📚 S1 Delphis Practice Papers (Edexcel & OCR) | S1 Delphis 模拟试卷（Edexcel 与 OCR）
The Delphis papers are a well-known set of unofficial practice papers for A Level Mathematics. This page collects the S1 (Statistics 1) Delphis papers for Edexcel, together with their matching mark schemes, so you can download a question paper and immediately check your answers against the official-style marking scheme. The OCR S1 Delphis papers are listed in the same place for reference.
Delphis 试卷是 A Level 数学圈里非常有名的一套非官方模拟卷。本页汇总了 Edexcel 考试局的 S1（Statistics 1，统计 1）Delphis 试卷，并附有对应的评分标准（mark scheme），你可以下载试卷后立刻对照答案批改。OCR 考试局的 S1 Delphis 试卷也在同一页面列出，方便查阅。
1. What Are the Delphis Papers? | 什么是 Delphis 试卷？
Delphis papers are unofficial practice papers written by experienced teachers and examiners rather than by the awarding bodies themselves. They are designed to mirror the style, length and difficulty of the real Edexcel and OCR modular papers, so students can practise on material that feels close to the genuine exam.
Delphis 试卷并非考试局官方出品，而是由经验丰富的教师和阅卷老师编写的非官方模拟卷。它们在题型风格、卷面长度和难度上都刻意模仿真实的 Edexcel、OCR 模块化试卷，因此学生练习时的体感与真正考试非常接近。
Because they are unofficial, they are especially valuable as extra practice. The supply of genuine past papers for any one module is limited, so Delphis papers effectively multiply the number of full-length S1 papers you can work through before the exam.
也正因它们是非官方的，作为额外练习就格外有价值。任何一个模块的官方真题数量都是有限的，Delphis 试卷相当于把考前可做的整套 S1 卷子数量成倍放大。
2. Why S1 Practice Matters So Much | 为什么 S1 刷题如此重要
S1 is often a student's first encounter with formal statistics in a maths course. The ideas - random variables, probability distributions, the normal distribution, correlation and regression - are conceptually different from the pure maths and mechanics that surround them.
S1 往往是学生在数学课程中第一次正式接触统计学。随机变量、概率分布、正态分布、相关与回归这些概念，与它周围的纯数和力学内容在思维上完全不同。
Unlike pure maths, where a wrong algebraic step usually still leaves some method marks, statistics questions reward correct interpretation. If you misread "given that" or confuse a discrete with a continuous distribution, you can lose the entire question. This makes timed practice on realistic papers essential.
纯数学里即使某一步代数算错，通常还能拿到方法分；但统计题奖励的是正确理解。如果你把 "given that"（已知）看漏了，或者把离散分布和连续分布搞混，整道题可能全丢。因此限时练习仿真卷是必不可少的。
3. The Edexcel S1 Delphis Papers: Full Download List | Edexcel S1 Delphis 试卷完整下载列表
Below is the complete set of Delphis S1 papers for Edexcel, from Delphis 01 through to Delphis 10. Each paper has two associated files: the question paper (QP) and the mark scheme (MS). Always download both, because the mark scheme is where the method marks are defined.
下面是 Edexcel 的 Delphis S1 全套试卷，从 Delphis 01 到 Delphis 10。每套卷对应两个文件：试卷（QP）和评分标准（MS）。建议两个都下载，因为方法分（method marks）的判定规则就写在评分标准里。
Delphis 01 QP – S1 Edexcel
Delphis 01 MS – S1 Edexcel
Delphis 02 QP – S1 Edexcel
Delphis 02 MS – S1 Edexcel
Delphis 03 QP – S1 Edexcel
Delphis 03 MS – S1 Edexcel
Delphis 04 QP – S1 Edexcel
Delphis 04 MS – S1 Edexcel
Delphis 05 QP – S1 Edexcel
Delphis 05 MS – S1 Edexcel
Delphis 06 QP – S1 Edexcel
Delphis 06 MS – S1 Edexcel
Delphis 07 QP – S1 Edexcel
Delphis 07 MS – S1 Edexcel
Delphis 08 QP – S1 Edexcel
Delphis 08 MS – S1 Edexcel
Delphis 09 QP – S1 Edexcel
Delphis 09 MS – S1 Edexcel
Delphis 10 QP – S1 Edexcel
Delphis 10 MS – S1 Edexcel
Mark schemes are formatted as QP first, then MS, so you can open the paper straight away and reveal the answers only after you have finished. If you prefer the original ordering (MS then QP), simply use the links in the table below.
