Preparations for IPM, MTSE, Olympiad, MAT, Scholarship,CBSE, ICSE & Board Math Exam

Friday, August 29, 2014

profit and loss

By selling an article for Rs 24 the profit percentage made is equal to the cost price of the article. Find the cost price of the article.

Answer: Rs 20.

remainder theorem

Without actually dividing prove that x⁴ + 2x³ – 2x² + 2x – 3 is exactly divisible by x² + 2x – 3

coordinate geometry

Show that the lines x = 0 and y = 0 trisect the line segment formed by joining the points (-10, -4) and (5,8). Find the point of trisection.

trigonometry

If A, B and C are interior angles of a triangle ABC, show Tan (A + B – C)/2 = cot C

circle

In the diagram given below, if AD = DC and AB = AC, then show that AP = 1/4 AB

Wednesday, August 27, 2014

15 Practice Questions for STD IX for IPM /IMO / MTSE with answers

15 Practice Questions for STD IX for IPM /IMO / MTSE with answers

15 Practice Questions for STD VIII for IPM /IMO / MTSE with answers

15 Practice Questions for STD VIII for IPM /IMO / MTSE with answers

geometry

ABCD is a square. With centre B and C and radius equal to the side of the square, circles are drawn to cut one another at E inside the square. What is the measure of angle BDE?

geometry

ABCD is a square. P is a point in the square such that triangle ABP is equilateral. What is the measure of angle PCB

Circle

A circle with radius 2 cm is placed against a right angle. Another small circle is placed in the gap between the circle and the right angle. What is the radius of the smaller circle?

Three friends returning from a movie, stopped to eat at a restaurant. After the dinner, they paid their bill and noticed a bowl of mints at the front counter. Shikha took 1/3^rd of the mints, but returned four because she had a momentary pang of guilt. Farah then took ¼ of what was remaining but returned three for similar reasons. Aditi then took half of the remaining but threw back two into the bowl. The bowl had only 17 mints left when the raid was over. How many mints were originally in the bowl?

counting

In a network of railways, a small island has 15 stations. Find the number of different tickets to be printed for each class, if every station must have tickets for the other station.

LCM and HCF

Three wheels can complete 60, 36 and 24 rpm respectively. There is a red spot on each wheel that touches the ground at time zero. After how much time, all these spots will simultaneously touch the ground again?

geometry STD X

P, Q, S and R are points on the circumference of a circle of radius "r". such that PQR is an equilateral triangle and PS is the diameter of the circle. What is the perimeter of the quadrilateral PQRS?

IMO STD XII paper

IMO test Papers - STD. XI

IMO test paper

IMO test Papers --- STD X

probability

In a multiple choice question, there are four alternatives, of which one or more are correct. A candidate will get marks in the question only if he ticks all the correct answers. If the candidate ticks the answers at random but is allowed upto three chances to answer the question, then the probability that he will get marks in the question is .......................

function

If f(x) = 1 – 1/x, then f(f(1/x)) = ....................

miscellaneous equation

If α and β are the complex cube roots of unity, and x = a + b, y = aα+ bβ and z = aβ + bα, then the value of xyz =.............................

IMO Test Papers --- STD IX

ICSE Mock test paper 2015

12 Practice Questions for STD VIII IPM, MTSE, IMO

IMO papers

I have received more papers of IMO. I will post them shortly.

Sample test paper for ICSE 2015

Sample test paper for ICSE 2015
(you may choose to check the answers in the respective labels)

15 practice papers for IPM, MTSE, IMO for STD VIII

15 practice papers for IPM, MTSE, IMO for STD VIII (you may choose to refer to the answers under the respective labels)

15 Practice questions for Std VII

15 Practice questions for Std VII (you may choose to refer to the answers under the respective labels)

Thank you

I want to thank all those parents and students who have sent me the question papers of IPM mega finals and IMO. Thanks a ton for finding some time out of your busy schedule to send these question papers. They are immensely helpful to me and as you will find, they will be immensely helpful to all those who are looking for it.

I look forward to similar help in the future. Happy blogging.

shubhro and Nanu

IMO Test Paper for STD VIII

IMO Test Papers for STD. VII

IMO test paper for STD V

15 Practice Questions for IPM/ MAT/ MTSE Exam for STD VIII (time 1 Hour)

15 Practice Questions for IPM/ MAT/ MTSE Exam for STD VIII (time 1 Hour)

Answers are there under respective labels

In most of the competitive exams on math, one has to choose the correct answer.

i think this whole idea of choosing the correct answer is counterproductive. It sets the student's mind on "work backwards" mode.

I have taken an example from the MAT 2014 question paper to elucidate my point.

Look at question 45. A nice question, which most students will find slightly difficult. But then the smarter ones will simply add the results given and check for the one that satisfy the data given. (answer is D: 117 + 143 = 260, satisfies the condition).
The entire question thereby gets reduced to whether you can add.
This defeats the purpose of the exam which is to check the understanding of the concepts in math. whereas what has been achieved is the measure of "survival instinct".
This is not an exam for a job.

In the Question 45, the examiner wanted to know:
a) whether the child has developed a good understanding of HCF and LCM
b) whether the child is able to mine the data given and translate the data into relevant information
c) to translate the data to information, does the child have the mental alertness and understanding to juggle and manipulate the data suitably, which is an absolute requirement for students who want to excel in higher maths.

The " choose the correct answer" misses all of this by a mile.

Rather then learning the trade the child is exposed to the tricks of the trade.

