Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 2009-03-10 03:53:14

ganesh
Moderator
Registered: 2005-06-28
Posts: 14,437

Question Bank : Age Group 14-15 : XI

1. Find the equation of the straight line joining the point of intersection of 3x - y + 9 = 0 and
2y + x - 4 = 0 to the point of intersection of 2x + y = 4 and 2y = x + 3.

2. The vertices of a triangle ABC are A (-3, 3), B (-1, -4), and C (5, -2). M and N are the midpoints of AB and AC. Show that MN is parallel to BC and

.

3. Find the equation of the line parallel to the Y axis and passing through the point of intersection of 3x - 4y - 9 = 0 and x - 4y - 2 = 0.

4. Find the orthocenter of the triangle whose vertices are (-2, 1), (-1, -4), and (0, -5).

5. Prove that the line segments joining the mid points of the adjacent sides of a rhombus form a rectangle.

6. ABCD is a trapezium with AB || CD. The diagonals AC and BD intersect at E. If
Δ AED ||| Δ BEC, prove that AD = BC.

7. Two circles intersect each other internally at P. If ACP and BDP are the lines meeting the two circles at A, B and C, D respectively, prove that

.

8. Show that

.

9. If A = 30°, and B = 60°, verify that
(i) sin(A + B) = sin A cos B + cos A sin B
(ii) cos(A + B) = cos A cos B - sinA sin B.

10. From the top of a building 60 meters high, the angle of depression of the top and bottom of a tower are observed to be 30° and 60° respectively. Find the height of the tower.


Character is who you are when no one is looking.

Offline

#2 2013-03-24 07:21:58

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,636

Re: Question Bank : Age Group 14-15 : XI

Hi;

4) The orthocenter is located at (-10,-7).

Last edited by bobbym (2013-03-24 08:00:48)


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

#3 2013-03-25 05:45:30

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,791
Website

Re: Question Bank : Age Group 14-15 : XI

What is the meaning of |||?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

Online

#4 2013-03-25 05:53:17

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,522

Re: Question Bank : Age Group 14-15 : XI

Maybe it is supposed to be a sign for congruence? dunno


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

Offline

#5 2013-03-25 05:58:15

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,791
Website

Re: Question Bank : Age Group 14-15 : XI

Then question 6 would be not a question at all.


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

Online

#6 2013-04-04 20:49:06

hammana
Member
Registered: 2012-03-02
Posts: 48

Re: Question Bank : Age Group 14-15 : XI

Hi Agnishom

Question 6 means probably that triangles AED and BEC are similar . We have to proof that: 

if EB/EA=EC/ED, then AD=BC.

EB/EA=EC/ED -->EB*ED=EA*EC --> A,B,C,D are concyclic --> AD=BC

Offline

#7 2013-04-04 23:56:52

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 16,791
Website

Re: Question Bank : Age Group 14-15 : XI

1. How does that make them concyclic?
2. How can you say that the opposite sides of a concyclic quadrilateral are equal?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

Online

Board footer

Powered by FluxBB