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 [(x - a)/(b + c)] + [(x - b)/(c + a)] + [(x - c)/(a + b)] = 3, then find the value of x:
Q.2
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.3
Find the quadratic equation whose roots are reciprocal of the roots of the equation 3x2 - 20x + 17 = 0.
Q.4
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.5
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.6
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.7
Which term is numerically greatest term in the expansion of (3 + 2x)49, when x = 1/5?
Q.8
The houses of a row are numbered consecutively from 1 to 49. If there is a value of x such that the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it. Find the value of x.
Q.9
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.10
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?
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Answers to Sample Questions from CREST Olympiads:
Q.1
b
Q.2
c
Q.3
a
Q.4
b
Q.5
b
Q.6
a
Q.7
c
Q.8
d
Q.9
c
Q.10
b
Answers to Sample Questions from CREST Olympiads:
Q.1 : b | Q.2 : c | Q.3 : a | Q.4 : b | Q.5 : b | Q.6 : a | Q.7 : c | Q.8 : d | Q.9 : c | Q.10 : b
