Toán [Event] HMF's Mathematics Contest - Round 2

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Không mở trả lời sau này.

Darkness Evolution

Duke of Mathematics
Thành viên
27 Tháng năm 2020
620
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Vĩnh Phúc
THCS Vĩnh Yên
Câu 4: To form a beautiful patterned cube, An cuts a piece of cardboard and draws patterns on the squares, creating the following shape:
dKJpZRkyBSOmCYcXZFJMnlAlZFDTgzUP9IykWnaT5AvoxMb7rDtsue9-RDzwRY4Cf4VrP79lQoxu-ggfQ_clqXH1gtVizG5MyBN_Kx5gbYD7GE0OzgKgasI1F6GCj3gwr3FRr9xF

Thus: The cube that An has after folding the above sample can be:
WtoWi3C8re_VdyF5-hqu5cyRxAl-rpFweHjbAbYzr3qJjYC6OMDTAqHQao-j_8YG0cGnJsoAfKQ6A7TxIUoZ01VyYrJKSe4RKT4hgzi2_EKKvdwgffcOWsUpKhTkLHr0bNB9gfV-

Câu 5: sẽ có lúc 20:40
Answer: B; C; D; E
 

Tiểu Bạch Lang

Cựu TMod Toán|Duchess of Mathematics
Thành viên
9 Tháng tư 2020
1,049
1,064
181
18
Hải Dương
THPT Chuyên Nguyễn Trãi

kido2006

Cựu TMod Toán
Thành viên
26 Tháng một 2018
1,693
2
2,652
401
Bắc Ninh
THPT Chuyên Bắc Ninh

Tungtom

King of Mathematics
Thành viên
7 Tháng sáu 2019
507
1,460
146
Thanh Hóa
Trường THPT Nông Cống 2

kido2006

Cựu TMod Toán
Thành viên
26 Tháng một 2018
1,693
2
2,652
401
Bắc Ninh
THPT Chuyên Bắc Ninh
Câu 1: In a soccer tournament with 4 teams A,B,C,D; 3 predictions are made
a) Team A is second, Team B is first
b) Team B is second, Team D is third
c) Team C is second, Team D is fourth
All the predictions have 1 correct and 1 wrong. Predict the order of each team.
Câu 2 sẽ có lúc 20:10
B C D A

If A second [tex]\rightarrow[/tex] D is third & fourth (nonsense)
So B first [tex]\Rightarrow D-3^{rd}[/tex][tex]\rightarrow C-2{nd}\rightarrow A-fourth[/tex]
 

Darkness Evolution

Duke of Mathematics
Thành viên
27 Tháng năm 2020
620
1,103
146
16
Vĩnh Phúc
THCS Vĩnh Yên
Câu 5:
A high-rise building (starts at the same base height and has 1 unit of floor) is surrounded by streets, the heights of the building is shown in the following chart:

TC1IeocEZHRixOYBnXGVs3d8OXv_JvC8mrjnbYyrEYq2uH8fm74NNmUyZr_Vod7K4S3-KVYeaoIcBV8oFCqAljm8UXxAHuO-o0x3YfgxffR_O0xec5YJJpcMykeOdJR8WdlsMVfN

One day, it rains heavily and floods the low area of the property. Since taller buildings surround the lower area, the water cannot be drained out. It just keeps rising up. The image is illustrated below:

1cyJqhdm1p3JZUTdELeRRxXXsDJZsBgLZK4fZaTq-42r5FwF36XpWB_htlO2EFVbYUj38egUIZTBFNMvm6eqcCROVFN8awmWpy61aHJwJCmn6n0zAqvTyVXg-ip30hEHZXvM_RUv

Key:
- Blue area represents rainwater.
- Brown columns represent buildings.

Knowing that the outer buildings are located on the edges, which will not be affected by the "water retention" since the water drains down the street.

Thus, the area of building that is flooded with ____ unit(s) of floor.
Câu 6: sẽ có lúc 20:50
Answer: 1 unit
 

Tiểu Bạch Lang

Cựu TMod Toán|Duchess of Mathematics
Thành viên
9 Tháng tư 2020
1,049
1,064
181
18
Hải Dương
THPT Chuyên Nguyễn Trãi
Câu 5:
A high-rise building (starts at the same base height and has 1 unit of floor) is surrounded by streets, the heights of the building is shown in the following chart:

TC1IeocEZHRixOYBnXGVs3d8OXv_JvC8mrjnbYyrEYq2uH8fm74NNmUyZr_Vod7K4S3-KVYeaoIcBV8oFCqAljm8UXxAHuO-o0x3YfgxffR_O0xec5YJJpcMykeOdJR8WdlsMVfN

One day, it rains heavily and floods the low area of the property. Since taller buildings surround the lower area, the water cannot be drained out. It just keeps rising up. The image is illustrated below:

1cyJqhdm1p3JZUTdELeRRxXXsDJZsBgLZK4fZaTq-42r5FwF36XpWB_htlO2EFVbYUj38egUIZTBFNMvm6eqcCROVFN8awmWpy61aHJwJCmn6n0zAqvTyVXg-ip30hEHZXvM_RUv

Key:
- Blue area represents rainwater.
- Brown columns represent buildings.

Knowing that the outer buildings are located on the edges, which will not be affected by the "water retention" since the water drains down the street.

Thus, the area of building that is flooded with ____ unit(s) of floor.
Câu 6: sẽ có lúc 20:50
The area of building that is flooded with __1__ unit(s) of floor.
 

