, 9
By
Mahabir Singh
MTG Learning Media (P) Ltd.
New Delhi | Gurgaon
,Corporate Office : Plot 99, Sector 44 Institutional area, Gurgaon -122 003 (HR) Telefax: 0124-6601200
Regd. Office : 406, Taj Apt., Ring Road, Adjacent Safdarjung Hospital, New Delhi - 110 029.
Web: mtg.in Email:
© Copyright reserved.
All the rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted, in any form
or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the Publisher.
Most children perform well below their DOWNLOADABLE
true potential in exams…!
Research has shown that providing students with right tools and strategies that build skills
for preparing for a test can help them overcome test anxiety and other associated
symptoms, while improving their ability to prepare for and perform in critical testing.
Do you want to help your child to perform at his/her true potential in
NCO/NSO/IMO/IEO/IGKO? FOR LEVEL - 1
Presenting Olympiad Skill Development System
Why OSDS is necessary even if you have Workbooks
and Previous Years’ Papers
Whereas workbooks and previous years’ papers are necessary for the basic level of preparation,
OSDS is at advanced level because of the following features: FOR LEVEL - 1
Identical pattern: It is a digital product, hence you get updated at the eleventh hour with all
information to match the current pattern.
At par with the standard of the questions: Level of difficulty is near to actual paper.
OMR answer sheet: Updated OMR sheets are provided to let students develop excellent exam
taking skills.
Exam like environment: Solutions are not provided with questions hence, students are forced to
attempt questions as if they are appearing for exam. FOR
OR LEVEL-1
LEVEL 1 and LEVEL
LEVEL-2
Reduces surprises and anxiety: Students are better prepared with OSDS and thus reduces
surprises and anxiety.
Detailed answers: Detailed explanations are provided. This helps in deriving the correct answer.
Time management: Practising question papers at par with the difficulty level of actual exam
helps in managing time during exam.
FOR
OR LEVEL
LEVEL-11 and LEVEL
LEVEL-2
Our scientific system can help your child perform
better and score higher.
By using our simple to use system, see your child
perform better ! score higher ! be much more confident ! a lot more prompt !
Enjoy Olympiads and other similar tests with enhanced confidence level FOR LEVEL-1 and LEVEL-2
Want to know more? Visit mtg.in Or call 0124 6601200 NOW !
,Chapter 1 : Number Systems 5
Chapter 2 : Polynomials 8
Chapter 3 : Coordinate Geometry 11
Chapter 4 : Linear Equations in Two Variables 14
Chapter 5 : Introduction to Euclid’s Geometry 18
Chapter 6 : Lines and Angles 21
Chapter 7 : Triangles 24
Chapter 8 : Quadrilaterals 27
Chapter 9 : Areas of Parallelograms and Triangles 30
Chapter 10 : Circles 33
Chapter 11 : Constructions 36
Chapter 12 : Heron’s Formula 38
Chapter 13 : Surface Areas and Volumes 42
Chapter 14 : Statistics 46
Chapter 15 : Probability 50
Chapter 16 : Logical Reasoning 54
Hints & Explanations 58
S F International Mathematics Olympiad - 2017 83
(with Hints & Explanations)
,
, CHAPTER
1 NUMBER SYSTEMS
MATHEMATICAL REASONING
1. If 2x – 3 ·32x – 8 = 36, then the value of x is -18
______. 7. Rational number lies between
5
(A) 2 (B) 5 (C) 3 (D) 1 consecutive integers ______.
(A) –2 and –3 (B) –3 and –4
5 +2 + 5−2 (C) –4 and –5 (D) –5 and –6
2. If N = − 3−2 2 ,
5 +1
1 2
then N equals ______. 8. An irrational number between and
7 7
(A) 1 (B) 2 2 -1 is _____.
5 1 1 2 1 2
2 (A) + (B) ×
(C) (D) 2 7 7 7 7
2 5 +1
(C) 1 2 (D) None of these
3. Express the mixed recurring decimal 4.32 ´
7 7
p
in the form .
q 9. The denominator of
389 329 a + a2 − b2 a − a2 − b2
(A) (B) + is ______.
90 90
a − a2 − b2 a + a2 − b2
29 233
(C) (D) (A) a2 (B) b2
90 990
1 4a2 − 2b 2
4. If x = (7 + 4 3 ), then x + = ______. (C) a2 – b2 (D)
x b2
(A) 8 3 (B) 14 (C) 49 (D) 48 10. The ascending order of the surds 3 2, 6 3, 9 4
is ______.
7 3 2 5 3 2 (A) 9 4, 6 3, 3 2 (B) 9 4, 3 2, 6 3
5. − − =
( 10 + 3 ) ( 6 + 5) ( 15 + 3 2 )
(C) 3
2, 6 3, 9 4 (D) 6
3, 9 4, 3 2
______.
1 11. The greater number among 17 − 12 and
(A) 1 (B) 2 (C) (D) 3
2 11 − 6 is ______.
6. The rationalising factor of 5 a2b3c 4 is _____. (A) 17 − 12
(A) 5 3 2
a b c (B) 4 3 2 (B) 11 − 6
a b c
(C) Both are equal
3 3 2
(C) a b c (D) a3b 2c (D) Can’t be compared
CLASS 9 5
By
Mahabir Singh
MTG Learning Media (P) Ltd.
