CREST Mathematics Olympiad Class 10 Sample Paper

Q.1

A tower stands vertically on the ground. From a point on the ground which is 30 m away from the foot of a tower, the angle of elevation of the top of the tower is found to be 45⁰. Find the height of the tower.

Q.2

If tan A = 1/2 and tan B = 1/3, then which of the following is true?

Q.3

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

Q.4

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).

Q.5

The houses of a row are numbered consecutively from 1 to 49. If there is a value of x such that the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it. Find the value of x.

Q.6

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

Q.7

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

Q.8

Ken and Paul can complete a job in 40 days and 50 days, respectively. They worked on alternative days to complete it. Find the minimum possible time in which they could have completed it.

Q.9

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

Q.10

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