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 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.2
Find the values of a and b for which 3x3 - ax2 - 74x + b is a multiple of x2 + 2x - 24.
Q.3
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.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
Perpendiculars are drawn from the vertex of the obtuse angles of a rhombus to its sides. The length of each perpendicular is equal to a unit. The distance between their feet is equal to b units. Find the area of the rhombus.
Q.6
If 1/(a + b), 1/(b + c), and 1/(c + a) are in AP, then which of the following is true?
Q.7
Write the general term in the expansion of (x2 -y)6:
Q.8
The areas of two similar triangles are 81 cm2 and 49 cm2, respectively, then what will be the ratio of their corresponding medians?
Q.9
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?
Q.10
For an acute angle θ, sin θ + cos θ takes the greatest value when θ is:
Your Score: 0/10
Answers to Sample Questions from CREST Olympiads:
Q.1
b
Q.2
a
Q.3
a
Q.4
b
Q.5
c
Q.6
a
Q.7
b
Q.8
c
Q.9
d
Q.10
b
Answers to Sample Questions from CREST Olympiads:
Q.1 : b | Q.2 : a | Q.3 : a | Q.4 : b | Q.5 : c | Q.6 : a | Q.7 : b | Q.8 : c | Q.9 : d | Q.10 : b
