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
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.2
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.3
If the coefficients of rth term and (r + 1)th term in the expansion of (1 + x)20 are in the ratio 1:2, what is the value of r?
Q.4
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.5
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.6
For an acute angle θ, sin θ + cos θ takes the greatest value when θ is:
Q.7
If sin A = √3/2 and A is an acute angle, then find the value of (tanA - cot A)/(√3 + cosec A).
Q.8
30% of the items were sold at a profit of 40% while the remaining were sold at x% loss. If the overall loss is 10%, find the value of x.
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
Simplify the following expression: [(a - b)3 - (a + b)3 ]/2 + a(a2 + 3b2)
Your Score: 0/10
Answers to Sample Questions from CREST Olympiads:
Q.1
b
Q.2
c
Q.3
b
Q.4
a
Q.5
c
Q.6
b
Q.7
b
Q.8
c
Q.9
d
Q.10
d
Answers to Sample Questions from CREST Olympiads:
Q.1 : b | Q.2 : c | Q.3 : b | Q.4 : a | Q.5 : c | Q.6 : b | Q.7 : b | Q.8 : c | Q.9 : d | Q.10 : d
