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
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.
Q.2
If tan A = 1/2 and tan B = 1/3, then which of the following is true?
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 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.5
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.6
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.7
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.8
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.9
Find the value of x + y in the solution of the equations x/4 + y/3 = 5/12 and x/2 + y = 1:
Q.10
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:
Your Score: 0/10
Answers to Sample Questions from CREST Olympiads:
Q.1
c
Q.2
a
Q.3
a
Q.4
b
Q.5
d
Q.6
d
Q.7
d
Q.8
d
Q.9
b
Q.10
c
Answers to Sample Questions from CREST Olympiads:
Q.1 : c | Q.2 : a | Q.3 : a | Q.4 : b | Q.5 : d | Q.6 : d | Q.7 : d | Q.8 : d | Q.9 : b | Q.10 : c