上面按"先试卷、后评分标准"的顺序排列，方便你先打开试卷，做完后再看答案。如果你习惯原来的顺序（先 MS 后 QP），可以直接使用下表中的链接。
4. Download Table: Edexcel QP & MS Quick Reference | 下载速查表：Edexcel 试卷与评分标准
The table below lists every Edexcel Delphis S1 paper with its mark scheme in one row, so you can copy a link quickly or check which papers you have already completed.
下表把每一套 Edexcel Delphis S1 试卷和它的评分标准放在同一行，方便你快速复制链接，或者核对哪些卷子已经做过了。
| Paper | 试卷 | Mark Scheme (MS) | 评分标准 | Question Paper (QP) | 试卷文件 |
|---|---|---|
| Delphis 01 | Delphis 01 MS – S1 Edexcel | Delphis 01 QP – S1 Edexcel |
| Delphis 02 | Delphis 02 MS – S1 Edexcel | Delphis 02 QP – S1 Edexcel |
| Delphis 03 | Delphis 03 MS – S1 Edexcel | Delphis 03 QP – S1 Edexcel |
| Delphis 04 | Delphis 04 MS – S1 Edexcel | Delphis 04 QP – S1 Edexcel |
| Delphis 05 | Delphis 05 MS – S1 Edexcel | Delphis 05 QP – S1 Edexcel |
| Delphis 06 | Delphis 06 MS – S1 Edexcel | Delphis 06 QP – S1 Edexcel |
| Delphis 07 | Delphis 07 MS – S1 Edexcel | Delphis 07 QP – S1 Edexcel |
| Delphis 08 | Delphis 08 MS – S1 Edexcel | Delphis 08 QP – S1 Edexcel |
| Delphis 09 | Delphis 09 MS – S1 Edexcel | Delphis 09 QP – S1 Edexcel |
| Delphis 10 | Delphis 10 MS – S1 Edexcel | Delphis 10 QP – S1 Edexcel |
5. The OCR S1 Delphis Papers | OCR S1 Delphis 试卷
The Delphis series also includes papers written for the OCR specification. The table of contents for OCR is shorter here, but the papers follow the same philosophy: realistic statistics questions with full solutions provided separately.
Delphis 系列同样包含为 OCR 大纲编写的试卷。这里列出的 OCR 清单较短，但编写思路一致：贴近真题的统计题，并配有单独提供的完整解答。
Delphis 01 – S1 OCR
Delphis 02 – S1 OCR
Delphis 03 – S1 OCR
Delphis 04 – S1 OCR
Delphis 05 – S1 OCR
Delphis 06 – S1 OCR
Delphis 07 – S1 OCR
Delphis 08 – S1 OCR
Delphis 09 – S1 OCR
Delphis 10 – S1 OCR
If you are sitting OCR rather than Edexcel, use these papers in preference to the Edexcel ones, because the notation conventions and question phrasing differ slightly between the two specifications.
如果你考的是 OCR 而不是 Edexcel，请优先使用这些卷子，因为两个考纲在符号习惯和题干措辞上有细微差别。
6. The S1 Syllabus These Papers Cover | 这些试卷覆盖的 S1 考纲内容
Delphis S1 papers are written against the classic modular S1 specification, which covers the following topic areas. Each paper normally draws on several of them in combination.
