How to Graph Functions and Coordinates

Create new objects
[size=100]You may create new objects (e.g. points, lines, functions) by either using the [i]Graphics Tools[/i] provided in the [i]Toolbar[/i], or by entering their equations and coordinates into the[i] Algebra Input[/i] and pressing the [i]Enter [/i]key.[br][/size]
[size=100][table][tr][td nowrap][code]y = 3 x + 1[/code][/td][td]Enter the linear equation [code]y = 3*x + 1 [/code]into the [i]Algebra Input[/i] and press the [i]Enter [/i]key.[/td][/tr][tr][td nowrap][code]f(x) = x² + 2[/code][/td][td]Enter the function [code]f(x) = x^2 + 2[/code] into the [i]Algebra Input[/i] and press the [i]Enter [/i]key.[/td][/tr][tr][td nowrap][code]B = (2, 1)[/code][/td][td]Enter [code]B = (2, 1)[/code] into the [i]Algebra Input[/i] and press [i]Enter [/i]in order to create a new point. Create another new point [code]C = (-1, 3)[/code][/td][/tr][tr][td][center][icon][/icon][/center][/td][td]Select the [i]Line [/i]tool from the [i]Toolbar [/i]and click twice in the [i]Graphics View[/i] or on the two existing points [i]B[/i] and [i]C[/i] to create a line.[/td][/tr][/table][br][/size][u]Hint[/u]: Click on the [img][/img] keyboard icon in order to open a [b]virtual keyboard[/b].
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Modify existing objects
[size=100]You can drag existing objects in the [i]Graphics View[/i], or change their equations and coordinates in the [i]Algebra View[/i].[br][br][/size][table][tr][td][size=100]1.[/size][/td][td][size=100][icon][/icon][/size][/td][td][size=100]Select the [i]Move [/i]tool and drag objects in the [i]Graphics View[/i] to change their position.[/size][/td][/tr][tr][td][size=100]2.[/size][/td][td][br][/td][td][size=100]Double click on an object in the [i]Algebra View[/i] in order to directly change its equation or coordinates, or redefine it.[/size][/td][/tr][/table][size=100][br][/size]
Delete objects
[size=100]Sometimes, you may want to delete objects that you created in one of the following ways:[br][/size][list][*][size=100]Select the [img][/img] [i]Undo [/i]button in order to undo the last object(s) you created.[/size][/*][*][size=100]Use the [img][/img] [i]Delete[/i] tool in order to delete any object you created.[br][u]Hint[/u]: Click on the last [i]Tool[/i] icon in order to open the corresponding [i]Toolbox[/i]. Select the [img][/img] [i]Delete [/i]tool from the [i]Toolbox[/i] and click on the object(s) you want to delete.[/size][/*][/list][size=100][br][/size]

How to Use GeoGebra's 3D Graphics Tools

What are Tools?
[size=100]GeoGebra's [i]3D Graphics View [/i]provides a [i]Toolbar [/i]with a selection of [i]Tools[/i]. You may [b]activate a [/b][i][b]Tool[/b] [/i]by clicking on the button showing the corresponding icon.[br][br][b]Task[/b]: Create a sphere using the [icon]/images/ggb/toolbar/mode_sphere2.png[/icon] [i]Sphere with Center through Point[/i] tool.[br][/size][list=1][*][size=100]Select the tool [img][/img] [i][i]Sphere with Center through Point[/i][/i] from the [i]3D Graphics View Toolbar[/i].[/size][/*][*][size=100]Click twice in the [i]3D Graphics View[/i] in order to create a sphere.[/size][/*][*][size=100]Select the [img][/img] [i]Move [/i]tool and drag the points in order to change the sphere's size and / or position.[/size][/*][/list]
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How to move objects in the 3D coordinate system
[size=100]In order to move a point in the three-dimensional coordinate system, you can [b]switch between two modes[/b] by repeatedly clicking on the point while the [img][/img] [i]Move[/i] tool is activated:[br][list][*][b]Mode [i]xOy[/i]-plane[/b]: You may move the point parallel to the [i]xOy[/i]-plane without changing the [i]z[/i]-coordinate.[/*][*][b]Mode [i]z[/i]-axis[/b]: You may move the point parallel to the [i]z[/i]-axis without changing the [i]x[/i]- and [i]y[/i]-coordinates. [/*][/list][/size]
What are Toolboxes?
[size=100]GeoGebra's [i]Tools[/i] are organized in [i]Toolboxes[/i], containing similar [i]Tools [/i]or [i]Tools [/i]that generate the same type of new object. You can [b]open a [/b][i][b]Toolbox[/b] [/i]by clicking on a [i]Tool [/i]button and selecting a [i]Tool [/i]from the appearing list.[br][br][b]Task[/b]: Create a cube using the [icon]/images/ggb/toolbar/mode_cube.png[/icon] [i]Cube[/i] tool.[br][/size][list=1][*][size=100]Search the [i]Toolboxes [/i]for the [img][/img] [i]Cube[/i][i] [/i]tool.[br][/size][/*][*][size=100]Click twice in the [i]3D Graphics View[/i] in order to create a cube.[/size][br][/*][*][size=100]Select the [img][/img] [i]Move [/i]tool and drag the points in order to change the cube's size and / or position.[br][/size][/*][/list]
What are Tooltips?
[size=100]If you select a [i]Tool[/i], [b]a [i]Tooltip [/i]appears[/b] explaining how to use this [i]Tool[/i].[br][u]Hint[/u]: When you click on a [i]Tooltip[/i], a web page providing help for the selected [i]Tool [/i]opens in your browser window.[br][br][b]Task[/b]: Create a pyramid using the [icon]/images/ggb/toolbar/mode_pyramid.png[/icon] [i]Pyramid [/i]tool works[br][/size][list=1][*][size=100]Select the [img][/img] [i][size=100][i]Pyramid [/i][/size] [/i]tool.[/size][/*][*][size=100]Read the [i]Tooltip.[/i][/size][/*][*][size=100]Figure out how to use this tool in order to create a pyramid.[/size][br][/*][/list]

