Gaokao - National College Entrance Exam — Questions and Answers

Question 1: For a reaction with K >> 1, the equilibrium position lies:

Far to the right, heavily favouring products (Correct answer)
Far to the left, heavily favouring reactants
Exactly at the midpoint
Depends only on temperature

Correct answer: Far to the right, heavily favouring products

K >> 1 means [products] >> [reactants] at equilibrium; the reaction essentially goes to completion.

Question 2: In Chinese high school composition topics about life-changing experiences, which literary technique involves starting with a present moment and then flashing back to explain how the protagonist arrived there?

插叙 (intercalated narration)
倒叙 (reverse chronological narration / flashback) (Correct answer)
补叙 (supplementary narration)
顺叙 (chronological narration)

Correct answer: 倒叙 (reverse chronological narration / flashback)

'倒叙' means beginning with the ending or a present moment and then narrating past events that explain the current situation — the classic flashback structure.

Question 3: Read the passage and answer the question. Passage: The sharing economy — platforms like Airbnb and Uber — has disrupted traditional industries. Advocates argue it increases efficiency by making use of underutilized assets: spare rooms, idle cars. Critics point out that these platforms shift economic risk onto individual workers, who lack the benefits and protections of traditional employment. Regulators in many cities struggle to adapt rules designed for hotels and taxi companies to these new business models. What challenge do regulators face with sharing economy platforms?

Traditional rules for hotels and taxis do not easily apply to new platform-based models. (Correct answer)
Platform companies actively break all existing laws in every city.
Workers in the sharing economy earn too much money to receive protections.
Sharing economy platforms are too small to require regulation.

Correct answer: Traditional rules for hotels and taxis do not easily apply to new platform-based models.

The passage says regulators 'struggle to adapt rules designed for hotels and taxi companies to these new business models.'

Question 4: In classical Chinese, the particle '之' (zhī) can function as which of the following?

Only a personal pronoun
Only a possessive particle
Only a sentence-final modal particle
A structural particle, a pronoun, or a verb meaning 'to go to' (Correct answer)

Correct answer: A structural particle, a pronoun, or a verb meaning 'to go to'

'之' has multiple grammatical functions in classical Chinese: as a structural particle (like 的), a third-person pronoun (it/him/her), or occasionally a verb meaning 'to go to a place.'

Question 5: To find the dihedral angle along a common edge in a solid geometry problem, the most systematic method in Chinese high school is:

Assume it equals a face angle
Find the half-plane angle by constructing perpendiculars from a point on the edge to each face, forming the dihedral angle's measurement angle (Correct answer)
Measure it directly from a 3D figure
Use only the dot product formula without geometric construction

Correct answer: Find the half-plane angle by constructing perpendiculars from a point on the edge to each face, forming the dihedral angle's measurement angle

The standard method: pick a point on the edge, construct perpendiculars to the edge in each half-plane. The angle between these two perpendiculars is the dihedral angle.

Question 6: A rectangular box (cuboid) has dimensions 2 × 4 × 4. What is the radius of its circumscribed sphere?

2√3
3 (Correct answer)
2√6
√10

Correct answer: 3

The space diagonal of a cuboid with dimensions a × b × c is √(a²+b²+c²) = √(4+16+16) = √36 = 6. The circumscribed sphere's diameter equals the space diagonal, so R = 6/2 = 3.

Question 7: In redox reactions, the species that undergoes an increase in oxidation number has been:

Neither oxidised nor reduced
Oxidised (Correct answer)
Reduced
Hydrolysed

Correct answer: Oxidised

Oxidation is defined as an increase in oxidation number (loss of electrons); reduction is a decrease in oxidation number.

Question 8: A 60 W light bulb operates on a 120 V AC supply. The resistance of the filament during operation is:

60 Ω
120 Ω
240 Ω (Correct answer)
480 Ω

Correct answer: 240 Ω

P = V²/R → R = V²/P = 120²/60 = 240 Ω.