If you feel as strongly as I do about this issue do send in your comments. This will help us to

collectively pursue with the authorities.

shubhro

Monday, August 18, 2014

15 questions for STD VII ---- IPM, MTSE, and IMO, MAT

15 questions for STD VII ---- IPM, MTSE, and IMO, MAT

((you may choose to refer to the answers under the respective labels))

15 questions for STD IX --- IPM, MTSE, IMO

15 questions for STD IX --- IPM, MTSE, IMO

(all the questions are solved, look for answers under the respective labels)

IMO test paper for STD IV

IMO test papers for STD. III

IMO test paper for STD II

IMO test paper for STD I

numbers

Pages of a magazine are numbered starting from 1. Jack was asked to add up the page numbers, but he included one page twice and got a sum of 130. What was the page number that was included twice?

IPM mega finals 2014 STD VI

polynomials

if f(x) is a polynomial satisying P( x + 3/2) = P (x), for all real values of x. If P(5) = 2002, then find the Value of P(8)

time and work

A tank can be filled by one tap in 20 mins and by another tap in 25 mins.Both the taps are kept open for 5 mins and then the second tap is turned off. In how many minutes more is the tank completely filled?

LCM and HCF

On Ashok Marg three consecutive traffic change after 36,42 and 72 secs respectively. If the lights are first switched on at 9:00 A.M. sharp, at what time will they change simultaneously?

IMO STD IX

mensuration,

A circular swimming pool is surrounded by a concrete walk 4m wide. If the area of the walk is 11/25 of that of the pool, then the radius of the pool is ..................................

rationalization

If, x = 9 + 4√5 and xy = 1 then the value of 1/x² + 1/y² = ................................

circle

The ratio of area of a square inscribed in a semicircle to the area of a square inscribed in a quadrant of the same circle is.......................................

IMO STD X

MAT Question Paper STD V and STD VI - 2014

division and numbers

If the number 5a8b7c is completely divisible by 66 and if b + c = 11 and a + b = 14, then find the value of (a – b).

47^th question of MAT 2014 STD V and STD VI

Answer:

The sum of the numbers = 5 + 8 + 7 + a + b + c = 20 + a + b + c ------------------------- (1)

Substituting (a + b) = 14 in equation 1 we get

The sum of the numbers = 20 + 14 + c = 34 + c

Now since the number is completely divisible by 66, it must be divisible by 2, 3 and 11.

If the number is divisible by 2 then “c” has to be an even number or 0.

Also, since the number is divisible by 3, hence sum of numbers must be divisible by 3

c	Sum of the numbers = 34 + c	Selection
0	34	3 + 4 = 7 => not divisible by 3
2	36	3 + 6 = 9 => divisible by 3
4	38	3 + 8 = 11 => not divisible by 3
6	40	4 + 0 = 4 => not divisible by 3
8	42	4 + 2 = 6 => divisible by 3

Therefore, c can have only 2 possible values of 2 and 8 to satisfy the divisibility test of 2 and 3.

Now we have to check the divisibility test of 11.

i.e. the sum of the numbers in the even place – the sum of the numbers in the odd place should be a multiple of 11.

Now, sum of the numbers in the even place = 7 + 8 + 5 = 20

Sum of the numbers in the odd place = a + b + c = 14 + c

c	Sum of the numbers in even place - sum of number in odd place = absolute { 20 – (14 + c) }	Selection
2	4	=> not multiple of 11
8	2	=> not multiple of 11

So, I think no answer is possible with the given set of conditions.

HCF and LCM ----MAT 2014

question number 45 of MAT

The HCF of two numbers is “x” and the sum of the uncommon factors is 20 and the product of the uncommon factors is 99. If the sum of the two numbers is 260, then thee two possible numbers are......................................

STD V / STD VI MAT Guess paper

A few MAT guess question

A number m is divided by 5 and added to 8. The result is equal to 3m subtracted from 4. Find the value of m.
1100 boys and 700 girls sit for an exam. 42% of the boys and 30% of the girls pass. The percentage of the total who failed is .....................
The value of 2^-4 + 2^-5 + 2^-6 =.........
If the angles of a triangle are in the ratio of 4:5:6, then the largest angle measures.............
The length and the breadth of a park are in the ratio of 5:4. If the length were 10% more and the breadth were 10% less, then the area would have decreased by 1620 m2. Find the original length of the park.
30 men and 20 women attend a convocation. What was the ratio of the women to the total number of persons at the convocation?
one cup of milk has the same amount of Calcium as 16 oranges. 2 oranges have the same amount of Calcium as 4 eggs. how many eggs have the same amount of Calcium a one cup of milk?
In a polygon, the sum of all exterior angles is ..................
Find the value of 42 x 8 ÷ ½ + ²/₃
Nanu's age in 20 years will be 4 less than 3 times her age now. What is the age of Nanu?
Sonar is a device used to measure the time taken by sound waves from a ship to reach the bottom of the ocean and then back to the ship. The speed of sound in water is 1.5 km/ sec. If the ship has a sonar sounding of 6 secs, what is the approximate depth of the ocean floor blow the ship?
When nanu purchased 6 kg of rice, she was short by Rs 6. When she purchased 8 kg of same rice, she was short by Rs 14. how much money did nanu have?
A Tank can hold 32 litres. It is 4/5 full of oil. One quarter of the oil is transferred to a vat. How much oil is left in the tank?
Represent in decimal system: 8 + 2²³/₂₅ + ⁸/₁₀₀₀
_{The difference in the area of a large square and the area of a small square is 56 cm2. If the area of the smaller square is 25 cm2, then find the perimeter of the larger square.}
A number when rounded of to its nearest hundred and its nearest thousand is 235000. Then the smallest possible value of such a number is?
Represent in number: eight million 24 thousand, four hundred and eighty six.
Nanu saves Rs 20 of her pocket money every day. Her father saves Rs 500 per day. If both of them save their money for 20 days, then what is the difference in their saving?