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IKMC 2018 - Grades 11-12 - Self-study

Question 1

In the diagram you can see the calendar page of a certain month. Unfortunately ink has run across parts of the page. Which day of the week does the 27th of that month fall on?

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  1. Monday
  2. Wednesday
  3. Thursday
  4. Saturday
  5. Sunday

Question 2

Which expression has the greatest value?
  1. $2-0\cdot1+8$
  2. $2+0\cdot1\cdot8$
  3. $2\cdot0+1\cdot8$
  4. $2\cdot(0+1+8)$
  5. $2\cdot0+1+8$

Question 3

The diagram shows the floor plan of Renate's house. Renate enters her house from the terrace (Terrasse) and walks through every door of the house exactly once. Which room does she end up in?

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

Question 4

Thor has seven stones and a hammer. With his hammer he hits a stone and it breaks into five small stones. He does that a few times. Which of these numbers could be the number of stones he ends up with?
  1. 17
  2. 20
  3. 21
  4. 23
  5. 25

Question 5

The diagram shows an object made up of 12 dice glued-together. The object is dipped into some colour so that the entire outside is coloured in this new colour. How many of the small dice will have exactly four faces coloured in?

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  1. 8
  2. 9
  3. 10
  4. 11
  5. 12

Question 6

The following two statements are true: Some aliens are green and all others are purple. Green aliens live on Mars only. Which one of the following logical conclusions can be made?
  1. All aliens live on Mars.
  2. Only green aliens live on Mars.
  3. Some purple aliens live on Venus.
  4. All purple aliens live on Venus.
  5. No green aliens live on Venus.

Question 7

Four identical rhombuses (diamonds) and two squares are fitted together to form a regular octagon as shown. How big are the obtuse interior angles in the rhombuses?

Question illustration
  1. $135^\circ$
  2. $140^\circ$
  3. $144^\circ$
  4. $145^\circ$
  5. $150^\circ$

Question 8

There are 65 balls in a box, 8 of which are white, the rest are black. Up to 5 balls can be taken out of the box in one draw. It is not allowed to put any balls back into the box. What is the minimum number of draws which have to be made to be certain that at least one white ball is drawn from the box?
  1. 11
  2. 12
  3. 13
  4. 14
  5. 15

Question 9

The three faces of the rectangular brick have areas $A,B,C$ as shown. What is its volume?

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  1. $ABC$
  2. $\sqrt{ABC}$
  3. $\sqrt{AB+BC+CA}$
  4. $\sqrt[3]{ABC}$
  5. $2(A+B+C)$

Question 10

How many ways are there to write the number 1001 as the sum of two prime numbers?
  1. No way
  2. One
  3. Two
  4. Three
  5. More than three

Question 11

Two cubes of volumes $V$ and $W$ overlap as shown. 90% of the cube of volume $V$ lies outside the overlap, as does 85% of the cube of volume $W$. What relation holds?

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  1. $V=\frac23W$
  2. $V=\frac32W$
  3. $V=\frac{85}{90}W$
  4. $V=\frac{90}{85}W$
  5. $V=W$

Question 12

The five vases shown are filled with water. The filling rate is constant. For which of the five vases does the graph shown describe the height of the water h as a function of the time t?

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Question 13

Evaluate $|\sqrt{17}-5|+|\sqrt{17}+5|$.
  1. 10
  2. $2\sqrt{17}$
  3. $\sqrt{34}-10$
  4. $10-\sqrt{34}$
  5. 0

Question 14

An octahedron is inscribed into a die with side length 1. The vertices of the octahedron are the midpoints of the faces of the die. How big is the volume of the octahedron?

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  1. $\frac13$
  2. $\frac14$
  3. $\frac15$
  4. $\frac16$
  5. $\frac18$

Question 15

Triangle vertices are $A(p,q),B(r,s),C(t,u)$ as shown. The side midpoints are $M(-2,1),N(2,-1),P(3,2)$. Determine $p+q+r+s+t+u$.

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  1. 2
  2. $\frac52$
  3. 3
  4. 5
  5. Another value

Question 16

Before Real Madrid plays Manchester United, five predictions are made: (i) no draw; (ii) Real Madrid scores at least once; (iii) Real Madrid does not lose; (iv) Real Madrid wins; (v) exactly three goals are scored in total. Exactly three predictions come true. How many goals did Real Madrid score?
  1. 0
  2. 1
  3. 2
  4. 3
  5. Cannot be determined

Question 17

A regular pentagon is cut out of a page of lined paper. Step by step this pentagon is then rotated 21° counter clockwise about its midpoint. The result after step one is shown in the diagram. Which of the diagrams shows the situation when the pentagon fills the hole entirely again for the first time?

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Question 18

Which number is not a factor of $18^{2017}+18^{2018}$?
  1. 8
  2. 18
  3. 28
  4. 38
  5. 48

Question 19

Three of the cards shown will be dealt to Nadia, the rest to Riny. Nadia multiplies the three values of her cards and Riny multiplies the two values of his cards. It turns out that the sum of those two products is a prime number. Determine the sum of the values of Nadia’s cards.

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  1. 12
  2. 13
  3. 15
  4. 17
  5. 18

Question 20

Two rectangles make angles $40^\circ$ and $30^\circ$ with a straight line, as shown. What is angle $\alpha$?

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  1. $105^\circ$
  2. $120^\circ$
  3. $130^\circ$
  4. $135^\circ$
  5. Another value