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IKMC 2027 - Grades 9-10 - Self-study SET 11 - Thematic Batch 3

Question 1

The diagram shows a solid, where a represents a fixed given length. What is the area of quadrilateral ABCD?

Question illustration
  1. $4\sqrt{2} × a^2$
  2. a²
  3. $2\sqrt{2} × a^2$
  4. 4a²
  5. $\sqrt{2} × a^2$

Question 2

Sam writes A, B, C on the two sides of 11 cards, with different letters on the two sides of each card. Seven cards have A, eight have C, and four have both A and C. How many cards have both B and C?

Question illustration
  1. 2
  2. 3
  3. 4
  4. 5
  5. 7

Question 3

Four athletes dine around a round table: a shooter, a track-and-field athlete, a table-tennis player and a skateboarder. The shooter sits immediately to Andrea’s left. The track-and-field athlete sits opposite Ben. Eva and Filip sit next to each other. The person immediately to the table-tennis player’s left is Andrea or Eva. Which sport does Eva play?

Question illustration
  1. Shooting
  2. Track and field
  3. Table tennis
  4. Skateboarding
  5. Cannot be determined

Question 4

Julia is 6 years old, one sixth of her mother’s age. They share a birthday. How old will Julia be when her mother is twice her age?

Question illustration
  1. 14 years
  2. 24 years
  3. 30 years
  4. 32 years
  5. 36 years

Question 5

Asif, Usman and Sami have 30 balls altogether. Usman gives Sami 5, Sami gives Asif 4, and Asif gives Usman 2. They then have equal numbers. How many did Asif have initially?

Question illustration
  1. 15
  2. 13
  3. 11
  4. 9
  5. 8

Question 6

Winning tickets have at least five digits and at most three digits larger than 2. The drawn tickets are 1022,22222,102334,213343,3042531. How many win?

Question illustration
  1. 1
  2. 2
  3. 3
  4. 4
  5. 5

Question 7

Which expression is divisible by 3?

Question illustration
  1. 2009
  2. 2+0+0+9
  3. 200−9
  4. $2^9$
  5. (2+0)(0+9)

Question 8

In a race with 2009 runners, Hans beats three times as many people as finish before him. What is his finishing place?

Question illustration
  1. 503
  2. 501
  3. 500
  4. 1503
  5. 1507

Question 9

What is 20102010 divided by 2010?

Question illustration
  1. 11
  2. 101
  3. 1001
  4. 10001
  5. Not an integer

Question 10

Ivan scored 85% of all test points; Tibor scored 90%, only one point more. What was the maximum score?

Question illustration
  1. 5
  2. 17
  3. 18
  4. 20
  5. 25

Question 11

A zebra crossing has alternating white and black stripes, each 50 cm wide. It starts and ends white, and has 8 white stripes. What is the total width?

Question illustration
  1. 7 m
  2. 7.5 m
  3. 8 m
  4. 8.5 m
  5. 9 m

Question 12

Let $P=2\times3+3\times4+4\times5$, $Q=2^2+3^2+4^2$, $R=1\times2+2\times3+3\times4$. Which statement is true?

Question illustration
  1. $Q<P<R$
  2. $P<Q=R$
  3. $P<Q<R$
  4. $R<Q<P$
  5. $Q=P<R$

Question 13

11.11−1.111 equals:

Question illustration
  1. 9.009
  2. 9.0909
  3. 9.99
  4. 9.999
  5. 10

Question 14

The number 200013−2013 is not divisible by which number?

Question illustration
  1. 2
  2. 3
  3. 5
  4. 7
  5. 11

Question 15

The Kangaroo competition is held on the third Thursday in March each year. What is its earliest possible date in March?

Question illustration
  1. 14
  2. 15
  3. 20
  4. 21
  5. 22

Question 16

The MSC Fabiola holds a record as the largest container ship to enter San Francisco Bay. Its 12500 containers would stretch about 75 km placed end to end. Roughly how long is one container?

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  1. 6 m
  2. 16 m
  3. 60 m
  4. 160 m
  5. 600 m

Question 17

Which number is closest to $20.15\times51.02$?

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  1. 100
  2. 1000
  3. 10000
  4. 100000
  5. 1000000

Question 18

Mother hangs T-shirts in a line, then children put a single sock between any two T-shirts. There are 29 items in all. How many T-shirts?

Question illustration
  1. 10
  2. 11
  3. 13
  4. 14
  5. 15

Question 19

Four numbers have mean 9. Three are 5,9,12. What is the fourth?

Question illustration
  1. 6
  2. 8
  3. 9
  4. 10
  5. 36

Question 20

Ruth answers all 30 test questions, each right or wrong. She has 50% more right answers than wrong. How many right answers?

Question illustration
  1. 10
  2. 12
  3. 15
  4. 18
  5. 20