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31st July 2014, 01:00 PM
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Re: International Mathematics Olympiad Exam question paper for 12th class

As you are looking for International Mathematics Olympiad Exam question paper for 12th class, so on youre demand here I am providing same
The “Golden Rectangle” of the ancient Greeks was considered to have the most pleasing proportion of
any rectangle. The ratio of width (w) to height (h) of the rectangle is expressed in the following proportion
and is shown in the drawing below.
=
-
2
5 1
w
h
w
h
Jason is planning to paint a rectangular mural using the proportions of the “Golden Rectangle.” If the
mural is 15 meters wide, how high should it be?
(A) 1.6 meters (B) 9.3 meters (C) 16.5 meters (D) 24.2 meters (E) None of these.
2. The given table shows the boiling points in degrees Celsius for
some different elements.
Which of the following elements have boiling points that are lower
than –190°C ?
(A) chlorine and oxygen (B) oxygen and nitrogen
Element
Chlorine
Helium
Hydrogen
Nitrogen
Oxygen – 183.0
– 195.8
– 252.9
– 269.0
– 34.6
BOILING POINTS OF SOME ELEMENTS
Boiling Point (in °C)
(C) chlorine, helium, and hydrogen
(D) helium, hydrogen, and nitrogen (E) None of these.
3. A certain radioactive element decays over time according to the equation æ ö = è ø
300 1 ,
2
t
y A where A = the
number of grams present initially and t = time in years. If 1000 grams were present initially, how many
grams will remain after 900 years?
(A) 500 grams (B) 250 grams (C) 125 grams (D) 62.5 grams (E) None of these.
4. Which is the first incorrect step in simplifying 4
4 log ?
64
Step 1: = - 4 4 4
4 log log 4 log 64
64
Step 2 : = 1 – 16 Step 3 : = – 15
(A) Step 1 (B) Step 2 (C) Step 3
(D) Each step is correct (E) None of these.
5. Which of the following sentence is true about the graphs of y = 3 (x – 5) 2 + 1 and y = 3 (x + 5) 2 + 1 ?
(A) Their vertices are maximum (B) The graphs have the same shape with different vertices
(C) The graphs have different shapes with different vertices
(D) One graph has a vertex that is a maximum, while the other graph has a vertex that is a minimum
(E) None of these.
6. If
r r r
, , a b c are vectors such that c a b = +
r r r and
r r . a b = 0 then
(A) a 2 + b 2 + c 2 = 0 (B) a 2 – b 2 = c 2
(C) a 2 + b 2 = c 2 (D) = ´
r r r
c a b (E) None of these.
7. In 1790, the United States had a population of approximately
4,000,000 people, as shown on the graph below.
According to the graph, in what year had the population grown to
approximately twice that number?
(A) 1797 (B) 1808 (C) 1813
25
20
15
10
5
1790 1800 1810 1820 1830 1840 1850
Number of people (in millions)
U.S. POPULATION
(D) 1822 (E) None of these.
MATHEMATICAL REASONING
8. Which expression represents f(g(x)) if f (x) = x 2 – 1 and g(x) = x + 3?
(A) x 3 + 3x 2 – x – 3 (B) x 2 + 6x + 8 (C) x 2 + x + 2 (D) x 2 + 8 (E) None of these.
9. From a deck of card two are drawn. The probability that both are of same suit is
(A) 1
2
(B) 1
13
(C) 4
17
(D) 2
17
(E) None of these.







For more paper here I am providing pdf


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