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
What is the value of the expression [(a - b)3 + (b - c)3 + (c - a)3] / [(a - b)(b - c)(c-a)]?
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
The areas of two similar triangles are 81 cm2 and 49 cm2, respectively, then what will be the ratio of their corresponding medians?
Q.4
How many 5-digit odd numbers can be formed using the digits 2, 3, 5, 7, 8, and 9 if every digit can occur at most once in any number?
Q.5
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.6
If [(x - a)/(b + c)] + [(x - b)/(c + a)] + [(x - c)/(a + b)] = 3, then find the value of x:
Q.7
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.8
Solve and find the roots of the equation: 2(x2 - 6) = 3(x - 4)
Q.9
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.10
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.
Your Score: 0/10
Answers to Sample Questions from CREST Olympiads:
Q.1
d
Q.2
c
Q.3
c
Q.4
d
Q.5
b
Q.6
b
Q.7
c
Q.8
d
Q.9
b
Q.10
c
Answers to Sample Questions from CREST Olympiads:
Q.1 : d | Q.2 : c | Q.3 : c | Q.4 : d | Q.5 : b | Q.6 : b | Q.7 : c | Q.8 : d | Q.9 : b | Q.10 : c
