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
In the given figure, PQRS is a square of side 7√2 cm. With P and R as centres and PQ as radius, the arcs QAS and QBS are drawn, respectively. Find the area of the shaded region (in cm2).
Q.3
A square is drawn by joining midpoints of the sides of a square. Another square is drawn inside the second square in the same way and the process is continued indefinitely. If, the side of the first square is 16 cm, then what is the sum of the areas of all the squares?
Q.4
Simplify the following expression: [(a - b)3 - (a + b)3 ]/2 + a(a2 + 3b2)
Q.5
In the binomial expansion of (a - b)n, n ≥ 5 the sum of the 5th and 6th terms is zero. Find the value of a/b.
Q.6
Find the quadratic equation whose roots are reciprocal of the roots of the equation 3x2 - 20x + 17 = 0.
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
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
If sin A = √3/2 and A is an acute angle, then find the value of (tanA - cot A)/(√3 + cosec A).
Q.10
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?
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Answers to Sample Questions from CREST Olympiads:
Q.1
b
Q.2
d
Q.3
b
Q.4
d
Q.5
b
Q.6
a
Q.7
a
Q.8
a
Q.9
b
Q.10
d
Answers to Sample Questions from CREST Olympiads:
Q.1 : b | Q.2 : d | Q.3 : b | Q.4 : d | Q.5 : b | Q.6 : a | Q.7 : a | Q.8 : a | Q.9 : b | Q.10 : d
