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IKMC 2007 - Grades 5-6 - Self-study

Question 1

Asia walks from the left to the right and puts the numbers in her basket. Which of the following numbers can be in her basket?

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  1. 1, 2 and 4
  2. 2, 3 and 4
  3. 2, 3 and 5
  4. 1, 5 and 6

Question 2

Which piece fits together with the given one to form a rectangle?

Source caveat: option D is blank and C has a stray incomplete outline in both the supplied compilation and the official Pakistan PDF. This item is kept for manually assessed reasoning, not automatic single-choice grading.

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A) Question illustration

B) Question illustration

C) Question illustration

D) Figure missing in source

Question 3

A kangaroo takes 6 seconds for every 4 jumps. How long does it take her to do 10 jumps?
  1. 15
  2. 12
  3. 10
  4. 18

Question 4

$2007\div(2+0+0+7)-2\times0\times0\times7=?$
  1. 9
  2. 214
  3. 223
  4. 2007

Question 5

Usman, who is older than Ali by 1 year minus 1 day, was born on January 1, 2002. What is the date of Ali’s birth?
  1. January 2, 2003
  2. January 2, 2001
  3. December 31, 2000
  4. December 31, 2002

Question 6

The Carpenter’s shop has two machines A and B. A is a “printing machine” and B is a “turning machine”. What’s the right sequence to obtain an upright square with a vertical middle line starting from a blank upright square?

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  1. BBA
  2. ABB
  3. BAB
  4. BA

Question 7

If you cut a 1 meter cube into 1 decimeter cubes and put one on the other, what height will this structure have?
  1. 100 m
  2. 1 km
  3. 10 km
  4. 10 m

Question 8

Uzma cut a paper in the shape of a square with perimeter 20 cm into two rectangles. The perimeter of one rectangle was 16 cm. What was the perimeter of the second rectangle?
  1. 8 cm
  2. 9 cm
  3. 12 cm
  4. 14 cm

Question 9

In a square grid Hina colours the small squares that lie on the two diagonals. What is the size of the grid if Hina altogether colours 9 small squares?
  1. $3\times3$
  2. $4\times4$
  3. $5\times5$
  4. $8\times8$

Question 10

In three adjacent faces of a cube, diagonals are drawn as shown in the figure. Which of the following nets is that of the given cube?

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

Question 11

There were 60 birds at three trees. At one moment 6 birds flew away from the first tree, 8 from the second and 4 from the third. Then there were the same number of birds at each tree. How many birds were at the second tree at the beginning?
  1. 24
  2. 22
  3. 21
  4. 20

Question 12

Two 9 cm × 9 cm squares overlap to form a 9 cm × 13 cm rectangle as shown. Find the area of the region in which the two squares overlap.

Question illustration
  1. $36\text{ cm}^2$
  2. $45\text{ cm}^2$
  3. $54\text{ cm}^2$
  4. $63\text{ cm}^2$

Question 13

Imran let a pigeon out at 7.30 a.m. to deliver a message to Saad. The pigeon delivered the envelope at 9.10 a.m. A pigeon flies 4 km in 10 minutes. What was the distance between Saad and Imran?
  1. 14 km
  2. 20 km
  3. 40 km
  4. 56 km

Question 14

A parallelogram is divided into two parts P1 and P2 as shown. Which sentence is surely true?

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  1. P2 has a bigger perimeter than P1
  2. P2 has a smaller perimeter than P1
  3. P2 has a smaller area than P1
  4. P1 and P2 have the same perimeter

Question 15

The squares are formed by intersecting the segment $AB$ of 24 cm by the broken line $AA_1A_2\ldots A_{12}B$ (see the figure). Find the length of $AA_1A_2\ldots A_{12}B$.

Source recovery: the compilation and official Pakistan PDF omit the figure. The matching original figure below is from Austrian Benjamin 2007, Q17; labels and the 24 cm statement match.

Question illustration
  1. 72 cm
  2. 96 cm
  3. 56 cm
  4. 106 cm

Question 16

The 2007th letter in the sequence KANGAROOKANGAROOKANG… is:
  1. O
  2. A
  3. N
  4. R

Question 17

Iqra is 10 years old. Her mother Asma is 4 times as old. How old will Asma be when Iqra is twice as old as she is now?
  1. 40 years
  2. 70 years
  3. 60 years
  4. 50 years

Question 18

To the right side of a given 2-digit number we write the same number, obtaining a 4-digit number. How many times as large as the 2-digit number is the 4-digit number?
  1. 100
  2. 101
  3. 10
  4. 11

Question 19

Ahmed thought of an integer. Umar multiplied it either by 5 or by 6. Ali added either 5 or 6 to the result. Tahir subtracted either 5 or 6. The obtained result was 73. What number did Ahmed think of?
  1. 10
  2. 11
  3. 12
  4. 14

Question 20

The multiplication shown uses each of the digits 1 to 9 exactly once. What is digit Y?

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  1. 5
  2. 4
  3. 1
  4. 8