CREST Mathematics Olympiad Class 10 Sample Paper

Q.1

A tower stands vertically on the ground. From a point on the ground which is 30 m away from the foot of a tower, the angle of elevation of the top of the tower is found to be 45⁰. Find the height of the tower.

Q.2

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

Q.3

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

Q.4

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.5

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

Q.6

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

Q.7

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.8

Ken and Paul can complete a job in 40 days and 50 days, respectively. They worked on alternative days to complete it. Find the minimum possible time in which they could have completed it.

Q.9

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.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.