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
If the first, second and last terms of an AP are a, b and c, respectively, then the sum is:
Q.2
If 1/(a + b), 1/(b + c), and 1/(c + a) are in AP, then which of the following is true?
Q.3
Simplify the following expression: [(a - b)3 - (a + b)3 ]/2 + a(a2 + 3b2)
Q.4
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.5
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:
Q.6
If p1 and p2 are two odd prime numbers such that p1 > p2, then p12 - p22 is:
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
If cos x / (1 + cosec x) + cos x / (cosec x - 1) = 2, then which one of the following is one of the values of x?
Q.9
The average mark obtained by the students in a class is 43. If the average marks obtained by 25 boys are 40 and the average marks obtained by the girl students are 48, then what is the number of girl students in the class?
Q.10
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?
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Answers to Sample Questions from CREST Olympiads:
Q.1
c
Q.2
a
Q.3
d
Q.4
a
Q.5
b
Q.6
a
Q.7
b
Q.8
c
Q.9
a
Q.10
a
Answers to Sample Questions from CREST Olympiads:
Q.1 : c | Q.2 : a | Q.3 : d | Q.4 : a | Q.5 : b | Q.6 : a | Q.7 : b | Q.8 : c | Q.9 : a | Q.10 : a
