📚 Year 10 CCEA Science Formula and Theorem Quick Reference Handbook | Year 10 CCEA 科学：公式定理速查手册
This quick reference handbook covers the essential formulae, laws, and theorems required for Year 10 CCEA Science, spanning Physics, Chemistry, and Biology. Each section presents key relationships with worked examples, unit definitions, and practical tips to support revision and exam success.
这本速查手册涵盖了 Year 10 CCEA 科学课程中物理、化学和生物所必需的基本公式、定律和定理。每个小节都用实例、单位定义和实用技巧介绍了关键关系式，以帮助复习和考试成功。
1. Speed, Velocity and Acceleration | 速度、速率和加速度
Speed is the rate at which distance is covered, while velocity is speed in a given direction. Acceleration occurs when an object changes its velocity.
速率是距离随时间的变化率，而速度是带有方向的速率。当物体改变其速度时就会产生加速度。
v = d / t (average speed)
Here v is speed (m/s), d is distance (m), t is time (s). Velocity uses the same equation but with direction stated.
这里 v 是速率（米/秒），d 是距离（米），t 是时间（秒）。速度使用相同的公式，但需要指明方向。
a = (v - u) / t
Acceleration a (m/s²) is the change in velocity (v − u) divided by the time taken. A negative value indicates deceleration.
加速度 a（米/秒²）等于速度变化量（v − u）除以所用时间。负值表示减速。
Example: A car accelerates from 5 m/s to 25 m/s in 4 s. a = (25 − 5) / 4 = 5 m/s².
示例：一辆汽车在 4 秒内从 5 米/秒加速到 25 米/秒。a = (25 − 5) / 4 = 5 米/秒²。
2. Newton's Second Law and Force | 牛顿第二定律与力
An unbalanced force causes a mass to accelerate. The acceleration is directly proportional to the net force and inversely proportional to the mass.
不平衡的力会使物体加速。加速度与合力成正比，与质量成反比。
F = m a
Force F is measured in newtons (N), mass m in kilograms (kg), and acceleration a in m/s².
力 F 的单位是牛顿（N），质量 m 的单位是千克（kg），加速度 a 的单位是米/秒²。
, where g is gravitational field strength (approximately 9.8 N/kg on Earth, often rounded to 10 N/kg).
重量是一个特例：重量 W = m g，其中 g 是重力场强度（地球表面约 9.8 牛/千克，常取 10 牛/千克）。
2 kg object experiences a net force of 10 N. Its acceleration a = F / m = 10 / 2 = 5 m/s².
示例：一个 2 千克的物体受到 10 牛的合力，其加速度 a = F / m = 10 / 2 = 5 米/秒²。
3. Work, Energy and Power | 功、能与功率
Work is done when a force moves an object through a distance. Energy is the capacity to do work, and power is the rate at which work is done.
力使物体在力的方向上移动一段距离时就做了功。能量是做功的能力，功率是做功的速率。
W = F d
Work W (J) equals force F (N) multiplied by distance d (m) in the direction of the force.
功 W（焦耳）等于力 F（牛顿）乘以沿力方向的距离 d（米）。
Eₖ = ½ m v²
Kinetic energy Eₖ (J) depends on mass m (kg) and speed v (m/s).
动能 Eₖ（焦耳）取决于质量 m（千克）和速率 v（米/秒）。
Eₚ = m g h
Gravitational potential energy Eₚ (J) is gained by lifting an object of mass m to height h against gravity g.
重力势能 Eₚ（焦耳）是将质量为 m 的物体反抗重力 g 提升高度 h 所获得的能量。
P = E / t = W / t
Power P (W) is energy transferred or work done per unit time.
功率 P（瓦特）是单位时间内转移的能量或做的功。
rough 8 m. Eₚ = 500 × 10 × 8 = 40 000 J. If this takes 20 s, power = 40 000 / 20 = 2000 W.
示例：一台起重机将 500 千克的重物提升 8 米，Eₚ = 500 × 10 × 8 = 40 000 焦耳。如果用时 20 秒，功率 = 40 000 / 20 = 2000 瓦。
4. Ohm's Law and Electrical Circuits | 欧姆定律与电路
For a metallic conductor at constant temperature, the current flowing is directly proportional to the potential difference across it.
对于恒温下的金属导体，流经的电流与其两端的电势差成正比。
V = I R
Voltage V (V), current I (A), and resistance R (Ω) form this fundamental relationship.
电压 V（伏特）、电流 I（安培）和电阻 R（欧姆）构成这一基本关系。
series circuits: Rₜₒₜₐₗ = R₁ + R₂ + ... ; current is the same everywhere, voltage divides.
在串联电路中：总电阻 Rₜₒₜₐₗ = R₁ + R₂ + ... ；各处电流相等，电压按比例分配。
s: 1/Rₜₒₜₐₗ = 1/R₁ + 1/R₂ + ... ; voltage across each branch is the same, current divides.
