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
In ∆ABC, ∠B = 90⁰. P, Q and R are the midpoints of AB, BC and AC, respectively. Which of the following options can be the vertices of a cyclic quadrilateral?
Q.2
If the sum of the roots of the equation ax2 + bx + c = 0 is equal to the sum of their squares, then which one of the following is correct?
Q.3
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.4
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.5
If 1/(a + b), 1/(b + c), and 1/(c + a) are in AP, then which of the following is true?
Q.6
If sin A = √3/2 and A is an acute angle, then find the value of (tanA - cot A)/(√3 + cosec A).
Q.7
Find the values of a and b for which 3x3 - ax2 - 74x + b is a multiple of x2 + 2x - 24.
Q.8
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.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
Solve and find the roots of the equation: 2(x2 - 6) = 3(x - 4)
Your Score: 0/10
Answers to Sample Questions from CREST Olympiads:
Q.1
b
Q.2
c
Q.3
a
Q.4
a
Q.5
a
Q.6
b
Q.7
a
Q.8
b
Q.9
b
Q.10
d
Answers to Sample Questions from CREST Olympiads:
Q.1 : b | Q.2 : c | Q.3 : a | Q.4 : a | Q.5 : a | Q.6 : b | Q.7 : a | Q.8 : b | Q.9 : b | Q.10 : d
