Std X
Geogebra
Q. 1 . Fill in the blanks : (1 mark each)
1) The
menu command used for hiding the axes is View->
Axes
2) The
tool used for the measurement of an interior angle is the angle tool.
3) Click
Edit -> Object Properties to
show and edit all the created objects.
4) Constructed
objects and graphs of functions are shown in the Graphics view.
5) An
angle bisector can be constructed by clicking the angle bisector tool , and three points of the angle in succession.
Q. 2. State whether the following statements are
true or False.
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1.
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Midpoint of a segment can be found without using the ‘ Mid Point or
Center’ tool or the Input Bar
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False
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2.
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When using the Graphics view , it is necessary coordinate axes.
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False
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3.
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Commands In Geogebra can be selected from the list next to the input
field on the Input Bar.
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True
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4.
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When a segment is drawn using the ‘Segment with given Length from the
point’ tool, moving the end-point moving the end-point of the segment changes
the length of the segment.
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True
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5.
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With the ‘ New Point ‘ tool selected, clicking at the intersection of
two objects adds a new point at the intersection.
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True
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6.
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GeoGebra can be used to Solve Simultaneous equations Geometrically.
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True
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7.
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The GeoGebra screen [window] is divided into three parts.(March 14)
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True
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8.
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By Default, the Geogebra window displays three parts – Algebra ,
Graphics and Spread sheet.
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False.
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9.
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The Command to draw Histogram [{List Of data } {List of Class
boundries}]
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True
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Q. 3
Multiple Choice Questions: ( Single Correct Answer) (1 mark each)
(1) Geogebra was created by Markus Hohenwarter
a) CDAC b) Google c) Markus
Hohenwarter d) Judith
Hohenwarter
(2) A file created in
Geogebra is saved with the .ggb extension.
a) .ggb b)
.gba c)
.ggr d)
.gbr
(3) A segment of
fixed length is drawn using the Segment with fixed length tool.
a) .segment between
two points b) . Segment with fixed length
c) .Vector from point
d) Fixed Segment
4) A histogram of a
data list is drawn by Typing the histogram
command in the Input bar.
(a) Selecting ‘Create Histogram’ command from the
right-click menu
(b) Selecting ‘Create List ‘ command from the right- click
menu
(c) Using the ‘Regular Polygon’ tool
(d) Typing the
histogram command in the Input bar
5) The Mode[] command
in GeoGebra must be supplied with data
list as parameter.
(a) Coordinates (b) histogram (c) data list (d) list of class boundaries
6) The input bar is used to input data required for
calculations and geometric constructions.(March ’14)
(a) Scroll bar (b) input
bar (c) output bar (d) menu bar
Q.4. Rewrite the
following statements by selecting two correct options : (2 marks each)
1) Every object in
GeoGebra has algebraic
and geometric representations
(a) algebraic (b) text (c) geometric (d) spreadsheet
2) In GeoGebra, you
can do different _______and ________ construction and processes easily with the
help of set of instructions.
(a) Geometric (b) geographic (c) biological (d) algebraic
3) Class boundaries
specified in the Histogram[] command determines ________ and ___________ of
each bar of the histogram.
(a) Height (b) width (c) position (d) shading
4) The Input bar in
GeoGebra has ________and _________.
(a) Settings button
(b) input field (c) Undo/ Redo
button (d) command button
5) Two tools in
GeoGebra to draw a circle of specific radius are Circle
with Centre and Radius and Circle with Centre through Point .
(a) Circle with
Centre and Radius (b) Circle with Centre through Point
(c) Compass (d) Circle through Three Points
6) Different
complicated theorems
and geometrical constructions
can be understood very clearly with the of GeoGebra .
(a) Questions (b) GK (c) theorems (d) geometrical
Q.5. Match the
following :(1 mark for each option)
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Column A
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Column B
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1. Regular Polygon
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(a)
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2. Midpoint or Centre
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(b)
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3. Angle with Given Size
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(c)
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4. Circle with Centre through Point
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(d)
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5. Angle Bisector
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(e)
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Ans. (1)-- b
(2) –d
(3)--e
(4) --a
(5) –c
Q.6 Answer the following questions : ( 2 marks each)
1) What are
the main parts of the GeoGebra window ? Give names of the different parts of
the GeoGebra window.
Ans. The different parts of the
GeoGebra window are (i) Title bar (ii) Menu bar (iii) Tool bar (iv) Algebra View (v) Graphic View and (vi) Input bar
2) Explain
Graphics View and Algebra View in GeoGebra.
Graphics View: Using the construction tools
available in the Toolbar you can do geometric constructions in the Graphics
View with the mouse. Select any construction tool from the Toolbar and read the
Toolbar Help (next to the Toolbar) in order to find out how to use the selected
tool. Any object you create in the Graphics View also has an algebraic
representation in the Algebra View.
Every icon in the Toolbar represents a toolbox that contains a
selection of similar construction tools. In order to open a toolbox, you need
to click on the small arrow in the lower right corner of the Toolbar icon.
