﻿ Maths Olympiad (CMO) Sample Paper & Questions for Class 10

# CREST Mathematics Olympiad Class 10 Sample Paper

Sample PDF of CREST Mathematics Olympiad for Class 10:

## Syllabus:

Section 1: Real Numbers, Polynomials, Pair of Linear Equations in Two Variables, Quadratic Equations, Arithmetic Progressions, Triangles, Coordinate Geometry, Introduction to Trigonometry, Some Applications of Trigonometry, Circles, Constructions, Areas Related to Circles, Surface Areas and Volumes, Statistics, Probability.

Achievers Section: Higher Order Thinking Questions - Syllabus as per Section 1

 Q.1 If the first, second and last terms of an AP are a, b and c, respectively, then the sum is:
 Q.2 Find the values of a and b for which 3x3 - ax2 - 74x + b is a multiple of x2 + 2x - 24.
 Q.3 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.
 Q.4 For an acute angle θ, sin θ + cos θ takes the greatest value when θ is:
 Q.5 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.6 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.7 Which among the following is a singleton set?
 Q.8 A square is drawn by joining midpoints of the sides of a square. Another square is drawn inside the second square in the same way and the process is continued indefinitely. If, the side of the first square is 16 cm, then what is the sum of the areas of all the squares?
 Q.9 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.10 The arithmetic mean of the squares of the first n natural number is: