Practice Questions - Arithmetic Progression

GeoGebra Tutorial - 2 Points and Lines

Let us Start : Perform the following actions 

• Go to Options , select Font Size and choose 18 points 
• Go to Options , select Point Capturing and then select Fixed On Grid.
• Finally to select labeling of points , go to Options select Labelling then select New Points Only. 
• Go to View , select Grid. 

• Click on the point button and place a point at (3,2) using the left click on your mouse.
• Click back on the arrow (Move Button) and then drag your point around. Notice the coordinates change on the point itself and in the Algebra window.
•   Click in the Input Field and type (-2,-4) and press Enter.
• Click on the Line through two points button  and then click on the two points on the screen to construct a line through these two points.
• Click on the arrow ( move button )   and


•   click any where on the line and drag the line. You can see the equation of line changes in algebra window.
• Click on any of the two points and drag the line. You will get the same result.
• Save your file in a folder. GeoGebra by default assigns .ggb extension to files.
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GeoGebra Tutorial - I Introduction

Introduction 

GeoGebra is a dynamic mathematics software that joins geometry , algebra and calculus. GeoGebra is an interactive geometry system. You can do constructions with points , vectors , segments , lines and conic sections as well as functions while changing them dynamically afterwards. At the same time equations and coordinates can be entered directly. Thus GeoGebra has the ability to deal with variables for numbers , vectors and points.

GeoGebra User Interface

Input Field  : Here you can enter the equation for a graph , coordinates of a point or one of GeoGebra’s commands. A list of commands is viewable by clicking on the ‘ Command’ drop down menu near the Input Field.

Geometry Window: This is the window where a graphical representation of your input (graphs, points , lines etc) is displayed.

Algebra Window : This window is on the LHS of the Geometry Window. Every geometrical object will have an algebraic representation in this window. You can open and close the Algebra Window using the View Menu.

Toolbar : This consists of a row of buttons. Which ever button you have selected to use will have a blue border. Each button has a drop down arrow at the bottom right of the button. This drop down arrow reveals more buttons. The active buttons will display some brief instructions on how the button works.

Tangram - I

The tangram ("seven boards of skill") is a dissection puzzle consists of seven flat shapes, called tans, which are put together to form other shapes. The objective of the puzzle is to form a specific shape (given only an outline) using all seven pieces, which may not overlap. It was originally invented in China at some unknown point in history, and then carried over to Europe by trading ships in the early 19th century. It became very popular in Europe for a time then, and then again during World War I. It is one of the most popular dissection puzzles in the world. 

Shapes 

Choosing a unit of measurement so that the seven shapes can be assembled to form a square of side one unit and having area one square unit, the seven shapes are: 

•  2 large right triangles (Shape 1 and 2) 
•  1 medium right triangle (Shape 3) 
•  2 small right triangle (Shape 4 and 6) 
•  1 square (Shape 5) 
•  1 parallelogram (Shape 7)

 Of these seven shapes, the parallelogram is unique in that it has no reflection symmetry but only rotational symmetry, and so its mirror image can be obtained only by flipping it over. Thus, it is the only shape that may need to be flipped when forming certain shapes. This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

Practice Sheet - Quadratic Equations