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 tan A = 1/2 and tan B = 1/3, then which of the following is true?
Q.2
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.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
What is the value of the expression [(a - b)3 + (b - c)3 + (c - a)3] / [(a - b)(b - c)(c-a)]?
Q.5
Which term is numerically greatest term in the expansion of (3 + 2x)49, when x = 1/5?
Q.6
The volume of a pyramid whose base is an equilateral triangle is 12 cm3. If the height of the pyramid is 3√3 cm, then find the length of each side of the base:
Q.7
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.8
Solve and find the roots of the equation: 2(x2 - 6) = 3(x - 4)
Q.9
Find the values of a and b for which 3x3 - ax2 - 74x + b is a multiple of x2 + 2x - 24.
Q.10
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).
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Answers to Sample Questions from CREST Olympiads:
Q.1
a
Q.2
a
Q.3
b
Q.4
d
Q.5
c
Q.6
c
Q.7
a
Q.8
d
Q.9
a
Q.10
b
Answers to Sample Questions from CREST Olympiads:
Q.1 : a | Q.2 : a | Q.3 : b | Q.4 : d | Q.5 : c | Q.6 : c | Q.7 : a | Q.8 : d | Q.9 : a | Q.10 : b
