On the afternoon of June 9th, the Ho Chi Minh City Department of Education and Training announced that, following public concerns about a flaw in question 5 of the 10th grade entrance exam in Mathematics, the Department had reviewed the matter and responded.
Specifically, the problem involves a real-world phenomenon: the process of boiling water in an electric kettle. This investigation focuses on only a short phase of the water boiling process; the start time of the investigation (t = 0) is not the start time of the water boiling process.
Problem 5 from the Mathematics entrance exam for 10th grade in public schools in Ho Chi Minh City, academic year 2023-2024.
Based on the data collected during this process, mathematically it can be described as a diagram and represented by a function that students have learned in the curriculum. Therefore, with their mathematical knowledge and skills (linear functions, graphs of linear functions, points on graphs, systems of linear equations with two variables, calculations, etc.), students can solve the requirements of the problem.
"According to the regulations and grading guidelines, cases where students provide solutions that differ from the grading guidelines but are still reasonable will be considered and evaluated," the Ho Chi Minh City Department of Education and Training emphasized.
Previously, after the 2023-2024 10th grade entrance exam concluded, some opinions suggested that question 5 of the exam contained a physics error: The question gives power P along with the unit W, so the coefficients a and b in the formula P = at + b should have corresponding units of W/s and W. If the student's answer or solution only provides the number without the unit, it is incorrect.
If the understanding is to find the time t from t = 0 for P(t) = 105W, then the data "boiling water" is misleading and irrelevant to the problem. If we still maintain the understanding that we are finding the time to boil water with a power of 105W, many complications arise. Suppose we boil m (kg) of water from T1 (°C) to T2 (°C), with specific heat capacity C (J/kgC), then the required heat is Q = mc(T2-T1).
Writing about boiling water with a fixed power is misleading because it lacks the data on the starting temperature, the mass of water, and the specific heat capacity of water. Furthermore, solving it this way is irrelevant to the given function P(t), and only involves applying the work W = Pt = 105.t and solving the equation Q = W to find the unknown t.
Because the power P(t) changes with time t, the formula to be performed is W = integral [P(t') dt'] from t' = 0 to t' = t (the time to be found) and solve Q = W to find the unknown t. Understood in this way, the knowledge of integration is outside the curriculum and the data 105 W becomes ambiguous.
Furthermore, while the data provided in the exam can be solved using formulas, a deeper analysis from a physics perspective might confuse students.
Lam Ngoc
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