劍橋 A-Level 物理 9702 結構題模擬卷（10 題・100 分・2 小時）

2026-10-29

TUTORZONE 原創模擬卷 · 劍橋 A-Level 物理 9702 結構題（Paper 4）

本卷照劍橋 A-Level 物理 9702 結構題卷（Paper 4）的卷制編寫：全卷 10 題、100 分、2 小時，涵蓋力學、材料、波、電學、量子物理、圓周運動、理想氣體與放射性衰變；所有數值由程式自算並核對。

卷制速覽

項目	內容
試卷	9702 Paper 4 結構題（A Level）
題數	10 題（36 部分）
分數	100 分
時限	2 小時
佔比	A Level 總分 38%
計算機	准用非程式計算機

題目（100 分）

全卷 10 題、36 部分，須寫出計算步驟；除特別指明外，非準確值取 3 位有效數字，重力加速度取 9.81 m s⁻²。

1. （9 分）運動學與自由落體

(a) A car accelerates uniformly from rest and reaches a speed of 25 m s⁻¹ in 8.0 s. Calculate its acceleration and the distance travelled in this time.（3 分）

(b) The car then travels a further 210 m in 6.0 s with constant acceleration. Calculate its speed at the end of this 6.0 s.（3 分）

(c) A stone is released from rest at the top of a cliff and reaches the sea 2.6 s later. Calculate the height of the cliff and the speed of the stone on impact. Take g = 9.81 m s⁻² and ignore air resistance.（3 分）

2. （10 分）力矩與平衡

(a) A uniform plank AB of length 3.2 m and weight 180 N rests on a pivot placed 0.80 m from A. A load of weight W hangs from B and the plank is in equilibrium. Calculate W by taking moments about the pivot.（3 分）

(b) Calculate the upward force exerted by the pivot on the plank.（3 分）

(c) The load W is removed and a load of weight 40 N is hung 0.50 m from A. State and explain whether the plank is now in equilibrium.（4 分）

3. （9 分）功、能量與功率

(a) A pump raises 240 kg of water per minute through a vertical height of 12 m into a tank. Calculate the useful output power of the pump. Take g = 9.81 m s⁻².（3 分）

(b) The efficiency of the pump is 65 %. Calculate the input power to the pump.（3 分）

4. （11 分）材料與楊氏模量

(a) A steel wire of length 2.00 m and diameter 0.30 mm hangs vertically and carries a mass of 1.60 kg at its lower end. Show that the tensile stress in the wire is about 2.2 × 10⁸ Pa.（3 分）

(b) The wire extends by 2.2 mm. Calculate the strain in the wire.（2 分）

(d) State what is meant by the limit of proportionality and explain why the extension is directly proportional to the load only below this limit.（3 分）

5. （10 分）駐波與弦上波

(a) A string of length 0.90 m is fixed at both ends. Its mass per unit length is 5.0 × 10⁻⁴ kg m⁻¹ and the tension is 45 N. Calculate the speed of transverse waves on the string.（3 分）

(b) Calculate the frequency of the first harmonic of the string.（3 分）

(d) Explain why a stationary wave pattern is produced on the string.（2 分）

6. （11 分）電動勢與內阻

(a) A battery of e.m.f. 12.0 V and internal resistance 0.80 Ω is connected to a resistor of resistance 5.2 Ω. Calculate the current in the circuit.（3 分）

(b) Calculate the terminal potential difference of the battery.（2 分）

(d) Calculate the efficiency of the battery and state where the lost energy goes.（3 分）

7. （10 分）光電效應

(a) Light of wavelength 4.8 × 10⁻⁷ m is incident on a metal of work function 2.20 eV. Calculate the energy of one photon in electronvolts. Take h = 6.63 × 10⁻³⁴ J s and c = 3.00 × 10⁸ m s⁻¹.（3 分）

(b) Calculate the maximum kinetic energy of the emitted photoelectrons, in joules.（3 分）

(d) The intensity of the light is doubled while the wavelength is unchanged. State and explain the effect on the maximum kinetic energy of the photoelectrons.（2 分）

8. （10 分）圓周運動

(a) A car of mass 1200 kg travels at a constant speed of 12 m s⁻¹ round a horizontal circular path of radius 25 m. Calculate its centripetal acceleration and the resultant force on the car.（3 分）

(b) The maximum frictional force between the tyres and the road is 0.65 times the weight of the car. Calculate the maximum speed at which the car can travel on this path.（3 分）

(d) State the direction of the resultant force on the car and explain why the speed is constant although a force acts on the car.（2 分）

9. （11 分）理想氣體

(a) A cylinder contains 0.050 mol of an ideal gas at a temperature of 300 K and a volume of 1.2 × 10⁻³ m³. Calculate the pressure of the gas. Take R = 8.31 J K⁻¹ mol⁻¹.（3 分）

(b) The gas is heated at constant volume until its temperature is 450 K. Calculate the new pressure.（3 分）

(d) Use the kinetic theory of gases to explain why the pressure of the gas increases when it is heated at constant volume.（3 分）

10. （9 分）放射性衰變

(a) The activity of a radioactive source falls from 4800 Bq to 600 Bq in 36 hours. Calculate the half-life of the source.（3 分）

(b) Calculate the decay constant of the source in s⁻¹.（3 分）

答案與評分要點

以下為每部分參考答案與評分要點：M 為方法分、A 為答案分、B 為獨立分、C 為補充分。

第 1 題 · 9 分

(a) a = 3.1 m s⁻²; s = 100 m

M1 uses a = (v − u)/t; A1 3.1 m s⁻²; A1 s = ½(u + v)t = 100 m.

(b) a = 3.3 m s⁻², so v = 45 m s⁻¹

M1 uses s = ut + ½at² with u = 25; A1 a = 3.3 m s⁻²; A1 v = 45 m s⁻¹.

C1 uses s = ½gt²; A1 33 m; C1 uses v = gt; A1 26 m s⁻¹.

第 2 題 · 10 分

(a) W = 60 N

M1 moment of weight = 180 × (1.6 − 0.80) = 144 N m; A1 W × 2.40 = 144; A1 W = 60 N.

(b) 240 N

C1 adds the two downward forces; A1 60 + 180; A1 240 N.

(c) No — the anticlockwise moment about the pivot is only 12 N m, less than the 144 N m clockwise moment of the weight, so the plank rotates clockwise (B end down).

M1 anticlockwise moment = 40 × 0.30; A1 12 N m; B1 compares with 144 N m; B1 states the plank rotates clockwise, B end down.

第 3 題 · 9 分

(a) P = 471 W

C1 uses mgh/t; A1 240 × 9.81 × 12 / 60; A1 471 W.

(b) 724 W

C1 efficiency = useful/input; A1 input = 471/0.65; A1 724 W.

C1 wasted power = 724 − 471 = 253 W; A1 energy = 253 × 60; A1 1.5 × 10⁴ J.

第 4 題 · 11 分

(a) A = 7.07 × 10⁻⁸ m², stress = 2.22 × 10⁸ Pa

C1 A = πd²/4; A1 7.1 × 10⁻⁸ m²; A1 stress = F/A = 2.2 × 10⁸ Pa.

(b) 2.2 × 10⁻³ (no unit)

C1 strain = extension/original length; A1 1.1 × 10⁻³.

C1 E = stress/strain; A1 2.0 × 10¹¹; B1 unit Pa (or N m⁻²).

(d) Limit of proportionality is the point beyond which extension is no longer proportional to load; below it the ratio stress/strain is constant, so extension doubles when the load doubles.

B1 defines the limit; B1 states constant ratio of stress to strain below it; B1 links doubling of load to doubling of extension.

第 5 題 · 10 分

(a) v = 300 m s⁻¹

C1 uses v = √(T/μ); A1 substitutes 45 and 5.0 × 10⁻⁴; A1 300 m s⁻¹.

(b) 167 Hz

C1 λ = 2L = 1.80 m; A1 f = v/λ; A1 167 Hz.

C1 f₂ = 2f₁; A1 333 Hz with λ = 0.90 m.

