Gaokao - National College Entrance Exam — Questions and Answers

Question 1: If f''(a) = 0 and f'''(a) ≠ 0, then x = a is:

An inflection point (Correct answer)
A local maximum
A local minimum
A saddle point

Correct answer: An inflection point

f''(a) = 0 with f'''(a) ≠ 0 means the concavity changes at x = a, making it an inflection point.

Question 2: In an arithmetic sequence, a₃ = 7 and a₇ = 15. What is a₁?

2
4
5
3 (Correct answer)

Correct answer: 3

From a₃ = a₁ + 2d = 7 and a₇ = a₁ + 6d = 15, subtracting gives 4d = 8, d = 2, so a₁ = 7 − 4 = 3.

Question 3: Read the passage and answer the question. Passage: The Silk Road was not a single road but a network of trade routes connecting China to Central Asia, the Middle East, and ultimately Europe. For centuries, merchants transported silk, spices, and other luxury goods across these routes. The Silk Road was also a conduit for the exchange of ideas, religions, and technologies. Buddhism, Islam, and paper-making all spread along these routes, illustrating that trade has always involved more than the movement of goods. What broader point does the author make about the Silk Road?

It was primarily important for moving silk to European markets.
Paper-making was invented along the Silk Road trade routes.
It was the main reason Buddhism became the dominant religion in China.
It shows that trade involves the exchange of culture and ideas, not only goods. (Correct answer)

Correct answer: It shows that trade involves the exchange of culture and ideas, not only goods.

The final sentence explicitly states the Silk Road illustrates that trade involves more than goods — it also spreads ideas, religions, and technologies.

Question 4: What alternative options are available for students who do not meet university cut-off scores?

Applying to universities abroad that accept Gaokao scores. (Correct answer)
Enrolling in vocational colleges. (Correct answer)
Changing their chosen major within the same university.
Retaking the Gaokao the following year. (Correct answer)

Correct answer: Applying to universities abroad that accept Gaokao scores.

For students who do not achieve the required Gaokao scores for university admission, retaking the exam the following year is a very common alternative. Many dedicate another year to intensive study to improve their scores and secure a place in their desired university. Other options include vocational colleges or studying abroad, but retaking is a direct path to re-entry into the university application system.

Question 5: The word '走' (zǒu) in classical Chinese most commonly means:

To walk
To leave
To run (Correct answer)
To travel

Correct answer: To run

In classical Chinese, '走' means 'to run' (rapid movement). 'To walk' in classical Chinese is '行' (xíng) or '步' (bù). Modern Chinese '走' means 'to walk,' illustrating semantic change.

Question 6: The 'induced fit' model of enzyme action states that:

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

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 7: A rectangular box has side lengths of 2, 3, and 6. What is the surface area of the sphere that circumscribes this box?

196π
14π
49π (Correct answer)
24.5π

Correct answer: 49π

The diameter of the circumscribing sphere is equal to the space diagonal of the rectangular box. The square of the diagonal is d² = l² + w² + h² = 2² + 3² + 6² = 4 + 9 + 36 = 49. So, the diameter d = 7, and the radius R = 3.5. The surface area of the sphere is A = 4πR² = 4π(3.5)² = 4π(12.25) = 49π.

Question 8: A regular triangular prism has base edge length 4 and height 6. What is its total surface area?

72 + 4√3
48 + 4√3
72 + 8√3 (Correct answer)
48 + 8√3

Correct answer: 72 + 8√3

Two equilateral triangle bases: 2 × (√3/4 × 4²) = 8√3. Three rectangular lateral faces: 3 × (4 × 6) = 72. Total = 72 + 8√3.

Question 9: A bag contains 3 red balls and 5 blue balls. If one ball is drawn at random, what is the probability of drawing a red ball?

5/8
1/4
3/8 (Correct answer)
3/5

Correct answer: 3/8

There are 3 red balls out of 8 total, so the probability is 3/8.

Question 10: Which measure of central tendency is most affected by an extreme outlier in a dataset?

Median
Mean (Correct answer)
Mode
Range

Correct answer: Mean

The mean incorporates every value arithmetically, so a single extreme outlier can shift it significantly.

Question 11: Which organelle is responsible for producing ATP through cellular respiration, often called the 'powerhouse of the cell'?

Chloroplast
Mitochondria (Correct answer)
Golgi apparatus
Endoplasmic reticulum

Correct answer: Mitochondria

Mitochondria perform aerobic respiration, generating the majority of the cell's ATP through oxidative phosphorylation.

Question 12: A fair six-sided die is rolled twice. What is the probability of getting a sum of 7?

5/36
1/9
7/36
1/6 (Correct answer)

Correct answer: 1/6

There are 6 favorable pairs (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) out of 36 total outcomes, giving 6/36 = 1/6.

Question 13: A satellite orbits Earth at radius R with period T. If it moves to orbit at radius 4R, what is its new period?

8T (Correct answer)
16T
4T
2T

Correct answer: 8T

Kepler's Third Law: T² ∝ R³. If R increases by factor 4, then T² increases by factor 4³ = 64, so T increases by factor 8. New period = 8T.

Question 14: What is the purpose of the Chinese subject in the Gaokao?

To test creative writing skills. (Correct answer)
To measure mathematical problem-solving.
To evaluate understanding of classical Chinese literature. (Correct answer)
To assess reading comprehension and analytical ability. (Correct answer)

Correct answer: To test creative writing skills.

The Chinese subject in the Gaokao comprehensively assesses various language skills, including reading comprehension, analytical ability, and a significant component dedicated to creative writing. The essay portion, in particular, evaluates a student's capacity to articulate complex ideas, construct coherent arguments, and demonstrate originality. This ensures a holistic evaluation of their linguistic and expressive capabilities.

Question 15: Read the passage and answer the question. Passage: Many people believe that multitasking increases productivity. However, cognitive scientists have found the opposite to be true. The human brain does not truly perform two tasks simultaneously; instead, it switches rapidly between tasks, incurring a 'switching cost' each time. This cost reduces accuracy and slows overall completion time, making multitaskers less efficient than those who focus on one task at a time. What can be inferred from the passage about multitasking?

It is only harmful when performed by beginners.
It is useful for creative tasks but not analytical ones.
It is not as efficient as it is commonly believed to be. (Correct answer)
It helps the brain become more flexible over time.

Correct answer: It is not as efficient as it is commonly believed to be.

The passage directly contradicts the popular belief in multitasking by citing scientific evidence of reduced accuracy and slower completion.

Question 16: 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 (Correct answer)
√3/3
1/3
√2/2

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 17: Which of the following salts will produce a neutral aqueous solution?

Na₂CO₃ (sodium carbonate)
NH₄Cl (ammonium chloride)
NaCl (sodium chloride) (Correct answer)
CH₃COONa (sodium acetate)

Correct answer: NaCl (sodium chloride)

NaCl is formed from a strong acid (HCl) and a strong base (NaOH); neither ion hydrolyses, giving a neutral solution.

Question 18: A regular pyramid has a square base with side 6 and four equilateral triangular lateral faces. What is the height of the pyramid?

6
√18
3√2 (Correct answer)
3

Correct answer: 3√2

Wait — if lateral faces are equilateral with side 6, the slant height = 6 (from apex to base edge midpoint? No — equilateral triangle side = base edge = 6, so lateral edge = 6). Height h = √(lateral edge² - (half diagonal)²) = √(36 - 18) = √18 = 3√2.

Question 19: The sum of an infinite geometric series is 9 and the first term is 3. What is the common ratio?

3/4
1/2
2/3 (Correct answer)
1/3

Correct answer: 2/3

Using S = a₁/(1 − q), we get 9 = 3/(1 − q), so 1 − q = 1/3 and q = 2/3.

Question 20: Read the passage and answer the question. Passage: The ozone layer, located in the stratosphere, shields Earth from harmful ultraviolet (UV) radiation. In the 1980s, scientists discovered a thinning of the ozone layer — particularly over Antarctica — caused largely by chlorofluorocarbons (CFCs) used in refrigerants and aerosols. The Montreal Protocol of 1987 phased out CFCs globally and is considered one of the most successful international environmental agreements. The ozone layer is now slowly recovering. What does the Montreal Protocol demonstrate, according to the passage?

The ozone layer has fully recovered from CFC damage.
Scientists discovered the ozone hole after the Montreal Protocol.
CFCs were harmless and should not have been banned.
International cooperation can successfully address global environmental problems. (Correct answer)

Correct answer: International cooperation can successfully address global environmental problems.

The passage calls the Montreal Protocol one of the most successful environmental agreements and notes the ozone layer is recovering, demonstrating that global cooperation can work.

Question 21: Benzene reacts with bromine in the presence of FeBr₃ catalyst. What type of reaction occurs?

Nucleophilic substitution
Free radical substitution
Addition reaction
Electrophilic substitution (Correct answer)

Correct answer: Electrophilic substitution

Benzene undergoes electrophilic aromatic substitution (EAS) with Br₂/FeBr₃. FeBr₃ activates Br₂ to form the electrophile Br⁺.

Question 22: The Nanjing Massacre (南京大屠杀, 1937-1938) occurred during:

The Chinese Civil War
The Boxer Rebellion
The Japanese occupation of Nanjing following the fall of the Chinese capital during the Second Sino-Japanese War (Correct answer)
The First Sino-Japanese War (1894-1895)

Correct answer: The Japanese occupation of Nanjing following the fall of the Chinese capital during the Second Sino-Japanese War

After capturing Nanjing (then China's capital) in December 1937 during the Second Sino-Japanese War, Japanese forces killed an estimated 200,000-300,000 Chinese civilians and prisoners of war over six weeks.

Question 23: The solubility product Ksp of AgCl is 1.8×10⁻¹⁰. The molar solubility of AgCl in pure water is:

3.6×10⁻¹⁰ M
1.8×10⁻¹⁰ M
9.0×10⁻¹¹ M
1.34×10⁻⁵ M (Correct answer)

Correct answer: 1.34×10⁻⁵ M

AgCl → Ag⁺ + Cl⁻; if s = molar solubility, then Ksp = s² → s = √(1.8×10⁻¹⁰) ≈ 1.34×10⁻⁵ M.

Question 24: 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?

Space programs are too expensive and should be cut.
NASA should focus exclusively on developing consumer products.
Space technology always has immediate practical uses on Earth.
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 25: Which of the following organic compounds can decolorize both acidic potassium permanganate (KMnO4) solution and bromine water?

Ethane
Benzene
Ethene (Correct answer)
Ethanol

Correct answer: Ethene

Ethene contains a carbon-carbon double bond (C=C). This unsaturated bond can undergo an addition reaction with bromine water and an oxidation reaction with acidic KMnO4, causing both reagents to lose their color. Saturated compounds like ethane do not react, while ethanol only reacts with KMnO4.

Question 26: A parabola has the equation y² = 8x. What are the coordinates of its focus?

(2, 0) (Correct answer)
(0, 2)
(-2, 0)
(4, 0)

Correct answer: (2, 0)

The standard form y² = 4px gives focus at (p, 0). Here 4p = 8 so p = 2, giving focus (2, 0).

Question 27: The First United Front (第一次国共合作, 1923-1927) was an alliance between:

The KMT and Japan
The CPC and warlord armies
The Chinese Communist Party (CPC) and the Nationalist Party (KMT/Guomindang) (Correct answer)
The CPC and the Soviet Union

Correct answer: The Chinese Communist Party (CPC) and the Nationalist Party (KMT/Guomindang)

The First United Front was a coalition between the CPC and the KMT under Sun Yat-sen, formed to fight northern warlords. It broke down in 1927 with Chiang Kai-shek's Shanghai Massacre.

Question 28: Which of the following is a MAJOR environmental consequence of large-scale deforestation in tropical rainforests?

Increased albedo leading to regional cooling
Reduction in river discharge due to decreased runoff
Loss of biodiversity, soil erosion, and disruption of the regional hydrological cycle (Correct answer)
Increased precipitation due to more exposed soil surface area

Correct answer: Loss of biodiversity, soil erosion, and disruption of the regional hydrological cycle

Tropical deforestation removes the canopy that intercepts rainfall, disrupts transpiration (reducing precipitation recycling), causes soil erosion, and destroys habitat for 50%+ of Earth's species.

Question 29: Which structural pattern is most commonly recommended for Gaokao argumentative essays?

Five-paragraph format identical to English essays
Stream-of-consciousness narrative
Question-answer dialogue format
Introduction (引论) → Body with multiple argument points (本论) → Conclusion (结论) (Correct answer)

Correct answer: Introduction (引论) → Body with multiple argument points (本论) → Conclusion (结论)

Chinese argumentative essays (议论文) follow a three-part structure: 引论 (introduction/establishing the thesis), 本论 (body with supporting arguments and evidence), and 结论 (conclusion/restatement). This mirrors Western essay structure but with Chinese-specific conventions.

Question 30: What is the primary function of the nucleolus within the nucleus?

Packaging of chromosomes during cell division
Synthesis and processing of ribosomal RNA (rRNA) (Correct answer)
DNA replication and repair
Transcription of mRNA from protein-coding genes

Correct answer: Synthesis and processing of ribosomal RNA (rRNA)

The nucleolus is the site of rRNA gene transcription and ribosomal subunit assembly; it disappears during mitosis and reforms after division.

Question 31: In a stem-and-leaf plot, which part represents the last digit of each data value?

Branch
Stem
Leaf (Correct answer)
Root

Correct answer: Leaf

In a stem-and-leaf plot, leaves represent the trailing digits while stems represent the leading digits.

Question 32: The concept of '仁' (rén, benevolence) in Confucian thought is best described as:

Strict adherence to ritual protocol
The highest virtue encompassing love for others, humaneness, and proper moral conduct in relationships (Correct answer)
Scholarly knowledge of classical texts
Physical courage in battle

Correct answer: The highest virtue encompassing love for others, humaneness, and proper moral conduct in relationships

'仁' is the central virtue in Confucianism, meaning benevolence, humaneness, and love for others. Confucius said '仁者爱人' (The benevolent person loves others).

Question 33: The Henderson-Hasselbalch equation pH = pKa + log([A⁻]/[HA]) is used to calculate the pH of:

Strong acid solutions
Strong base solutions
Buffer solutions (Correct answer)
Pure water

Correct answer: Buffer solutions

The Henderson-Hasselbalch equation applies to buffer solutions containing a weak acid and its conjugate base.

Question 34: For the sequence aₙ = n × 2ⁿ, what is a₄?

80
64 (Correct answer)
32
48

Correct answer: 64

Substituting n = 4: a₄ = 4 × 2⁴ = 4 × 16 = 64.

Question 35: In the 'speeding father' story, what does the father's final silence most likely represent?

Confusion about what the child meant.
Anger at being corrected by his child.
A sudden realization of his hypocrisy and a sense of shame. (Correct answer)
Deciding to ignore the child and continue speeding.

Correct answer: A sudden realization of his hypocrisy and a sense of shame.

The father's silence is a turning point. It's not just an admission of being wrong, but a moment of profound realization and introspection, possibly accompanied by shame. The child's simple, principle-based logic has defeated his adult, consequence-based logic, forcing him to reflect on his own values.

Question 36: The Xinhai Revolution (辛亥革命, 1911) led to:

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

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 37: A mutation that disrupts the signal peptide of a secretory protein would most likely cause the protein to:

Remain in the cytoplasm instead of entering the ER (Correct answer)
Be degraded immediately in the nucleus
Be transported directly to lysosomes
Accumulate in the mitochondrial matrix

Correct answer: Remain in the cytoplasm instead of entering the ER

Signal peptides direct ribosomes to the rough ER; without a functional signal peptide, the ribosome translates the protein in the cytoplasm rather than threading it into the ER lumen.

Question 38: A 5 kg box is pushed across a horizontal floor by a 30 N horizontal force. The coefficient of kinetic friction between the box and floor is 0.4. What is the acceleration of the box? (g = 10 m/s²)

2 m/s² (Correct answer)
4 m/s²
1 m/s²
6 m/s²

Correct answer: 2 m/s²

Normal force N = mg = 5 × 10 = 50 N. Friction force f = μN = 0.4 × 50 = 20 N. Net force = 30 − 20 = 10 N. By Newton's Second Law, a = F_net / m = 10 / 5 = 2 m/s².

Question 39: The Marco Polo Bridge Incident (七七事变) of July 7, 1937 is historically significant because it:

Marked the beginning of Japan's full-scale invasion of China and the Second Sino-Japanese War (Correct answer)
Triggered China's entry into World War I on the side of the Allied Powers
Led to the formation of the First United Front between the CCP and KMT
Resulted in the Nationalist government relocating its capital from Nanjing to Wuhan

Correct answer: Marked the beginning of Japan's full-scale invasion of China and the Second Sino-Japanese War

The clash between Japanese and Chinese troops near Beijing on July 7, 1937 escalated into Japan's full-scale invasion, launching the Second Sino-Japanese War (1937–1945), also called the War of Resistance Against Japanese Aggression (抗日战争).

Question 40: A 500 g ball traveling at 4 m/s is acted on by a constant net force for 2 seconds, accelerating it to 8 m/s in the same direction. What is the magnitude of the net force?

4 N
1 N (Correct answer)
2 N
0.5 N

Correct answer: 1 N

Mass m = 0.5 kg. Change in velocity Δv = 8 − 4 = 4 m/s over t = 2 s, so a = 4/2 = 2 m/s². By Newton's Second Law, F = ma = 0.5 × 2 = 1 N.

Question 41: In projectile motion (抛体运动), what happens to the horizontal velocity component throughout the flight (ignoring air resistance)?

It remains constant (Correct answer)
It decreases due to gravity
It increases due to gravity
It becomes zero at the highest point

Correct answer: It remains constant

In projectile motion without air resistance, the horizontal direction has no force acting on it, so horizontal velocity remains constant throughout the flight (Newton's First Law).

Question 42: '征集志愿' (Supplementary Enrollment Rounds) in the Gaokao system are triggered when:

Provincial authorities reallocate quota from over-subscribed universities to under-subscribed ones
A student's first-choice university rejects their application and they must resubmit immediately
Students request to change their major preference after receiving an admission offer
Universities still have unfilled enrollment slots after a main admissions batch concludes, and eligible non-admitted students may apply again (Correct answer)

Correct answer: Universities still have unfilled enrollment slots after a main admissions batch concludes, and eligible non-admitted students may apply again

After each major admission batch (e.g., 本科一批, 本科二批), if certain universities still have unfilled spots, a 征集志愿 round is opened. Students who were not admitted in that batch and whose scores meet the remaining requirements can submit new preferences for those vacancies. This gives students a second opportunity within the same batch cycle.

Question 43: Read the passage and answer the question. Passage: Green architecture seeks to design buildings that minimize environmental impact. Features include solar panels, green roofs planted with vegetation, rainwater harvesting systems, and materials with low carbon footprints. Beyond environmental benefits, green buildings often have lower long-term operating costs due to energy savings, though the initial construction costs are typically higher than conventional buildings. According to the passage, what is a financial disadvantage of green buildings?

They require expensive solar panels that rarely work.
Their long-term operating costs are higher than conventional buildings.
Their rainwater systems increase water bills.
They cost more to build initially than conventional buildings. (Correct answer)

Correct answer: They cost more to build initially than conventional buildings.

The passage explicitly states that initial construction costs are typically higher, though long-term operating costs are lower.

Question 44: A circle passes through the origin and has center at (3, 4). What is the equation of this circle?

(x-3)² + (y-4)² = 5
x² + y² = 25
(x+3)² + (y+4)² = 25
(x-3)² + (y-4)² = 25 (Correct answer)

Correct answer: (x-3)² + (y-4)² = 25

The radius is the distance from center (3,4) to origin (0,0): r = √(9+16) = 5. Equation: (x-3)² + (y-4)² = 25.

Question 45: China's Reform and Opening Up Policy (改革开放) launched in 1978 was initiated by:

Hua Guofeng as a continuation of previous policies
The National People's Congress independently
Mao Zedong before his death in 1976
Deng Xiaoping at the Third Plenary Session of the 11th Central Committee of the CPC (Correct answer)

Correct answer: Deng Xiaoping at the Third Plenary Session of the 11th Central Committee of the CPC

The Third Plenary Session of the 11th Central Committee (十一届三中全会, December 1978) marked Deng Xiaoping's rise and launched the reform era: shifting focus from class struggle to economic development.

Question 46: ∫₀¹ x·e^x dx equals:

e - 2 (Correct answer)
1
e - 1
2 - e

Correct answer: e - 2

Integrate by parts: u=x, dv=eˣdx; ∫x·eˣdx = x·eˣ - eˣ + C; evaluated 0 to 1: (e - e) - (0 - 1) = 0 + 1 = 1. Recheck: [x·eˣ - eˣ]₀¹ = (e - e) - (0 - 1) = 0 + 1 = 1. Hmm — that gives 1. Actually (1·e¹ - e¹) - (0·e⁰ - e⁰) = (e-e) - (0-1) = 0+1 = 1.

Question 47: Three resistors of 6 Ω, 3 Ω, and 2 Ω are connected in parallel. What is the equivalent resistance?

2 Ω
0.5 Ω
11 Ω
1 Ω (Correct answer)

Correct answer: 1 Ω

1/R = 1/6 + 1/3 + 1/2 = 1/6 + 2/6 + 3/6 = 1; R = 1 Ω.

Question 48: Read the passage and answer the question. Passage: Public transportation systems are central to sustainable urban development. Buses and trains can move large numbers of people efficiently, reducing traffic congestion and carbon emissions compared to private cars. Cities with well-developed transit networks also show lower rates of road accidents. Despite these benefits, many governments underinvest in public transit, often because its costs are highly visible while its benefits — reduced congestion, fewer accidents, cleaner air — are diffuse and harder to quantify. Why do governments often underinvest in public transit, according to the passage?

Public transit is generally more expensive to operate than private cars.
The benefits of transit are spread out and difficult to measure precisely. (Correct answer)
Governments prefer investing in road construction instead.
Public transit systems have poor safety records in most cities.

Correct answer: The benefits of transit are spread out and difficult to measure precisely.

The passage says governments underinvest because the benefits are 'diffuse and harder to quantify' even though they are real.

Question 49: A cell biologist treats cells with colchicine, which disrupts microtubule polymerization. Which process would be MOST directly affected?

DNA replication
Lipid synthesis in the smooth ER
Protein synthesis at ribosomes
Chromosome separation during mitosis (Correct answer)

Correct answer: Chromosome separation during mitosis

Colchicine prevents spindle fiber formation by binding to tubulin, arresting cells in metaphase and preventing chromosome movement to the poles.

Question 50: If f(x) = x²·sin(1/x) for x ≠ 0 and f(0) = 0, is f differentiable at x = 0?

No, f is not continuous at 0
Yes, f'(0) = 0 (Correct answer)
Yes, f'(0) = 1
No, the limit does not exist

Correct answer: Yes, f'(0) = 0

f'(0) = lim_{h→0} h²sin(1/h)/h = lim h·sin(1/h) = 0 (squeeze: |h·sin(1/h)| ≤ |h| → 0).

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%

To Pass

Checking for saved progress...

Exam Rules

You can skip questions and return to them later
Flag questions for review before submitting
No feedback shown until you submit the entire exam
Unanswered questions count as wrong — answer everything
10 pretest questions are mixed in and don't affect your score
Timer auto-submits when time runs out
Your progress is auto-saved every 30 seconds