CREST Mathematics Olympiad Class 10 Sample Paper

Q.1

Simplify the following expression:
[(a - b)³ - (a + b)³ ]/2 + a(a² + 3b²) 

Q.2

If sin A = √3/2 and A is an acute angle, then find the value of (tanA - cot A)/(√3 + cosec A).

Q.3

Inside a triangular park, there is a flower bed forming a similar triangle. Around the flower bed runs a uniform path of such a width that the sides of the park are exactly double the corresponding sides of the flower bed. Find the ratio of the area of the path to the flower bed.

Q.4

Find the value of x + y in the solution of the equations x/4 + y/3 = 5/12 and x/2 + y = 1:

Q.5

If the coefficients of r^th term and (r + 1)^th term in the expansion of (1 + x)²⁰ are in the ratio 1:2, what is the value of r?

Q.6

If [(x - a)/(b + c)] + [(x - b)/(c + a)] + [(x - c)/(a + b)] = 3, then find the value of x:

Q.7

The areas of two similar triangles are 81 cm² and 49 cm², respectively, then what will be the ratio of their corresponding medians?

Q.8

The arithmetic mean of the squares of the first n natural number is:

Q.9

If α, β are the roots of the equation x² - 2x + 3 = 0, then find the equation whose roots are 1/α² and 1/β².

Q.10

The volume of a pyramid whose base is an equilateral triangle is 12 cm³. If the height of the pyramid is 3√3 cm, then find the length of each side of the base: