of change of any function over a given interval.
Examples of ways to deal with the ambiguous case of the sine rule when solving obtuse triangles.
Some tips on working within eActivities including working with text or calculation rows, deleting strips and adding strip help.
Many multiple-step math problems can be programmed into an eActivity. This example uses Herons method to find the area of a triangle given three side lengths.
Strip Help is a great way to add hints on what to do within any strip in an eActivity.
Lock, Unlock, Delete, Move Folder and Rename eActivities. Also create a new folder.
Store and solve all your commonly used formulae as strips in eActivities.
How to import external data in comma separated variable (csv) file format into the Spreadsheet app and then into the Statistics app.
Simulate throwing 120 six-sided dice in a spreadsheet and display the resulting distribution as a histogram.
Smooth time series data in a spreadsheet using moving averages, fit a regression line and calculate residuals.
Use a spreadsheet to examine the balance of an annuity.
Use a spreadsheet to examine the balance of a reducible interest loan.
Create a flexible Compound Interest spreadsheet using Absolute and Relative cell references and format cells to 2dp.
Create a flexible Simple Interest spreadsheet using Absolute and Relative cell references and extend by copying and pasting multiple columns.
Create a pie chart, determine the percentages represented by each sector and dynamically modify.
Create a geometric sequence including the sum of terms and extend using Tap and Drag technique.
Create the Fibonacci sequence, adjust columns widths, use the Fill Range command to extend the sequence and display very long integers.
Create a simple sequence and then extend the spreadsheet using Cut and Paste technique.
A quick introduction to the common data types – text, number and formula – and some useful spreadsheet tools.
Calculate a confidence interval for a proportion from supplied summary data in the statistics application.
Calculate a confidence interval for a mean from supplied summary data in the statistics application.
Calculate inverse normal probabilities in Statistics using the Calc menu and Inverse Normal CD tool.
After finding a linear regression model for a bivariate data set, residuals are calculated and plotted to check suitability of linear model.
Substitute a value into a recently calculated regression line to determine a predicted value.
Vary the class intervals when summarising data with a histogram. Also shows use of the randList() command to create a list of random numbers.
Create an xyLine of time series data.
Create a scatterplot and then calculate and plot the least squares linear regression line through the data.
Calculate two variable statistics from paired data.
Create a histogram from a frequency table.
Create a histogram from a single list of scores.
Create several boxplots in a single graph to compare their distributions.
Create a boxplot from a frequency table.
Create a boxplot from a single list of scores.
Calculate one variable statistics from a frequency table.
Calculate one variable statistics from a single list of scores.
Graph parametric functions using ParamType, adjust basic view window settings and become aware of some limitations.
Graph a polar function using r=Type, adjust basic view window settings and become aware of some limitations.
Evaluate and illustrate trapped areas in Graph and Table using Analysis, G-Solve tools.
Evaluate and illustrate area trapped between x-axis and function in Graph and Table using Analysis, G-Solve tools.
Draw the graph of a function in y1 and automatically draw the graph of its first (and second if required) derivatives.
Solve a linear programming problem with 4 constraints in Graph and Table.
Evaluate and illustrate definite integrals in Graph and Table using Analysis, G-Solve tools.
Find the equation of the tangent to a curve in Graph and Table using the Analysis, Sketch, Tangent function.
Use the Modify tool when graphing to vary the parameters of a graph. In this example we vary a and b when y = ( x + a )^2 + b.
Show the gradient of a function on screen when tracing along its graph.
Jump to any exact coordinate whilst tracing along one of several functions in graph.
Solve y = 2 – 5x and y = -3x^2 + 4x + 2 graphically by first drawing the functions and then finding the points of intersection.
Solve y = 3x – 4 and y = 6 – 2x graphically by first drawing the functions and then finding the points of intersection.
Graph y = 4^x using the Graph & Table application, including use of Zoom facility.
Graph y = x^2 + 3x – 4 using the Graph & Table application, including setting the View Window.
Graph 3x + 2y =12 using the Main application, including use of Resize.
Graph y = 2x + 3 using the Graph & Table application, including setting the View Window.
Important settings that should be taken in Graph & Table before trying any of the activities in this section.
Use the differential equation solver with a simple growth and decay question.
How to express a as the subject of the equation t = 2a + 3b in Main.
Solve simultaneously the equations 2x – 3y = -1 and x + y = 7 using the Solve command in Main.
Solve simultaneously the equations 2x – 3y = -1 and x + y = 7 using the 2D simultaneous template in Main.
Solving the quadratic equation x^2 + 6x + 5 = 0 with the solve command in Main.
Solve the equation 7x – 3 = 2x + 4 using the solve command in Main.
Solve the equation 7x – 3 = 2x + 4 using a traditional step by step approach in Main.
Important actions that should be taken in Main before trying any of the activities in this section.
Find the gradient at a point of an implicitly defined function in Main.
Find a volume of revolution in Main and graphically.
Find indefinite and definite integrals in Main using either Interactive, S or the 2D template.
Find the equation of the tangent to a curve in Main using the tanLine function.
Differentiation basics in Main using either Interactive, diff or the 2D template. Also higher orders and any variable.
Learn how to over-ride the selected angle setting when working with trig functions in Main.
Temporarily and permanently assign and delete values to variables in Main. Useful for substitution.
Generate random numbers and simulate throwing dice using the rand() and randlist() functions in Main.
Rounding to a given number of decimal places or significant figures.
Determine the Highest Common Factor or Lowest Common Multiple of two numbers.
Simplification and addition of algebraic fractions
Some basic calculation techniques including evaluation of expressions and substitution.
Some basic editing methods in Main, including drag, cut, copy and paste.
Settings in Main we recommend you should make to ensure your initial experience of Classpad and these help sheets is hassle free.
A brief welcome to ClassPad II Help Series and a preview of some of the new features and apps that come with OS2
A guided tour of the most commonly used areas of the Classpad keyboard.
Calculate a confidence interval for a mean when sample data has been entered in the statistics application.
Calculate normal probabilities in Statistics using the Calc menu and Normal CD tool.
Enter and graph piecewise defined functions in Graph and Table.
Draw a random sample from X~N(60,144) in Main and calculate mean and SD. Also analyse in Statistics.
Use the toPol and toRect functions to convert between polar and rectangular coordinates with vectors or complex numbers.
Basic complex number entry and calculations, including finding magnitude, argument and conversion between forms.
Create your own cis function for making complex number entry simpler.
Create and reflect a triangle in the line y=-x in Geometry. Also, tips on using other transformations.
Calculate binomial probabilities in Statistics using the Calc menu and Binomial PD tool.
Calculate normal probabilities in Main using the Interactive menu and normCDF function.
Draw a random sample from X~Bin(24,1/6) in Main and calculate mean and SD. Also analyse in Statistics.
Calculate binomial probabilities in Main using the Interactive menu and BinomialPDF function.
Calculate inverse normal probabilities in Main using the Interactive menu and invNormCDF function.
Basic matrix creation, editing and calculations in Main, including determinants and inverses.
Define, use and graph piecewise functions in Main. OS3.04 and later.
Define f(x) and g(x), then find f(g(1)), graph g(f(x)) and find all h(x) where g(f(x))=g(h(x)).
The library folder sits in the Other Data memory of Classpad but functions or programs stored in them are also available in eActivities.
Basic settings, inserting and deleting rows in the Statistics application.
Solving the inequality 3 – 4x > 9 using both a step by step approach and also the solve command in Main.
Convert vectors between Cartesian and polar forms, find unit vectors, angle between vectors and dot products.
Use of the Math and 2D tabs in entering simple calculations when in Main.
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