CREST Mathematics Olympiad Class 10 Sample Paper

Q.1

If 1/(a + b), 1/(b + c), and 1/(c + a) are in AP, then which of the following is true?

Q.2

Solve and find the roots of the equation:
2(x² - 6) = 3(x - 4)

Q.3

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

Q.4

The angles of elevation of the top of a tower from two points at distances m and n metres are complementary. If the two points and the base of the tower are on the same straight line, then what will be the height of the tower?

Q.5

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.6

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.7

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

Q.8

The volume of a pyramid whose base is an equilateral triangle is 12 cm³. If the height of the pyramid is 3√3 cm, then find the length of each side of the base:

Q.9

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

Q.10

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.