Lê Tự Đông

Prince of Mathematics
Thành viên
23 Tháng mười hai 2018
928
860
146
Đà Nẵng
THPT chuyên Lê Quý Đôn Đà Nẵng
Câu 5:
A high-rise building (starts at the same base height and has 1 unit of floor) is surrounded by streets, the heights of the building is shown in the following chart:

TC1IeocEZHRixOYBnXGVs3d8OXv_JvC8mrjnbYyrEYq2uH8fm74NNmUyZr_Vod7K4S3-KVYeaoIcBV8oFCqAljm8UXxAHuO-o0x3YfgxffR_O0xec5YJJpcMykeOdJR8WdlsMVfN

One day, it rains heavily and floods the low area of the property. Since taller buildings surround the lower area, the water cannot be drained out. It just keeps rising up. The image is illustrated below:

1cyJqhdm1p3JZUTdELeRRxXXsDJZsBgLZK4fZaTq-42r5FwF36XpWB_htlO2EFVbYUj38egUIZTBFNMvm6eqcCROVFN8awmWpy61aHJwJCmn6n0zAqvTyVXg-ip30hEHZXvM_RUv

Key:
- Blue area represents rainwater.
- Brown columns represent buildings.

Knowing that the outer buildings are located on the edges, which will not be affected by the "water retention" since the water drains down the street.

Thus, the area of building that is flooded with ____ unit(s) of floor.
Câu 6: sẽ có lúc 20:50
1
 

kido2006

Cựu TMod Toán
Thành viên
26 Tháng một 2018
1,693
2
2,652
401
Bắc Ninh
THPT Chuyên Bắc Ninh
Câu 5:
A high-rise building (starts at the same base height and has 1 unit of floor) is surrounded by streets, the heights of the building is shown in the following chart:

TC1IeocEZHRixOYBnXGVs3d8OXv_JvC8mrjnbYyrEYq2uH8fm74NNmUyZr_Vod7K4S3-KVYeaoIcBV8oFCqAljm8UXxAHuO-o0x3YfgxffR_O0xec5YJJpcMykeOdJR8WdlsMVfN

One day, it rains heavily and floods the low area of the property. Since taller buildings surround the lower area, the water cannot be drained out. It just keeps rising up. The image is illustrated below:

1cyJqhdm1p3JZUTdELeRRxXXsDJZsBgLZK4fZaTq-42r5FwF36XpWB_htlO2EFVbYUj38egUIZTBFNMvm6eqcCROVFN8awmWpy61aHJwJCmn6n0zAqvTyVXg-ip30hEHZXvM_RUv

Key:
- Blue area represents rainwater.
- Brown columns represent buildings.

Knowing that the outer buildings are located on the edges, which will not be affected by the "water retention" since the water drains down the street.

Thus, the area of building that is flooded with ____ unit(s) of floor.
Câu 6: sẽ có lúc 20:50
1 unit(s) of floor.
 

Tungtom

King of Mathematics
Thành viên
7 Tháng sáu 2019
507
1,460
146
Thanh Hóa
Trường THPT Nông Cống 2
Câu 5:
A high-rise building (starts at the same base height and has 1 unit of floor) is surrounded by streets, the heights of the building is shown in the following chart:

TC1IeocEZHRixOYBnXGVs3d8OXv_JvC8mrjnbYyrEYq2uH8fm74NNmUyZr_Vod7K4S3-KVYeaoIcBV8oFCqAljm8UXxAHuO-o0x3YfgxffR_O0xec5YJJpcMykeOdJR8WdlsMVfN

One day, it rains heavily and floods the low area of the property. Since taller buildings surround the lower area, the water cannot be drained out. It just keeps rising up. The image is illustrated below:

1cyJqhdm1p3JZUTdELeRRxXXsDJZsBgLZK4fZaTq-42r5FwF36XpWB_htlO2EFVbYUj38egUIZTBFNMvm6eqcCROVFN8awmWpy61aHJwJCmn6n0zAqvTyVXg-ip30hEHZXvM_RUv

Key:
- Blue area represents rainwater.
- Brown columns represent buildings.

Knowing that the outer buildings are located on the edges, which will not be affected by the "water retention" since the water drains down the street.

Thus, the area of building that is flooded with ____ unit(s) of floor.
Câu 6: sẽ có lúc 20:50
the area of building that is flooded with 3 unit(s) of floor.
 

Darkness Evolution

Duke of Mathematics
Thành viên
27 Tháng năm 2020
620
1,103
146
16
Vĩnh Phúc
THCS Vĩnh Yên

Lê Tự Đông

Prince of Mathematics
Thành viên
23 Tháng mười hai 2018
928
860
146
Đà Nẵng
THPT chuyên Lê Quý Đôn Đà Nẵng

Tiểu Bạch Lang

Cựu TMod Toán|Duchess of Mathematics
Thành viên
9 Tháng tư 2020
1,049
1,064
181
18
Hải Dương
THPT Chuyên Nguyễn Trãi

Tungtom

King of Mathematics
Thành viên
7 Tháng sáu 2019
507
1,460
146
Thanh Hóa
Trường THPT Nông Cống 2
Câu 6: 1 rabbit saw 9 elephants while going to the river.
Every elephant saw 3 monkeys going to the river.
Each monkey had 1 tortoise in each hand.
How many animals were going to the river?
10 animals.
1 rabit saw 9 elephants while going to the river, but it doesn't mean 9 elephants were going to the river.
Every elephant saw 3 monkeys going to the river, and each monkey had tortoise in each hand.
So, the sum is: $1+3+3*2=10$
 

kido2006

Cựu TMod Toán
Thành viên
26 Tháng một 2018
1,693
2
2,652
401
Bắc Ninh
THPT Chuyên Bắc Ninh
Status
Không mở trả lời sau này.
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