📚 AS Mathematics Unit 5 Mark Scheme June 2019 – Common Mistakes & How to Avoid Them | AS 数学 单元5 2019年6月 评分标准 常见错误与规避
The June 2019 AS Unit 5 mark scheme (typically Mechanics 1 or an applied maths paper) reveals a set of recurring errors that cost students valuable marks. Understanding these pitfalls can transform a grade from a C to an A. This article uses actual mark scheme notes to highlight what examiners wanted to see, and where candidates consistently slipped up.
2019年6月AS单元5的评分标准（通常对应力学1或应用数学卷）暴露了一系列反复出现的错误，这些错误让学生损失了许多分数。理解这些陷阱可以把成绩从C提升到A。本文利用评分标准中的真实批注，指出考官想看到什么，以及考生最容易在哪里失手。
1. Misapplying Constant Acceleration Equations (SUVAT) | 误用匀加速运动公式
t when s was unknown but t was also unknown. The mark scheme repeatedly penalised working that failed to identify the missing variable. Always list u, v, a, s, t before selecting an equation.
很多考生选错了匀加速运动公式，常试图用 v = u + at 却同时缺少 s 和 t。评分标准多次惩罚了未能识别缺失变量的做法。选择方程前，一定要先列出 u, v, a, s, t。
negative when decelerating. In one question, candidates lost marks because they wrote 25 = 100 + 2 × a × 50 instead of using negative initial velocity correctly.
一个经典错误是使用 v² = u² + 2as 时代入速度值却忘了平方，或者在减速时忘了让加速度取负值。在某道题中，考生因写成 25 = 100 + 2 × a × 50 而没有正确使用负初速度而失分。
2. Sign Conventions in Vertical Motion | 竖直运动中的符号约定
8 as positive in both upward and downward motion, causing sign errors in displacement and final velocity. In June 2019, a 4-mark question on a ball thrown vertically saw over half of students mix signs.
当物体向上抛出或在重力作用下下落时，评分标准要求一致的正方向。很多考生在向上和向下运动中都将 g = 9.8 设为正，导致位移和末速度出现符号错误。2019年6月一道关于竖直上抛小球的4分题，超过一半的学生混淆了符号。
ity and acceleration follow that convention. For example, if upwards is positive, then g = – explicitly awarded method marks only when signs were consistent with the chosen direction.
一定要画一个粗略的箭头标明所选正方向，然后确保位移、速度和加速度都遵循这个约定。例如，若向上为正，则 g = –9.8 m s⁻²。评分标准明确表示，只有符号与所选方向一致时才给方法分。
3. Misreading Velocity–Time Graphs | 误读速度–时间图
Velocity–time graph questions were a rich source of mistakes. Candidates confused area with gradient, using the slope to find distance travelled. The mark scheme required the area under the graph for distance, and gradient for acceleration only. Several candidates also assumed acceleration was zero when the line was straight but non‑horizontal.
速度–时间图问题是错误的丰产田。考生混淆了面积和斜率，用斜率求行驶距离。评分标准要求用图像下的面积求距离，仅用斜率求加速度。还有考生在直线倾斜但非水平时误以为加速度为零。
In one part, a trapezium area calculation was needed, yet candidates frequently forgot to halve the sum of parallel sides or used the wrong base. The mark scheme often allowed a follow-through if the shape was split correctly, but arithmetic slips still cost accuracy marks.
有道题需要计算梯形面积，但考生经常忘记将平行边之和除以2，或用错底边。如果图形拆分正确，评分标准通常允许后续跟进，但计算错误仍然丢失准确分。
4. Resolving Forces: Missing Perpendicular Components | 力的分解：遗漏垂直分量
When resolving a force into components on an inclined plane, a common error was to confuse sine and cosine, or to forget that the weight always acts vertically downwards. In June 2019, a 6-mark equilibrium problem penalised those who resolved weight without accounting for the angle of the slope, writing mg instead of mg sin θ or mg cos θ.
在斜面上分解力时，一个常见错误是混淆正弦和余弦，或忘记重力始终竖直向下。2019年6月一道6分的平衡题惩罚了那些分解重力却没有考虑斜面角度的考生，他们直接写 mg 而不是 mg sin θ 或 mg cos θ。
Always draw a clearly labelled free-body diagram with all forces, then use the correct adjacent/opposite reasoning. The mark scheme gave diagrams marks only when all forces were present and arrows were pointing in the correct sense.
一定要画出标注清晰的受力图，包含所有力，然后使用正确的邻边/对边推理。只有所有力都存在且箭头方向正确时，评分标准才给受力图分。
5. Connected Particles: Tension Direction and Whole-System Approach | 连接体：张力方向与整体法
In pulley or tow-bar problems, candidates frequently misdirected the tension force on free-body diagrams, drawing it in the same direction on both particles. The mark scheme insisted on tension pulling away from each body. Another widespread mistake was attempting to solve by isolating particles when a whole-system equation would have been faster and less error-prone.
在滑轮或拖杆问题中，考生经常在隔离体图上画错张力方向，在两个物体上画成同一方向。评分标准坚持张力应从每个物体拉离。另一个普遍错误是试图隔离求解，而使用整体系统方程本可以更快且不易出错。
pulley system, the mark scheme awarded full marks for writing a combined equation like m₁g – ion of a light inextensible string was stated. Many lost method marks by writing separate equations with incorrect signs for tension.
对于光滑滑轮系统，只要说明假设轻绳且不可伸长，写出如 m₁g – m₂g = (m₁ + m₂)a 的组合方程，评分标准就给满分。许多考生因单独写方程时张力符号错而丢了方法分。
6. Friction: Direction and Limiting Equilibrium Confusion | 摩擦力：方向与极限平衡混淆
Candidates often assumed friction always opposes motion without considering whether the body was about to slide up or down the slope. In June 2019, a ladder slip question required friction pointing up the wall, but many drew it down. The mark scheme explicitly stated that the direction of friction must oppose the relative motion or tendency of motion.
考生常假设摩擦力总是阻碍运动，而不考虑物体即将向上还是下滑动。2019年6月一道梯子滑动题要求摩擦力指向墙上方，但很多人画成了向下。评分标准明确指出，摩擦力方向必须与相对运动或运动趋势相反。
se, friction is less than μR. Incorrectly using the equality led to overdetermined systems and impossible solutions.
另一个关键错误是混淆 F = μR 与 F ≤ μR。当系统处于极限平衡时，F = μR；否则摩擦力小于 μR。错误地使用等式导致系统过约束和不可能的解。
7. Moments: Perpendicular Distance Mistakes | 力矩：垂直距离错误
Moments questions regularly tripped students who took the wrong perpendicular distance from a force’s line of action to the pivot. The mark scheme required distances measured at right angles to the force. In a non-uniform rod problem, many candidates used the slant length instead of the horizontal or vertical component distance, losing all method marks.
力矩问题经常让那些取了错误垂直距离（从力的作用线到支点）的学生栽跟头。评分标准要求沿垂直于力的方向测量距离。在一道非均匀杆题中，许多考生用了斜长而不是水平或垂直分量距离，丢掉了所有方法分。
Always resolve the force into components parallel and perpendicular to the lever arm, then take moments of components. The mark scheme gave credit for correct component distances even if the final answer was numerically wrong, provided the moment equation was set up accurately.
始终将力分解为平行和垂直于力臂的分量，然后对分力取矩。只要力矩方程建立准确，即便最终答案数值有误，评分标准也对正确的距离分量给分。
8. Units and Significant Figures in Final Answers | 最终答案的单位与有效数字
Losing a mark for forgetting units or giving answers to an inappropriate number of significant figures was surprisingly common. The June 2019 mark scheme deducted a mark for answers without units when the quantity had physical dimensions (e.g., velocity in m s⁻¹, force in N). It also demanded answers rounded to 2 or 3 significant figures as per general instruction, unless the question stated otherwise.
因忘记写单位或有效数字不当而丢分的情况出乎意料地普遍。2019年6月评分标准规定，当物理量有量纲时（如速度用 m s⁻¹，力用 N），不写单位扣一分。它还要求除非题目另有说明，答案要按总要求四舍五入到2或3位有效数字。
Candidates who wrote 14.676 N instead of 14.7 N or 15 N lost the accuracy mark despite having correct method. The mark scheme usually prints a final answer line and expected unit; any discrepancy triggers the penalty.
考生写14.676 N而不是14.7 N或15 N，即便方法正确也丢了准确度分。评分标准通常会印出最终答案线和期望的单位；任何差异都会触发扣分。
9. Interpretation and Modelling Assumptions | 解释与建模假设
Examiners routinely set 1‑2 mark questions asking “Explain what is meant by...” or “State one modelling assumption you have made”. In June 2019, candidates lost these easy marks by giving vague answers like “friction is ignored” without specifying particle, string, or smooth surface. The mark scheme required precise wording such as “the string is light and inextensible” or “the particle is modelled as a point mass”.
考官通常设置1‑2分的题，问“解释……的含义”或“说出你使用的一个建模假设”。2019年6月，考生因给出“忽略摩擦”等模糊答案而丢掉了这些容易的分，却没有指出是质点、细绳还是光滑表面。评分标准要求精确措辞，如“轻绳且不可伸长”或“质点被建模为一个点质量”。
Another pitfall was failing to link the assumption to the specific context. For example, when asked about constant acceleration, candidates wrote “acceleration is constant” instead of “the car’s acceleration is constant, so we can use SUVAT equations”. The mark scheme expected application, not just a generic statement.
另一个陷阱是没有把假设与具体情境联系起来。例如，问到匀加速时，考生写“加速度恒定”而不是“汽车的加速度恒定，因此我们可以使用SUVAT方程”。评分标准期待应用，而不只是一个笼统的陈述。
10. Impulse and Momentum: Vector Direction | 冲量与动量：矢量方向
In impulse– uld have been straightforward vector calculations. The mark scheme emphasized that I = m(v – s velocity reversed; forgetting the minus sign on the rebound resulted in a doubled error.
在冲量–动量问题中，很多学生把速度当作速率，忽略了方向，在本来应该简单的矢量计算上丢了分。评分标准强调 I = m(v – u) 是矢量方程；u 和 v 的正确符号至关重要。球垂直撞墙后速度反向，反弹时忘记负号导致错误加倍。
A typical mistake observed in the series was writing impulse = 0.5 × 8 – 6 = 1 N s without accounting for opposite directions. The mark scheme showed that 0.5 × (–8) – 0.5 × 6 = – N s. Method marks were only given when signs were consistent with a stated positive sense.
该系列考试中观察到的一个典型错误是写出冲量 = 0.5 × 8 – 0.5 × 6 = 1 N s，而没有考虑相反方向。评分标准显示，应写为 0.5 × (–8) – 0.5 × 6 = –7 N s，大小为7 N s。只有符号与声明的正方向一致时才给方法分。
Published by TutorHao | Mathematics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图