New Delhi | Gurgaon
,Corporate Office : Plot 99, Sector 44 Institutional area, Gurgaon -122 003 (HR) Telefax: 0124-6601200
Regd. Office : 406, Taj Apt., Ring Road, Adjacent Safdarjung Hospital, New Delhi - 110 029.
Web: mtg.in Email:
© Copyright reserved.
All the rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted, in any form
or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the Publisher.
Most children perform well below their DOWNLOADABLE
true potential in exams…!
Research has shown that providing students with right tools and strategies that build skills
for preparing for a test can help them overcome test anxiety and other associated
symptoms, while improving their ability to prepare for and perform in critical testing.
Do you want to help your child to perform at his/her true potential in
NCO/NSO/IMO/IEO/IGKO? FOR LEVEL - 1
Presenting Olympiad Skill Development System
Why OSDS is necessary even if you have Workbooks
and Previous Years’ Papers
Whereas workbooks and previous years’ papers are necessary for the basic level of preparation,
OSDS is at advanced level because of the following features: FOR LEVEL - 1
Identical pattern: It is a digital product, hence you get updated at the eleventh hour with all
information to match the current pattern.
At par with the standard of the questions: Level of difficulty is near to actual paper.
OMR answer sheet: Updated OMR sheets are provided to let students develop excellent exam
taking skills.
Exam like environment: Solutions are not provided with questions hence, students are forced to
attempt questions as if they are appearing for exam. FOR
OR LEVEL-1
LEVEL 1 and LEVEL
LEVEL-2
Reduces surprises and anxiety: Students are better prepared with OSDS and thus reduces
surprises and anxiety.
Detailed answers: Detailed explanations are provided. This helps in deriving the correct answer.
Time management: Practising question papers at par with the difficulty level of actual exam
helps in managing time during exam.
FOR
OR LEVEL
LEVEL-11 and LEVEL
LEVEL-2
Our scientific system can help your child perform
better and score higher.
By using our simple to use system, see your child
perform better ! score higher ! be much more confident ! a lot more prompt !
Enjoy Olympiads and other similar tests with enhanced confidence level FOR LEVEL-1 and LEVEL-2
Want to know more? Visit mtg.in Or call 0124 6601200 NOW !
,Chapter 1 : Number Systems 5
Chapter 2 : Polynomials 8
Chapter 3 : Coordinate Geometry 11
Chapter 4 : Linear Equations in Two Variables 14
Chapter 5 : Introduction to Euclid’s Geometry 18
Chapter 6 : Lines and Angles 21
Chapter 7 : Triangles 24
Chapter 8 : Quadrilaterals 27
Chapter 9 : Areas of Parallelograms and Triangles 30
Chapter 10 : Circles 33
Chapter 11 : Constructions 36
Chapter 12 : Heron’s Formula 38
Chapter 13 : Surface Areas and Volumes 42
Chapter 14 : Statistics 46
Chapter 15 : Probability 50
Chapter 16 : Logical Reasoning 54
Hints & Explanations 58
S F International Mathematics Olympiad - 2017 83
(with Hints & Explanations)
,
, CHAPTER
1 NUMBER SYSTEMS
MATHEMATICAL REASONING
1. If 2x – 3 ·32x – 8 = 36, then the value of x is -18
______. 7. Rational number lies between
5
(A) 2 (B) 5 (C) 3 (D) 1 consecutive integers ______.
(A) –2 and –3 (B) –3 and –4
5 +2 + 5−2 (C) –4 and –5 (D) –5 and –6
2. If N = − 3−2 2 ,
5 +1
1 2
then N equals ______. 8. An irrational number between and
7 7
(A) 1 (B) 2 2 -1 is _____.
5 1 1 2 1 2
2 (A) + (B) ×
(C) (D) 2 7 7 7 7
2 5 +1
(C) 1 2 (D) None of these
3. Express the mixed recurring decimal 4.32 ´
7 7
p
in the form .
q 9. The denominator of
389 329 a + a2 − b2 a − a2 − b2
(A) (B) + is ______.
90 90
a − a2 − b2 a + a2 − b2
29 233
(C) (D) (A) a2 (B) b2
90 990
1 4a2 − 2b 2
4. If x = (7 + 4 3 ), then x + = ______. (C) a2 – b2 (D)
x b2
(A) 8 3 (B) 14 (C) 49 (D) 48 10. The ascending order of the surds 3 2, 6 3, 9 4
is ______.
7 3 2 5 3 2 (A) 9 4, 6 3, 3 2 (B) 9 4, 3 2, 6 3
5. − − =
( 10 + 3 ) ( 6 + 5) ( 15 + 3 2 )
(C) 3
2, 6 3, 9 4 (D) 6
3, 9 4, 3 2
______.
1 11. The greater number among 17 − 12 and
(A) 1 (B) 2 (C) (D) 3
2 11 − 6 is ______.
6. The rationalising factor of 5 a2b3c 4 is _____. (A) 17 − 12
(A) 5 3 2
a b c (B) 4 3 2 (B) 11 − 6
a b c
(C) Both are equal
3 3 2
(C) a b c (D) a3b 2c (D) Can’t be compared
CLASS 9 5