(d) Waves travelling along the string reflect at the fixed end and the reflected and incident waves have the same frequency and speed, so they superpose to give nodes and antinodes.

B1 mentions reflection at a fixed end; B1 mentions superposition of the two waves of the same frequency travelling in opposite directions.

第 6 題 · 11 分

(a) I = 2 A

C1 total resistance = 5.2 + 0.80; A1 I = 12.0/6.0; A1 2.0 A.

(b) 10.4 V

C1 V = E − Ir; A1 10.4 V.

C1 P = I²R; A1 2.0² × 5.2; A1 20.8 W.

(d) 86.7 % ; the lost energy heats the battery itself (internal resistance).

C1 efficiency = VI/EI; A1 86.7 %; B1 states energy is dissipated as thermal energy inside the battery.

第 7 題 · 10 分

(a) 2.59 eV

C1 E = hc/λ; A1 4.14 × 10⁻¹⁹ J; A1 2.59 eV.

(b) 6.2 × 10⁻²⁰ J

C1 uses hf = φ + KEmax; A1 0.39 eV; A1 6.2 × 10⁻²⁰ J.

C1 uses λ₀ = hc/φ; A1 5.7 × 10⁻⁷ m.

(d) No change: the maximum kinetic energy depends only on photon energy and work function; doubling intensity only doubles the number of photoelectrons per second.

B1 no change in maximum kinetic energy; B1 explanation in terms of photon energy being unchanged and only the rate of emission increasing.

第 8 題 · 10 分

(a) a = 5.76 m s⁻²; F = 6.91 × 10³ N

C1 a = v²/r; A1 5.8 m s⁻²; A1 F = ma = 6.9 × 10³ N towards the centre.

(b) 12.6 m s⁻¹

C1 sets μmg = mv²/r; A1 v = √(μgr); A1 13 m s⁻¹.

C1 T = 2πr/v; A1 13 s.

(d) Towards the centre of the circle; the force is perpendicular to the velocity, so it changes the direction of motion but does no work on the car.

B1 force directed towards the centre; B1 force perpendicular to velocity, so no work is done and the speed stays constant.

第 9 題 · 11 分

(a) 1.04 × 10⁵ Pa

C1 uses pV = nRT; A1 substitutes 0.050, 8.31 and 300; A1 1.0 × 10⁵ Pa.

(b) 1.56 × 10⁵ Pa

C1 uses p/T constant at constant volume; A1 p₂ = p₁ × 450/300; A1 1.6 × 10⁵ Pa.

C1 uses 3/2 kT; A1 6.2 × 10⁻²¹ J.

(d) Molecules move faster, so they hit the walls more often and each collision changes momentum by a larger amount; force on the walls per unit area therefore increases.

B1 molecules have greater mean speed; B1 greater rate of collisions with the walls; B1 greater change of momentum per collision, so higher pressure.

第 10 題 · 9 分

(a) 12 hours

C1 recognises 4800 → 600 is three half-lives; A1 36/3; A1 12 hours.

(b) 1.6 × 10⁻⁵ s⁻¹

C1 λ = ln2/T½ with T½ in seconds (43 200 s); A1 1.6 × 10⁻⁵; A1 unit s⁻¹.

C1 four half-lives elapse; A1 4800/2⁴; A1 300 Bq.

常見失分位

用 v = u + at 時忘記帶單位方向，位移與路程混淆，令 Q1 的距離寫成 200 m。
力矩題目只看力的大細，沒有乘力臂，或把支點兩邊的力臂寫反。
楊氏模量把直徑當半徑代入 A = πd²/4，面積大四倍，E 亦細四倍。
計算效率時用 input/output 而不是 useful/input，或漏寫百分號。
光電子的最大動能與光強度混為一談，以為加光就會加大動能。

時間分配

題目	分數	建議時間
第 1–2 題	19 分	約 23 分鐘
第 3–4 題	20 分	約 24 分鐘
第 5–6 題	21 分	約 25 分鐘
第 7–8 題	20 分	約 24 分鐘
第 9–10 題	20 分	約 24 分鐘

下載與列印

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題目卷 PDF · 答案與評分要點 PDF

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