📚 Year 10 AQA Science: Formula & Theorem Quick Reference Handbook | Year 10 AQA 科学：公式定理速查手册
Welcome to your essential quick reference for all the key formulas, equations, and theorems you will encounter in Year 10 AQA Combined Science or Separate Sciences. This handbook breaks down each relationship in physics, chemistry, and biology, giving you the standard symbols, SI units, and worked examples in both English and Chinese to reinforce your understanding. Use it for revision, homework, or practical work.
欢迎使用这份必备速查手册，这里汇总了 Year 10 AQA 综合科学或独立科学课程中所有关键公式、方程和定理。本手册逐一拆解物理、化学和生物中的重要关系，提供标准符号、国际单位以及中英双语示例，帮助你巩固理解。可用于复习、作业或实验操作。
1. Kinetic Energy & Gravitational Potential Energy | 动能与重力势能
Kinetic energy is the energy an object possesses due to its motion. It depends on mass and the square of velocity.
动能是物体因运动而具有的能量，它与质量和速度的平方成正比。
Eₖ = ½ m v²
Where Eₖ is kinetic energy in joules (J), m is mass in kilograms (kg), and v is velocity in metres per second (m/s).
其中 Eₖ 为动能，单位焦耳 (J)；m 为质量，单位千克 (kg)；v 为速度，单位米/秒 (m/s)。
Gravitational potential energy is the energy stored in an object because of its height above the ground. It depends on mass, gravitational field strength, and height.
重力势能是物体因离地高度而储存的能量，它与质量、引力场强度和高度有关。
Eₚ = m g h
Where Eₚ is gravitational potential energy (J), g is gravitational field strength (9.8 N/kg on Earth), and h is height (m).
其中 Eₚ 为重力势能 (J)，g 为引力场强度（地球取 9.8 N/kg），h 为高度 (m)。
2. Work Done, Power & Efficiency | 做功、功率与效率
Work is done when a force moves an object through a distance. Energy is transferred mechanically.
当力使物体移动一段距离时就做了功，能量以机械方式传递。
W = F s
W is work done (J), F is force (N), s is distance moved in the direction of the force (m).
W 为做功 (J)，F 为力 (N)，s 为沿力方向移动的距离 (m)。
Power is the rate at which energy is transferred or work is done.
功率是能量传递或做功的速率。
P = E ÷ t and P = W ÷ t
Where P is power in watts (W), E or W is energy transferred or work done (J), and t is time (s).
其中 P 为功率，单位瓦特 (W)；E 或 W 为传递的能量或做的功 (J)；t 为时间 (s)。
Efficiency is the proportion of useful output energy to total input energy. No device is 100% efficient due to wasted energy, often as heat.
效率是指有用输出能量占总输入能量的比例。由于能量耗散（通常为热），没有设备能达到 100% 效率。
Efficiency = (Useful output energy transfer ÷ Total input energy transfer) × 100%
Symbol version: (Euseful out / Etotal in) × 100%. Efficiency can also be expressed as a decimal.
符号形式：(E有用输出 / E总输入) × 100%。也可用小数表示。
3. Electrical Charge & Current | 电荷与电流
Electric current is a flow of charge. The size of the current is the rate of flow of charge.
电流是电荷的流动。电流的大小即电荷流动的速率。
Q = I t
Q is charge in coulombs (C), I is current in amperes (A), and t is time in seconds (s).
Q 为电荷，单位库仑 (C)；I 为电流，单位安培 (A)；t 为时间，单位秒 (s)。
When current flows through a component, charge carriers transfer energy. The potential difference (voltage) indicates how much energy is transferred per unit charge.
当电流流过元件时，载流子传递能量。电势差（电压）表示每单位电荷传递的能量。
4. Potential Difference & Resistance | 电势差与电阻
Potential difference (V) is the work done per unit charge. Ohm’s Law states that, at constant temperature, current through a resistor is directly proportional to the potential difference across it.
电势差 (V) 是每单位电荷做的功。欧姆定律指出，在温度恒定时，通过电阻器的电流与两端电压成正比。
V = I R
V is potential difference in volts (V), I is current (A), R is resistance in ohms (Ω).
V 为电压，单位伏特 (V)；I 为电流 (A)；R 为电阻，单位欧姆 (Ω)。
Combining with Q = I t, energy transferred in a circuit component can also be found.
结合 Q = I t，也能计算出电路元件中传递的能量。
5. Electrical Power & Energy Transferred | 电功率与电能
Electrical power depends on both current and potential difference. This is used to rate appliances.
