Cambridge IGCSE · thinka 原创模拟试题

2025 Cambridge IGCSE Sciences - Co-ordinated (Double) (0654) 模拟试题及答案详解

Thinka Nov 2025 (V1) Cambridge IGCSE-Style Mock — Sciences - Co-ordinated (Double) (0654)

120 120 分钟2025
An original Thinka practice paper modelled on the structure and difficulty of the Nov 2025 (V1) Cambridge IGCSE Sciences - Co-ordinated (Double) (0654) paper. Not affiliated with or reproduced from Cambridge.

甲部: Biology

Answer all questions. Write your answers in the spaces provided.
4 题目 · 40
题目 1 · structured
10
A student investigates the response of young oat seedlings to gravity.
Several germinating seedlings are placed horizontally in a dark box.

(a) (i) Describe the expected response of the shoots of these seedlings after 48 hours. [1]

(ii) State the term used to describe this specific response of the shoot to gravity. [1]

(iii) Explain how auxins control this response in the shoot. [3]

(b) (i) Define the term *hormone* as used in humans. [2]

(ii) Adrenaline is a hormone released during a 'fight or flight' situation.
State three physiological effects of adrenaline on the human body. [3]
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解题

(a) (i) The shoots will grow / bend upwards.

(ii) Negative gravitropism (or negative geotropism).

(iii) Auxin is produced in the shoot tip and moves downwards due to gravity, accumulating on the lower side of the horizontal shoot. A higher concentration of auxin on the lower side promotes faster cell elongation compared to the upper side, causing the shoot to bend upwards.

(b) (i) A hormone is a chemical substance, produced by a gland and carried by the blood, which alters the activity of one or more specific target organs.

(ii) Any three of:
- increased heart rate
- increased breathing rate
- dilated pupils
- increased blood glucose concentration
- diversion of blood flow to the muscles / away from the digestive system.

评分标准

(a) (i)
- shoots grow / bend upwards [1] (Reject: grow towards light)

(ii)
- negative gravitropism / negative geotropism [1]

(iii)
- auxin is made in the shoot tip [1]
- auxin moves / diffuses to the lower side of the shoot [1]
- high concentration of auxin on the lower side stimulates cell elongation, causing the shoot to bend upwards [1]

(b) (i) Any two from:
- chemical substance produced by a gland [1]
- transported in the blood / plasma [1]
- alters the activity of one or more specific target organs [1]

(ii) Any three from:
- increased heart rate [1]
- increased breathing rate [1]
- widened / dilated pupils [1]
- increased blood glucose level [1]
- diversion of blood to muscles / away from gut [1]
题目 2 · structured
10
Table 2.1 shows the percentage composition of inspired air and expired air.

**Table 2.1**
| Gas | Percentage in inspired air / % | Percentage in expired air / % |
| :--- | :---: | :---: |
| nitrogen | 78 | 78 |
| oxygen | 21 | 16 |
| carbon dioxide | 0.04 | 4.00 |
| water vapour | variable | saturated |

(a) (i) Explain the difference in the percentage of oxygen between inspired and expired air. [2]

(ii) Explain the difference in the percentage of carbon dioxide between inspired and expired air. [2]

(b) The gas exchange surface in the human lungs is adapted for efficient diffusion.

(i) Name the structures in the lungs where gas exchange occurs. [1]

(ii) Describe three features of these structures that make gas exchange efficient. [3]

(c) Goblet cells and ciliated cells work together to protect the gas exchange system from pathogens.

Describe the roles of these cells. [2]
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解题

(a) (i) The percentage of oxygen is lower in expired air because oxygen diffuses from the alveoli into the blood capillaries in the lungs, as it is needed by cells for aerobic respiration.

(ii) The percentage of carbon dioxide is higher in expired air because carbon dioxide is produced as a waste product of cellular respiration and diffuses from the blood capillaries into the alveoli to be exhaled.

(b) (i) Alveoli (or air sacs).

(ii) Three of:
- thin walls (one cell thick) which provide a short diffusion distance
- very large surface area for diffusion
- surrounded by a dense network of capillaries to maintain a steep concentration gradient
- moist lining which allows gases to dissolve before diffusing.

(c) Goblet cells secrete sticky mucus that traps inhaled dust, dirt, and pathogens. Ciliated cells have tiny hair-like projections (cilia) that beat in unison to sweep the mucus up and out of the trachea and airways toward the throat to be swallowed.

评分标准

(a) (i)
- oxygen diffuses into the blood / is absorbed in the lungs [1]
- because it is used for respiration [1]

(ii)
- carbon dioxide is produced during respiration [1]
- and diffuses out of the blood into the lungs / alveoli to be exhaled [1]

(b) (i)
- alveoli / air sacs [1] (Accept: alveolus)

(ii) Any three from:
- thin walls / one cell thick [1]
- large surface area [1]
- surrounded by a dense network of capillaries / good blood supply [1]
- moist lining [1]

(c)
- goblet cells secrete / produce mucus which traps pathogens / dust [1]
- ciliated cells have cilia that sweep / beat the mucus upwards / away from the lungs [1]
题目 3 · structured
10
Table 3.1 shows four structures of the female reproductive system and their functions.

(a) Complete Table 3.1 by filling in the name of each structure and its corresponding function. [4]

**Table 3.1**
| Structure | Name of structure | Function of structure |
| :---: | :--- | :--- |
| **A** | ......................................... | releases progesterone and estrogen |
| **B** | oviduct | .......................................................................................... |
| **C** | ......................................... | site of implantation of the zygote / fetus development |
| **D** | cervix | .......................................................................................... |

(b) (i) Describe the role of the placenta in supporting the developing fetus. [3]

(ii) Explain why the blood of the mother and the blood of the fetus do not mix in the placenta. [2]

(c) State the number of chromosomes in a human zygote. [1]
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解题

(a)
- **A**: ovary
- **B function**: site of fertilisation / transport of egg from ovary to uterus
- **C**: uterus
- **D function**: ring of muscle at opening of uterus / holds developing fetus in place during pregnancy

(b) (i) The placenta allows oxygen, glucose, amino acids, and antibodies to diffuse from the maternal blood to the fetal blood. It also allows carbon dioxide and urea to diffuse from the fetal blood to the maternal blood for excretion, and it secretes hormones (like progesterone) to maintain the uterine lining during pregnancy.

(ii) The bloods do not mix to prevent high maternal blood pressure from damaging delicate fetal capillaries, and to protect the fetus from maternal immune responses (or mismatched blood groups causing agglutination).

(c) 46 (or 23 pairs).

评分标准

(a) 1 mark for each correct entry:
- **A**: ovary [1]
- **B function**: site of fertilisation / transport of egg to uterus [1]
- **C**: uterus (or womb) [1]
- **D function**: keeps fetus in place / ring of muscle at entrance to uterus [1]

(b) (i) Any three from:
- allows diffusion of oxygen / nutrients / glucose / amino acids from mother to fetus [1]
- allows diffusion of carbon dioxide / urea from fetus to mother [1]
- secretes progesterone / hormones to maintain pregnancy [1]
- provides passive immunity / transfers antibodies [1]

(ii) Any two from:
- high maternal blood pressure would damage fetal capillaries [1]
- prevents mismatch of blood groups / agglutination [1]
- protects fetus from some pathogens / toxins in maternal blood [1]

(c)
- 46 (or 23 pairs) [1]
题目 4 · structured
10
Eutrophication is a serious environmental problem in aquatic ecosystems caused by human activities.

(a) (i) State two human activities that can lead to eutrophication. [2]

(ii) Describe the sequence of events that occurs in a freshwater lake after fertilizer runoff occurs, leading to the death of fish. [5]

(b) Deforestation can also harm ecosystems and contribute to climate change.

(i) Explain how deforestation contributes to an increase in atmospheric carbon dioxide levels. [2]

(ii) State one other negative consequence of deforestation on land. [1]
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解题

(a) (i) Runoff / leaching of chemical fertilizers from agricultural land, and discharge of untreated sewage into water bodies.

(ii)
1. Fertilizer runoff increases nutrient levels in the water, causing rapid growth of algae (an algal bloom).
2. The algal bloom covers the surface, blocking sunlight from reaching plants underneath.
3. Underwater plants die due to lack of light for photosynthesis.
4. Decomposers (bacteria) feed on the dead plant matter and multiply rapidly.
5. The bacteria respire aerobically, depleting dissolved oxygen levels in the water, which causes fish to die of suffocation.

(b) (i) Deforestation reduces the number of trees available to absorb carbon dioxide from the atmosphere during photosynthesis. Additionally, when cut trees are burned or decay, they release stored carbon back into the atmosphere as carbon dioxide.

(ii) Soil erosion (or flooding / habitat destruction / loss of biodiversity).

评分标准

(a) (i) 1 mark for each correct activity:
- leaching / runoff of fertilizers [1]
- release of untreated sewage / animal waste [1]

(ii) Any five from:
- increased growth of algae / algal bloom on surface [1]
- algae block light from reaching submerged plants [1]
- submerged plants die due to lack of photosynthesis [1]
- bacteria / decomposers multiply rapidly as they feed on dead plants [1]
- bacteria respire aerobically [1]
- oxygen concentration in water decreases / depleted [1]
- fish die from lack of oxygen [1]

(b) (i)
- fewer trees to photosynthesize and absorb carbon dioxide [1]
- burning of wood / decay of cut trees releases carbon dioxide [1]

(ii) Any one from:
- soil erosion [1]
- flooding [1]
- habitat destruction / loss of biodiversity [1]

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乙部: Chemistry

Answer all questions. Refer to the Periodic Table where necessary.
4 题目 · 40
题目 1 · structured
10
Crude oil (petroleum) is a mixture of hydrocarbons. It is separated into useful fractions. (a) (i) Name the process used to separate crude oil into fractions. [1] (ii) Explain how this process separates the different fractions. [2] (b) One of the fractions is naphtha. Naphtha can be cracked to produce smaller, more useful molecules. (i) Describe the conditions needed for cracking. [2] (ii) Complete the chemical equation for the cracking of decane, \(C_{10}H_{22}\), to produce propene, \(C_3H_6\), and one other hydrocarbon: \(C_{10}H_{22} \rightarrow C_3H_6 + \text{....................}\). [1] (c) Propene is an unsaturated hydrocarbon. (i) State what is meant by the term unsaturated. [1] (ii) Describe a chemical test to distinguish propene from propane. State the result with propene. [3]
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解题

(a) (i) Fractional distillation. (ii) Crude oil is heated and vaporised. The vapour rises up a fractionating column which is hot at the bottom and cooler at the top. The fractions condense at different heights depending on their boiling points. (b) (i) High temperature and a catalyst (e.g., alumina or silica). (ii) \(C_7H_{16}\). (c) (i) It contains a carbon-carbon double bond (\(C=C\)). (ii) Add aqueous bromine (bromine water) to both hydrocarbons. Propene turns the orange-brown bromine water colourless (decolourises it). Propane does not react and the mixture remains orange-brown.

评分标准

(a) (i) Fractional distillation [1]. (ii) Crude oil is heated/vaporised [1]; fractions condense at different temperatures/boiling points [1]. (b) (i) High temperature / heat (approx. 500-600 °C) [1]; catalyst (alumina/silica/zeolite) [1]. (ii) \(C_7H_{16}\) [1]. (c) (i) Contains a double bond (\(C=C\)) [1]. (ii) Test: add bromine water / aqueous bromine [1]; result with propene: turns colourless / decolourises [1]; result with propane: remains orange/brown [1].
题目 2 · structured
10
Zinc chloride, \(ZnCl_2\), is an ionic compound. It can be electrolysed when molten using carbon electrodes. (a) (i) State the name of the positive electrode. [1] (ii) Identify the products formed at each electrode: Positive electrode and Negative electrode. [2] (iii) Explain why zinc chloride must be molten to conduct electricity. [2] (b) Aqueous copper(II) sulfate can also be electrolysed. (i) When aqueous copper(II) sulfate is electrolysed using inert carbon electrodes, a gas is produced at the positive electrode. Name this gas and describe a test to identify it. [2] (ii) Describe the observation at the negative electrode during this electrolysis. [1] (iii) If copper electrodes are used instead of carbon electrodes, state and explain what happens to the mass of the positive electrode. [2]
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解题

(a) (i) Anode. (ii) Positive electrode: chlorine gas; Negative electrode: zinc. (iii) In solid zinc chloride, the ions are held in fixed positions in a giant lattice and cannot move. When molten, the giant structure breaks down and the ions are free to move and carry the electric current. (b) (i) Oxygen gas. Test: relights a glowing splint. (ii) A pink-brown solid is deposited on the electrode. (iii) The mass of the positive electrode decreases because the copper atoms lose electrons to form copper ions, which dissolve into the solution.

评分标准

(a) (i) Anode [1]. (ii) Chlorine / \(Cl_2\) [1]; zinc / \(Zn\) [1]. (iii) Ions in solid are in fixed positions/cannot move [1]; ions in molten state are free to move and carry charge [1]. (b) (i) Oxygen / \(O_2\) [1]; Test: relights a glowing splint [1]. (ii) Pink/brown/red-brown solid deposit [1]. (iii) Mass decreases [1]; copper atoms oxidised to copper ions / \(Cu \rightarrow Cu^{2+} + 2e^-\)[1].
题目 3 · structured
10
Soluble salts can be prepared by reacting dilute acids with metal oxides. A student prepares a sample of zinc sulfate crystals by reacting zinc oxide with dilute sulfuric acid. (a) (i) Write the word equation for this reaction. [1] (ii) Suggest why zinc oxide is added in excess to the sulfuric acid. [1] (iii) Describe how the excess zinc oxide is removed from the reaction mixture. [1] (iv) Explain how dry crystals of zinc sulfate are obtained from the zinc sulfate solution. [3] (b) The student tests the zinc sulfate solution to identify the ions present. (i) Describe a chemical test to show the presence of sulfate ions in the solution, including the positive result. [2] (ii) Describe the observations when a few drops of aqueous sodium hydroxide are added to a solution containing zinc ions, followed by an excess of the sodium hydroxide. [2]
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解题

(a) (i) zinc oxide + sulfuric acid -> zinc sulfate + water. (ii) To ensure all of the dilute sulfuric acid has reacted. (iii) By filtration (the excess zinc oxide remains on the filter paper as residue). (iv) Heat the solution to evaporate most of the water until a saturated solution is formed. Leave the hot solution to cool so that crystals form. Filter off the crystals and dry them between filter papers. (b) (i) Add dilute hydrochloric acid followed by aqueous barium chloride. A white precipitate is formed. (ii) A white precipitate forms with a few drops of sodium hydroxide. The white precipitate dissolves in excess sodium hydroxide to form a colourless solution.

评分标准

(a) (i) zinc oxide + sulfuric acid -> zinc sulfate + water [1]. (ii) To ensure all acid is fully reacted/neutralised [1]. (iii) Filtration [1]. (iv) Heat/evaporate solution to crystallization point / saturated solution [1]; cool to allow crystal growth [1]; filter and dry crystals between filter papers [1]. (b) (i) Acidify with dilute hydrochloric acid / nitric acid AND add aqueous barium chloride / barium nitrate [1]; white precipitate [1]. (ii) White precipitate formed initially [1]; precipitate dissolves in excess to give a colourless solution [1].
题目 4 · structured
10
Air is a mixture of gases. (a) (i) Complete the sentences to show the approximate percentage composition by volume of clean, dry air: Nitrogen is approximately ........% of air, and Oxygen is approximately ........% of air. [2] (ii) Carbon dioxide is a greenhouse gas. State the name of one other greenhouse gas. [1] (iii) Explain how greenhouse gases contribute to global warming. [2] (b) Water from natural sources must be treated to make it safe to drink. (i) State the names of two processes used in water treatment and explain the purpose of each. [4] (ii) Describe a chemical test to show the presence of water. State the observation for a positive result. [1]
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解题

(a) (i) Nitrogen is 78% (accept 78% to 80%); Oxygen is 21% (accept 20% to 21%). (ii) Methane (or water vapour). (iii) Greenhouse gases absorb infrared radiation reflected/radiated from the Earth's surface and trap heat in the atmosphere. (b) (i) Filtration: to remove insoluble solids/particles from the water; Chlorination: to kill harmful bacteria/microorganisms. (ii) Add the liquid to anhydrous copper(II) sulfate. It turns from white to blue. (Alternatively, add to anhydrous cobalt(II) chloride, which turns from blue to pink).

评分标准

(a) (i) Nitrogen: 78% [1]; Oxygen: 21% [1]. (ii) Methane / water vapour [1]. (iii) Greenhouse gases absorb infrared radiation [1]; trapped heat warms the atmosphere / prevents heat from escaping into space [1]. (b) (i) Filtration [1]; to remove suspended insoluble solids [1]; Chlorination [1]; to kill bacteria/pathogens [1]. (ii) Anhydrous copper(II) sulfate turns blue (OR anhydrous cobalt(II) chloride turns pink) [1].

部分 C: Physics

Answer all questions. Take the acceleration of free fall to be 9.8 m/s^2.
4 题目 · 40
题目 1 · structured
10
Fig. 1.1 shows a speed-time graph for a runner during a 10-second race.

[Insert Description of Fig. 1.1: The graph starts at time \(t = 0\text{ s}\) with speed \(v = 0\text{ m/s}\). The speed increases at a constant rate until time \(t = 4.0\text{ s}\), reaching a speed of \(8.0\text{ m/s}\). From \(t = 4.0\text{ s}\) to \(t = 10.0\text{ s}\), the speed remains constant at \(8.0\text{ m/s}\).]

(a) (i) Describe the motion of the runner between \(t = 0\text{ s}\) and \(t = 4.0\text{ s}\). [1]
(ii) Calculate the acceleration of the runner during the first 4.0 seconds of the race. State the unit of your answer. [3]
(iii) Calculate the total distance travelled by the runner during the 10.0 seconds. [3]

(b) The runner has a mass of \(65\text{ kg}\).
(i) Calculate the kinetic energy of the runner when they are running at their constant maximum speed of \(8.0\text{ m/s}\). [2]
(ii) State the name of the main form of energy stored in the runner's body that is converted into kinetic energy as they accelerate. [1]
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解题

(a) (i) The line is a straight diagonal going upwards, representing constant acceleration (or uniform acceleration).
(ii) Acceleration is calculated using the formula:
\(a = \frac{\Delta v}{\Delta t}\)
\(a = \frac{8.0\text{ m/s} - 0\text{ m/s}}{4.0\text{ s}} = 2.0\text{ m/s}^2\)
The unit for acceleration is \(\text{m/s}^2\) (or \(\text{m s}^{-2}\)).
(iii) The total distance is the area under the speed-time graph. This can be calculated as the area of a trapezium, or the sum of the areas of a triangle (from 0 to 4 s) and a rectangle (from 4 to 10 s):
\(\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height} = 0.5 \times 4.0\text{ s} \times 8.0\text{ m/s} = 16.0\text{ m}\)
\(\text{Area of rectangle} = \text{base} \times \text{height} = (10.0\text{ s} - 4.0\text{ s}) \times 8.0\text{ m/s} = 6.0\text{ s} \times 8.0\text{ m/s} = 48.0\text{ m}\)
\(\text{Total distance} = 16.0\text{ m} + 48.0\text{ m} = 64\text{ m}\)

