Answers to one-page math problems in the 9th grade gifted student exam

Many students (even teachers) were surprised when they encountered a one-page exam in the city's excellent student exam, but in fact the solution to the problem was very simple.

As we have seen through some math problems of AMC, Kangaroo, SASMO... the math problems behind the problem are not too difficult, but to solve them students must read the problem, extract information and understand the mathematical nature of the question.

For Vietnamese students, this problem is difficult, while they solve technical problems many times more difficult very well. Therefore, many students (and even many teachers) were surprised when they encountered the following one-page test (problem number 6 out of 6 math problems) in the 9th grade excellent student exam of Ho Chi Minh City in the 2015-2016 school year. Please read and solve it together.

Topic:

On the afternoon of March 13, the Dau Tieng - Phuoc Hoa Lake Irrigation Exploitation Company announced that it had finished releasing water to push back the salinity into the Saigon River. This is the fifth water release since the beginning of the year, helping Saigon residents ensure water for daily life and agriculture.

The water discharge with a capacity of 30 m3/s lasted for 3 days, and saltwater was pushed out to the river mouths. According to this unit, after the discharge, the water level in the lake was about 20 m high, with a reserve of nearly 850 million m3.

Although it helps downstream water plants operate, many experts expressed concern because the reserves in upstream lakes are low while the drought and salinity are forecast to last until May. Currently, the lakes have to work together to release water to push back the salinity to serve agriculture and production activities.

Regarding the cause of saltwater intrusion, Mr. Pham The Vinh - Southern Institute of Water Resources Research - said that the severe drought and saltwater intrusion occurred because of the prolonged El Nino, causing very little rain in the Southern region. In addition, the high tides lasting until February and March caused saltwater to penetrate deep into river mouths.

Mr. Bui Thanh Giang - Deputy General Director of Saigon Water Supply Company (Sawaco) - said that this year, the water reserves in upstream lakes have decreased sharply. In particular, the water storage capacity of the Dau Tieng - Phuoc Hoa lake system on the upper Saigon River is currently only about 70%. The flow of Tri An lake on the Dong Nai River is only about 80% of the annual average.

Regarding the long-term solution, Sawaco proposed that the Ho Chi Minh City People's Committee allow the construction of a raw water reservoir for the Saigon River water source with funding from the budget. In addition, the unit also proposed improving water treatment technology, but this requires high investment and operating costs. (Source: VnExpress.net).

a) Please tell me how much water Dau Tieng Lake has released in the past 3 days?

b) If we continue to discharge 20% of the existing water volume to prevent salinity (at the above discharge rate), how many days will this work take?

Assuming the anti-salt water discharge takes place continuously from today (March 22) to May 15, calculate the amount of water the lake has discharged during this period.

Prize:

The solution is actually very simple. The important thing is that we read, understand and draw out the necessary information. And in real-life situations, we can ask ourselves questions like the above to draw conclusions from the information we receive. People say that hearing 1 and knowing 2, 3 is from this ability to deduce.

In the general math program, we have focused too much on technical issues (e.g. simplifying expressions, solving equations, proving inequalities) and neglected reading comprehension and modeling. No wonder a student exclaimed, "Teacher, I feel so discouraged reading the questions!"

Let’s look at the answer to see how simple this problem is. Simple yet interesting, not only because of its practicality, but also because of its academic value: reading, extracting necessary information and processing information appropriately are essential skills for everyone.

Dr. Tran Nam Dung
University of Science, Vietnam National University, Ho Chi Minh City

According to VnExpress