online user counter

MATHMAA

# KVS Sample Papers

KVS Sample Papers has KVS  math olympiad sample papers with answers which help the students who appear for KVS Junior Mathematical Olympiad .

Here are the questions and solutions .

Sample paper 1 :

Time: 3hrs                                                             M.M:100

Each question carry 10 marks.

1Q)  If a, b , c are measures which form a triangle for all n=2,3,4...etc, Prove  that $$\sqrt[n]{a}, \sqrt[n]{b}, \sqrt[n]{c}$$
also form a triangle .

2Q) A square sheet of paper PQRS is so folded that the point Q fall on the mid point M of RS. Prove that the crease will divide BC in the ratio 5:3 .

3Q) Prove that in any triangle ABC, if one angle is $$120^{\circ}$$, the triangle formed by the feet of the angle bisectors is a right  angled.

4Q) a) Find all the integers which are equal to 11 times the sum of their digits.

KVS Sample Papers

b) Prove that $$3a^{4}-4a^{3}b+b^{4} \geq 0$$, for all real numbers a and b.

5Q) In triangle ABC, the area is $$\frac{1}{2}bc sq.units$$. AD is a median to BC. Prove that $$\angle ABC = \frac{1}{2}\angle ADC$$.

6Q) Solve the inequality, |x-1|+|x+1| < 4.

7Q) Prove that, if the coefficients of the quadratic equation $$ax^{2}+bx+c =0$$ are odd integers, then the roots of the equation cannot be rational numbers .

8Q) Given real numbers x, y, and z such that x+y+z=3, $$x^{2}+y^{2}+z^{2}=5 , x^{3}+y^{3}+z^{3}=7$$ . Find the value of $$x^{4}+y^{4}+z^{4}$$.

9Q) If x and y are positive numbers such that x+y=1, find the maximum value of $$x^{4}y+xy^{4}$$.