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 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.2
The arithmetic mean of the squares of the first n natural number is:
Q.3
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.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
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.6
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.7
What is the value of the expression [(a - b)3 + (b - c)3 + (c - a)3] / [(a - b)(b - c)(c-a)]?
Q.8
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.9
Solve and find the roots of the equation: 2(x2 - 6) = 3(x - 4)
Q.10
Which term is numerically greatest term in the expansion of (3 + 2x)49, when x = 1/5?
Your Score: 0/10
Answers to Sample Questions from CREST Olympiads:
Q.1
c
Q.2
c
Q.3
b
Q.4
b
Q.5
a
Q.6
d
Q.7
d
Q.8
b
Q.9
d
Q.10
c
Answers to Sample Questions from CREST Olympiads:
Q.1 : c | Q.2 : c | Q.3 : b | Q.4 : b | Q.5 : a | Q.6 : d | Q.7 : d | Q.8 : b | Q.9 : d | Q.10 : c