Algebra view: In the Algebra View,
mathematical objects are organized as free and dependent objects. If you create
a new object without using any other existing objects, it is classified as a
free object. If your newly created object was created by using other existing
objects, it is classified as a dependent object.
Using the Input Bar you can directly enter algebraic
expressions in GeoGebra. After hitting the Enter key your algebraic
input appears in the Algebra View while its graphical
representation is automatically displayed in the Graphics View.
3) Draw the following
construction tools [ in GeoGebra] : (i) Polygon (ii) Angle.
4) Give the uses of the following tools in GeoGebra.
Q- 7) Answer the
following (4 marks each)
1)
What is GeoGebra OR Write short note on Geogebra
?
Ans. Geogebra is a free, open source and
multiplatform software that combines dynamic geometry , algebra, calculus,
spreadsheet, graphing and statistics.Geogebra is one easy – to use package. The name ,
GeoGebra is derived from Geometry and Algebra. GeoGebra was created by Markus Hohenwarter in
2001-02 as part of his Masters and PhD project in Mathematics. Students can
learn mathematics using computer with the help of software called ‘Geogebra’ . It was specially designed for middle school
and high school students and has won several prestigious awards. GeoGebra is
multi-faceted tool. It can be used as both teaching & a learning tool.
2)
What would you use to
type the equation for drawing graph in Geogebra.?
Ans In Geogrbra, a graph is drawn by typing its equation in the
input field of the Input bar and pressing the Enter key. The rules for the
algebraic input are as follows.
(1) Only x and y in
lower case can be used as variables.
(2) A linear equation
in two variables can be entered in standard form.
3. Give two methods to find mean, mode and
median of given data.
To find out mean
median and mode of a list of sample data, the list may be created in two ways
in Geogebra, namely, using input bar or the spreadsheet view.
Method 1 : In the input field of the input bar, type
the sample data as a comma delimited list with in braces (Curly brackets). It
may be named using lower or upper case letters. If no names are given, the
program names them as list1, list2 etc. The Algebra View displays the list and
its name under free objects.
Method 2: Enable the spreadsheet View from the View
menu. Enter the data in the first column or row. Select all data by dragging
the mouse and select Create List from the right- click context menu. The
algebra view displays the list and its name.(L1, L2, etc) under dependent
objects.
Suppose a list has been created with a name L1. To find the
mean, median and mode of the list, type each command with the list name
enclosed within square brackets in the input bar, Mean [L1],Median [L1],
Mode [L1] and press enter key. The algebra view displays the values under
dependent objects.
Q 5. Solve the following examples using GeoGebra.
5. Construct an equilateral triangle PQR and measure
its angles.
Ans. Steps for Solution :
(1) First we have to select view menu in that we have to click on axes
option for getting clear screen.
(2) For construction of an equilateral triangle, select ‘regular polygon’
tool .
(3) Create an equilateral triangle by selecting two base points. Then a window
will open to specify the number of sides, then type 3 and click on ‘OK’
(4) To measure the angle , click on angle tool from the construction tool
and select the points in counter clockwise.
6. Construct a regular polygon with 6 side . Use
‘polygon’ tool.
Ans. Steps for Solution :
(1) First we have to select view menu in that we have to click on axes
option for getting clear screen.
(2) For construction of an regular polygon, select ‘regular polygon’ tool .
(3) Select two base points A and B.
(4) Type the number of sides of the polygon (Enter ‘6’)
8. Draw angle with measurement 133o and
bisect it with ‘angle bisector’ tool.
Ans. Steps for Solution :
(1) First we have to select view menu in that we have to click on axes
option for getting clear screen.
(2) Select the ‘angle with given size’ . option and select two points on
the graphic section and enter the measurement of the angle (133o)
(3) Then the third point will be displayed. Then select segment between two
points and select the points in the order.
(4) Select the angle bisector and select the points in the order (A,B,A’)
10. Draw a circle with radius
3.1 cm and draw tangents to the circle from points 6.5 cm away from centre.
Ans. Steps for Solution :
(1) First we have to select view menu in that we have to click on axes
option for getting clear screen.
(2) For drawing circle with given radius we have taken ‘circle with centre
and radius ‘ tool.
(3) We have inputed given radius 3.1 cm in input window which was displayed
on screen and click on ‘OK’ option for getting circle.
(4) Select ‘segment with fixed length ‘ option from the tool and click on
the centre of the circle. Then the input box will appear to enter the length,
type 6.5 in the input box, a line will be drawn by joining the centres and the
point B which is 6.5 cm away from the centre.
(5) For construction of tangent , select ‘tangent tool’ after that click on
the point B which is 6.5 cm away from the centre and on circumference of circle
respectively. Tangent will be constructed at that point.
12. Plot the points A(4,-3) and B(-2,5) join them and find
equation of line and write the steps for solution.
Ans. Steps for Solution :
(1) Here we want axes for establishing given points . For that we have
selected ‘Axes’ and ‘Grid’ tool view menu.
(2) We have taken ‘New Point’ tool for plotting given points.
(3) For drawing line, click on ‘line through two points’ tool.
(4) Now the Algebra view shows the equation 4x+3y=7
