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IKMC 2015 - Grades 7-8 - Self-study

Question 1

My umbrella has KANGAROO written on top, as shown. Which picture also shows my umbrella?

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Question 2

Four identical small rectangles form the large rectangle shown. Its shorter side is 10 cm. How long is its longer side?

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  1. 10 cm
  2. 20 cm
  3. 30 cm
  4. 40 cm
  5. 50 cm

Question 3

Which number is closest to $2.015\times 510.2$?
  1. 0.1
  2. 1
  3. 10
  4. 100
  5. 1000

Question 4

The net of a cube with numbered faces is shown. Sasha adds the numbers on opposite faces correctly. What three totals does she get?

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  1. 4,6,11
  2. 4,5,12
  3. 5,6,10
  4. 5,7,9
  5. 5,8,8

Question 5

Which number is not an integer?
  1. $\frac{2011}1$
  2. $\frac{2012}2$
  3. $\frac{2013}3$
  4. $\frac{2014}4$
  5. $\frac{2015}5$

Question 6

A journey from Koice to Poprad through Preov lasts 130 minutes. Koice to Preov takes 35 minutes. How long does Preov to Poprad take?
  1. 95 minutes
  2. 105 minutes
  3. 115 minutes
  4. 165 minutes
  5. 175 minutes

Question 7

The diagram is the net of a triangular prism. Which edge coincides with UV when the net is folded?

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  1. WV
  2. XW
  3. XY
  4. QR
  5. RS

Question 8

A triangle has side lengths 6,10,11. An equilateral triangle has the same perimeter. What is its side length?
  1. 18
  2. 11
  3. 10
  4. 9
  5. 6

Question 9

On the ground, Simon the squirrel never goes more than 5 m from his tree trunk and always stays at least 5 m from the doghouse. Which picture best shows the region he can visit?
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Question 10

A cyclist rides at 5 metres per second. Each wheel has circumference 125 cm. How many complete turns does each wheel make in 5 seconds?
  1. 4
  2. 5
  3. 10
  4. 20
  5. 25

Question 11

In a class, no two boys were born on the same weekday and no two girls in the same month. Adding any new boy or any new girl would make one of these conditions fail. How many children are in the class?
  1. 18
  2. 19
  3. 20
  4. 24
  5. 25

Question 12

The centre of the top square is directly above the common edge of the two lower squares. Every square has side 1. What is the area of the shaded region?

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  1. $\frac 34$
  2. $\frac 78$
  3. $1$
  4. $1\frac 14$
  5. $1\frac 12$

Question 13

Replace each asterisk in $2*0*1*5*2*0*1*5*2*0*1*5=0$ by either + or − to make the equation true. What is the smallest number of plus signs?
  1. 1
  2. 2
  3. 3
  4. 4
  5. 5

Question 14

During a rainstorm,15 litres of water fall per square metre. How much does the level rise in an open-air swimming pool?
  1. 150 cm
  2. 0.15 cm
  3. 15 cm
  4. 1.5 cm
  5. It depends on the pool size

Question 15

A bush has 10 branches. Each has either 5 leaves only or 2 leaves and 1 flower. Which could be the total number of leaves?

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  1. 45
  2. 39
  3. 37
  4. 31
  5. None of A–D

Question 16

The mean mathematics-test score was 6. Exactly 60% of students passed, and their mean score was 8. What was the mean score of those who failed?
  1. 1
  2. 2
  3. 3
  4. 4
  5. 5

Question 17

One corner of a square is folded to its centre, making an irregular pentagon. The areas of the pentagon and square are consecutive integers. What is the area of the square?

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  1. 2
  2. 4
  3. 8
  4. 16
  5. 32

Question 18

Rachel adds three side lengths of a rectangle and gets 44 cm. Heather adds three side lengths of the same rectangle and gets 40 cm. What is the perimeter?
  1. 42 cm
  2. 56 cm
  3. 64 cm
  4. 84 cm
  5. 112 cm

Question 19

Some unit segments have the indicated colours. Luis colours every remaining segment red, blue or green so that each triangle has one side of each colour. What colour can segment x have?

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  1. Only green
  2. Only red
  3. Only blue
  4. Either red or blue
  5. Impossible

Question 20

Irina asks five students how many of them studied yesterday. Pol says none, Berta one, Ona exactly two, Eugeni exactly three, Gerard exactly four. Those who did not study lie and those who studied tell the truth. How many studied?
  1. 0
  2. 1
  3. 2
  4. 3
  5. 4