CREST Mathematics Olympiad Class 10 Sample Paper

Q.1

If the first, second and last terms of an AP are a, b and c, respectively, then the sum is:

Q.2

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.3

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?

Q.4

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.5

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.6

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

Q.7

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.8

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

Q.9

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.10

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.