CREST Mathematics Olympiad Class 10 Sample Paper

Q.1

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.2

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.3

In the given figure, AB || DE and the area of the parallelogram ABFD is 24 cm². Find the areas of triangles AFB, AGB, and AEB.

Q.4

How many 5-digit odd numbers can be formed using the digits 2, 3, 5, 7, 8, and 9 if every digit can occur at most once in any number?

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

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

Q.7

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

Q.8

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.9

Find the quadratic equation whose roots are reciprocal of the roots of the equation 3x² - 20x + 17 = 0.

Q.10

30% of the items were sold at a profit of 40% while the remaining were sold at x% loss. If the overall loss is 10%, find the value of x.