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
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.2
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.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
The following steps are involved in finding a number, if the positive number is less than its square by 30. Arrange them in sequential order: (A) x2 - x - 30 = 0 (B) x = 6 (C) x2 - x = 30 (D) (x + 5) (x - 6) = 0
Q.5
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.6
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.7
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.8
Two vertices of a triangle are (5, -1) and (-2, 3). If the orthocentre of the triangle is the origin, find the third vertex.
Q.9
What is the value of the expression [(a - b)3 + (b - c)3 + (c - a)3] / [(a - b)(b - c)(c-a)]?
Q.10
A certain strain of virus occurs three times every 25 minutes. In how much time will it become 729 times its initial value?
Your Score: 0/10
Answers to Sample Questions from CREST Olympiads:
Q.1
d
Q.2
b
Q.3
c
Q.4
a
Q.5
c
Q.6
c
Q.7
b
Q.8
d
Q.9
d
Q.10
c
Answers to Sample Questions from CREST Olympiads:
Q.1 : d | Q.2 : b | Q.3 : c | Q.4 : a | Q.5 : c | Q.6 : c | Q.7 : b | Q.8 : d | Q.9 : d | Q.10 : c
