Ôn tập kiến thức tổng hợp

• Factor the quadratic: \(x^2-5x+6=(x-2)(x-3)\).
• Identify the roots: x=2 and x=3 split the number line into three intervals: \((‑\infty,2),\;(2,3),\;(3,+\infty)\).
• Test a point in each interval: Choose x=0 for the first interval, x=2.5 for the middle, and x=4 for the last.
  • At x=0: \((0-2)(0-3)=6>0\) → inequality false.
  • At x=2.5: \((2.5-2)(2.5-3)=0.5\times(-0.5)=-0.25
  • At x=4: \((4-2)(4-3)=2\times1=2>0\) → inequality false.
• Combine the true intervals: The solution set is the open interval \((2,3)\).

Key takeaway: For a quadratic that opens upward (positive leading coefficient), the expression is negative between its two real roots.

2. Basic Probability with Two Dice

When two fair six‑sided dice are rolled simultaneously, each die has outcomes {1,…,6}. The sample space contains 6×6=36 equally likely ordered pairs.

• List the pairs that sum to 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1). There are 6 favorable outcomes.
• Compute the probability: \(P=\frac{6}{36}=\frac{1}{6}\).

Practice question: What is the probability of obtaining a total of 8? (Answer: \(\frac{5}{36}\)).

3. Literary Devices: Metonymy (Hoán Dụ)

In the Vietnamese sentence “Nhà báo ấy là một cây bút sắc sảo”, the phrase cây bút (literally “pen”) stands for the journalist himself. This is an example of metonymy, a figure of speech where a thing is called by the name of something closely associated with it.

• Difference from other devices:
  • Comparison (so sánh) uses “like” or “as”.
  • Repetition (điệp ngữ) repeats a word for emphasis.
  • Personification (nhân hóa) attributes human qualities to non‑human entities.
• Why it works: The pen is the primary tool of a writer; using it to represent the writer creates a vivid, concise image.

4. Cause‑Result Relationships in Compound Sentences

The sentence “Vì trời mưa nên chúng em nghỉ học” contains two clauses linked by the conjunction vì… nên. This structure expresses a cause‑result (nguyên nhân – kết quả) relationship:

• Cause (nguyên nhân): "trời mưa" – the rain.
• Result (kết quả): "chúng em nghỉ học" – we skip class.

Understanding these connectors helps in both reading comprehension and writing clear arguments.

5. Electrical Circuits: Equivalent Resistance of Parallel Resistors

When resistors are connected in parallel, the total (equivalent) resistance R_eq is found using the reciprocal formula:

\[\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2}\]

• Given R_1 = 6\,\Omega and R_2 = 3\,\Omega:
  • \(\frac{1}{R_{eq}} = \frac{1}{6}+\frac{1}{3}=\frac{1}{6}+\frac{2}{6}=\frac{3}{6}=\frac{1}{2}\)
  • Therefore, R_eq = 2\,\Omega.

Tip: For two resistors, you can also use the shortcut \(R_{eq}=\frac{R_1R_2}{R_1+R_2}\).

6. Chemical Equilibrium: Le Chatelier’s Principle

The reaction N₂(g) + 3H₂(g) ⇌ 2NH₃(g) involves gases. Increasing the pressure shifts the equilibrium toward the side with fewer gas moles. Compare the mole counts:

• Reactant side: 1 (N₂) + 3 (H₂) = 4 moles.
• Product side: 2 (NH₃) = 2 moles.

Because 2 < 4, the system responds by producing more NH₃. Hence the shift is forward (chiều thuận), toward ammonia formation.

7. Cell Biology: Chromosome Numbers in Meiosis

For a diploid organism with a chromosome complement 2n = 8, meiosis reduces the number by half. During the telophase of meiosis I (kì sau của nguyên phân), each daughter cell contains the full set of chromosomes but each chromosome consists of two sister chromatids. Therefore, the number of individual chromatids (often called “nhiễm sắc thể đơn” in Vietnamese) is:

• Each of the 4 chromosomes (n = 4) has 2 chromatids → 4 × 2 = 8 chromatids.
• Thus, there are 8 single chromatids in each cell at that stage.

Remember: after meiosis I, chromosome number is halved, but each chromosome is still duplicated.

8. Vietnamese History: The Battle of Bạch Đằng (938)

The decisive victory at Bạch Đằng River in 938 AD was led by Ngô Quyền. He employed a clever tactic of planting hidden iron‑tipped stakes in the riverbed, waiting for the tide to recede, and then ambushing the invading Nam Hán (Southern Han) fleet. This battle marked the end of Chinese domination and the beginning of an independent Vietnamese state.

• Key figures: Ngô Quyền (commander) vs. the Southern Han army.
• Historical significance: Established the first Vietnamese dynasty after centuries of foreign rule.

9. Consolidated Practice Quiz

Test your understanding with the original questions. Review the explanations above if you encounter difficulty.

1. What is the solution set of x²‑5x+6?
   Answer: (2,3)
2. Probability that two dice sum to 7?
   Answer: \(\frac{1}{6}\)
3. In the phrase “cây bút” used for a journalist, the literary device is?
   Answer: Hoán dụ (metonymy)
4. The relationship expressed by “Vì trời mưa nên chúng em nghỉ học” is?
   Answer: Nguyên nhân – kết quả (cause‑result)
5. Equivalent resistance of 6 Ω and 3 Ω in parallel?
   Answer: 2 Ω
6. Increasing pressure in the N₂ + 3H₂ ⇌ 2NH₃ system shifts the equilibrium?
   Answer: Forward, toward ammonia
7. Number of single chromatids after meiosis I for 2n=8?
   Answer: 8
8. Who led the victory at Bạch Đằng in 938?
   Answer: Ngô Quyền, defeating the Nam Hán army