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
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.2
Find the values of a and b for which 3x3 - ax2 - 74x + b is a multiple of x2 + 2x - 24.
Q.3
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.4
Inside a triangular park, there is a flower bed forming a similar triangle. Around the flower bed runs a uniform path of such a width that the sides of the park are exactly double the corresponding sides of the flower bed. Find the ratio of the area of the path to the flower bed.
Q.5
In the given figure, AB || DE and the area of the parallelogram ABFD is 24 cm2. Find the areas of triangles AFB, AGB, and AEB.
Q.6
The houses of a row are numbered consecutively from 1 to 49. If there is a value of x such that the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it. Find the value of x.
Q.7
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.8
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.9
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.10
Find the value of x + y in the solution of the equations x/4 + y/3 = 5/12 and x/2 + y = 1:
Your Score: 0/10
Answers to Sample Questions from CREST Olympiads:
Q.1
d
Q.2
a
Q.3
a
Q.4
d
Q.5
b
Q.6
d
Q.7
d
Q.8
a
Q.9
d
Q.10
b
Answers to Sample Questions from CREST Olympiads:
Q.1 : d | Q.2 : a | Q.3 : a | Q.4 : d | Q.5 : b | Q.6 : d | Q.7 : d | Q.8 : a | Q.9 : d | Q.10 : b