Question 9: Two charges +Q and −Q are separated by distance d. The electric potential at the midpoint between them is:

2kQ/d
−kQ/(d/2)
Zero (Correct answer)
kQ/(d/2)

Correct answer: Zero

Potential is a scalar; V = kQ/(d/2) + k(−Q)/(d/2) = 0.

Question 10: A frequency table shows scores: 60 (5 students), 70 (8 students), 80 (7 students), 90 (5 students). What is the mode?

80
60
90
70 (Correct answer)

Correct answer: 70

The mode is 70 because it appears most frequently (8 students).

Question 11: A homozygous dominant plant (TT) is crossed with a homozygous recessive plant (tt). What fraction of offspring will be heterozygous?

0
1/2
1 (Correct answer)
1/4

Correct answer: 1

All offspring of a TT × tt cross inherit one T and one t allele, making 100% (all) of them heterozygous Tt.

Question 12: In the right triangular prism ABC-A₁B₁C₁, ∠BCA = 90°, and AC = BC = CC₁ = 1. What is the cosine of the dihedral angle B₁-AC₁-B?

√2/2
√3/3
2√2/3 (Correct answer)
1/3

Correct answer: 2√2/3

Set up a coordinate system with C at (0,0,0). Then A=(1,0,0), B=(0,1,0), C₁=(0,0,1), B₁=(0,1,1). The two planes are Plane(B,A,C₁) and Plane(B₁,A,C₁). A normal vector to Plane(B,A,C₁) is n₁ = vector(AC₁) × vector(AB) = (1,0,1) × (-1,1,0) = (-1,-1,1). A normal vector to Plane(B₁,A,C₁) is n₂ = vector(AC₁) × vector(AB₁) = (1,0,1) × (-1,1,1) = (-1,-2,1). The cosine of the angle θ between the planes is |n₁·n₂| / (|n₁||n₂|) = |1+2+1| / (√3 * √6) = 4/√18 = 4/(3√2) = 2√2/3.

Question 13: The Treaty of Nanking (1842), which concluded the First Opium War, is considered a major turning point in Chinese history because it:

Led to the immediate legalization of the opium trade.
Caused the Taiping Rebellion to break out.
Marked the beginning of the erosion of China's sovereignty. (Correct answer)
Established formal diplomatic relations between China and Britain on an equal footing.

Correct answer: Marked the beginning of the erosion of China's sovereignty.

The Treaty of Nanking was the first of the 'unequal treaties' imposed on China by Western powers. By forcing the cession of Hong Kong, the opening of treaty ports, and the payment of indemnities, it began the erosion of Chinese sovereignty and marked the start of China's semi-colonial, semi-feudal period.

Question 14: An object rests on a horizontal table. Which statement correctly describes the weight of the object and the normal force exerted by the table on the object?

They act in the same direction and together keep the object stationary
They form an action-reaction pair according to Newton's Third Law
The normal force is always greater than the weight
They are equal in magnitude but act on the same object and are NOT an action-reaction pair (Correct answer)

Correct answer: They are equal in magnitude but act on the same object and are NOT an action-reaction pair

Weight and normal force are equal in magnitude and opposite in direction, but both act on the same object — they are a balanced force pair (Newton's First Law), not an action-reaction pair. An action-reaction pair (Newton's Third Law) always acts on two different objects. The true reaction to the object's weight is the gravitational pull the object exerts on the Earth.

Question 15: Which of the following is the equation of a hyperbola with real axis along the y-axis?

y²/9 - x²/4 = 1 (Correct answer)
y²/9 + x²/4 = 1
x²/4 + y²/9 = 1
x²/9 - y²/4 = 1

Correct answer: y²/9 - x²/4 = 1

A hyperbola with real axis along the y-axis has the form y²/a² - x²/b² = 1. Option A matches this form.

Question 16: The International Monetary Fund (IMF) and the World Bank were both established at the Bretton Woods Conference in 1944. What is the primary distinction between their roles?

