Mathematics Academy

GeoGebra Hindi Interface

noreply@blogger.com (Sanjay Gulati) — Fri, 15 Feb 2013 16:52:00 +0000

यह एक जावा एप्लेट है जिसे www.geogebra.org से जियोजेब्रा प्रयोग कर बनाया गया है।ऐसा लगता है कि आपके कंप्यूटर में जावा स्थापित नहीं है, कृपया www.java.com पर जायें।

Practice Sheet - Height and Distance

noreply@blogger.com (Sanjay Gulati) — Wed, 05 Dec 2012 01:59:00 +0000

GeoGebra Tutorial - 6 Triangle and Angles

noreply@blogger.com (Sanjay Gulati) — Fri, 09 Nov 2012 15:03:00 +0000

In this tutorial we will construct a triangle and measure its internal angles.

Click on File Menu and select New. (This will open a new GeoGebra window)
Click on the drop down arrow of the Line through Two Points and choose the Segment between Two Points button

Construct a triangle using Segment between Two Points button. You will see in the Algebra Window , the three segments (sides of triangle) are represented by their lengths.

To see which length corresponds to which side , click on the Move Tool (arrow) and hover the mouse over one of the sides to see the corresponding length light up.
Now to measure internal angles of the triangle , select the Angle Button and click once on vertices B , A and C in that order. This will give you measure of ∠BAC. (Make sure that you select the vertices in clockwise direction. Anti-clockwise selection will give you reflex angle.

Similarly, measure ∠CBA and ∠ACB.
Now, drag the vertices using Move Button (Arrow). If you drag enough, you will notice reflex angles appearing. To stop this, right click on an angle in Algebra or Geometry Window, and choose Object Properties.Under Basic Tab un-check the Allow Reflex Angle check box and close the Object Properties box.

Check your settings have been applied by dragging the vertices of your triangle.

GeoGebra Tutorial - 5 Translating Functions

noreply@blogger.com (Sanjay Gulati) — Mon, 05 Nov 2012 14:55:00 +0000

In this tutorial we will see how the equation of a function changes dynamically when we drag its graph.

Click on File Menu and select New. (This will open a new GeoGebra window)
Click in the Input Field and type f(x) = x³
Drag the curve around to see that its equation changes dynamically

After Translation

GeoGebra Tutorial - 4 Moving the Screen

noreply@blogger.com (Sanjay Gulati) — Wed, 31 Oct 2012 15:28:00 +0000

GeoGebra allows you to move our construction around into a better position. To do this we use the Move Drawing Pad button

Click on the Move Drawing Pad button and use the left mouse button to drag the screen around.
Click on the Move Button when moving drawing pad is complete.
Click on the Undo Button (arrow mark on the upper right corner) to move back to the last position. If you keep clicking, it will return to the original position.

Tip : Hold down the Ctrl key and use the left mouse button to move the screen around. This will save a few clicks.

GeoGebra Tutorial - 3 Editing Objects and Properties

noreply@blogger.com (Sanjay Gulati) — Sat, 27 Oct 2012 11:14:00 +0000

In continuation of GeoGebra Tutorial series let us see how we can edit objects and their properties.

Right clicking any object in the Algebra window or Geometry window will show the list of available editing options for that object.
If you double click on any object in Algebra window , GeoGebra will allow you to redefine that object. Double click on point A in the Algebra window and change coordinates to (2,3).
Right click on point A in the Algebra window to see the available options for that object.

Right click on any object in the Algebra or Geometry window and choose Object Properties.

With this dialog box you can change color , label , name , caption , thickness etc. for the selected object.

Practice Questions - Arithmetic Progression

noreply@blogger.com (Sanjay Gulati) — Fri, 26 Oct 2012 01:16:00 +0000

GeoGebra Tutorial - 2 Points and Lines

noreply@blogger.com (Sanjay Gulati) — Sat, 20 Oct 2012 14:46:00 +0000

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.

GeoGebra Tutorial - I Introduction

noreply@blogger.com (Sanjay Gulati) — Thu, 18 Oct 2012 15:50:00 +0000

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

noreply@blogger.com (Sanjay Gulati) — Sun, 14 Oct 2012 12:57:00 +0000

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

noreply@blogger.com (Sanjay Gulati) — Wed, 10 Oct 2012 15:26:00 +0000

NTSE Practice Sheet - Cubes and Cuboids

noreply@blogger.com (Sanjay Gulati) — Sun, 30 Sep 2012 02:31:00 +0000

NTSE Practice Questions - Classification of Numbers

noreply@blogger.com (Sanjay Gulati) — Thu, 20 Sep 2012 15:05:00 +0000

Direction : Choose the number which is different from others in the group.

