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 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.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
The volume of the vessel, in the form of a right circular cylinder, is 448π cm3 and its height is 7 cm. What is the radius of its base?
Q.4
Which term is numerically greatest term in the expansion of (3 + 2x)49, when x = 1/5?
Q.5
If sin A = √3/2 and A is an acute angle, then find the value of (tanA - cot A)/(√3 + cosec A).
Q.6
The shadow of a pole standing on a horizontal plane is d metre longer when the Sun's altitude is α than when it is β. What is the height of the pole?
Q.7
Two regular polygons are such that the ratio between their number of sides is 1:2 and the ratio of measures of their interior angles is 3:4. Find the number of sides of each polygon.
Q.8
The volume of a pyramid whose base is an equilateral triangle is 12 cm3. If the height of the pyramid is 3√3 cm, then find the length of each side of the base:
Q.9
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.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
c
Q.3
d
Q.4
c
Q.5
b
Q.6
c
Q.7
a
Q.8
c
Q.9
d
Q.10
c
Answers to Sample Questions from CREST Olympiads:
Q.1 : b | Q.2 : c | Q.3 : d | Q.4 : c | Q.5 : b | Q.6 : c | Q.7 : a | Q.8 : c | Q.9 : d | Q.10 : c