在并联电路中：1/Rₜₒₜₐₗ = 1/R₁ + 1/R₂ + ... ；各支路两端电压相等，电流按比例分配。
Charge Q = I t and energy transferred E = V I t (or E = V Q).
电荷量 Q = I t，转移的能量 E = V I t（或 E = V Q）。
Example: Two 4 Ω resistors in parallel have Rₜₒₜₐₗ = 1/(1/4 + 1/4) = 2 Ω.
示例：两个 4 欧姆的电阻并联，总电阻 Rₜₒₜₐₗ = 1/(1/4 + 1/4) = 2 欧姆。
5. Wave Equation | 波动方程
All waves obey the wave equation, linking velocity, frequency and wavelength.
所有波都遵循波动方程，它将波速、频率和波长联系起来。
v = f λ
Wave speed v (m/s) equals frequency f (Hz) multiplied by wavelength λ (m). The same equation applies to sound, light and water waves.
波速 v（米/秒）等于频率 f（赫兹）乘以波长 λ（米）。同样的方程适用于声波、光波和水波。
Period T = 1 / f. Frequency is the number of complete waves per second.
周期 T = 1 / f。频率是每秒完整波的个数。
sound wave has frequency 500 Hz and wavelength 0.68 m. Its speed v = 500 × 0.68 = 340 m/s.
示例：一声波频率为 500 赫兹，波长为 0.68 米，其速度 v = 500 × 0.68 = 340 米/秒。
6. Chemical Equations and Quantity Calculations | 化学方程式与物质的量计算
Chemical reactions are represented by balanced symbol equations, showing the conservation of mass. The relative atomic mass (Aᵣ) of elements and relative formula mass (Mᵣ) of compounds are used to calculate reacting masses.
化学反应用配平的符号方程表示，体现了质量守恒。元素的相对原子质量（Aᵣ）和化合物的相对式量（Mᵣ）用于计算反应质量。
n = m / M
ance n (mol) = mass m (g) ÷ molar mass M (g/mol). Molar mass equals the Aᵣ or Mᵣ in grams.
物质的量 n（摩尔）= 质量 m（克） ÷ 摩尔质量 M（克/摩尔）。摩尔质量在数值上等于 Aᵣ 或 Mᵣ，单位为克。
To find the mass of a product from a given mass of reactant: (i) convert masses to moles; (ii) use the mole ratio from the balanced equation; (iii) convert moles back to mass.
从给定反应物质量求产物质量：(i) 将质量换算为摩尔；(ii) 利用配平方程式中的摩尔比；(iii) 将摩尔换算回质量。
MgCl₂ formed. Molar mass of MgCl₂ = 24 + (2 × 35.5) = 95 g/mol. Mass = 0.10 × 95 = 9.5 g.
示例：Mg + 2HCl → MgCl₂ + H₂。2.4 克 Mg（Ar = 24）反应。Mg 的摩尔数 = 2.4/24 = 0.10 mol。摩尔比 Mg : MgCl₂ = 1:1，生成 0.10 mol MgCl₂。MgCl₂ 摩尔质量 = 24 + (2×35.5) = 95 g/mol。质量 = 0.10×95 = 9.5 克。
7. Acids, Bases and pH Scale | 酸、碱与 pH 标度
Acids are proton (H⁺) donors; bases are proton acceptors. The pH scale measures the concentration of hydrogen ions in a solution. Universal indicator or a pH probe gives a numerical value from 0 (strongly acidic) to 14 (strongly alkaline).
酸是质子（H⁺）的给予体；碱是质子接受体。pH 标度衡量溶液中氢离子的浓度。通用指示剂或 pH 探针给出 0（强酸性）至 14（强碱性）的数值。
+ base → salt + water (neutralisation); acid + carbonate → salt + water + carbon dioxide.
关键反应：酸 + 碱 → 盐 + 水（中和）；酸 + 碳酸盐 → 盐 + 水 + 二氧化碳。
The test for hydrogen gas: a lit splint gives a 'squeaky pop'. For carbon dioxide: limewater turns milky.
氢气检验：点燃的木条会发出“噗”的爆鸣声。二氧化碳检验：石灰水变浑浊。
hydrochloric acid reacts with sodium hydroxide to form the salt sodium chloride and water.
示例：HCl + NaOH → NaCl + H₂O。盐酸与氢氧化钠反应生成氯化钠盐和水。
8. Reactivity Series and Redox | 反应性序列与氧化还原
The reactivity series lists metals in order of their tendency to lose electrons and form positive ions. A more reactive metal can displace a less reactive metal from its compound.
反应性序列按金属失去电子形成正离子的倾向性排列。较活泼的金属能将较不活泼的金属从其化合物中置换出来。
Oxidation is loss of electrons; reduction is gain of electrons (OIL RIG). In terms of oxygen, oxidation is gain of oxygen, reduction is loss of oxygen.
氧化是失电子；还原是得电子（OIL RIG）。从氧的角度看，氧化是得氧，还原是失氧。
Common reactivity order: K > Na > Ca > Mg > Al > Zn > Fe > (H) > Cu > Ag.
常见反应性顺序：K > Na > Ca > Mg > Al > Zn > Fe > (H) > Cu > Ag。
u. Iron is more reactive than copper, so it displaces copper from copper sulfate solution.
示例：Fe + CuSO₄ → FeSO₄ + Cu。铁比铜活泼，因此能从硫酸铜溶液中置换出铜。
9. Cell Structure and Functions | 细胞结构与功能
All living organisms are made of cells. Plant and animal cells share common structures but also have differences.
所有生物体都由细胞构成。植物细胞和动物细胞既有共同的结构，也有不同之处。
| Organelle | Function | Present in |
|---|---|---|
| Nucleus | Contains genetic material; controls cell activities | Both |
| Cytoplasm | Site of chemical reactions | Both |
| Cell membrane | Controls entry and exit of substances | Both |
| Mitochondria | Site of aerobic respiration | Both |
| Ribosomes | Protein synthesis | Both |
| Cell wall | Provides support (made of cellulose) | Plants only |
| Chloroplasts | Site of photosynthesis; contain chlorophyll | Plants only |
| Permanent vacuole | Contains cell sap; maintains turgor | Plants only |
Bacterial cells are prokaryotic: they lack a true nucleus and membrane-bound organelles. Their genetic material is a single loop of DNA.
细菌细胞是原核细胞：它们没有真正的细胞核和膜包被的细胞器。其遗传物质是一条环状的 DNA。
10. Enzymes and Factors Affecting Rates | 酶与反应速率影响因素
Enzymes are biological catalysts made of protein. They speed up reactions by lowering activation energy and remain unchanged at the end.
酶是由蛋白质构成的生物催化剂。它们通过降低活化能来加快反应，并且在反应结束时本身保持不变。
The lock-and-key model: the enzyme's active site is complementary to the shape of the substrate. Once bound, the substrate is converted to products.
锁钥模型：酶的活性部位与底物的形状互补。一旦结合，底物便转化为产物。
Factors affecting enzyme activity: temperature, pH, substrate concentration. Each enzyme has an optimum temperature and pH. Extremes can denature the enzyme, changing the shape of the active site irreversibly.
影响酶活性的因素：温度、pH、底物浓度。每种酶都有最适温度和最适 pH。极端条件会使酶变性，永久改变活性部位的形状。
Example: Amylase breaks down starch into maltose. Its optimum pH is around 7; at very low pH it denatures.
示例：淀粉酶将淀粉分解为麦芽糖，其最适 pH 约为 7；在极低 pH 下它会变性。
11. Photosynthesis and Respiration | 光合作用与呼吸作用
Photosynthesis is the process by which plants produce glucose using light energy. Aerobic respiration releases energy from glucose in the presence of oxygen.
光合作用是植物利用光能制造葡萄糖的过程。有氧呼吸在氧气存在下从葡萄糖中释放能量。
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂ (photosynthesis, light energy required)
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂（光合作用，需要光能）
C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + energy (aerobic respiration)
C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + 能量（有氧呼吸）
Factors limiting photosynthesis: light intensity, carbon dioxide concentration, temperature. The rate can be measured by the volume of oxygen produced per unit time.
限制光合作用的因素：光照强度、二氧化碳浓度、温度。速率可通过单位时间内产生的氧气体积来衡量。
acid (less efficient, produces oxygen debt). In yeast: glucose → ethanol + carbon dioxide.
肌肉中的无氧呼吸：葡萄糖 → 乳酸（效率较低，产生氧债）。在酵母中：葡萄糖 → 乙醇 + 二氧化碳。
12. Genetics and Inheritance | 遗传学与遗传
Genes are sections of DNA that code for proteins. Alleles are different forms of a gene. The combination of alleles makes up the genotype; the observable characteristic is the phenotype.
基因是编码蛋白质的 DNA 片段。等位基因是基因的不同形式。等位基因的组合构成基因型；可观察到的特征即为表现型。
A dominant allele (e.g. B for brown eyes) masks a recessive allele (b for blue eyes). A homozygous individual has two identical alleles (BB or bb); a heterozygous individual has two different alleles (Bb).
显性等位基因（如决定棕色眼睛的 B）会掩盖隐性等位基因（决定蓝色眼睛的 b）。纯合子个体有两个相同的等位基因（BB 或 bb），杂合子个体有两个不同的等位基因（Bb）。
genotypic ratio is 1 BB : 2 Bb : 1 bb, giving a phenotypic ratio of 3 dominant : 1 recessive.
庞尼特方格用于预测遗传杂交的结果。在两个杂合亲本（Bb × Bb）的单基因杂交中，预期的基因型比例为 1 BB : 2 Bb : 1 bb，表现型比例为 3 显性 : 1 隐性。
Example: If brown eyes (B) are dominant, two heterozygous brown-eyed parents could produce a blue-eyed child (bb) with a probability of 25%.
示例：如果棕色眼睛（B）为显性，那么两个均为杂合子的棕色眼睛父母有 25% 的概率生下一个蓝眼睛的孩子（bb）。
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