📚 AQA A-level Maths June 2018 Pure & Statistics Markscheme: Examiner Notes | AQA A-level 数学 2018年6月纯数与统计评分方案：考官要点
The June 2018 AQA A-level Mathematics Pure and Statistics mark scheme is more than a list of final answers. It shows exactly where method marks, accuracy marks and explanation marks are awarded, and it reveals the standard of written reasoning examiners expect at A-level.
2018年6月 AQA A-level 数学纯数与统计评分方案不仅仅是一份最终答案表。它准确标出了方法分、答案分和解释分在哪里给出，也揭示了考官在 A-level 阶段对书面推理水平的要求。
1. How to Use the June 2018 Mark Scheme | 如何使用2018年6月评分方案
Many students read the mark scheme backwards: they check only the final answer. However, AQA awards the majority of marks for a clear method, correct substitution and valid conclusions.
很多学生用错误的方式读评分方案：只核对最终答案。然而，AQA 大部分分数是给清晰的解题方法、正确的代入和有效的结论。
Each marking point is coded M for method, A for accuracy, B for independent accuracy or statement, and E for explanation. Learn what each code requires.
每个评分点用 M 表示方法、A 表示答案、B 表示独立的准确答案或陈述、E 表示解释。要弄清每个代码要求什么。
A correct answer without working often scores zero in Pure questions because the method cannot be verified. In Statistics, a bare probability may score only one mark.
纯数题中，只写正确答案而不展示过程通常得零分，因为无法验证方法。统计题中，只写出一个概率值可能只得一分。
- M1 – one method mark for a correct route | M1——一条正确解题路径的方法分
- A1 – one accuracy mark for a correct intermediate or final value | A1——一个正确中间值或最终值的答案分
- B1 – one independent mark, often for a definition, sketch feature or quoted formula | B1——一个独立得分点，通常给定义、图像特征或引用的公式
- E1 – one explanation mark for interpreting a result in context | E1——一个在背景下解释结果的解释分
2. Pure Topic 1: Binomial Expansion and Approximations | 纯数考点1：二项展开与近似
In the June 2018 paper, a typical Pure question asked for the first four terms of (1 + ax)n in ascending powers of x, followed by an approximation of a given value.
在2018年6月的试卷中，一道典型纯数题要求写出 (1 + ax)n 按 x 升幂排列的前四项，随后进行给定数值的近似计算。
The mark scheme gives M1 for the correct binomial coefficient structure, A1 for each simplified term, and a final A1 for using x within the validity range |ax| < 1.
评分方案给出 M1 给正确的二项式系数结构，A1 给每一个化简后的项，最后的 A1 给在有效范围 |ax| < 1 内代入 x。
Common errors include forgetting the sign of x, miscopying n(n - 1)/2!, and writing the coefficient as nC2 instead of n choose 2. The mark scheme penalises these as accuracy errors only if the method is clear.
常见错误包括忘记 x 的符号、抄错 n(n - 1)/2!、以及把系数写成 nC2 而不是组合数。评分方案只在方法清晰时把这些作为答案错误扣分。
(1 + x)ⁿ = 1 + nx + [n(n – 1)/2!] x² + [n(n – 1)(n – 2)/3!] x³ + …
3. Pure Topic 2: Trigonometric Equations and Identities | 纯数考点2：三角方程与恒等式
θ to reduce a quadratic in one trig function, then solving for θ within a given interval.
2018年6月的三角题要求使用 sin²θ + cos²θ = 1 或 tan θ = sin θ / cos θ 将一个三角函数的二次式化简，然后在给定区间内求解 θ。
The mark scheme awards M1 for substituting the identity, M1 for forming a correct quadratic, A1 for each correct root, and M1 for finding all secondary solutions in the range.
评分方案给 M1 分用于恒等式代入，M1 分用于列出正确的二次方程，A1 分给每一个正确的根，M1 分给在区间内求出所有第二解。
Do not cancel sin θ or cos θ from both sides unless you state why it cannot be zero. Mark schemes require explicit checking of excluded values.
