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 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.2
If tan A = 1/2 and tan B = 1/3, then which of the following is true?
Q.3
What is the value of the expression [(a - b)3 + (b - c)3 + (c - a)3] / [(a - b)(b - c)(c-a)]?
Q.4
Which among the following is a singleton set?
Q.5
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.6
Find the quadratic equation whose roots are reciprocal of the roots of the equation 3x2 - 20x + 17 = 0.
Q.7
In the adjoining figure, the bottom of the glass has a hemispherical raised portion. If the glass is filled with orange juice, then find the quantity of juice which a person will get:
Q.8
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.9
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.10
A square is drawn by joining midpoints of the sides of a square. Another square is drawn inside the second square in the same way and the process is continued indefinitely. If, the side of the first square is 16 cm, then what is the sum of the areas of all the squares?
Your Score: 0/10
Answers to Sample Questions from CREST Olympiads:
Q.1
c
Q.2
a
Q.3
d
Q.4
c
Q.5
a
Q.6
a
Q.7
b
Q.8
a
Q.9
b
Q.10
b
Answers to Sample Questions from CREST Olympiads:
Q.1 : c | Q.2 : a | Q.3 : d | Q.4 : c | Q.5 : a | Q.6 : a | Q.7 : b | Q.8 : a | Q.9 : b | Q.10 : b