The IMF provides short-term balance-of-payments assistance to member countries, while the World Bank focuses on long-term development financing for developing nations (Correct answer)
The IMF promotes military stability while the World Bank funds peacekeeping operations
The IMF exclusively serves developed nations while the World Bank serves only the poorest countries
The IMF regulates international currency exchange rates by fixing them, while the World Bank prints a global reserve currency

Correct answer: The IMF provides short-term balance-of-payments assistance to member countries, while the World Bank focuses on long-term development financing for developing nations

The IMF's core mandate is to ensure international monetary system stability and provide short-term financing to members facing balance-of-payments crises. The World Bank's mandate is long-term economic development and poverty reduction through project loans and grants to developing countries. Though both emerged from Bretton Woods, they serve complementary but distinct functions.

Question 17: The core ideology of the Self-Strengthening Movement (洋务运动) in the late 19th century can be best summarized by which phrase?

“Democracy and Science” (民主与科学)
“Drive out the Manchus, Revive China” (驱除鞑虏，恢复中华)
“Chinese learning as the essence, Western learning for practical use” (中学为体，西学为用) (Correct answer)
“Support the Qing, Exterminate the Foreigners” (扶清灭洋)

Correct answer: “Chinese learning as the essence, Western learning for practical use” (中学为体，西学为用)

This phrase encapsulates the movement's goal: to adopt Western technology and industry ('Western learning for practical use') to strengthen the nation, while preserving the traditional Confucian social and political order ('Chinese learning as the essence'). The movement sought modernization without fundamental institutional change.

Question 18: Which of the following functions is NOT differentiable at x = 0?

f(x) = |x| (Correct answer)
f(x) = x³
f(x) = sin(x)
f(x) = x²

Correct answer: f(x) = |x|

The left and right derivatives of |x| at x = 0 are -1 and +1 respectively; since they differ, |x| is not differentiable at 0.

Question 19: If f(x) = x³ - 3x, the maximum value of f on [-2, 3] is:

20
9
2
18 (Correct answer)

Correct answer: 18

f'(x) = 3x²-3 = 3(x²-1) = 0 at x = ±1; f(-2) = -8+6 = -2; f(-1) = -1+3 = 2; f(1) = 1-3 = -2; f(3) = 27-9 = 18; maximum = 18.

Question 20: Read the passage and answer the question. Passage: Forests regulate the water cycle in ways many people do not realize. Trees absorb rainwater through their roots and release it gradually back into the atmosphere through a process called transpiration. Deforested areas experience more extreme flooding after heavy rain because the soil cannot absorb water as effectively without tree roots. Conversely, these areas suffer more severe droughts between rainy seasons. What role does transpiration play according to the passage?

It is a process exclusive to tropical rainforests.
It prevents trees from absorbing water during droughts.
It helps trees release absorbed water gradually back into the atmosphere. (Correct answer)
It causes flooding by releasing too much water into rivers.

Correct answer: It helps trees release absorbed water gradually back into the atmosphere.

The passage directly states transpiration is the process by which trees release absorbed water back into the atmosphere.

Question 21: In the pyramid P-ABCD, the base ABCD is a rectangle. E is the midpoint of the side PD. Let plane α be the plane passing through points A, E, and C. What is the relationship between line PB and plane α?

PB lies within plane α
The relationship is uncertain
PB intersects plane α
PB is parallel to plane α (Correct answer)

Correct answer: PB is parallel to plane α

Let O be the intersection of the diagonals AC and BD of the rectangle. Connect EO. In triangle PBD, E is the midpoint of PD and O is the midpoint of BD, so EO is the midsegment. Therefore, EO is parallel to PB. Since EO lies within plane AEC (plane α) and PB does not, PB is parallel to plane α.

Question 22: Read the passage and answer the question. Passage: Overfishing is depleting marine ecosystems at an alarming rate. When fish populations are reduced faster than they can reproduce, stocks collapse — sometimes permanently. The collapse of the Grand Banks cod fishery off Canada in the 1990s left tens of thousands of fishermen without work and has not recovered to this day. International agreements on fishing quotas exist, but enforcement is difficult on the open seas. What lesson does the Grand Banks example illustrate?

Canadian fishermen were the main cause of global overfishing.
International fishing agreements are highly effective at protecting fish stocks.
Overfishing can permanently destroy fish populations and the communities dependent on them. (Correct answer)
Cod is the most commercially valuable fish in the world.

Correct answer: Overfishing can permanently destroy fish populations and the communities dependent on them.

The Grand Banks collapse illustrates that overfishing can permanently destroy stocks and devastate dependent communities.

Question 23: The unit of momentum in the SI system is:

kg·m/s (Correct answer)
J/s
N·m
kg·m/s²

Correct answer: kg·m/s

Momentum p = mv. Units: kg × m/s = kg·m/s. This is also equivalent to N·s (Newton-second), since N = kg·m/s².

Question 24: Which stage of mitosis is characterized by chromosomes aligned along the cell's equatorial plate?

Anaphase
Prophase
Metaphase (Correct answer)
Telophase

Correct answer: Metaphase

During metaphase, condensed chromosomes are aligned along the metaphase plate by balanced tension from spindle fibers attached to kinetochores on each sister chromatid.

Question 25: Read the passage and answer the question. Passage: Libraries have traditionally been repositories of books. Yet modern libraries increasingly serve as community hubs: offering free internet access, hosting job-skill workshops, providing quiet study spaces, and even lending tools and seed collections. These changes reflect a shift in purpose from simply storing knowledge to actively serving community needs. The phrase 'repositories of books' most likely means:

Places that produce and publish books.
Places where books are stored and kept. (Correct answer)
Places that sell books to the public.
Places that review and rate books.

Correct answer: Places where books are stored and kept.

'Repository' means a place where things are stored; the contrast with active community services reinforces this meaning.

Question 26: How many structural isomers does butane (C₄H₁₀) have?

2 (Correct answer)
3
1
4

Correct answer: 2

Butane has 2 isomers: n-butane (straight chain: CH₃CH₂CH₂CH₃) and isobutane/2-methylpropane (branched: (CH₃)₃CH).

Question 27: The Nanjing Massacre (南京大屠杀, December 1937 – January 1938) refers to:

The Nationalist government's violent suppression of student-led protests in the capital
The systematic mass killing of an estimated 300,000 Chinese civilians and prisoners of war by Japanese forces after Nanjing fell (Correct answer)
The Allied aerial bombardment of Japanese-occupied Nanjing during World War II
The Communist purge of Nationalist officials after the People's Liberation Army captured Nanjing in 1949

Correct answer: The systematic mass killing of an estimated 300,000 Chinese civilians and prisoners of war by Japanese forces after Nanjing fell

After Japanese forces captured the then-Chinese capital Nanjing in December 1937, they committed widespread atrocities over approximately six weeks — killing an estimated 300,000 civilians and POWs. Also known as the Rape of Nanjing, it remains a defining and deeply contested episode in Sino-Japanese history.

Question 28: The range of f(x) = 2sin(x) + 1 for x ∈ [0, π] is:

[0, 3]
[1, 3] (Correct answer)
[-1, 3]
[-2, 3]

Correct answer: [1, 3]

sin(x) ∈ [0, 1] for x ∈ [0, π]; so 2sin(x) ∈ [0, 2]; f(x) = 2sin(x)+1 ∈ [1, 3].

Question 29: The process of 'isostasy' in physical geography explains why:

Ocean basins sink due to the weight of ocean water above them
Continental crust rises after the removal of ice sheet weight during deglaciation (Correct answer)
Mountains erode at the same rate they are uplifted by tectonic forces
Sea level rises when ocean water temperature increases due to thermal expansion

Correct answer: Continental crust rises after the removal of ice sheet weight during deglaciation

Isostatic rebound (post-glacial rebound) occurs because the removal of heavy ice sheets reduces crustal loading, allowing the mantle to flow back and the crust to rise; Scandinavia is rising ~1 cm/year.

