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IKMC 2016 - Grades 9-10 - Self-study

Question 1

Four numbers have mean 9. Three are 5,9,12. What is the fourth?
  1. 6
  2. 8
  3. 9
  4. 10
  5. 36

Question 2

Which number is closest to $\frac{17\times0.3\times20.16}{999}$?
  1. 0.01
  2. 0.1
  3. 1
  4. 10
  5. 100

Question 3

Ruth answers all 30 test questions, each right or wrong. She has 50% more right answers than wrong. How many right answers?
  1. 10
  2. 12
  3. 15
  4. 18
  5. 20

Question 4

Four of these coordinate points are vertices of a square. Which point is not a vertex of that square?
  1. (−1;3)
  2. (0;−4)
  3. (−2;−1)
  4. (1;1)
  5. (3;−2)

Question 5

A positive integer x leaves remainder 3 on division by 6. What remainder does 3 x leave on division by 6?
  1. 4
  2. 3
  3. 2
  4. 1
  5. 0

Question 6

How many weeks equal 2016 hours?
  1. 6
  2. 8
  3. 10
  4. 12
  5. 16

Question 7

Before learning negative signs, Lucas counts backwards as …,3,2,1,0,00,000,0000,… . What is 000+0000 in his notation?
  1. 1
  2. 00000
  3. 000000
  4. 0000000
  5. 00000000

Question 8

A strange die has faces−1,2,−3,4,−5,6. Throw two such dice. Which total cannot occur?
  1. 3
  2. 4
  3. 5
  4. 7
  5. 8

Question 9

How many exchanges of directly adjacent letters are needed to change VELO into LOVE step by step?
  1. 3
  2. 4
  3. 5
  4. 6
  5. 7

Question 10

Sven writes five different positive one-digit integers. No two sum to 10. Which number must he have written?
  1. 1
  2. 2
  3. 3
  4. 4
  5. 5

Question 11

Let $a+5=b^2-1=c^2+3=d-4$. Which of a, b, c, d is largest?
  1. a
  2. b
  3. c
  4. d
  5. impossible to determine

Question 12

A 3 × 3 grid has unit squares, with circles inscribed in two of them as shown. What is the distance between the circles?

Question illustration
  1. $2\sqrt2-1$
  2. $\sqrt2+1$
  3. $2\sqrt2$
  4. 2
  5. 3

Question 13

In a knock-out tennis tournament, six of the quarterfinal, semifinal, final results are: Bella beat Ann; Celine beat Donna; Gina beat Holly; Gina beat Celine; Celine beat Bella; Emma beat Farah. Which result is missing?
  1. Gina beat Bella
  2. Celine beat Ann
  3. Emma beat Celine
  4. Bella beat Holly
  5. Gina beat Emma

Question 14

What percentage of the triangle’s area is shaded as shown?

Question illustration
  1. 80%
  2. 85%
  3. 88%
  4. 90%
  5. impossible to determine

Question 15

Jill makes a multiplicative magic square using 1,2,4,5,10,20,25,50,100 once each. Products in every row, column and both diagonals are equal. The start is shown. What belongs in the question-mark cell?

Question illustration
  1. 2
  2. 4
  3. 5
  4. 10
  5. 25

Question 16

Jack holds six circular pipes of diameter 2 cm with a taut rubber band in either arrangement shown. Compare the band lengths.

Question illustration
  1. Left is $\pi$ cm shorter
  2. Left is4 cm shorter
  3. Right is $\pi$ cm shorter
  4. Right is4 cm shorter
  5. Both equal

Question 17

Eight unmarked envelopes contain 1,2,4,8,16,32,64,128. Eve chooses some, Alie takes the rest. Eve’s sum is 31 more than Alie’s. How many envelopes did Eve choose?
  1. 2
  2. 3
  3. 4
  4. 5
  5. 6

Question 18

Color a 3 × 3 grid so each row, column and both diagonals contain three different colors. What is the least number of colors?

Question illustration
  1. 3
  2. 4
  3. 5
  4. 6
  5. 7

Question 19

A cube has four marked angles as shown. What is their sum?

Question illustration
  1. 315°
  2. 330°
  3. 345°
  4. 360°
  5. 375°

Question 20

There are 2016 kangaroos, each grey or red, and both colors occur. For each kangaroo K take number of opposite-color kangaroos divided by number of same-color kangaroos, including K. What is the sum of all 2016 fractions?
  1. 2016
  2. 1344
  3. 1008
  4. 672
  5. more information needed