CREST Mathematics Olympiad Class 10 Sample Paper

Q.1

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.2

Two vertices of a triangle are (5, -1) and (-2, 3). If the orthocentre of the triangle is the origin, find the third vertex.

Q.3

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

Q.4

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

Q.5

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.6

Which term is numerically greatest term in the expansion of (3 + 2x)⁴⁹, when x = 1/5?

Q.7

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.8

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

Q.9

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

Q.10

The volume of the vessel, in the form of a right circular cylinder, is 448π cm³ and its height is 7 cm. What is the radius of its base?