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VTMO 2019 — Grade 4 — semifinal

Question 1

Which calculation result is incorrect?
  1. $1\times1:1\times1=1$
  2. $2:2+2:2=2$
  3. $3\times3-3+3=3$
  4. $(4-4):4+4=4$
  5. $5+5\times(5-5)=5$

Question 2

Linh is $5$ years older than Minh. How old is Minh when Linh is $35$?
  1. $20$
  2. $25$
  3. $30$
  4. $35$
  5. $40$

Question 3

Select the figure with exactly half its area shaded.

Question illustration
  1. Figure $A$
  2. Figure $B$
  3. Figure $C$
  4. Figure $D$
  5. Figure $E$

Question 4

A container full of water weighs $13 \,\mathrm{kg}$; with half the water it weighs $7 \,\mathrm{kg}$. What is the empty weight in kg?
  1. $1$
  2. $2$
  3. $5$
  4. $6$
  5. $3$

Question 5

Four congruent rectangles are assembled as shown. Each small rectangle’s long side is $9 \,\mathrm{cm}$. Find the combined perimeter.

Question illustration
  1. $36 \,\mathrm{cm}$
  2. $42 \,\mathrm{cm}$
  3. $45 \,\mathrm{cm}$
  4. $48 \,\mathrm{cm}$
  5. $54 \,\mathrm{cm}$

Question 6

Thanh’s family keeps ducks and sheep with $140$ legs total. Which option is possible?
  1. $60$ ducks, $10$ sheep
  2. $50$ ducks, $15$ sheep
  3. $40$ ducks, $16$ sheep
  4. $35$ ducks, $18$ sheep
  5. $30$ ducks, $20$ sheep

Question 7

A bus departs every $24$ minutes, with a departure at $06 : 06$. Minh arrives at $06 : 40$. How many minutes must he wait?
  1. $6$
  2. $14$
  3. $20$
  4. $24$
  5. $34$

Question 8

In the figure sequence, how many white triangles are in figure $6$?

Question illustration
  1. $22$
  2. $14$
  3. $16$
  4. $18$
  5. $20$

Question 9

An and Binh play: the loser gives one card to the winner each round. An wins $4$ rounds, and Binh ends with $2$ more cards than he started with. How many rounds were played?
  1. $6$
  2. $8$
  3. $9$
  4. $10$
  5. $12$

Question 10

Each unit square has area $2$ square centimeters. Find the shaded area.

Question illustration
  1. $15$
  2. $21$
  3. $20$
  4. $30$
  5. $28$

Question 11

Numbers $1$ through $32$ are evenly spaced in order around a circle. Diameters pair opposite numbers. Which is opposite $12$?
  1. $28$
  2. $27$
  3. $23$
  4. $25$
  5. $29$

Question 12

Color the cardboard so regions sharing an edge differ. What is the fewest colors?

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

Question 13

Fill the magic square with $2$ through $10$, each once, so rows, columns and diagonals have equal sums. Find $x$.

Question illustration
  1. $2$
  2. $3$
  3. $5$
  4. $6$
  5. $8$

Question 14

Fold the net into a cube. Which three faces meet at $P$?

Question illustration
  1. $BEF$
  2. $ACF$
  3. $BCF$
  4. $ABE$
  5. $ABF$

Question 15

Choose one entry from each row and each column of the $3 \times 3$ table, and multiply the three. What is the maximum?

Question illustration
  1. $45$
  2. $162$
  3. $168$
  4. $105$
  5. $504$

Question 16

Roll a six-sided die twice. How many ordered outcomes sum to $7$?

Question 17

A matchstick grid $1 \times 1$ uses $4$ sticks and $2 \times 2$ uses $12$ as shown. How many does an $8 \times 8$ grid need?

Question illustration

Question 18

An odometer reads palindrome $42924$. What is the least additional distance to reach the next palindrome?

Question 19

An drives east $10 \,\mathrm{km}$, north $5$, east $3$, south $11$, west $13$. How far is the final position from the start?

Question 20

Fill $1 \text{--} 9$ once each in $a = 3 \times 3$ table. Top row contains $1 , 8 , 6$; bottom row $9 , 4 , 2$. The right column excludes $8 , 3 , 5 , 1 , 9 , 4$; the left excludes $6 , 4 , 3 , 1 , 7 , 2$. What is in the center?