电功率取决于电流和电势差，用于衡量电器功率。
P = I V
P is power (W), I is current (A), V is potential difference (V).
P 为功率 (W)，I 为电流 (A)，V 为电压 (V)。
lculated from power and time. When combined with P = I V, this gives a second useful form.
传递的能量可由功率和时间计算，结合 P = I V 可得另一种形式。
E = P t and E = I V t
E is energy transferred (J). Both equations appear regularly on the AQA equation sheet.
E 为传递的能量 (J)。这两个公式都经常出现在 AQA 公式表中。
6. Density & Specific Heat Capacity | 密度与比热容
Density is mass per unit volume. It determines whether objects float or sink and is a property of materials.
密度是单位体积的质量，决定物体浮沉，也是材料的属性。
ρ = m ÷ V
ρ (rho) is density in kilograms per metre cubed (kg/m³), m is mass (kg), V is volume (m³). For irregular solids, volume can be measured by displacement.
ρ（rho）为密度，单位千克每立方米 (kg/m³)；m 为质量 (kg)，V 为体积 (m³)。测量不规则固体体积可用排水法。
Specific heat capacity is the energy required to raise the temperature of 1 kg of a substance by 1 °C.
比热容是将 1 kg 物质升高 1 °C 所需的能量。
ΔE = m c Δθ
ΔE is change in thermal energy (J), m is mass (kg), c is specific heat capacity (J/kg°C), Δθ is temperature change (°C).
ΔE 为内能变化 (J)，m 为质量 (kg)，c 为比热容 (J/kg°C)，Δθ 为温度变化 (°C)。
7. Latent Heat & Particle Model | 潜热与粒子模型
During a change of state, the temperature remains constant while energy is absorbed or released as latent heat. This is explained by the particle model.
物态变化时，温度保持不变，能量以潜热形式吸收或释放。这可用粒子模型解释。
E = m L
E is energy (J), m is mass (kg), L is specific latent heat (J/kg) — for fusion (solid ↔ liquid) or vaporisation (liquid ↔ gas).
E 为能量 (J)，m 为质量 (kg)，L 为比潜热 (J/kg) —— 熔化潜热（固 ↔ 液）或汽化潜热（液 ↔ 气）。
The particle model also helps explain gas pressure and temperature: increasing temperature raises the average kinetic energy of particles, increasing the frequency and force of collisions with container walls.
粒子模型还有助于解释气体压强与温度：升温使粒子平均动能增大，碰撞器壁的频率和力度加大。
8. Speed & Acceleration | 速度与加速度
Speed is the distance travelled per unit time. In a distance–time graph, the gradient equals speed.
速度是单位时间移动的距离。在距离-时间图中，斜率等于速度。
v = s ÷ t
v is speed (m/s), s is distance (m), t is time (s). For objects moving with constant velocity, this formula holds.
v 为速度 (m/s)，s 为距离 (m)，t 为时间 (s)。适用于匀速直线运动。
Acceleration is the rate of change of velocity. It can be calculated from change in velocity over time or using the equation of motion.
加速度是速度变化的速率，可通过速度变化量除以时间计算，也可用运动方程。
a = Δv ÷ t
a is acceleration (m/s²), Δv is change in velocity (m/s). In a velocity–time graph, the gradient is acceleration, and the area under the graph equals distance travelled.
a 为加速度 (m/s²)，Δv 为速度变化 (m/s)。在速度-时间图中，斜率表示加速度，图线下的面积等于移动距离。
9. Resultant Force & Newton’s Second Law | 合力与牛顿第二定律
Newton’s Second Law describes how an object accelerates when a resultant force acts on it. Acceleration is proportional to force and inversely proportional to mass.
牛顿第二定律描述物体在合力作用下的加速情况：加速度与合力成正比，与质量成反比。
F = m a
F is resultant force (N), m is mass (kg), a is acceleration (m/s²).
F 为合力 (N)，m 为质量 (kg)，a 为加速度 (m/s²)。
Weight is a force caused by gravity: W = m g. Remember: mass (kg) is not the same as weight (N).
重力是由引力引起的力：W = m g。注意：质量 (kg) 与重力 (N) 不同。
10. Chemical Quantities: Moles & Concentration | 化学计量：摩尔与浓度
The mole is the unit for amount of substance. The mass of one mole of a substance is its relative formula mass (Mr) in grams.
摩尔是物质的量的单位。1 摩尔物质的质量等于其相对式量 (Mr) 以克为单位。
Number of moles = mass (g) ÷ Mr
Or n = m ÷ M, where n is moles (mol), m is mass (g), M is molar mass (g/mol).
