CREST Mathematics Olympiad Class 10 Sample Paper

Q.1

In the adjoining figure, the bottom of the glass has a hemispherical raised portion. If the glass is filled with orange juice, then find the quantity of juice which a person will get:

Q.2

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

Q.3

The arithmetic mean of the squares of the first n natural number is:

Q.4

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.5

Find the values of a and b for which 3x³ - ax² - 74x + b is a multiple of x² + 2x - 24.

Q.6

In ∆ABC, ∠B = 90⁰. P, Q and R are the midpoints of AB, BC and AC, respectively. Which of the following options can be the vertices of a cyclic quadrilateral?

Q.7

If α, β are the roots of the equation x² - 2x + 3 = 0, then find the equation whose roots are 1/α² and 1/β².

Q.8

If tan A = 1/2 and tan B = 1/3, then which of the following is true?

Q.9

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.10

Two vertices of a triangle are (5, -1) and (-2, 3). If the orthocentre of the triangle is the origin, find the third vertex.