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
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.2
The areas of two similar triangles are 81 cm2 and 49 cm2, respectively, then what will be the ratio of their corresponding medians?
Q.3
Solve and find the roots of the equation: 2(x2 - 6) = 3(x - 4)
Q.4
If 1/(a + b), 1/(b + c), and 1/(c + a) are in AP, then which of the following is true?
Q.5
Find the value of x + y in the solution of the equations x/4 + y/3 = 5/12 and x/2 + y = 1:
Q.6
A bag contains 63 cards (numbered 1, 2, 3, ….., 63). Two cards are picked at random from the bag (one after another and without replacement). What is the probability that the sum of the numbers of both the cards drawn is even?
Q.7
In the given figure, PQRS is a square of side 7√2 cm. With P and R as centres and PQ as radius, the arcs QAS and QBS are drawn, respectively. Find the area of the shaded region (in cm2).
Q.8
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.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
Write the general term in the expansion of (x2 -y)6:
Your Score: 0/10
Answers to Sample Questions from CREST Olympiads:
Q.1
b
Q.2
c
Q.3
d
Q.4
a
Q.5
b
Q.6
d
Q.7
d
Q.8
d
Q.9
b
Q.10
b
Answers to Sample Questions from CREST Olympiads:
Q.1 : b | Q.2 : c | Q.3 : d | Q.4 : a | Q.5 : b | Q.6 : d | Q.7 : d | Q.8 : d | Q.9 : b | Q.10 : b
