 # CREST Mathematics Olympiad Class 10 Sample Papers

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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 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 The arithmetic mean of the squares of the first n natural number is:
 Q.3 If sin A = √3/2 and A is an acute angle, then find the value of (tanA - cot A)/(√3 + cosec A):
 Q.4 Write the general term in the expansion of (x2 -y)6:
 Q.5 If p1 and p2 are two odd prime numbers such that p1 > p2, then p12 - p22 is:
 Q.6 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 of the corresponding sides of the flower bed. Find the ratio of the area of the path to the flower bed:
 Q.7 A three digits 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.8 Two regular polygons are such that the ratio between their number of sides is 1:2 and the ratio of measures of their interior angles is 3:4. Find the number of sides of each polygon:
 Q.9 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:
 Q.10 Kiran and Pavan 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:

Sample PDF of CREST Mathematics Olympiad for Class 10: