📚 OCR Science: Calculation Questions Masterclass | OCR 科学：计算题专项训练
Mastering calculations is essential for success in OCR Science examinations, whether you are taking Combined Science or the separate sciences. This article provides targeted practice on the most common calculation types across Physics, Chemistry, and Biology. Work through each section carefully, pay attention to unit conversions, and learn to avoid the typical mistakes that cost marks in the exam.
掌握计算题对于在 OCR 科学考试中取得成功至关重要，无论你参加的是综合科学还是单独科学。本文针对物理、化学和生物学中最常见的计算类型进行专项训练。请仔细学习每个部分，注意单位转换，并学会避免考试中导致失分的典型错误。
1. Speed, Distance and Time | 速度、距离与时间
Speed is a scalar quantity that describes how fast an object is moving. It is calculated by dividing the distance travelled by the time taken. In the exam, you will often need to rearrange the formula to find distance or time.
速度是描述物体运动快慢的标量。它等于物体运动的路程除以所用的时间。考试中你经常需要将公式变形来求距离或时间。
The core relationship is expressed as v = s / t (or speed = distance / time). The standard units are metres (m) for distance, seconds (s) for time, and metres per second (m/s) for speed. If a question gives distance in kilometres or time in minutes, you must convert them first.
核心关系表示为 速度 = 距离 / 时间。标准单位是距离用米(m)，时间用秒(s)，速度用米每秒(m/s)。如果题目给出的距离单位是千米或时间单位是分钟，你必须先进行换算。
A typical mistake is using inconsistent units. For example, if a cyclist covers 36 km in 2 hours, converting to m/s: 36 km = 36000 m and 2 hours = 7200 s, so speed = 36000 / 7200 = 5 m/s. Always check whether the question expects the answer in m/s or km/h.
典型的错误是使用不一致的单位。例如，一个骑行者 2 小时行驶 36 km，要转换成 m/s： 36 km = 36000 m，2 小时 = 7200 s，所以速度 = 36000 / 7200 = 5 m/s。务必检查题目期望的答案单位是 m/s 还是 km/h。
2. Acceleration and Newton’s Second Law | 加速度与牛顿第二定律
Acceleration is the rate of change of velocity. It can be calculated using a = (v – u) / t, where v is the final velocity (m/s), u is the initial velocity (m/s), and t is the time (s). The unit of acceleration is metres per second squared (m/s²).
加速度是速度的变化率。可以用公式 a = (v – u) / t 计算，其中 v 是末速度(m/s)，u 是初速度(m/s)，t 是时间(s)。加速度的单位是米每二次方秒(m/s²)。
Newton’s second law connects force, mass, and acceleration: F = m × a. Force (F) is measured in newtons (N), mass (m) in kilograms (kg), and acceleration in m/s². Many exam questions require you to use F = m a after first finding the acceleration from motion data.
牛顿第二定律将力、质量和加速度联系起来：F = m × a。力(F)的单位是牛顿(N)，质量(m)的单位是千克(kg)，加速度的单位是 m/s²。许多考题要求你先从运动数据求出加速度，再使用 F = m a。
It is vital to use mass in kilograms, not grams. If a resultant force of 120 N acts on a mass of 800 g, convert to 0.8 kg, then a = F / m = 120 / 0.8 = 150 m/s². Forgetting to convert grams to kilograms is a common error.
使用质量时务必使用千克，而不是克。如果一个 120 N 的合力作用在 800 g 的物体上，转换成 0.8 kg，然后 a = F / m = 120 / 0.8 = 150 m/s²。忘记将克换算为千克是一个常见错误。
When an object decelerates, the initial velocity is greater than the final velocity, producing a negative acceleration. Always include the negative sign in your answer unless the question asks for deceleration as a magnitude.
当物体减速时，初速度大于末速度，会产生负加速度。除非题目要求减速的数值大小，否则答案中务必包含负号。
3. Kinetic Energy and Gravitational Potential Energy | 动能与重力势能
Kinetic energy (KE) is the energy an object possesses due to its motion. The formula is KE = ½ × m × v², where m is mass (kg) and v is speed (m/s). The energy is measured in joules (J).
动能(KE)是物体由于运动而具有的能量。公式为 KE = ½ × m × v²，其中 m 是质量(kg)，v 是速度(m/s)。能量的单位是焦耳(J)。
Gravitational potential energy (GPE) is the energy stored in an object because of its height above the ground: GPE = m × g × h. Here m is mass (kg), g is gravitational field strength (9.8 N/kg or approximately 10 N/kg on Earth), and h is height (m).
重力势能(GPE)是物体因距地面有一定高度而储存的能量：GPE = m × g × h。其中 m 是质量(kg)，g 是引力场强度(地球表面为 9.8 N/kg 或近似取 10 N/kg)，h 是高度(m)。
OCR often asks you to use conservation of energy. For a falling object with no air resistance, the loss in GPE equals the gain in KE. For instance, if a 2 kg ball falls 5 m, GPE lost = 2 × 10 × 5 = 100 J. This becomes KE, so 100 = ½ × 2 × v², solving gives v = √100 = 10 m/s.
OCR 经常考察能量守恒。对于一个没有空气阻力的下坠物体，重力势能的减少量等于动能的增加量。例如，一个 2 kg 的球下落 5 m，减少的 GPE = 2 × 10 × 5 = 100 J。它转化为 KE，即 100 = ½ × 2 × v²，解得 v = √100 = 10 m/s。
Always square the velocity correctly when using the KE formula. A common slip is to multiply m by v and then halve, instead of squaring v first. Show each step clearly to avoid arithmetic mistakes.
使用动能公式时必须先将速度正确平方。常见的失误是先乘质量再除二，而没有先平方速度。解题时逐步清晰地展示运算过程以避免算术错误。
4. Efficiency and Power | 效率与功率
Efficiency is a measure of how much useful energy or power output is obtained from a system compared to the total energy or power input. It is normally expressed as a decimal or percentage: Efficiency = Useful output energy / Total input energy (or useful power output / total power input).
效率衡量一个系统获得的有用能量或功率输出与总输入能量或功率的比值。通常用小数或百分比表示：效率 = 有用输出能量 / 总输入能量 (或有用输出功率 / 总输入功率)。
Efficiency can never be greater than 1 (or 100%) due to conservation of energy. In practical questions, some energy is always transferred to less useful stores, such as thermal energy in the surroundings. A motor lifting a load might have a useful power output of 50 W and a total input of 80 W, so efficiency = 50/80 = 0.625 or 62.5%.
效率不可能大于 1 (或 100%)，因为能量守恒。在实际问题中，总有一部分能量转移到不大有用的能量储存中，比如周围环境的热能。一个提升重物的马达可能有 50 W 的有用输出功率和 80 W 的总输入功率，因此效率 = 50/80 = 0.625 或 62.5%。
Power is the rate of doing work or transferring energy. Two forms of the power equation are common: P = E / t (where E is energy transferred in J, t is time in s) and P = W / t (where W is work done). Power is measured in watts (W), where 1 W = 1 J/s.
功率是做功或传递能量的速率。两个常用功率公式是：P = E / t (E 为传递的能量，单位 J；t 为时间，单位 s) 和 P = W / t (W 为做功)。功率的单位是瓦特(W)，1 W = 1 J/s。
If a question asks for the power of an appliance that uses 3600 J in 2 minutes, convert minutes to seconds first: 2 min = 120 s. Then P = 3600 / 120 = 30 W.
如果题目问一个用电器在 2 分钟内使用了 3600 J 能量，要求它的功率，要先将分钟转化为秒：2 分钟 = 120 s。然后 P = 3600 / 120 = 30 W。
5. Density | 密度
Density is the mass per unit volume of a material. The equation is ρ = m / V, where ρ (rho) is density (kg/m³ or g/cm³), m is mass, and V is volume. A solid block’s volume can often be found from its dimensions, while the volume of an irregular solid can be measured by displacement.
密度是物质单位体积的质量。公式为 密度 = 质量 / 体积，通常表示为 ρ = m / V，其中 ρ 是密度(kg/m³ 或 g/cm³)，m 是质量，V 是体积。规则固体的体积通常可通过尺寸求得，而不规则固体的体积可用排水法测量。
In the lab, a eureka can or measuring cylinder is used to find the volume of an irregular object by the rise in water level. Record the volume in cm³ or m³ as required. If the mass of a stone is 150 g and it causes the water level to rise from 50 cm³ to 80 cm³, the volume is 30 cm³, so density = 150 / 30 = 5 g/cm³.
在实验室中，可使用溢水罐或量筒，通过水位上升来求不规则物体的体积。根据要求以 cm³ 或 m³ 记录体积。如果一块石头的质量是 150 g，它使水面从 50 cm³ 上升到 80 cm³，则体积为 30 cm³，密度 = 150 / 30 = 5 g/cm³。
OCR may ask you to convert between g/cm³ and kg/m³. The conversion factor is 1 g/cm³ = 1000 kg/m³. To go from g/cm³ to kg/m³, multiply by 1000. Thus a density of 2.7 g/cm³ equals 2700 kg/m³. Be careful with unit multipliers.
OCR 可能要求你在 g/cm³ 和 kg/m³ 之间转换。换算关系是 1 g/cm³ = 1000 kg/m³。要将 g/cm³ 换算为 kg/m³，乘以 1000。因此 2.7 g/cm³ 等于 2700 kg/m³。使用换算因子时要当心。
6. Moles and Molar Mass | 摩尔与摩尔质量
The mole is the unit for amount of substance. The number of moles (n) is calculated by n = m / M, where m is the mass of the substance in grams (g) and M is the molar mass (in g/mol). The molar mass is the mass of one mole of the substance, numerically equal to the relative formula mass (Mr).
摩尔是物质的量的单位。摩尔数(n)用 n = m / M 计算，其中 m 是物质的质量(单位：g)，M 是摩尔质量(单位：g/mol)。摩尔质量是一摩尔该物质的质量，数值上等于相对式量(Mr)。
To find the Mr, you sum the relative atomic masses (Ar) of all atoms in the chemical formula. For water, H₂O: Ar of H = 1, O = 16, so Mr = (2 × 1) + 16 = 18. The molar mass of water is 18 g/mol.
要计算 Mr，将化学式中所有原子的相对原子质量(Ar)相加。对于水 H₂O：H 的 Ar = 1，O = 16，因此 Mr = (2 × 1) + 16 = 18。水的摩尔质量是 18 g/mol。
When given a mass, you can find moles. How many moles are in 36 g of water? n = 36 g / 18 g/mol = 2.0 mol. To find mass from moles: mass = n × M. What is the mass of 0.5 mol of CO₂? CO₂ Mr = 12 + (2 × 16) = 44, so mass = 0.5 × 44 = 22 g.
已知质量，可以求摩尔数。36 g 水有多少摩尔？n = 36 g / 18 g/mol = 2.0 mol。已知摩尔数求质量：质量 = n × M。0.5 mol CO₂ 的质量是多少？CO₂ 的 Mr = 12 + (2 × 16) = 44，因此质量 = 0.5 × 44 = 22 g。
7. Concentration and Titration Calculations | 浓度与滴定计算
Concentration is a measure of how much solute is dissolved in a given volume of solution. It is commonly expressed in g/dm³ or mol/dm³. The formulas are: Concentration (g/dm³) = mass of solute (g) / volume of solution (dm³) and Concentration (mol/dm³) = number of moles / volume (dm³).
浓度是衡量在一定体积溶液中溶有多少溶质的量。常用单位是 g/dm³ 或 mol/dm³。公式为：浓度(g/dm³) = 溶质质量(g) / 溶液体积(dm³) 和 浓度(mol/dm³) = 溶质摩尔数 / 体积(dm³)。
Always convert volume to dm³ before carrying out these calculations. 1 dm³ = 1000 cm³. So 250 cm³ = 0.25 dm³. OCR titration questions typically require you to calculate the unknown concentration of an acid or alkali using results from a neutralisation reaction.
在进行这些计算之前，务必先将体积换算为 dm³。1 dm³ = 1000 cm³，所以 250 cm³ = 0.25 dm³。OCR 的滴定问题通常要求你利用中和反应的结果计算未知酸或碱的浓度。
The titration calculation uses the mole ratio from the balanced equation. For a reaction between sodium hydroxide and hydrochloric acid: NaOH + HCl → NaCl + H₂O, the ratio is 1:1. The key equation is n = c × V, where c is concentration in mol/dm³ and V in dm³. At the equivalence point, the moles of acid equal the moles of alkali based on the ratio.
滴定计算使用化学方程式给出的摩尔比。对于氢氧化钠和盐酸的反应：NaOH + HCl → NaCl + H₂O，比为 1:1。核心公式是 n = c × V，其中 c 为浓度(mol/dm³)，V 为体积(dm³)。在等当点，根据摩尔比，酸的摩尔数等于碱的摩尔数。
If 25.0 cm³ of NaOH solution required 20.0 cm³ of 0.100 mol/dm³ HCl for neutralisation, find the concentration of NaOH. Moles of HCl = 0.100 × 0.0200 = 0.00200 mol. Because of 1:1 ratio, moles NaOH = 0.00200 mol. Concentration of NaOH = 0.00200 / 0.0250 = 0.0800 mol/dm³.
如果 25.0 cm³ 的 NaOH 溶液需要 20.0 cm³ 的 0.100 mol/dm³ HCl 进行中和，求 NaOH 的浓度。HCl 的摩尔数 = 0.100 × 0.0200 = 0.00200 mol。由于 1:1 比例，NaOH 的摩尔数 = 0.00200 mol。NaOH 的浓度 = 0.00200 / 0.0250 = 0.0800 mol/dm³。
8. Percentage Yield and Atom Economy | 百分产率与原子经济
Percentage yield compares the actual mass of product obtained from a reaction to the theoretical maximum mass predicted by stoichiometry. The formula is Percentage yield = (actual yield / theoretical yield) × 100.
百分产率是将反应实际获得的产物质量与根据化学计量预测的理论最大质量进行比较。公式为 百分产率 = (实际产量 / 理论产量) × 100。
Yields are rarely 100% because of incomplete reactions, side reactions, and losses during purification. When you calculate theoretical yield, first use moles to find the expected mass of product from the limiting reactant. Then apply the yield formula.
由于反应不完全、副反应和提纯过程中的损失，产率很少达到 100%。计算理论产量时，首先利用摩尔数从限量反应物求出预期产物质量，然后应用产率公式。
Atom economy measures the efficiency of a reaction in incorporating atoms from reactants into the desired product. Atom economy = (Mr of desired product / sum of Mr of all reactants) × 100. A higher atom economy means a more sustainable process with less waste.
原子经济性衡量反应中反应物原子纳入目标产物的效率。原子经济性 = (目标产物的 Mr / 所有反应物 Mr 之和) × 100。原子经济性越高，意味着过程越可持续，废料越少。
When a question provides actual yield and the balanced equation, start by calculating the number of moles of the known reactant or product, scale according to the mole ratio, convert to mass to find theoretical yield, and finally compute percentage yield. Being methodical prevents errors.
当题目给出实际产量和配平的方程式时，先从已知反应物或产物的摩尔数开始，按照摩尔比换算，再转化为质量求出理论产量，最后计算百分产率。有条不紊的解题思路可避免错误。
9. Magnification and Unit Conversions in Biology | 生物放大倍数与单位转换
In biology, magnification is calculated using Magnification = size of image / size of real object. Both sizes must be in the same units. The formula can be rearranged to find the actual size of a specimen: Actual size = image size / magnification.
在生物学中，放大倍数用公式 放大倍数 = 图像大小 / 实物大小 计算。两个大小必须使用相同单位。该公式可变形来求样本的实际大小：实际大小 = 图像大小 / 放大倍数。
Typical units are millimetres (mm), micrometres (µm), and nanometres (nm). Conversions: 1 mm = 1000 µm; 1 µm = 1000 nm. When measuring an image with a ruler, you usually get a value in mm, which you often need to convert to µm for cell sizes.
典型单位有毫米(mm)、微米(µm)和纳米(nm)。换算关系为：1 mm = 1000 µm；1 µm = 1000 nm。当用直尺测量图像时，通常会得到一个毫米值，而细胞大小往往需要换算为微米。
If a cell image measures 15 mm in a micrograph with a magnification of ×3000, the actual size = 15 mm / 3000 = 0.005 mm = 5 µm. Always present your answer in the most appropriate unit – for cells, micrometres are standard.
如果一个细胞图像在一张放大倍数为 ×3000 的显微照片上量得 15 mm，实际大小 = 15 mm / 3000 = 0.005 mm = 5 µm。务必用最合适的单位呈现答案——对细胞而言，微米是标准单位。
In estimating the length of an organelle, you may need to use a scale bar. Measure the scale bar in mm, determine its value in µm, and apply the ratio to the measured structure. Check that the magnification calculated makes sense (e.g. ×1000–×10 000 for light microscopes, up to ×500 000 for electron microscopes).
在估算细胞器长度时，可能需要用到比例尺。用毫米量出比例尺的长度，确定其代表的微米值，然后按比例推算所测结构的大小。检查求出的放大倍数是否合理(光学显微镜约为 ×1000–×10000，电子显微镜可达 ×500000)。
10. Genetic Probability and Ratios | 遗传概率与比例
Genetic crosses in OCR Biology often require you to calculate probabilities and ratios of offspring genotypes and phenotypes. Monohybrid inheritance follows Mendel’s laws, and you use a Punnett square to show the possible combinations of alleles.
OCR 生物学中的遗传杂交题常要求计算子代基因型和表现型的概率与比例。单基因遗传遵循孟德尔定律，你可用庞纳特方格表示所有可能的等位基因组合。
If both parents are heterozygous for a trait (e.g. Aa ×
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