(b) (i) Kinetic energy is calculated using the formula:
\(E_k = \frac{1}{2} m v^2\)
\(E_k = 0.5 \times 65\text{ kg} \times (8.0\text{ m/s})^2 = 0.5 \times 65 \times 64 = 2080\text{ J}\) (or \(2.08\text{ kJ}\))
(ii) The body uses chemical energy from food reserves to produce muscular movement.

评分标准

(a) (i)
- Constant / uniform acceleration [1] (Reject: just 'acceleration' or 'speed increases')

(ii)
- \(a = \frac{\Delta v}{\Delta t}\) or \(\frac{8.0}{4.0}\) [1]
- \(2.0\) [1]
- \(\text{m/s}^2\) or \(\text{m s}^{-2}\) [1]

(iii)
- distance = area under graph (stated or shown in working) [1]
- calculation of either triangle area (\(16\text{ m}\)) or rectangle area (\(48\text{ m}\)) [1]
- \(64\text{ m}\) [1]

(b) (i)
- \(E_k = \frac{1}{2} m v^2\) or \(0.5 \times 65 \times 8.0^2\) [1]
- \(2080\text{ J}\) (or \(2.08\text{ kJ}\)) [1]

(ii)
- Chemical (energy) [1]
题目 2 · structured
10
(a) Fig. 2.1 shows a ray of light travelling from air into a rectangular glass block.

[Insert Description of Fig. 2.1: A light ray is incident on the top surface of a glass block at an angle of incidence of \(45.0^\circ\) to the normal. It refracts as it enters the glass, bending towards the normal.]

(i) State what happens to the speed of light as it enters the glass block from the air. [1]
(ii) The angle of incidence is \(45.0^\circ\). The refractive index of the glass block is \(1.50\). Calculate the angle of refraction. [3]
(iii) The light ray travels through the glass and reaches the bottom boundary where it meets air again. State the two conditions required for total internal reflection to occur at this boundary. [2]

(b) A sound wave is produced by a loudspeaker vibrating in air.
(i) Describe how the sound wave is transmitted through the air in terms of air particles. [2]
(ii) The frequency of the sound wave is \(250\text{ Hz}\) and its speed in air is \(340\text{ m/s}\). Calculate the wavelength of this sound wave. [2]
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解题

(a) (i) The speed of light decreases (slows down) because glass is optically denser than air.
(ii) Use the refractive index formula:
\(n = \frac{\sin i}{\sin r}\)
Rearranging for \(\sin r\):
\(\sin r = \frac{\sin i}{n} = \frac{\sin 45.0^\circ}{1.50}\)
\(\sin r = \frac{0.7071}{1.50} = 0.4714\)
\(r = \sin^{-1}(0.4714) \approx 28.1^\circ\)
(iii) Total internal reflection can only happen if:
1. The light is travelling in the more optically dense medium (glass) towards the less dense medium (air).
2. The angle of incidence is greater than the critical angle for the glass-air boundary.

(b) (i) The loudspeaker cone vibrates back and forth, pushing on nearby air molecules. These vibrations are passed along as air particles collide, creating longitudinal waves consisting of compressions (regions of high pressure where particles are close together) and rarefactions (regions of low pressure where particles are spread apart).
(ii) Use the wave equation:
\(v = f \lambda\)
Rearranging for wavelength \(\lambda\):
\(\lambda = \frac{v}{f} = \frac{340\text{ m/s}}{250\text{ Hz}} = 1.36\text{ m}\)

评分标准

(a) (i)
- Decreases / slows down [1]

(ii)
- \(n = \frac{\sin i}{\sin r}\) (or rearranged) [1]
- \(\sin r = \frac{\sin 45^\circ}{1.50}\) or \(\sin r = 0.4714\) [1]
- \(28.1^\circ\) (Accept: \(28^\circ\) or \(28.13^\circ\)) [1]

(iii)
- Ray must be travelling from a more dense medium to a less dense medium [1]
- Angle of incidence must be greater than the critical angle [1]

(b) (i)
- Particles vibrate / oscillate back and forth parallel to wave direction [1]
- Creating compressions and rarefactions (or passing energy via collisions) [1]

(ii)
- \(\lambda = \frac{v}{f}\) or \(\frac{340}{250}\) [1]
- \(1.36\text{ m}\) [1]
题目 3 · structured
10
Fig. 3.1 shows a circuit diagram containing a \(12.0\text{ V}\) battery connected to two resistors in parallel.

[Insert Description of Fig. 3.1: A circuit diagram shows a \(12.0\text{ V}\) battery connected to a parallel network of two resistors, \(R_1\) and \(R_2\). The resistance of \(R_1\) is \(6.0\text{ }\Omega\) and the resistance of \(R_2\) is \(12.0\text{ }\Omega\).]

(a) (i) Show that the combined resistance of the two parallel resistors is \(4.0\text{ }\Omega\). [2]
(ii) Calculate the total current flowing from the battery. [2]
(iii) State the potential difference (voltage) across resistor \(R_1\). [1]

(b) (i) Calculate the electrical power dissipated in resistor \(R_2\). [2]
(ii) An additional resistor of resistance \(12.0\text{ }\Omega\) is now connected in series with the battery, before the parallel branch.
State and explain what happens to the current in resistor \(R_1\). [3]
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解题

(a) (i) For parallel resistors:
\(\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2}\)
\(\frac{1}{R_p} = \frac{1}{6.0} + \frac{1}{12.0} = \frac{2}{12.0} + \frac{1}{12.0} = \frac{3}{12.0}\)
\(R_p = \frac{12.0}{3} = 4.0\text{ }\Omega\)
(ii) The total current \(I\) from the battery is:
\(I = \frac{V}{R_p} = \frac{12.0\text{ V}}{4.0\text{ }\Omega} = 3.0\text{ A}\)
(iii) In a parallel circuit, the voltage across each parallel branch is equal to the voltage of the supply (if there are no other series components).
Voltage across \(R_1 = 12.0\text{ V}\).

(b) (i) Power \(P\) dissipated in a resistor can be calculated using \(P = \frac{V^2}{R}\) or \(P = I^2 R\).
Using \(P = \frac{V^2}{R}\) for resistor \(R_2\):
\(P = \frac{(12.0\text{ V})^2}{12.0\text{ }\Omega} = \frac{144}{12.0} = 12.0\text{ W}\)
Alternatively, current in \(R_2\) is \(I_2 = \frac{12.0\text{ V}}{12.0\text{ }\Omega} = 1.0\text{ A}\), so \(P = I_2 \times V = 1.0\text{ A} \times 12.0\text{ V} = 12.0\text{ W}\).
(ii) Connecting a resistor in series with the parallel branch:
1. Increases the total resistance of the circuit (from \(4.0\text{ }\Omega\) to \(4.0 + 12.0 = 16.0\text{ }\Omega\)).
2. This decreases the total current in the circuit.
3. Because current flows through the new series resistor, there is a potential drop across it, leaving less voltage across the parallel branch (and thus less voltage across \(R_1\)).
4. Since \(I_1 = \frac{V_{\text{parallel}}}{R_1}\), a lower voltage across \(R_1\) results in a decreased current through \(R_1\).

评分标准

(a) (i)
- \(\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2}\) or \(\frac{1}{6} + \frac{1}{12}\) [1]
- \(\frac{3}{12}\) leading to \(R_p = 4.0\text{ }\Omega\) [1]

(ii)
- \(I = \frac{V}{R}\) or \(\frac{12.0}{4.0}\) [1]
- \(3.0\text{ A}\) [1]

(iii)
- \(12.0\text{ V}\) [1]

(b) (i)
- \(P = \frac{V^2}{R}\) or \(P = I V\) with \(I_2 = 1.0\text{ A}\) [1]
- \(12.0\text{ W}\) [1]

(ii)
- Current through \(R_1\) decreases [1]
- Total resistance of the circuit increases (which decreases total current) [1]
- Voltage across parallel branch / resistor \(R_1\) decreases [1]
题目 4 · structured
10
(a) (i) Describe the nature of an alpha (\(\alpha\)) particle and a beta-minus (\(\beta^-\)) particle. [2]
(ii) An isotope of polonium, Polonium-210 (\(\text{}^{210}_{84}\text{Po}\)), decays by alpha emission to form an isotope of lead (\(\text{Pb}\)).
The nuclear equation for this decay is:
\[ \text{}^{210}_{84}\text{Po} \rightarrow \text{}^{A}_{Z}\text{Pb} + \text{}^{4}_{2}\alpha \]
State the value of \(A\) and the value of \(Z\). [2]
- \(A = \) ______
- \(Z = \) ______
(iii) State the number of neutrons in a lead-206 (\(\text{}^{206}_{82}\text{Pb}\)) nucleus. [1]

(b) A sample of Polonium-210 has an initial activity of \(800\text{ Bq}\). The half-life of Polonium-210 is 138 days.
(i) Define the term half-life. [1]
(ii) Calculate the activity of the sample of Polonium-210 after 414 days. [2]
(iii) State which of alpha (\(\alpha\)), beta (\(\beta\)), or gamma (\(\gamma\)) radiation is the most ionising, and describe one hazard of ionising radiation to human body cells. [2]
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解题

(a) (i) An alpha particle is a helium nucleus, consisting of 2 protons and 2 neutrons. A beta-minus particle is a high-energy, high-speed electron emitted from the nucleus.
(ii) In a nuclear reaction, the mass numbers and atomic numbers must balance on both sides of the equation.
For mass numbers: \(210 = A + 4 \Rightarrow A = 210 - 4 = 206\).
For atomic numbers: \(84 = Z + 2 \Rightarrow Z = 84 - 2 = 82\).
(iii) Number of neutrons = \(\text{nucleon number } (A) - \text{proton number } (Z) = 206 - 82 = 124\).

(b) (i) Half-life is defined as the time taken for half the nuclei of a radioactive isotope in a sample to decay (or the time taken for the activity of a sample to decrease to half of its initial value).
(ii) Number of half-lives elapsed:
\(n = \frac{414\text{ days}}{138\text{ days}} = 3\text{ half-lives}\)
After 1 half-life: \(800\text{ Bq} \rightarrow 400\text{ Bq}\)
After 2 half-lives: \(400\text{ Bq} \rightarrow 200\text{ Bq}\)
After 3 half-lives: \(200\text{ Bq} \rightarrow 100\text{ Bq}\)
(iii) Alpha radiation is the most strongly ionising because of its relatively large mass and \(+2\) charge. Ionising radiation is hazardous because it can damage DNA, leading to mutations, causing cancers, or directly destroying cells.

评分标准

(a) (i)
- Alpha: helium nucleus / 2 protons and 2 neutrons [1]
- Beta: high-speed / high-energy electron [1]

(ii)
- \(A = 206\) [1]
- \(Z = 82\) [1]

(iii)
- \(124\) [1]

(b) (i)
- Time taken for half the radioactive nuclei in a sample to decay (or for activity / count rate to halve) [1]

(ii)
- Shows that 3 half-lives have elapsed (\(\frac{414}{138} = 3\)) [1]
- \(100\text{ Bq}\) [1]

(iii)
- Alpha (radiation) [1]
- Cell mutation / cancer / cell damage / cell death [1]

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