The Class 10 Maths Olympiad Sample Paper is a great tool for students to practise advanced concepts, improve accuracy, and get familiar with the Olympiad format.
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
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.2
If tan A = 1/2 and tan B = 1/3, then which of the following is true?
Q.3
If the first, second and last terms of an AP are a, b and c, respectively, then the sum is:
Q.4
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.5
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.6
How many 5-digit odd numbers can be formed using the digits 2, 3, 5, 7, 8, and 9 if every digit can occur at most once in any number?
Q.7
f(x) = x4 - 2x3 + 3x2 - ax + b is a polynomial such that when it is divided by (x - 1) and (x + 1), the remainders are 5 and 19, respectively. Determine the remainder when f(x) is divided by (x - 2).
Q.8
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.9
If p1 and p2 are two odd prime numbers such that p1 > p2, then p12 - p22 is:
Q.10
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:
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Answers to Sample Questions from CREST Olympiads:
Q.1
c
Q.2
a
Q.3
c
Q.4
d
Q.5
c
Q.6
d
Q.7
b
Q.8
c
Q.9
a
Q.10
b
Answers to Sample Questions from CREST Olympiads:
Q.1 : c | Q.2 : a | Q.3 : c | Q.4 : d | Q.5 : c | Q.6 : d | Q.7 : b | Q.8 : c | Q.9 : a | Q.10 : b
