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

What is the value of the expression [(a - b)³ + (b - c)³ + (c - a)³] / [(a - b)(b - c)(c-a)]?

Q.3

If the sum of the roots of the equation ax² + bx + c = 0 is equal to the sum of their squares, then which one of the following is correct?

Q.4

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

Q.5

The average weight of A, B and C is 84 kg. If D joins the group, the average weight of the group becomes 80 kg. If another man E who weighs 3 kg more than D replaces A, then the average of B, C, D and E becomes 79 kg. What is the weight of A ?

Q.6

The shadow of a pole standing on a horizontal plane is d metre longer when the Sun's altitude is α than when it is β. What is the height of the pole?

Q.7

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.8

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.9

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.10

A three-digit number was chosen at random. Find the probability that its hundred's digit, ten's digit and unit's digit are consecutive integers in descending order.