CREST Mathematics Olympiad Class 10 Sample Paper

Q.1

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.2

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.3

Two regular polygons are such that the ratio between their number of sides is 1:2 and the ratio of measures of their interior angles is 3:4. Find the number of sides of each polygon.

Q.4

If the first, second and last terms of an AP are a, b and c, respectively, then the sum is:

Q.5

If 3y + 4x = 1, y = x + 5 and 5y + bx = 3 are concurrent, find the value of 'b'.

Q.6

A three-digit number was chosen at random. Find the probability that its hundred's digit, ten's digit and unit's digit are consecutive integers in descending order.

Q.7

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

Q.8

If cos x / (1 + cosec x) + cos x / (cosec x - 1) = 2, then which one of the following is one of the values of x?

Q.9

The shadow of a pole standing on a horizontal plane is d metre longer when the Sun's altitude is α than when it is β. What is the height of the pole?

Q.10

f(x) = x⁴ - 2x³ + 3x² - ax + b is a polynomial such that when it is divided by (x - 1) and (x + 1), the remainders are 5 and 19, respectively. Determine the remainder when f(x) is divided by (x - 2).