a.579 b.885 c.696 d.398
a.3-27 b.4-64 c.7-353 d.6-216
a.124 b.235 c.789 d.510
a.5188 b.9238 c.8244 d.6311
a.9 b.3 c.19 d.15
a.7654 b.4567 c.9876 d.4321
a.1472 b.3848 c.2683 d.4210
a.83-75 b.58-50 c.49-32 d.25-17
a.325 b.207 c.711 d.23
a.1365 b.5713 c.3175 d.7531
a.212 b.343 c.757 d.511
a.95-82 b.69-45 c.55-42 d.48-34
a.14 b.36 c.28 d.21
a.5 b.11 c.7 d.9
a.67,19 b.71,11 c.41,19 d.61,15
a.3-5 b.5-3 c.6-2 d.7-3
a.49 b.85 c.12 d.81
a.49 b.97 c.98 d.77
a.6 b.18 c.7 d.3
a.48-134 b.40-110 c.18-48 d.30-80
a.22,4,5 b.34,4,8 c.37,4,9 d.54,4,13
a.9-3 b.½- 1/8 c.⅓ – ½ d.24-6
a.2731 b.1357 c.2571 d.2357
a.3642 b.4249 c.7586 d.1745
a.34 b.36 c.42 d.48
a. 8314 b. 2709 c.1315 d.2518
a. 51 b. 144 c. 64 d. 121
a. 2384 b. 1592 c. 3756 d. 3629
a. 325 b. 326 c. 178 d. 639
a. 372164 b. 376821 c. 318951 d. 319446

NTSE Practice Sheet - Number Series

noreply@blogger.com (Sanjay Gulati) — Tue, 18 Sep 2012 15:34:00 +0000

1.   1 , 3, 6, 10 , 15 ,……..
a) 21 b) 20 c) 18 d) 22
2.   2 , 5l 11 , 23 , 46 , ……
a) 94 b) 95 c) 90 d) 96
3.   2 , 5, 12 , 27 , ……
a) 54 b) 57 c) 56 d) 58
4.   2 , 5, 17 , 71 , ……
a) 360 b) 355 c) 357 d) 358
5.   2 , 6 , 12 , 20 , ……
a) 25 b) 24 c) 30 d) 28
6.   0 , 2 , 6 , 12 , ……
a) 20 b) 22 c) 25 d) 26
7.   2 , 10 , 30 , 64 , …….
a) 132 b) 135 c) 136 d) 130
8.   1 , 1, 2, 4, 3, 9, 4, 16, 5, …..
a) 6 b) 25 c) 20 d) 7
9.   4 , 0 , 8 , 6 , 24 , 24 , 96 , 60 , ……
a) 120 b) 360 c) 460 d) 125
10. 45 , 54 , 57 , 75 , 79 , ……
a) 81 b) 83 c) 97 d) 95
11. 4, 9, 19, 34, 54, ?, 109
a) 89 b) 84 c)74 d)79
12. 1, 6, 13, 22, 33, ?
(a) 44 (b) 45 (c)46 (d)47
13. 3, 15, 35, 63, 99, ?
(a) 144 (b)143 (c)121 (d)169
14. 3, 6, 15, ?, 123, 366
(a)34 (b)59 (c)42 (d)60
15. 80, 64, 48, 32, 16, ?
(a) 4 (b) 0 (c) 8 (d) 1
16. 1, 9, 17, 33, 49, 73, ?
(a) 97 (b) 98 (c) 99 (d) 100
17. 121, 225, 361, ?
(a) 441 (b) 484 (c) 529 (d) 729
18. 9, 81, 90, 810, 819, ?
(a) 7371 (b) 900 (c) 8100 (d) 1638
19. 5, 3, 6, 2, 7, 1, ?
(a) 0 (b) 2 (c) 4 (d) 8
20. 3, 12, 48, 192, ?
(a) 202 (b) 301 (c) 768 (d) 689
21. 2, 3, 5, 6, 7, 9, 10, 11, 13, ?
(a) 12 (b) 15 (c) 14 (d) 16
22. 4, 32, 128, ?
(a) 128 (b) 144 (c) 192 (d) 256
23. 2, 4, 8, 3, 9, 27, 4, 16, ?
(a) 64 (b) 32 (c) 48 (d) 24
24. 23,29,31,37,?,43
(a) 39 (b) 38 (c) 42 (d) 41
25. 5, 16, 49, 104, ?
(a) 117 (b) 148 (c) 170 (d) 181
26. 4,8,7,7,10,6,13,5,?
(a) 16 (b) 6 (c) 12 (d) 9
27. 1 , 5 , 21 , ? , 341
(a) 65 (b) 78 (c) 58 (d) 85

NTSE Practice Questions - Direction Sense

noreply@blogger.com (Sanjay Gulati) — Sun, 16 Sep 2012 16:00:00 +0000

Select the correct answer from among the four given choices.

