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

Write the general term in the expansion of (x² -y)⁶:

Q.3

In ∆ABC, ∠B = 90⁰. P, Q and R are the midpoints of AB, BC and AC, respectively. Which of the following options can be the vertices of a cyclic quadrilateral?

Q.4

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

Q.5

In the adjoining figure, the bottom of the glass has a hemispherical raised portion. If the glass is filled with orange juice, then find the quantity of juice which a person will get:

Q.6

W borrowed a certain sum of money from X at the rate of 10% per annum under simple interest and lent one-fourth of the amount to Y at 8% per annum under simple interest and the remaining amount to Z at 15% per annum under simple interest. If at the end of 15 years, W made a profit of $5850 in the deal, then find the sum that W had lent to Z.

Q.7

How many 5-digit odd numbers can be formed using the digits 2, 3, 5, 7, 8, and 9 if every digit can occur at most once in any number?

Q.8

If p₁ and p₂ are two odd prime numbers such that p₁ > p₂, then p₁² - p₂² is:

Q.9

For an acute angle θ, sin θ + cos θ takes the greatest value when θ is:

Q.10

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