CREST Mathematics Olympiad Class 10 Sample Paper

Q.1

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

Q.2

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

Q.3

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.4

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.5

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.6

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.7

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.8

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

Q.9

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.10

A certain strain of virus occurs three times every 25 minutes. In how much time will it become 729 times its initial value?