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
Write the general term in the expansion of (x2 -y)6:
Q.2
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.3
If α, β are the roots of the equation x2 - 2x + 3 = 0, then find the equation whose roots are 1/α2 and 1/β2.
Q.4
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.5
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.6
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.7
The average weight of A, B and C is 84 kg. If D joins the group, the average weight of the group becomes 80 kg. If another man E who weighs 3 kg more than D replaces A, then the average of B, C, D and E becomes 79 kg. What is the weight of A ?
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
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.10
W borrowed a certain sum of money from X at the rate of 10% per annum under simple interest and lent one-fourth of the amount to Y at 8% per annum under simple interest and the remaining amount to Z at 15% per annum under simple interest. If at the end of 15 years, W made a profit of $5850 in the deal, then find the sum that W had lent to Z.
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Answers to Sample Questions from CREST Olympiads:
Q.1
b
Q.2
d
Q.3
a
Q.4
d
Q.5
b
Q.6
c
Q.7
a
Q.8
d
Q.9
a
Q.10
c
Answers to Sample Questions from CREST Olympiads:
Q.1 : b | Q.2 : d | Q.3 : a | Q.4 : d | Q.5 : b | Q.6 : c | Q.7 : a | Q.8 : d | Q.9 : a | Q.10 : c
