﻿ Free Maths Olympiad (CMO) Sample Paper for Class 10 (PDF)

# CREST Mathematics Olympiad Class 10 Sample Paper

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## 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 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.2 Write the general term in the expansion of (x2 -y)6:
 Q.3 If the coefficients of rth term and (r + 1)th term in the expansion of (1 + x)20 are in the ratio 1:2, what is the value of r?
 Q.4 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.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 Simplify the following expression:[(a - b)3 - (a + b)3 ]/2 + a(a2 + 3b2)
 Q.7 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.8 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.9 A certain strain of virus occurs three times every 25 minutes. In how much time will it become 729 times its initial value?
 Q.10 Perpendiculars are drawn from the vertex of the obtuse angles of a rhombus to its sides. The length of each perpendicular is equal to a unit. The distance between their feet is equal to b units. Find the area of the rhombus.