# International Mathematics OIympiad Test Papers

9

SAMPLE PAPER

International

Mathematics Olympiad

The actual test paper has 50 questions. Time allowed : 60 minutes. There are 3 sections: 20 questions in sec tion I, 20 in section II and 10 in section III.

S Y L L A BU S

Section – I (Logical reasoning) : Mathematical operations, Series completion, Arithmetical Reasoning, Problems on c ubes and dice, Number ranking & Time sequence Test, Inserting missing character and general reasoning based on prescribed syllabus.

Section – II (Mathematical reasoning) : Number Sy stems, Polynomials, Coordinate Geometry, Linear Equations in Two Variables, Introduction to Euclid’s Geometry, Lines and Angles, Triangles, Quadrilaterals, Areas of Parallelograms and Triangles, Circ les, Constructions, Heron’s Formula, Surface Areas and Volumes, Statistics, Probability.

Section – III (Everyday Mathematics) : The Sy llabus of this section will be based on the syllabus of Mathematical Reasoning.

SOF

LOGICAL REASONING

1. A pples, cherries and grapes are arranged on a platter in the f ollowing f ashion: opposite sectors contain f ruit which is of equal value. To equal the value of two bunches of grapes, how much f ruit m ust be placed in the em pty sector?

(A )

(B )

(C)

?

(D)

2. There are twenty people working in an off ice. The f irst group of f ive works between 8.00 A .M. and 2.00 P.M. The second group of ten works between 10.00 A .M. and 4.00 P.M. And the third group of f ive works between 12 noon and 6.00 P.M. There are three computers in the off ice which all the em ployees f requently use. During which of the f ollowing hours are the com puters likely to be used most? (A ) 10.00 A .M. – 12 noon

(B ) 12 noon – 2.00 P.M.

(C) 1.00 P.M. – 3.00 P.M.

(D) 2.00 P.M. – 4.00 P.M.

3. If L denotes ¸ , M denotes ×, P denotes + and Q denotes –, then which of the following statements is true? 173

3

(A ) 32 P 8 L 16 Q 4 = –

(B ) 6 M 18 Q 26 L 13 P 7 =

13

2

38

(C) 11 M 3 4 L 17 Q 8 L 3 =

(D) 9 P 9 L 9 Q 9 M 9 = – 71

3

4. A student got twice as m any sum s wrong as he got right. If he attem pted 48 sum s in all, how m any did he solve correctly?

(A ) 12

(B ) 16

(C) 24

(D) 18

5. Find the m issing num ber :

1

2

4

584

2

(A ) 93 7

5

(B ) 82 4

3

2

3

4

694

3

2

2

6

7

?

2

(C) 76 9

1

2

1

(D) 67 8

6. In a certain code, ‘256’ m eans ‘you are good’; ‘6 37’ m eans ‘we are bad’ and ‘358’ m eans ‘good and bad’. W hich of the f ollowing r epresents ‘and’ in that code? (A ) 2

(B ) 5

(C) 8

(D) 3

7. Com plete the pattern. 6, 11, 21, 36, 56, (.....) (A ) 42

(B ) 51

(C) 81

(D) 91

MATHEMAT ICAL REASONING

8. In the accom panying dia gram , parallel lines l and m are cut by t ransversal t.

W hich statem ent about ang les 1 and 2 m ust be true? (A ) Ð1 @ Ð 2

(C) Ð1 i s t he suppl em en t of Ð 2

l

1

m

2

(B ) Ð1 i s t he com pl em en t of Ð 2

(D) Ð1 and Ð 2 are right angles

9. W hat values of a and b m ake quadr ilateral MNOP a parall elogram ? (A ) a = 1, b = 5

(B ) a = 5, b = 1

11

34

(C) a =

, b =

7

7

t

34

11

(D) a =

, b =

7

7

10. For the quadrilateral shown below, what is m Ð a + m Ð c? (A ) 53°

(B ) 137°

(C) 180°

(D) 233°

N

2

O

3 a – 2

b

13

M

4a + b

P

C

c

B 95 °

32 °

a

A

Cl ass 9

21

D

11. If a cylindrical barrel m easures 22 cm in diam eter, how m any cm will it roll in 8 revolutions along a sm ooth surf...

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