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IKMC 2011 - Grades 7-8 - Self-study

Question 1

Which of the following has the largest value?
  1. $2011^1$
  2. $1^{2011}$
  3. $1\times2011$
  4. $1+2011$
  5. $1\div2011$

Question 2

Elsa plays with tetrahedrons and cubes. She has 5 cubes and 3 tetrahedrons. How many faces are there in total?

Question illustration
  1. 42
  2. 48
  3. 50
  4. 52
  5. 56

Question 3

A zebra crossing has alternate white and black stripes, each of width 50 cm. The crossing starts and ends with a white stripe and has 8 white stripes in all. What is the total width of the crossing?
  1. 7 m
  2. 7.5 m
  3. 8 m
  4. 8.5 m
  5. 9 m

Question 4

My broken calculator divides instead of multiplying and subtracts instead of adding. I type $(12\times3)+(4\times2)$. What answer does the calculator show?
  1. 2
  2. 6
  3. 12
  4. 28
  5. 38

Question 5

My digital watch has just changed to show the time 20:11. How many minutes later will it next show a time with the digits 0,1,1,2 in some order?
  1. 40
  2. 45
  3. 50
  4. 55
  5. 60

Question 6

The medium square is formed by joining the midpoints of the large square. The small square is formed by joining the midpoints of the medium square. The small square has area 6 cm². What is the difference between the areas of the medium and large squares?

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  1. 6 cm²
  2. 9 cm²
  3. 12 cm²
  4. 15 cm²
  5. 18 cm²

Question 7

In my street there are 17 houses. On the even side the houses are numbered 2,4,6,…; on the odd side 1,3,5,… . I live in the last even-side house, number 12. My cousin lives in the last odd-side house. What is its number?
  1. 5
  2. 7
  3. 13
  4. 17
  5. 21

Question 8

Felix the Cat caught 12 fish in three days. Each day after the first he caught more fish than the previous day. On the third day he caught fewer fish than the first two days together. How many fish did he catch on the third day?
  1. 5
  2. 6
  3. 7
  4. 8
  5. 9

Question 9

Mary lists every 3-digit number whose digits add up to 8. What is the sum of the largest and smallest numbers in her list?
  1. 707
  2. 907
  3. 916
  4. 1000
  5. 1001

Question 10

The diagram shows an L-shape made from four small squares. Ria adds one extra small square to form a shape with a line of symmetry. In how many different ways can she do this?

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  1. 1
  2. 2
  3. 3
  4. 5
  5. 6

Question 11

What is the value of $\frac{2011\times2.011}{201.1\times20.11}$?
  1. 0.01
  2. 0.1
  3. 1
  4. 10
  5. 100

Question 12

Marie has 9 pearls weighing 1,2,3,4,5,6,7,8,9 g. She makes four rings, using two pearls on each. Their pearl totals are 17,13,7,5 g. What is the weight of the unused pearl?
  1. 1 g
  2. 2 g
  3. 3 g
  4. 4 g
  5. 5 g

Question 13

Hamster Fridolin sets out for the Land of Milk and Honey through the tunnels shown. There are 16 pumpkin seeds in the tunnels. What is the highest number he can collect without visiting any junction more than once?

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  1. 12
  2. 13
  3. 14
  4. 15
  5. 16

Question 14

Each region is coloured red (R), green (G), orange (O) or yellow (Y). Only three colours are shown. Any two regions that touch have different colours. What is the colour of region X?

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  1. red
  2. orange
  3. green
  4. yellow
  5. impossible to determine

Question 15

A teacher has marks 17,13,5,10,14,9,12,16. Which two can be removed without changing the average?
  1. 12 and 17
  2. 5 and 17
  3. 9 and 16
  4. 10 and 12
  5. 10 and 14

Question 16

A square piece of paper is cut into six rectangles as shown. The sum of their perimeters is 120 cm. What is the area of the square?

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  1. 48 cm²
  2. 64 cm²
  3. 110.25 cm²
  4. 144 cm²
  5. 256 cm²

Question 17

In three games FC Barcelona scored three goals and conceded one. The club won one game, drew one and lost one. What was the score in the game it won?
  1. 2–0
  2. 3–0
  3. 1–0
  4. 2–1
  5. 0–1

Question 18

Lali draws a segment DE of length 2 cm. How many different points F give a right-angled triangle DEF of area 1 cm²?
  1. 2
  2. 4
  3. 6
  4. 8
  5. 10

Question 19

The positive number a is less than 1 and b is greater than 1. Which value is largest?
  1. $a\times b$
  2. $a+b$
  3. $a\div b$
  4. $b$
  5. depends on a and b

Question 20

The net shown is folded into a cube. A dark line divides its surface into two identical parts as shown. The cube is unfolded. Which of the following can the paper look like?

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