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FMO 2021 - Grade 5 - International - Paper 10 - Sample

Question 1

Which figure should fill the cell containing the question mark?

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Question 2

Mr. Lee plants vegetables on $\frac 12$ of his garden and builds a pond on $\frac 13$ of the remaining land. He makes a path on the rest. The path has area 30 m². Find the garden’s area.
  1. 90 m²
  2. 60 m²
  3. 36 m²
  4. 80 m²
  5. 120 m²

Question 3

Find the value of the triangle in the operation chain, given that the circle is the smallest three-digit odd number.

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  1. 167
  2. 170
  3. 165
  4. 169
  5. 70

Question 4

A wall uses alternating gray and striped square tiles so that tiles of the same type do not share a side. Some fall off, leaving the white region shown with perimeter 90 cm. Find the total area, in cm², of the gray tiles that fell off.

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  1. 225
  2. 200
  3. 175
  4. 150
  5. 125

Question 5

A store sells rice in sacks of 50 kg or 80 kg. Which of the following cannot be the total weight of whole sacks sold in a day?
  1. 100 kg
  2. 130 kg
  3. 210 kg
  4. 180 kg
  5. 170 kg

Question 6

Alex folds a square sheet in half twice and makes the two cuts shown. How many pieces does he obtain?

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  1. 12
  2. 10
  3. 5
  4. 4
  5. 3

Question 7

Five runners’ finishing times are shown on equally spaced graph lines. After the winner finishes, 6 seconds pass before the third runner finishes. How many seconds does the last runner take?

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  1. 12
  2. 18
  3. 22
  4. 33
  5. 32

Question 8

Four friends own 240 books altogether. Arthur gives Ben 3 books, Ben gives Charles 4, Charles gives Derek 5, and Derek gives Arthur 6. They then have equal numbers. How many books did the friend with the fewest books originally own?
  1. 57
  2. 58
  3. 59
  4. 60
  5. 61

Question 9

Each grid cell has side length 1 cm. Find the total area of the four shapes, in cm².

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  1. 44
  2. 43
  3. 41
  4. 40
  5. 42

Question 10

A teacher gives each of 7 students one gift box. A box contains either 2 pens and 3 books, or 5 pens and 1 book. There are 17 pens altogether. How many books are there?
  1. 15
  2. 19
  3. 6
  4. 21
  5. 8

Question 11

Candace glues 25 white cubes into the arch shown and paints all surfaces red, except the bottom. How many unit cube faces are painted?

Interpretation note: the supplied answer excludes every downward-facing face, including the underside of the bridge. Use that source convention for this multiple-choice question. The alternative ground-contact interpretation is explained in the solution.

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  1. 74
  2. 79
  3. 82
  4. 70
  5. 86

Question 12

A box contains 10 red, 5 green, 6 blue and 14 black balls. Ally draws without looking. What is the minimum number she must draw to guarantee balls of all four colors?
  1. 29
  2. 30
  3. 31
  4. 32
  5. 33

Question 13

Eight identical rectangles, each of perimeter 36 cm, form the large square shown. Find the perimeter of that square.

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  1. 84 cm
  2. 96 cm
  3. 144 cm
  4. 72 cm
  5. 108 cm

Question 14

Find square + circle, using the three equations shown.

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  1. 42
  2. 66
  3. 48
  4. 57
  5. None of the above

Question 15

James places each integer 1 through 9 exactly once in a 3-by-3 grid. He calculates the sums of all three rows and all three columns. Five of those sums, in some order, are 12, 13, 15, 16 and 17. What is the sixth?

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  1. 17
  2. 16
  3. 15
  4. 14
  5. 13

Question 16

Lucy stacks cards to form the one-, two- and three-floor towers shown. How many cards does she need for a 20-floor tower?

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