How to Use GeoGebra's CAS Tools

What are Tools?
[size=100]GeoGebra provides a [i]Toolbar [/i]with a selection of [i]Tools [/i]specific for the CAS [i]View[/i]. You may [b]activate a [/b][i][b]Tool[/b] [/i]by clicking on the button showing the corresponding icon.[br][br][b]Task[/b]: Solve an equation using the [icon]/images/ggb/toolbar/mode_solve.png[/icon] [i]Solve[/i] tool[/size][list=1][*][size=100]Type the equation [code]3x + 1 = 10[/code] into the [i]CAS Input[/i].[/size][/*][*][size=100]Select the [img][/img] [i]Solve[/i] tool from the [i]CAS View Toolbar[/i].[br][u]Note[/u]: The equation is solved and the solution is shown underneath the equation.[/size][/*][/list]
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What are Tooltips?
[size=100]If you select a [i]Tool[/i], a [b][i]Tooltip [/i]appears[/b] explaining how to use this [i]Tool[/i].[br][u]Hint[/u]: Click on a [i]Tooltip[/i] in order to open a web page providing help for the selected [i]Tool[/i].[br][br][/size][b]Task[/b]: Factorize the term [code](x² - 4)[/code] using the [icon]/images/ggb/toolbar/mode_factor.png[/icon] [i]Factor [/i]tool.