不要从等式两边约去 sin θ 或 cos θ，除非你说明它为什么不为零。评分方案要求明确检查被排除的值。
4. Pure Topic 3: Differentiation and Stationary Points | 纯数考点3：微分与驻点
Differentiation questions tested the product rule, quotient rule and chain rule, often leading to stationary points and their nature.
微分题考查了积的法则、商的法则和链式法则，通常最后要求求驻点及其性质。
0, A1 for solving x, and M1 for evaluating the second derivative or checking the sign change.
评分方案给 M1 分给正确求导，M1 分给令 dy/dx = 0，A1 分给解出 x，M1 分给计算二阶导数或检查符号变化。
A very common mark-losing error is to state f''(x) > 0 is a minimum but then fail to write that it is a minimum point with both coordinates. Always quote the full point (x, y).
一个常见的失分错误是写了 f''(x) > 0 是最小值，却没有写出最小点的完整坐标。一定要写出完整的点 (x, y)。
5. Pure Topic 4: Integration by Substitution and Areas | 纯数考点4：换元积分法与应用
Integration by substitution questions in June 2018 required changing the limits, replacing dx correctly, and simplifying the integral before integrating.
2018年6月的换元积分题要求更换积分上下限、正确替换 dx，并在积分前化简被积函数。
The mark scheme awards M1 for a correct substitution of u and du/dx, M1 for converting the limits, and A1 for the final exact value. Decimalised answers lose the final A1 if exact form is demanded.
评分方案给 M1 分给正确替换 u 和 du/dx，M1 分给转换上下限，A1 分给最终精确值。如果要求精确形式，写成小数会失去最后的 A1。
mark scheme requires writing Area = ∫(y₂ - y₁) dx with clear limits before any evaluation.
面积题通常是对一条曲线减另一条曲线积分。评分方案要求在计算前写出 Area = ∫(y₂ - y₁) dx 并标清上下限。
6. Pure Topic 5: Proof and Sequences | 纯数考点5：证明与数列
A proof question in June 2018 Pure asked for a counterexample or exhaustion. The mark scheme gives full marks only for a logically complete statement, not for a numeric verification.
2018年6月纯数的一道证明题要求举反例或用穷举法。评分方案只给逻辑完整的陈述满分，不给只代入数字的验证满分。
d geometric series, including sum to infinity. Show the formula S∞ = a / (1 - r) only when |r| < 1.
数列题考查了等差与等比数列，包括无穷和。只有当 |r| < 1 时才能使用公式 S∞ = a / (1 - r)。
The mark scheme explicitly withholds the final A1 if the convergence condition is not checked or written.
如果收敛条件没有检查或写出，评分方案明确扣掉最后的 A1。
7. Statistics Topic 1: Discrete Random Variables and Expectation | 统计考点1：离散随机变量与期望
e table. You were expected to show ΣP(X = x) = 1, find E(X), and use E(X²) to find Var(X).
统计题从离散随机变量表开始。要求展示 ΣP(X = x) = 1，求 E(X)，并用 E(X²) 求 Var(X)。
babilities equals 1, M1 for using E(X) = Σ xP(X = x), and A1 for Var(X) = E(X²) - [E(X)]².
评分方案给 B1 分用于陈述或检验概率和为 1，M1 分用于使用 E(X) = Σ xP(X = x)，A1 分用于 Var(X) = E(X²) - [E(X)]²。
Always give the variance as an exact fraction or decimal to 3 significant figures unless told otherwise. The June 2018 mark scheme accepted both but required the method shown.
除非另有说明，方差要给出精确分数或三位有效数字。2018年6月评分方案两者都接受，但要求展示方法。
8. Statistics Topic 2: Binomial Distribution and Hypothesis Tests | 统计考点2：二项分布与假设检验
Hypothesis
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