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IMAS 2011 — Upper Primary Grades 5–6 — Round 1

Question 2

Lynne’s last class of the day starts at 2:30 pm. Each class lasts 45 minutes. When this class is over, what is the angle, the one less than $ 180^{\circ} $, which is formed by the hour hand and the minute hand of her watch?
  1. $ 90^{\circ} $
  2. larger than $ 90^{\circ} $
  3. Larger than $ 0^{\circ} $ and less than $ 90^{\circ} $
  4. $ 0^{\circ} $
  5. could not be determined

Question 3

Each small square in all the following figures has side length 1. Which figure has the largest area?
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Question 4

In which of the following figures does the shaded part occupy more than $ \frac{3}{4} $ of the total area?
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Question 5

Bruce is reading a story book. One of the stories takes up two consecutive pages, and the sum of the page numbers is 345. On which page does this story begin?
  1. 114
  2. 115
  3. 171
  4. 172
  5. 173

Question 6

If we copy the letters “MATHS” repeatedly, we get “MATHSMATHS...”. What is the 2011-th letter from the left?
  1. M
  2. A
  3. T
  4. H
  5. S

Question 7

From $2+2=2\times2$, we observe that the sum of the two numbers 2 and 2 is equal to their product. Of the following pairs of numbers, which has this property?
  1. 2 and $ \frac{2}{3} $
  2. 3 and $ \frac{3}{2} $
  3. 4 and $ \frac{4}{5} $
  4. 5 and $ \frac{6}{5} $
  5. 6 and $ \frac{7}{5} $

Question 8

A certain percentage of the area of the given figure is shaded.

What is this percentage?

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  1. 25%
  2. 27.5%
  3. 36.5%
  4. 37.5%
  5. 42.5%

Question 9

Thirty students are standing in a row. They start calling out 1, 2, 3, … from the left, and Mickey calls out 13. If the calling starts from the right instead, what number will Mickey call out?
  1. 18
  2. 17
  3. 16
  4. 14
  5. 13

Question 10

The box contains 20 balls numbered from 1 to 20, but identical otherwise. Eve draws a ball at random from the box. Which of the following outcome is the most likely?
  1. drawing the ball numbered 11.
  2. drawing balls that are of even number.
  3. drawing balls that ended with the digit 5, 6, 7, 8.
  4. drawing balls that contain the digit 1.
  5. drawing balls with a one-digit number.

Question 11

There is a pattern to the given sequence of figures.

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(1)

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(2)

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(3)

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(4)

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(5)

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(6)

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(7)

Which of the following will be the 2011-th figure of the sequence?
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Question 12

Woody has a rabbit which eats three carrots and one cabbage every two days. He is going on a 7-day holiday. At least how many carrots and cabbages must he leave behind for the rabbit? (Assume that all carrots are of the same size, as are the cabbages.)
  1. 9 carrots and 3 cabbages
  2. 10 carrots and 3 cabbages
  3. 11 carrots and 3 cabbages
  4. 10 carrots and 4 cabbages
  5. 11 carrots and 4 cabbages

Question 13

The given figure is the net of a cube, and each face is labeled with a letter. When the cube is formed, which letter is on the face opposite to the one labeled with the letter I?

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  1. A
  2. K
  3. M
  4. O
  5. S

Question 14

Mark's bicycle has a front wheel and a back wheel of different sizes. The front wheel advances 3 metres per revolution, and the back wheel advances 2 metres per revolution. Which statement accurately describes Mark's 6-kilometre trip from home to school?

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  1. The front wheel makes 3000 revolutions.
  2. The front wheel and the back wheel makes the same number of revolutions.
  3. The front wheel makes 1.5 times the number of revolutions of the back wheel.
  4. The front wheel run 1000 revolutions less than the back wheel.
  5. The back wheel run 1000 revolutions less than the front wheel.

Question 15

The given rectangle is formed of six small squares. If the perimeter of the rectangle is 30 centimetres, what is its area in square centimetre?

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  1. 24
  2. 36
  3. 54
  4. 150
  5. 216

Question 16

The given diagram shows five differently coloured disks. The orange disk is above the green disk but below all the others. The purple disk is above the blue disk but below the red disk. What is the colour of the disk labeled Z?

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  1. Red
  2. Orange
  3. Green
  4. Blue
  5. Purple

Question 17

Gia’s grandfather, a watchmaker, gives her a special watch. The long hand makes one revolution per hour, and the short hand makes one revolution per 24 hours. When Gia’s favorite television show starts, the positions of the two hands are as shown. At this moment, what is the standard time?

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  1. 18:20
  2. 19:20
  3. 19:25
  4. 19:30
  5. 20:25

Question 18

The given menu is from a restaurant serving a buffet dinner. What is the minimum expenditure for four adults and three children under 12 to eat there?

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Menu text: Adult: 30 dollars; child under 12: 25 dollars; Family Set A (1 adult and 1 child): 45 dollars; Family Set B (2 adults and 1 child): 70 dollars.
  1. 155 dollars
  2. 160 dollars
  3. 165 dollars
  4. 180 dollars
  5. 195 dollars

Question 19

Wendy throws three cubical dice, with the numbers 1, 2, 3, 4, 5 and 6 on the faces. Which of the following numbers cannot be the product of three numbers on the dice?
  1. 48
  2. 84
  3. 120
  4. 180
  5. 216

Question 20

Leon is given five wooden blocks:

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Which of the following blocks should be added so that he can make a $ 4 \times 4 \times 4 $ cube? (None of the blocks can be dissected)
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