CREST Mathematics Olympiad Class 10 Sample Paper

Q.1

A bag contains 63 cards (numbered 1, 2, 3, ….., 63). Two cards are picked at random from the bag (one after another and without replacement). What is the probability that the sum of the numbers of both the cards drawn is even?

Q.2

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.3

The following steps are involved in finding a number, if the positive number is less than its square by 30. Arrange them in sequential order:
(A) x² - x - 30 = 0
(B) x = 6
(C) x² - x = 30
(D) (x + 5) (x - 6) = 0

Q.4

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

Q.5

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.6

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

Q.7

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

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 average mark obtained by the students in a class is 43. If the average marks obtained by 25 boys are 40 and the average marks obtained by the girl students are 48, then what is the number of girl students in the class?

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).