SOF - IMO Level 2 Sample Papers for Class 10

Class 10 sample paper & practice questions for the level 2 of International Mathematics Olympiad (IMO) are given below. Syllabus for level 2 is also mentioned for these exams. You can refer these sample paper & quiz for preparing for the exam.

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Sample Questions from Olympiad Success:

Q.1

Q.2

Q.3

Q.4

Q.5

Q.6

Q.7

Q.8

Q.9

Q.10

Q.1	If (secθ + tanθ)/(secθ − tanθ) = 2 ⁵¹/₇₉, then find the value of sinθ.
a)	65/144
b)	39/72
c)	'35/72
d)	'91/144

Q.2	Find the quadratic equation whose roots are 3 and -1.
a)	x² + 4x + 3 = 0
b)	x² + 2x - 3 = 0
c)	x² - 2x - 3 = 0
d)	x² - 4x + 3 = 0

Q.3	In a family, each daughter has the same number of brothers as she has sisters and each son has twice as many sisters as he has brothers. How many sons are there in the family?
a)	4
b)	3
c)	5
d)	2

Q.4	In a right-angled triangle, the product of two sides is equal to half of the square of the third side i.e. hypotenuse. One of the acute angle must be?
a)	45°
b)	15°
c)	30°
d)	60°

Q.5	A bucket of height 16 cm made up of metal sheet is in the form of frustum of a right circular cone with radii of its lower and upper ends as 3 cm and 15 cm respectively. What is the slant height of the bucket?
a)	15 cm
b)	5 cm
c)	12 cm
d)	20 cm

Q.6	A cylinder is surmounted by a cone at one end, a hemisphere at the other end. The common radius is 3.5 cm, the height of the cylinder is 6.5 cm and the total height of the structure is 12.8 cm. The volume V of the structure lies between which of the following option?
a)	390 cm² and 400 cm²
b)	360 cm² and 370 cm²
c)	380 cm² and 390 cm²
d)	370 cm² and 380 cm²

Q.7	If OA and OB are radii and PA and PB are tangents to the circle, which of the following is quadrilateral OAPB?
a)	Rectangle
b)	Square
c)	Kite
d)	Parallelogram

Q.8	If the integer m and n are chosen at random between 1 and 100, then the probability that a number of the from 7^m + 7ⁿ is divisible by 5 equal to:
a)	1/8
b)	1/49
c)	1/4
d)	1/7

Q.9	Find the unit digit in the product (2467)¹⁵³ x (341)¹⁷².
a)	4
b)	7
c)	6
d)	8

Q.10	If one of the roots of quadratic equation 7y² - 50y + k = 0 is 7, then what is the value of k?
a)	1
b)	7
c)	50/7
d)	7/50

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Answers to Sample Questions from Olympiad Success:

Q.1 )a	Q.2 )c	Q.3 )b	Q.4 )a	Q.5 )d	Q.6 )d	Q.7 )c	Q.8 )a	Q.9 )b	Q.10 )b

Answers to Sample Questions from Olympiad Success:

Q.1 : a | Q.2 : c | Q.3 : b | Q.4 : a | Q.5 : d | Q.6 : d | Q.7 : c | Q.8 : a | Q.9 : b | Q.10 : b

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