Question 30: The monsoon climate of South and East Asia is primarily driven by:

Permanent high-pressure systems over the Tibetan Plateau year-round
Ocean currents that reverse direction between summer and winter
Volcanic activity that creates seasonal precipitation patterns
The ITCZ shifting location with the sun, creating seasonal wind reversals (Correct answer)

Correct answer: The ITCZ shifting location with the sun, creating seasonal wind reversals

Monsoons result from differential heating between the Asian landmass and the Indian Ocean, which shifts the ITCZ and creates seasonal pressure gradients that reverse wind direction and precipitation patterns.

Question 31: Read the passage and answer the question. Passage: Space exploration has produced technologies we use every day. Memory foam, water purification filters, scratch-resistant lenses, and even the cameras in smartphones all trace their origins to NASA research. Critics argue that space programs consume resources that could be better spent on Earth's problems. Supporters counter that the technology developed for space eventually improves life on Earth in ways that are difficult to predict in advance. What is the supporters' argument as described in the passage?

NASA should focus exclusively on developing consumer products.
Space technology always has immediate practical uses on Earth.
Space programs are too expensive and should be cut.
Investments in space eventually yield benefits for life on Earth. (Correct answer)

Correct answer: Investments in space eventually yield benefits for life on Earth.

Supporters argue that space technology eventually improves life on Earth, even if those benefits cannot be predicted in advance.

Question 32: Which of the following accurately describes how 'ENSO (El Niño–Southern Oscillation)' affects global climate patterns?

La Niña warms the eastern Pacific, causing flooding in Australia and drought in South America
ENSO only affects climate in the tropics and has no measurable impact on mid-latitudes
El Niño cools the Pacific Ocean, reducing tropical storm formation worldwide
El Niño warms the central-eastern Pacific, causing drought in Australia and flooding in coastal South America (Correct answer)

Correct answer: El Niño warms the central-eastern Pacific, causing drought in Australia and flooding in coastal South America

During El Niño, weakened trade winds allow warm water to accumulate in the central-eastern Pacific, disrupting normal precipitation patterns: drought in Australia/Indonesia, flooding in Peru/Ecuador.

Question 33: The Great Leap Forward (大跃进, 1958-1962) resulted in:

A massive famine causing tens of millions of deaths due to unrealistic production targets and agricultural collectivization failures (Correct answer)
Improved agricultural output through mechanization
Rapid successful industrialization ahead of schedule
Successful implementation of Soviet-style five-year plans

Correct answer: A massive famine causing tens of millions of deaths due to unrealistic production targets and agricultural collectivization failures

The Great Leap Forward's unrealistic steel and grain production targets, combined with the collectivization of agriculture into People's Communes, caused a catastrophic famine with an estimated 15-55 million excess deaths (1959-1961).

Question 34: The concept of 'comparative advantage' in agricultural geography suggests that regions should specialize in producing goods for which they:

Have the highest absolute productivity per worker
Have the largest area of arable land
Have historically grown the crop for the longest time
Can produce at a lower opportunity cost than other regions (Correct answer)

Correct answer: Can produce at a lower opportunity cost than other regions

Comparative advantage (Ricardo) means a region should specialize in the product where its opportunity cost is lowest relative to other regions, enabling mutually beneficial trade.

Question 35: If a random variable X follows a binomial distribution with n = 10 and p = 0.5, what is E(X)?

5 (Correct answer)
10
7.5
2.5

Correct answer: 5

The expected value of a binomial distribution is E(X) = n × p = 10 × 0.5 = 5.

Question 36: An electric dipole consists of charges +q and −q separated by distance d. The electric field at the midpoint between the charges is directed:

Zero
From −q toward +q
From +q toward −q (Correct answer)
Perpendicular to the dipole axis

Correct answer: From +q toward −q

Both charges produce fields at the midpoint; the +q field points away from +q (toward −q) and the −q field also points toward −q; they add in the same direction.

