## Wednesday, 1 May 2013

### Stuff for school kids (standard 5 to 10)

I thought of providing some stuff for students studying in the range 5th to 10th standard. This stuff is a combination of two sets. One is Math&Logic based and the other is Knowledge based. This stuff is a mix of some questions that are based on math fundamental concepts and remaining questions that are based on commonsensical and out-of-box thinking. These do not look like standard questions that are given in school-level exams but mostly resemble or can act as base for the math and logic aptitude sort of questions that are asked in various entrance exams. My primary intention is to inculcate in kids an interest and liking on maths. I strongly opine that math solving skills are very much needed to excel in diverse fields of studies ranging from Science, Engineering to Economics, Management studies etc.
To be frank on my part, I am starting this post with small number of questions at hand but I will try to enrich this bit bank by updating it from time to time.

Math and Logic Based Set:
1.      A number when used in denominator results in an 'undefined' value. What's that number?
2.      X is a number. If you add X to any other number you get the other number. If you subtract X from any other number, even then you get the other number. What is the number X?
3.      Y is a number. If you multiply Y with any other number you get the other number. If you divide any other number with Y, even then you get the other number. What is the number Y?
4.      It's a geometric figure and there is one point 'X' with in that figure. All points on that figure are equidistant from X. What is that geometric figure?What is the point X called?
5.      The one and only number which is even and prime is_____
6.   Which of the English alphabets are symmetric in shape when written in upper case? (If bisected vertically)
7.  Which of the English alphabets are symmetric in shape when written in upper case? (If bisected horizontally)
8.      How many two digit numbers having both identical digits are there?
9.    Consider a two digit number such that if you add it's two digits, you should get a sum of 9. How many such two digit numbers are possible?
10.  How many three digit numbers can be formed by using all the digits 0,1,2. Here repetition  of a digit in a number is not allowed.
11.  What are all the years in twenty first century that use all the four digits 0,1,2,3?
12.  What are all the years in twenty first century that are palindromes?
13.  Is 2013 a prime number?
14.  For a right triangle, if 24 and 25 are two sides then what is the other side?
15.  What is the square of 995?
16. Ram walked 6 m Eastwards and turned 90 degrees to his left and continued to walk for 8m and stopped there. At what distance and direction is the final point positioned with respect to the initial point if we join the two points by a straight line?
17.  Amar can do a work in 60 days and Akbar in 90 days. In how many days both of them can jointly do that work?
18.  Anthony started a journey by car to his home town which is 100 km away. He travels first 40 km at a speed of 40 kmph, next 40 km at a speed of 80 kmph and the remaining distance at a speed of 40 kmph. What is the average speed with which he travelled to reach the destination?
19. Given the radius of a circle is 5 cm, what is the distance between two points on the circle which are located exactly opposite to each other?
20.  “The radius of a circular path is 7 m. If I start at a point on the path and travel 88 m along the path, then I will reach the same point at which I have started”. Is this statement True/False?
21.  The statement “X/X = 1” does not work when X=____
22.  “Square root of 16 is 4”- is this sentence perfectly correct?
23.  “Square of 4 is 16”- is this sentence perfectly correct?
24.  If I say “A/B = C/D”, does it mean A=C and B=D?
25.  If I say “A*B = C*D”, does it mean either A=C or A=D?
26.  If XY = 0, then X must be___, irrespective of the value of Y.
27.  If XY = 1, then Y must be___, irrespective of the value of X.

Knowledge Based Set:
1.      That's an English word, which is an acronym representing all the four sides. What's it?
2.      We all remember him for his magic square. Who is that great Indian mathematician?
3.   The great Indian lady mathematician famously known for her quick calculations on large numbers (recently she has passed away)________
4.      The great Indian mathematician who invented Pujyam ('0') is ____
5.    “For a right angle triangle if 'a' is hypotenuse and 'b' and 'c' are sides then, a2=b2+c2” - whose theorem is this?
6.      “Any three points which are not collinear can form a triangle”. Is this statement True/False?
7.      “For any two points on a plane, if we join them by a straight line, it gives the shortest path”. Is this statement True/False?
8.      “In a right angle triangle, hypotenuse is the largest side”. Is this statement True/False?
9.    “In a right angle triangle, length of hypotenuse is the greater than sum of the lengths of other two sides”. Is this statement True/False?
10.  If the length and breadth of a rectangle are made equal, then it becomes a _____

Answers (Math & Logic Based Set):
1.      0
2.      0
Clue: X+0=0+X=X
3.      1
Clue: Y*1=1*Y=Y
4.      Circle, Centre of the circle
5.      2
6.  A,H,I,M,O,T,U,V,W,X (clue: If we bisect each of these letters vertically, the left and right portions appear as mirror images)
7.  D,E,H,I,K,O,X (clue: If we bisect each of these letters horizontally, the upper and lower portions appear as mirror images)
8.  9 (they are- 11,22,33,44,55,66,77,88,99)
9.  9 (they are- 18,81,27,72,36,63,45,54,90)
10. 4 (they are- 102,120,201,210)
11. 2013 and 2031
12. only one - 2002.
Notes:
Palindrome is a word or number with a unique property that when it is reversed, it yields the     same word or number
Clue: As it should belong to twenty first century we start with taking 20 as the first two digits.     To fulfill the condition of palindrome, the next two digits must be 0 and 2 respectively. Thus          2002 is the only palindrome in the twenty first century. Likewise, 2112 is the only palindrome        in the 22nd century.
13.  No
Notes: Try to factorize the number. 2013=11*183
14.  7
Notes: Let us try to use Pythagoras theorem. First let us find the squares of the given two           numbers. 25^2 = 625 and 24^2=576. Then let us check whether sum or difference of these two       squares is a perfect square.625+576 = 1201. We are not sure whether this is a perfect square or         not. So let us consider difference. 625-576=49=> this is square of 7 and hence 7 is the other   side. Here 25, which is biggest of the three sides is called hypotenuse.
15.  990025
short cut:
step-1:
consider the part of the number excepting the unit's digit 5 => 99
step-2:
multiply this with it's next number => 99*(99+1)=99*100=9900
step-3:
append 25 to the right side of 9900 => we get 990025
16.  10 m NE
17.  36
18.  50 kmph
19.  10 cm
20.  True
21.  0
22.  No. Square root of 16 is either +4 or -4
23.  Yes
24.  No
25.  No
26.  0
27.  0

1.      NEWS – North,East,West,South
2.      Srinivasa Ramanujam
3.      Shakuntala Devi
4.      Aryabhatta
5.      Pythagoras'
6.      True
7.      True
8.      True
9.      False
10.  Square