How to Input Data and Refer to Cells

Entering data and creating objects
[size=100]In GeoGebra’s [i]Spreadsheet View[/i] every cell has a specific name that allows you to directly address each cell.[br][u]Example[/u]: The cell in column [i]A[/i] and row [i]1[/i] is named [b]A1[/b].[br][br]You may use the [i]Spreadsheet [/i]cells in order to create mathematical objects that are directly displayed in the [i]Graphics View[/i] (e.g. points).[br][br][b]Task 1[/b][br][/size][table][tr][td][size=100]1.[/size][/td][td][center][size=100][b]A1[/b][/size][/center][/td][td][size=100][font=Arial]Enter the number [/font][code]10 [/code]into cell [b]A1[/b].[br][u]Hint[/u]: Always confirm your input by pressing the [i]Enter[/i] key.[/size][/td][/tr][tr][td][size=100]2.[/size][/td][td][center][size=100][b]B1[/b][/size][/center][/td][td][size=100]Enter the coordinates [code](-2, 2) [/code]into cell [b]B1[/b].[br][u]Note[/u]: The point [i]B1 = (-2, 2)[/i] is automatically shown in the [i]Graphics View[/i].[/size][/td][/tr][tr][td][size=100]3.[br][/size][/td][td][size=100][icon]/images/ggb/toolbar/mode_move.png[/icon][br][/size][/td][td][size=100]Select the [i]Move[/i] tool and drag point [i]B1[/i] in the [i]Graphics View[/i]. [br][u]Note[/u]: The [i]Spreadsheet View [/i]shows the current position of point [i]B1 [/i]in cell [b]B1[/b][i][/i].[br][/size][/td][/tr][tr][td][size=100]4.[br][/size][/td][td][size=100][icon]/images/ggb/toolbar/mode_delete.png[/icon][br][/size][/td][td][size=100]Delete the content of cell [b]B1[/b].[/size][/td][/tr][/table]
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Cell references
[size=100]You may refer to another cell by using its name in your new input.[br][u]Note[/u]: If the content of this cell is modified, the new input adapts automatically.[br][/size][size=100][br][b]Task 2[/b][br][/size][table][tr][td][size=100]1.[/size][/td][td][size=100][b]A1[/b][/size][/td][td][size=100]Change the number in cell [b]A1[/b] to [code]1.5[/code] and confirm your input.[/size][/td][/tr][tr][td][size=100]2.[/size][/td][td][center][size=100][b]B1[/b][/size][/center][/td][td][size=100]Enter the formula [code]= 2 * [/code]into cell [b]B1[/b] and then select cell [b]A1[/b] in order to insert its name into the formula. Confirm your input.[br][u]Note[/u]: GeoGebra calculates [i]2 * 1.5[/i] and displays the solution [i]3[/i] in cell [b]B1[/b].[br][/size][/td][/tr][tr][td][size=100]3.[br][/size][/td][td][b][size=100][/size][/b][center][size=100][b]A1[/b][br][/size][/center][/td][td][size=100]Change the content of cell [b]A1[/b] to [font=monospace]3[/font].[br][u]Note[/u]: The content of cell [b]B1[/b] automatically adapts to your changes.[/size][/td][/tr][/table][size=100][br][br][b]Task 3[/b][br][table][tr][td]1.[/td][td][b]C1[/b][/td][td]Enter the coordinates [code](A1, B1) [/code]into cell [b]C1[/b] and confirm your input.[br][u]Hint[/u]: Cell [b]C1[/b][i] now [/i]shows the coordinates [i](3, 6)[/i]. The corresponding Point [i]C1[/i] is automatically displayed in the [i]Graphics View[/i].[/td][/tr][tr][td]2.[/td][td][b]A1[/b][/td][td]Change the value of cell [b]A1[/b] to [code]2[/code].[br][u]Note[/u]: The coordinates in cell [b]C1[/b] and the corresponding point automatically adapt to your changes.[/td][/tr][/table][/size]

How to use the Probability Calculator

What is the Probability Calculator?
[size=100]The [i]Probability Calculator[/i] allows you to graph and explore a variety of probability distributions. Just select your preferred distribution (e.g. Normal distribution, Binomial distribution) and customize it by adjusting the parameters.[br][br][/size][u]Note[/u]: Each distribution has specific parameters you need to adjust (e.g. Normal distribution with mean [math]\mu[/math] and standard deviation [math]\sigma[/math]).
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Features of the Probability Calculator
[table][tr][td][icon][/icon][/td][td]Calculate the probability P([i]a[/i] [math]\le [/math]X [math]\le[/math] [i]b[/i]) of a distribution.[u]Note[/u]: You may adjust the interval limits [i]a[/i] and [i]b[/i] by either replacing their values in the formula, or by dragging them in the graph.[br][/td][/tr][tr][td][icon][/icon][/td][td]Calculate the probability P(X[math] \le [/math][i]x[/i]) of a left sided distribution. [/td][/tr][tr][td][icon][/icon][/td][td]Calculate the probability P([i]x[/i][math] \le  [/math]X)  of a right sided distribution. [/td][/tr][tr][td][icon][/icon][/td][td]Toggle between the graphs of the [i]probability density function[/i] and the [i]cumulative distribution function[/i].[/td][/tr][/table]

What is GeoGebra Exam?

[img][/img] GeoGebra Exam allows you and your students to use the power of GeoGebra during exams on paper (i.e. like a graphing calculator or pocket calculator) while restricting their access to the Internet or other software that should not be used during the exam.[br][br][img][/img] GeoGebra Exam...[br][list][*]... can easily be accessed at [url=][/url][/*][*]... runs in your browser, so no additional installations are required.[/*][*]... can be customized in case your students should not have access to the full power of GeoGebra (e.g. deactivate the GeoGebra CAS)[/*][*]... runs in full screen mode allowing no space for other information to be displayed on screen.[br][/*][*]... doesn't allow access to the Internet, the GeoGebra Materials platform, or files saved on the computer.[/*][/list]
GeoGebra Exam activated
GeoGebra Exam Alert
Leaving the [img][/img] GeoGebra Exam window triggers a visual alert that is easily detectable and recorded in the Exam Log.