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
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?
Q.3
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.
Q.4
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.5
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.6
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.7
If cos x / (1 + cosec x) + cos x / (cosec x - 1) = 2, then which one of the following is one of the values of x?
Q.8
Find the value of x + y in the solution of the equations x/4 + y/3 = 5/12 and x/2 + y = 1:
Q.9
If p1 and p2 are two odd prime numbers such that p1 > p2, then p12 - p22 is:
Q.10
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
Your Score: 0/10
Answers to Sample Questions from CREST Olympiads:
Q.1
c
Q.2
b
Q.3
c
Q.4
b
Q.5
a
Q.6
b
Q.7
c
Q.8
b
Q.9
a
Q.10
a
Answers to Sample Questions from CREST Olympiads:
Q.1 : c | Q.2 : b | Q.3 : c | Q.4 : b | Q.5 : a | Q.6 : b | Q.7 : c | Q.8 : b | Q.9 : a | Q.10 : a