即 n = m ÷ M，n 为物质的量 (mol)，m 为质量 (g)，M 为摩尔质量 (g/mol)。
Concentration of a solution is the amount of solute dissolved per unit volume. The most common unit in Year 10 is g/dm³.
溶液浓度指单位体积溶液中溶质的量。Year 10 常用单位为克每立方分米 (g/dm³)。
Concentration (g/dm³) = mass of solute (g) ÷ volume of solution (dm³)
You can also express concentration in mol/dm³: c = n ÷ V (V in dm³).
浓度也可用 mol/dm³ 表示：c = n ÷ V（V 单位 dm³）。
11. Rates of Reaction | 反应速率
The rate of a chemical reaction can be measured by how quickly a reactant is used up or a product is formed. Common methods involve measuring change in mass, volume of gas evolved, or colour change over time.
化学反应速率可通过反应物消耗或产物生成的快慢衡量。常用方法包括测量质量变化、产生气体体积或颜色随时间的变化。
Mean rate of reaction = quantity of reactant used or product formed ÷ time
For example, if 30 cm³ of carbon dioxide is produced in 60 seconds, the mean rate is 0.5 cm³/s.
例如，60 秒产生 30 cm³ 二氧化碳，则平均速率为 0.5 cm³/s。
The rate at any particular point on a graph is the gradient of the curve. Factors affecting rates include temperature, concentration, surface area, and catalysts.
曲线上任意点的瞬时速率等于该点切线斜率。影响速率的因素包括温度、浓度、表面积和催化剂。
12. Biology: Microscopy & Magnification | 生物：显微镜与放大倍数
Magnification is the number of times larger an image is compared to the real size of the object. The formula links image size, actual size, and magnification.
放大倍率是图像大小与实物大小的比值。该公式联系图像大小、实际大小和放大倍数。
Magnification = Image size ÷ Actual size
I = image size, A = actual size, M cell image is 40 mm long and the magnification is ×400, the actual size is 0.1 mm (or 100 µm).
I 为图像大小，A 为实际大小，M 为放大倍数。确保两者单位一致。典型问题：若细胞图像长 40 mm，放大倍数为 ×400，则实际大小为 0.1 mm（即 100 µm）。
Remember unit conversions: 1 mm = 1000 µm; 1 µm = 1000 nm. Always show working when rearranging.
记住单位换算：1 mm = 1000 µm；1 µm = 1000 nm。换算时务必展示步骤。
13. Key Unit Conversions & Prefixes | 重要单位换算与前缀
In all three sciences, you must be comfortable with standard form and prefixes. Common ones include:
在三门科学中，必须熟练运用科学记数法和前缀。常见前缀包括：
- centi (c) = 10⁻², so 1 cm = 0.01 m
- milli (m) = 10⁻³, 1 mm = 0.001 m
- micro (µ) = 10⁻⁶, 1 µm = 0.000 001 m
- nano (n) = 10⁻⁹, 1 nm = 0.000 000 001 m
- kilo (k) = 10³, 1 kg = 1000 g
- mega (M) = 10⁶, 1 MJ = 1 000 000 J
Centimetres to metres: divide by 100. Millimetres to metres: divide by 1000. Always convert to standard SI units before substituting into formulas unless the question uses consistent non-standard units.
厘米转米：除以 100。毫米转米：除以 1000。代入公式前一定要转换成标准国际单位，除非题目要求用一致的非标准单位。
14. Essential Practical Formula Rearrangements | 必做实验中的公式变形
re mass, temperature change, and electrical energy input. Rearrange ΔE = m c Δθ to find c: c = ΔE ÷ (m × Δθ).
许多必做实验涉及测量与公式应用。例如，比热容实验中测量质量、温度变化和输入的电能，可将 ΔE = m c Δθ 重排为 c = ΔE ÷ (m × Δθ)。
In density experiments, volume of a regular solid = length × width × height (V = l × w × h). For liquids, read the meniscus at eye level. For irregular objects, use V displaced = final reading – initial reading.
在密度实验中，规则固体的体积 = 长 × 宽 × 高 (V = l × w × h)。测量液体体积时视线应与凹液面底部平齐。测不规则物体时，V 排水 = 末读数 – 初读数。
the relationship c₁V₁ = c₂V₂ (when 1:1 ratio) is a useful extension after learning moles.
在化学滴定中（独立科学），尽管 Year 10 不要求计算浓度，但学习摩尔后，c₁V₁ = c₂V₂（等物质的量反应时）是一个有用的延伸。
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