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
The angles of elevation of the top of a tower from two points at distances m and n metres are complementary. If the two points and the base of the tower are on the same straight line, then what will be the height of the tower?
Q.2
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.3
Write the general term in the expansion of (x2 -y)6:
Q.4
Find the value of x + y in the solution of the equations x/4 + y/3 = 5/12 and x/2 + y = 1:
Q.5
Find the values of a and b for which 3x3 - ax2 - 74x + b is a multiple of x2 + 2x - 24.
Q.6
The average mark obtained by the students in a class is 43. If the average marks obtained by 25 boys are 40 and the average marks obtained by the girl students are 48, then what is the number of girl students in the class?
Q.7
The shadow of a pole standing on a horizontal plane is d metre longer when the Sun's altitude is α than when it is β. What is the height of the pole?
Q.8
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.9
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.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
c
Q.3
b
Q.4
b
Q.5
a
Q.6
a
Q.7
c
Q.8
c
Q.9
b
Q.10
b
Answers to Sample Questions from CREST Olympiads:
Q.1 : a | Q.2 : c | Q.3 : b | Q.4 : b | Q.5 : a | Q.6 : a | Q.7 : c | Q.8 : c | Q.9 : b | Q.10 : b