Question 37: Read the passage and answer the question. Passage: Satellite technology has revolutionized navigation. Before GPS, travelers relied on paper maps, compasses, and local knowledge to find their way. Today, GPS receivers — built into smartphones — can pinpoint a user's location to within a few meters anywhere on Earth. While this technology has made navigation vastly more convenient, concerns have been raised about over-reliance: some research suggests people's innate spatial reasoning skills are declining because they no longer practice navigation independently. What concern about GPS is raised in the passage?

GPS devices are too expensive for widespread public use.
People may lose natural navigation skills by relying too heavily on GPS. (Correct answer)
GPS signals are unreliable in bad weather conditions.
GPS technology poses a security risk by tracking user locations.

Correct answer: People may lose natural navigation skills by relying too heavily on GPS.

The passage raises the concern that over-reliance on GPS is causing a decline in people's innate spatial reasoning and navigation skills.

Question 38: In an electrochemical cell, oxidation occurs at the:

Anode (Correct answer)
Cathode
Both electrodes simultaneously
Salt bridge

Correct answer: Anode

By definition, oxidation (loss of electrons) occurs at the anode, whether in a galvanic cell or an electrolytic cell.

Question 39: A sex-linked recessive trait is carried on the X chromosome. If the mother is a carrier (X^A X^a) and the father is unaffected (X^A Y), what percentage of their sons will be affected?

0%
25%
50% (Correct answer)
100%

Correct answer: 50%

Sons receive either X^A (unaffected) or X^a (affected) from the mother with equal probability, so 50% of sons are affected.

Question 40: In China's compulsory history curriculum, the May Fourth Movement of 1919 is primarily characterized as a turning point because it:

Marked the beginning of a new democratic revolution led by the proletariat (Correct answer)
Formalized China's alliance with the Soviet Union during the Cold War
Established the People's Republic of China as a sovereign state
Ended the Qing Dynasty and introduced a republican system of government

Correct answer: Marked the beginning of a new democratic revolution led by the proletariat

The May Fourth Movement is taught in Chinese compulsory history as the start of the New Democratic Revolution, shifting leadership from the bourgeoisie to the working class (proletariat) under Marxist influence — a foundational distinction in the official curriculum narrative.

Question 41: Which phenomenon demonstrates that the cell membrane is selectively permeable?

Small nonpolar molecules cross freely while large polar molecules require protein channels (Correct answer)
The membrane dissolves in water, allowing unrestricted transport
All molecules can freely diffuse across the membrane given sufficient time
Active transport uses ATP to move all molecules equally

Correct answer: Small nonpolar molecules cross freely while large polar molecules require protein channels

Selective permeability means small nonpolar molecules (O₂, CO₂) pass freely while large or charged molecules (glucose, ions) require specific transport proteins.

Question 42: A Gaokao essay prompt shows an image of a person at a crossroads. What type of prompt is this?

命题作文 (titled essay)
图画材料作文 (picture-based material essay) (Correct answer)
续写作文 (continuation essay)
话题作文 (topic essay)

Correct answer: 图画材料作文 (picture-based material essay)

'图画材料作文' uses a visual image as the prompt. Students interpret the symbolic meaning of the image (e.g., crossroads = life choices) and write an argumentative essay based on their interpretation.

Question 43: The 'induced fit' model of enzyme action states that:

Only substrates with exactly the right shape can bind to the active site
Enzymes are permanently altered after each catalytic reaction
The active site changes shape to fit the substrate upon binding (Correct answer)
Substrate binding is entirely random and non-specific

Correct answer: The active site changes shape to fit the substrate upon binding

In the induced fit model, substrate binding causes the enzyme's active site to change shape, forming a more complementary fit that stabilizes the transition state.

Question 44: The Xinhai Revolution (辛亥革命, 1911) led to:

A military dictatorship under Yuan Shikai from the start
A constitutional monarchy
The overthrow of the Qing Dynasty and the establishment of the Republic of China (Correct answer)
The establishment of the PRC

Correct answer: The overthrow of the Qing Dynasty and the establishment of the Republic of China

The Xinhai Revolution, beginning with the Wuchang Uprising (October 10, 1911), led to the abdication of the last Qing Emperor Puyi and the founding of the Republic of China (中华民国) on January 1, 1912, under Sun Yat-sen.

