Macmillan TI-Nspire supplement

Transcription

1 February 2011 Contents Changes to the hardware the touchpad... 1 Changes to the software OS version The Home screen... 2 Page layout... 4 Calculator page menu changes... 5 Systems of equations... 5 Polynomials... 6 Calculus... 8 Graph page menu changes... 9 Zoom setting... 9 Special values... 9 Statistics changes Multiple boxplots Frequency plots Normal distribution probabilities with shading This supplement explains the new features and main differences between the TI-Nspire touchpad calculators with operating system version 2.1 and older versions of the calculators and software. It is designed to be used with the following Macmillan Senior Mathematics publications: MathsWorld Mathematical Methods CAS Units 1&2 second edition MathsWorld Mathematical Methods CAS Units 3&4 second edition It may also be useful to teachers and students using MathsWorld General Mathematics Units 1&2 and MathsWorld Further Mathematics Units 3&4, although the technology tips and screenshots in these books are written for the older TI 83, TI 84 and TI 89 calculators.

2 Changes to the hardware the touchpad The new TI-Nspire handhelds have changed their appearance. The following pictures show the keypad for the earlier handheld (with clickpad) and the new handheld (with touchpad). The main differences in keys and layout on the new touchpad version are as follows: the top third are navigation keys (escape, tab etc.), including a new Scratchpad key (see below) and a new doc key that activates the document management menu (essentially this is the Tools menu that could be obtained via the spanner icon above the home key on the 'clickpad' version) the middle third comprises mathematical and numeric keys; the mathematical keys have different functions on their left and right sides (except the enter key); all trigonometric functions (including sec, cosec etc.) are accessed via the trig key; and symbols such as >, < and importantly the with operator are found by pressing ctrl + = the bottom third are alpha keys and some special character symbol keys (for example, the π key, which also includes symbols for i, and e). Copyright Macmillan Education Australia

3 Changes to the software OS version 2 The operating system for the TI-Nspire handheld calculator is constantly being upgraded, very often as a result of suggestions from users. There are a number of changes in the upgrade from OS version 1.7 to OS version 2 (versions 2.0 and 2.1 have been released to date and a new version is due in 2011). In brief, there is a new Home screen interface and there is some new functionality. However, these changes should be regarded as incremental; for users familiar with OS version 1.7 an upgrade to version 2 will not lead to any real difficulties in operating the CAS calculator. The Home screen The following screenshots show the Home screens in OS versions 1.7 and 2. The Home screen in OS version 2 shows document management on the right and a new Scratchpad on the left. Tabbing to the New Doc icon in version 2 has the same effect as tabbing to the corresponding icon in version 1.7. Alternatively you can click on one of the 6 icons; these are the same, except for the Graphs & Geometry icon: it has been replaced by an icon for Graphs and an icon for Geometry. The screenshots below show the difference. To select the application desired, scroll to the item and press enter or simply type the number. Copyright Macmillan Education Australia

4 The Scratchpad can be used to make mathematical calculations and/or draw graphs without creating a document (whereas applications like Geometry, Lists & Spreadsheets etc. are only available within a document). Think of working on Scratchpad as doing some basic work on a physical scratchpad that you expect to discard afterwards. If you select Scratchpad or the Calculate icon, a Scratch Calculate page opens (all functionality other than programming is available); if you choose the Graph icon, a Scratch Graph page opens (all graphing functionality is available but geometry functionality is not available). In version 2 you can access and then easily change settings by clicking on the icon; you can also still change your mind and save the results of Scratch Calculate and/or Scratch Graph by clicking on Scratchpad and selecting Save to Document. Alternatively, you can start afresh by selecting Clear Scratchpad. Copyright Macmillan Education Australia

5 Page Layout There are some new options in the Documents menu (called Tools in version 1.7): Delete Application, Group and Ungroup (see the screenshot below left). These are useful when you have multiple applications open on one page, for example when you draw a graph and add a table, as shown in the screenshot below right. In version 1.7 the best way to get back to a full-screen mode of your graph is to undo your previous selections by repeating ctrl + z. In version 2 you can delete the table (when it is the highlighted application) to return to the graph in full-screen mode or you can choose to Ungroup the applications so that both graph and table are available on different pages, as shown in the following screenshots. The screenshot below right shows that the graph and the table have been ungrouped : the graph is now on page 1.1 and the table on page 1.2. Copyright Macmillan Education Australia

6 Calculator page menu changes The main changes are as follows. Systems of equations Below screenshots show the Algebra menu in version 1.7 (on the left) and in version 2 (on the right); note new menu item 6 in version 2 for solving a system of equations. Selecting this new menu item yields two new options: Solve System of Equations and Solve System of Linear Equations. Accessing the first option results in the screenshot below left and pressing OK gives the template menu in the screenshot below right; this simplifies the use of the solve command in version 1.7. This template allows you to solve linear (and some non-linear) systems of equations. Copyright Macmillan Education Australia

7 Accessing the second option results in the screenshot below left and pressing OK gives the template menu in the screenshot below right. In this case only linear systems can be solved. The outputs are slightly different, as shown in the screenshot below. Polynomials The Algebra: Polynomial Tools submenu has some additional commands, as shown in the screenshot below. Copyright Macmillan Education Australia

