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
Inside a triangular park, there is a flower bed forming a similar triangle. Around the flower bed runs a uniform path of such a width that the sides of the park are exactly double the corresponding sides of the flower bed. Find the ratio of the area of the path to the flower bed.
Q.2
For an acute angle θ, sin θ + cos θ takes the greatest value when θ is:
Q.3
If [(x - a)/(b + c)] + [(x - b)/(c + a)] + [(x - c)/(a + b)] = 3, then find the value of x:
Q.4
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.5
If tan A = 1/2 and tan B = 1/3, then which of the following is true?
Q.6
If α, β are the roots of the equation x2 - 2x + 3 = 0, then find the equation whose roots are 1/α2 and 1/β2.
Q.7
The areas of two similar triangles are 81 cm2 and 49 cm2, respectively, then what will be the ratio of their corresponding medians?
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 the first, second and last terms of an AP are a, b and c, respectively, then the sum is:
Q.10
If 1/(a + b), 1/(b + c), and 1/(c + a) are in AP, then which of the following is true?
Your Score: 0/10
Answers to Sample Questions from CREST Olympiads:
Q.1
d
Q.2
b
Q.3
b
Q.4
b
Q.5
a
Q.6
a
Q.7
c
Q.8
a
Q.9
c
Q.10
a
Answers to Sample Questions from CREST Olympiads:
Q.1 : d | Q.2 : b | Q.3 : b | Q.4 : b | Q.5 : a | Q.6 : a | Q.7 : c | Q.8 : a | Q.9 : c | Q.10 : a