Question 45: Read the passage and answer the question. Passage: The Renaissance was a cultural movement that emerged in Italy during the 14th century and gradually spread across Europe. It was characterized by a renewed interest in the art, literature, and philosophy of ancient Greece and Rome. Renaissance thinkers championed humanism — the idea that human beings, rather than divine authority, are the center of intellectual and artistic inquiry. This shift had profound effects on science, philosophy, and the arts. According to the passage, what was 'humanism'?

A scientific theory developed during the Renaissance period.
A religious movement that replaced Christianity in Renaissance Europe.
The practice of translating ancient Greek texts into Latin.
The belief that humans, not divine authority, are the central focus of thought. (Correct answer)

Correct answer: The belief that humans, not divine authority, are the central focus of thought.

The passage explicitly defines humanism as placing human beings at the center of intellectual and artistic inquiry.

Question 46: Two independent events A and B have P(A) = 0.5 and P(B) = 0.6. What is P(A ∩ B)?

0.30 (Correct answer)
0.55
0.10
1.10

Correct answer: 0.30

For independent events, P(A ∩ B) = P(A) × P(B) = 0.5 × 0.6 = 0.30.

Question 47: Essay Prompt: A father speeds on the highway. His child reminds him it's wrong. The father dismisses it, saying there are no cameras. The child replies, "But we have the word 'Safety' on our wall at home." The father falls silent. What is the core theme an essay on this topic should address?

The importance of modern surveillance in enforcing traffic laws.
The necessity of upholding principles and rules regardless of external supervision. (Correct answer)
How children should be educated about traffic safety from a young age.
The conflict between generations and their different views on rules.

Correct answer: The necessity of upholding principles and rules regardless of external supervision.

The central conflict is between external rules (cameras, police) and internal principles ('Safety' on the wall). The father's silence indicates his realization that true safety and morality come from within, not from fear of punishment. An essay should explore this theme of self-discipline and abiding by principles even when unobserved.

Question 48: The hydrolysis of the salt CH₃COONa in water produces a solution that is:

Neutral (pH = 7)
pH depends on concentration only
Acidic (pH < 7)
Basic (pH > 7) (Correct answer)

Correct answer: Basic (pH > 7)

CH₃COO⁻ hydrolyses: CH₃COO⁻ + H₂O ⇌ CH₃COOH + OH⁻; the weak acid anion produces OH⁻, making the solution basic.

Question 49: The mean of five numbers is 10. If four of the numbers are 8, 9, 11, and 13, what is the fifth number?

7
9 (Correct answer)
11
10

Correct answer: 9

Total sum = 5 × 10 = 50; fifth number = 50 − (8+9+11+13) = 50 − 41 = 9.

Question 50: In a cube ABCDA'B'C'D' with side length 'a', what is the sine of the angle between the line A'B and the plane BDD'B'?

√3/2
√3/3
1/2 (Correct answer)
√2/2

Correct answer: 1/2

Set up a coordinate system with D at the origin (0,0,0). Then A'=(a,0,a), B=(a,a,0). The vector for line A'B is v = B - A' = (0, a, -a). The plane BDD'B' is the plane x=y, so its normal vector is n = (1, -1, 0). The sine of the angle θ between a line and a plane is given by sin(θ) = |v · n| / (|v| * |n|) = |(0)(1) + (a)(-1) + (-a)(0)| / (sqrt(a²+a²) * sqrt(1²+1²)) = a / (a√2 * √2) = a / (2a) = 1/2.

Gaokao - National College Entrance Exam

The Gaokao is China's national university entrance examination testing Chinese language, mathematics, English, and elective subjects including physics, chemistry, biology, and history.

Questions

150 min

Time Limit

60%

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Sources & references

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