Rahul was facing East. He walked 4 km forward and then after turning to his right walked 3 km. Again he turned to his right and walked 3 km. Again he turned to his right and walked 4 km. After this , he turned back. Which direction was he facing at that time? a) East b) West c) North d) South
While facing East you turn to your left and walk 10 yards, then turn to your left and walk 10 yards and now you turn 45° towards your right and go straight to cover 25 yards. Now , in which direction are you from starting point ? a) North-East b) South-West c) East d) North-West
A direction pole was situated on the crossing. Due to an accident the pole turned in such a manner that the pointer which was showing East , started showing South. One traveler went to the wrong direction thinking it to be West. In what direction actually he was trevelling ? a) South-West b) East c) West d) North
Ashok goes 30 metres North then turns right and walks 40 metres, then again turns right and walks 40 metres.. How many metres is he away from his original position? a) 0 m b) 10 m c) 20 m d) 40 m
Ajay starts walking straight towards East. After walking 75 m he turns towards left and walks 25 m straight. Again he turns to the left and walks a distance of 40 m straight. Again he turns to the left and walks a distance of 25 m. How far is he from this starting point ? a) 140 m b) 50 m c) 35 m d) 115 m
Rakesh walks 30 m towards East. Then he turns to his right and walks 20 m. Then again turning to his right , he walks 30 m. How far and in which direction is he from his original position. a) 20 m , North b) 20 m , South c) 50 m , West d) 80 m , West
One morning after sunrise , Sunil was standing facing a pole. The shadow of the pole fell exactly to his right , which direction was he facing ? a) East b) South c) West d) Data Inadequate
One morning after sunrise , Vikram and Shailesh were standing in a town with their backs towards each other. Vikram’s shadow fell exactly towards left hand side. Which direction was Shailesh facing ? a) East b) West c) North d) South
The town of Loni is located on Yellow Lake. The town of Siera is West of Loni. Ballar is East of Dogri but West of Takra and Siera. If they are all in the same district which town is the farthest West ?a) Loni b) Ballar c) Siera d) Dogri
If South-East is called East. North – West is called West. South – West is called South and so on, what will North be called ? a) East b) North-East c) North-West d) South
Lokesh’s school bus is facing North when it reaches his school. After starting from Lokesh’s house , it turns right twice and then left before reaching the school. What direction was the bus facing when it left the bus stop in from of Lokesh’s house ? a) North b) South c) East d) West
Suman is 40 m South-West of Ashok. Prakash is 40 m South-East of Ashok. Prakash is in which direction of Suman ? a) South b) West c) East d) North-East
If I stand on my head with my face pointing Southwards , in which direction will my right hand point ? a) West b) North c) East d) South-East
A watch reads 4.30. If the minute hand points East , In what direction will the hour hand point ? a) North b) North-West c) South-East d) North-East

Direction (15 – 18) :
i. Six flats on a floor in two rows facing North and South are allotted to P , Q , R , S , T and U.
ii. Q gets a North facing flat and is not next to S.
iii. S and U gets diagonally opposite flats.
v. R , next to U gets a South facing flat and T gets a North facing flat.

15. Which of the following combinations get South facing flats ?
a) QTS b) UPT c) URP d) Data inadequate

16. Whose flat is between Q and S ?
a) T b) U c) R d) P
17. If the flats of T and P are interchanged , whose flat will be next to that of U ?
a) P b) Q c) R d) T

18. The flats of which of the other pairs than SU is diagonally opposite to each other ?
a) QP b) QR c) PT d) TS

Direction (19 – 20) : The following questions are based on the diagram given below :

19. From the original position given in the above figure . A and B move one arm length clockwise and then cross over to the corners diagonally opposite : C and D move one
arm length anti-clockwise and cross over the corner diagonally opposite. The original
configuration ADBC has now changed to a) CBDA b) BDAC c) DACB d) ACBD

20. From the original position , B and D move one and half length of sides clockwise and anti-clockwise respectively. Which one of the following statement is true ?

a) B and D are both at the mid point between A and C

b) D is at the mid-point between A and C and B at the corner originally occupied by C.

c) B is at the mid-point between A and C, and D at the corner originally occupied by A

d) B and D are both at the midpoint between A and D.

Trigonometric Identities - III

noreply@blogger.com (Sanjay Gulati) — Sun, 09 Sep 2012 16:03:00 +0000

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

Trigonometric Identities - II

noreply@blogger.com (Sanjay Gulati) — Sat, 08 Sep 2012 15:44:00 +0000

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

Trigonometric Identities - I

noreply@blogger.com (Sanjay Gulati) — Fri, 07 Sep 2012 14:33:00 +0000

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 Questions - Solution of Triangles

noreply@blogger.com (Sanjay Gulati) — Thu, 06 Sep 2012 15:42:00 +0000

Practice Questions - Identities and Complementary Angles

noreply@blogger.com (Sanjay Gulati) — Mon, 03 Sep 2012 16:34:00 +0000

Practice Questions - Trigonometric Identities

noreply@blogger.com (Sanjay Gulati) — Sun, 02 Sep 2012 15:52:00 +0000

Practice Questions - Trigonometric Ratios - II

noreply@blogger.com (Sanjay Gulati) — Fri, 31 Aug 2012 23:44:00 +0000

Practice Questions - Trigonometric Ratios

noreply@blogger.com (Sanjay Gulati) — Fri, 31 Aug 2012 00:13:00 +0000

Sample Paper - Class IX - SA - I

noreply@blogger.com (Sanjay Gulati) — Wed, 29 Aug 2012 08:21:00 +0000

Sample Question Paper - Class X - SA - I

noreply@blogger.com (Sanjay Gulati) — Tue, 28 Aug 2012 00:08:00 +0000