VTMO 2026 - Grade 5 - Semifinal - SET 12 - Self-study

Question 1

The diagram shows a net of a die. Which face is opposite the face marked with a diamond?

1. Triangle
2. Circle
3. Semicircle
4. Plus sign
5. Arrow

Question 2

An assembles six wooden pieces into a square: two identical large triangles, two identical medium triangles, one small triangle and one square. What is the difference between the sum of the six pieces’ perimeters and the perimeter of the assembled square? A side of a large triangle is 10 cm, as marked.

1. 20 cm
2. 30 cm
3. 100 cm
4. 10 cm
5. 50 cm

Question 3

Colour the faces of the solid shown so that any two faces sharing an edge have different colours. What is the least number of colours needed?

1. 2
2. 3
3. 4
4. 6
5. 8

Question 4

An initially has 40 sweets. First, Bình gives An 20 sweets; then An gives Bình 30 sweets. Finally, Bình gives An one fifth of Bình’s sweets, and the two children then have equal amounts. How many sweets did Bình have initially?

1. 20
2. 30
3. 40
4. 50
5. 60

Question 5

The triangle and the square in the diagram have the same perimeter. The square has side length 4 cm. What is the perimeter of the combined outer shape, in centimetres?

1. 12
2. 24
3. 26
4. 28
5. 32

Question 6

At the start of summer, Trung is 150 cm tall. By the end of summer, his height has increased by 5%. How tall is he then?

1. 157
2. 157.5
3. 158
4. 158.5
5. 165

Question 7

Calculate $51.17\div7.31$.

1. 5
2. 7
3. 6
4. 8
5. 13

Question 8

In July of a certain year, three Fridays fall on even-numbered dates and three Saturdays fall on odd-numbered dates. What day of the week is 5 September of that year?

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

Question 9

A group of pupils is travelling by bus, with the same number on each bus. Just before departure, one bus breaks down. Its pupils are divided equally among the remaining buses, adding 3 pupils to each. Each remaining bus now carries 27 pupils. How many pupils are travelling?

1. 216
2. 218
3. 224
4. 240
5. 254

Question 10

A jar weighs 16.5 kg when it is half full of water and 11.5 kg when it is one third full. How much does the empty jar weigh, in kilograms?

1. 1
2. 1.5
3. 2
4. 2.5
5. 3

Question 11

Bon’s square garden is divided into four equal smaller squares to grow four kinds of vegetables. A total of 120 m of fencing is used for the outer boundary and the two internal dividing lines, as shown. What is the area of the whole garden, in square metres?

1. 100
2. 196
3. 225
4. 400
5. 324

Question 12

Some equal small squares are used to form a large square, with 3 small squares left over. Which of the following could be the original number of small squares?

1. 103
2. 102
3. 97
4. 107
5. 108

Question 13

Every corner of the boundary in the diagram is a right angle. The shaded region has area $A$ and perimeter $P$. Find $A+P$.

Question 14

Fresh fruit juice contains 80% water. To concentrate it, 75% of that water is removed. What percentage of the concentrated juice is water?

Question 15

Two containers hold water. First, pour from container 1 into container 2 an amount equal to the water already in container 2. Then pour from container 2 into container 1 an amount equal to the water now in container 1. Both containers then hold 32 litres. How many litres did each hold initially? Give container 1’s amount, then container 2’s.

Question 16

Two four-digit numbers have a difference of 6789. What is the smallest possible sum of the two numbers?

Question 17

An has $2/3$ as many sweets as Bình. Bình has $3/4$ as many as Châu, and Châu has $4/5$ as many as Dũng. What fraction of An’s amount does Dũng have? If Dũng’s amount represents 15 equal parts, how many such parts does An’s amount represent? Give the fraction first, then the number of parts.

Question 18

A square has a side equal to the width of a rectangle. The rectangle has perimeter 100 cm and length 40 cm. Find the perimeter of the square, in centimetres.

1. 100
2. 10
3. 20
4. 40
5. 50

Question 19

Lam uses four of the five types of pieces shown to form the figure below. Each type may be used more than once. Which piece cannot be used?

1. three-square strip
2. two-square strip
3. 2-by-2 square
4. T-shaped piece
5. L-shaped piece

Question 20

Which expression below has value 7?

1. $4\times5+6\times3$
2. $4\times5+6\div3$
3. $6\div3+5\times4$
4. $3\times4\div6+5$
5. $3+4\times5\times6$