8 The first menu brings up easy-to-use wizards, as shown in the following two screenshots. The wizard in the screenshot below right is used to find the roots of the quadratic 2x 2 + 3x + 1 = 0. The result is shown in the screenshot below left. Alternatively, selecting the menu item Real Roots of Polynomial gives you the prompt for manual entry, as shown in the screenshot below right. Note that the polyroots prompt is equivalent to the zeros command, available in the Algebra menu in either version (version 1.7 on the left; version 2 on the right). Copyright Macmillan Education Australia

9 Calculus The Calculus menu has a wizard for the derivative at a point. Insert the numerical value as required and press OK. The prompt for manual entry of the algebraic expression appears; enter the algebraic expression required (see the screenshots below). Note that templates for derivatives and integrals are available in the Math Template palette for version 2, as they were in version 1.7. In the Statistics menu, the item Key Stats in version 1.7 has been given the more appropriate name List Math in version 2; all items in this submenu remain the same. Copyright Macmillan Education Australia

10 Graph page menu changes The main changes are as follows. Zoom setting In the Window/Zoom menu, a Zoom Decimal option has been added (see screenshot below left). This enables automatic tracing in 0.1 increments (note that the Trace Step can still be changed to a user-defined value in the Trace Settings submenu of the Trace menu). Special values The Analyze Graph menu allows the user to find significant points on a graph (zeros, minimums/ maximums, inflection) and locate an intersection point of two graphs (the intersection tool in the Points & Lines menu is still available as well). Graphical tools for the derivative and integral are located in this menu (the integral tool is no longer available in the Measurement menu). In version 1.7 significant points are found using the trace key and hints, as shown in the three screenshots below left (you place a range with the maximum in this range). In version 2 the calculation is done via the Analyze Graph menu, as shown in the three screenshots below right (you select a lower bound and then an upper bound with the maximum between these bounds). Copyright Macmillan Education Australia

11 The derivative at a point can be found interactively via the Analyze Graph menu. Press the menu key and select Analyze Graph: dy/dx, then open a bracket (. A darkened x-value appears (related to where the pointer is on the screen), as shown in the screenshot below left. Overwrite it with the value you want. Thus for the gradient at x = 2, simply type 2 and press enter. A point is placed at this x-value and the gradient revealed, in this case 0.7, as shown in the screenshot below right (the coordinates of the point are not shown; use Actions: Coordinates and Equations to show these if required). The point can be dragged around the curve and the gradient will be updated. Copyright Macmillan Education Australia

12 The integral over a range of values can also be found interactively via the Analyze Graph menu. Press the menu key and select Analyze Graph: Integral, then open a bracket ( when prompted for the lower bound. A darkened x-value appears (related to where your pointer is on the screen), as shown in the screenshot below left. Overwrite it with the value you want. Thus for the integral from x = 3 to x = 1, simply type 3 for the lower bound and press enter. Repeat this process for the upper bound. Points are placed at the x-values chosen and the integral is revealed, in this case 4.27, as shown in the screenshot below right (the coordinates of the points are not shown; use Actions: Coordinates and Equations to show these if required). Note that either point can be dragged around the curve and the integral will be updated. Copyright Macmillan Education Australia

13 Statistics changes The main changes are as follows. Multiple boxplots In version 1.7 multiple boxplots were tedious to prepare. In version 2 it is easier to show multiple boxplots on a single page. For example, the Lists & Spreadsheet page in the screenshot below left shows some percentage scores of a group of paramedics on an initial test (test 1) of emergency procedures and a later re-test (test 2) to determine how well they could recall these procedures. The screenshot below right shows a boxplot of the results of test 1 on a Data & Statistics page. For a boxplot of the results of test 2 on the same axes, press the menu key and select Plot Properties: Add X Variable. This option is not available a second time in version 1.7 (it is greyed out), but it can be repeatedly selected in version 2. Select test2 from the list of available variables and both boxplots are revealed (see the screenshots below). Copyright Macmillan Education Australia

14 Frequency plots In version 2 it is now easy to create a frequency plot. For example, the List & Spreadsheet page in the screenshot below left shows the frequency of 1, 2, 3 and 4 child families for a class at a school. To create a frequency plot on a Data & Statistics page, press the menu key and select Plot Properties: Add X Variable with Frequency (see screenshot below right). Fill in the dialog box, then press OK to reveal the frequency plot (see the screenshots below). Switch to a boxplot for this frequency data if required, as shown in the screenshot below. Copyright Macmillan Education Australia

15 Normal distribution probabilities with shading In version 2 it is easy to find a probability for a normal distribution and visualise it by automatically shading the corresponding area. In a Lists & Spreadsheet page, press the menu key and select Statistics: Distributions: Normal Cdf (see the screenshot below left). A new wizard feature is the Draw button: Shade area. To find and visualise Pr(10 X 20) for a normal distribution with mean 15 and standard deviation 4, enter the values, as shown in the screenshot below right. Press OK twice to reveal the screenshot below left. Ungroup the pages if required (see earlier comments on page layout) to give a better view of the curve and the area corresponding to the probability (see screenshots below). A useful feature is that you can grab either the lower limit or the upper limit on the Data & Statistics page to explore how the probability changes as the limit chosen is moved. Copyright Macmillan Education Australia