Delphis S1 试卷是按经典模块化 S1 考纲编写的，涵盖以下主题。每套卷子通常会把其中若干主题组合起来考查。
- Representation and summary of data: histograms, box plots, stem-and-leaf | 数据的表示与概括：直方图、箱线图、茎叶图
- Measures of location and spread: mean, median, mode, range, IQR, variance, standard deviation | 位置与离散程度的度量：平均数、中位数、众数、极差、四分位距、方差、标准差
- Probability: Venn diagrams, tree diagrams, conditional probability, independence | 概率：韦恩图、树形图、条件概率、独立性
- Discrete random variables: probability distributions, E(X), Var(X), E(aX + b) | 离散随机变量：概率分布、E(X)、Var(X)、E(aX + b)
- The binomial distribution B(n, p) | 二项分布 B(n, p)
- The normal distribution: standardising with z, inverse normal problems | 正态分布：用 z 值标准化、正态分布的反向求解
- Correlation and regression: scatter diagrams, r, least squares regression line y = a + bx | 相关与回归：散点图、相关系数 r、最小二乘回归直线 y = a + bx
Knowing the syllabus map is useful because it tells you what the Delphis papers can and cannot test. If a topic is not on the list, a Delphis question on it would be off-specification.
熟悉考纲地图很有用，因为它界定了 Delphis 试卷能考什么、不能考什么。如果某个主题不在清单里，那么 Delphis 出现相关题目就属于超纲。
7. Key Formulas to Have Ready | 必须熟记的核心公式
The S1 formulae are relatively few, but the exam expects you to recall several of them from memory. Note that in the modular S1 paper the formulae booklet does not always supply everything, so memorising these is the safe option.
S1 的公式数量不算多，但考试要求你凭记忆复现其中若干条。注意在模块化 S1 试卷中，公式手册未必把所有公式都给出，所以背下来才是最稳妥的。
E(X) = Σ x P(X = x)
Var(X) = Σ x² P(X = x) − [E(X)]²
E(aX + b) = a E(X) + b, Var(aX + b) = a² Var(X)
X ~ B(n, p) ⇒ E(X) = np, Var(X) = np(1 − p)
z = (x − μ) ÷ σ
b = Sₓᵧ ÷ Sₓₓ, a = ȳ − b x̄
= 1 − Φ(z) and P(Z < −z) = 1 − Φ(z). These symmetry moves appear in almost every S1 paper.
对于正态分布，要记住标准正态概率由 Φ(z) = P(Z ≤ z) 给出，并且由对称性可得 P(Z > z) = 1 − Φ(z)，P(Z < −z) = 1 − Φ(z)。这些对称性变换几乎在每一套 S1 试卷里都会出现。
8. How to Use the Papers: A Four-Stage Revision Cycle | 如何使用这些试卷：四阶段复习循环
Simply downloading ten papers and "doing them" is rarely effective. A structured cycle produces far better results. Here is a cycle that works well for S1.
单纯下载十套卷子然后"做完"往往效果有限。有结构的循环会带来明显更好的结果。下面这个循环对 S1 很有效。
- Stage 1 - Untimed first pass | 阶段一：不限时首做。 Work slowly with notes open. The goal is understanding, not speed. | 打开笔记慢慢做，目标是理解而不是速度。
- Stage 2 - Mark with the MS | 阶段二：用地评标准批改。 Use the Delphis mark scheme and record which marks you lost and why. | 用 Delphis 评分标准批改，记录丢分点和原因。
- Stage 3 - Timed redo | 阶段三：限时重做。 Return to the same paper a week later under exam timing, typically 1 hour 30 minutes for S1. | 一周后按考试时间重做同一套卷，S1 通常为 1 小时 30 分钟。
- Stage 4 - Error log | 阶段四：错题本。 Write every lost mark into a log and review it before the next paper. | 把每一处丢分写进错题本，在下一套卷前先复习。
Run this cycle on Delphis 01, then 02, and so on. By Delphis 10 you will have seen most of the question styles the specification can produce.
先对 Delphis 01 走完这个循环，再做 02，依次类推。做到 Delphis 10 时，你基本见过了这一考纲能出的大部分题型。
9. Common S1 Mistakes the Delphis Papers Expose | Delphis 试卷暴露出的 S1 常见错误
Because the Delphis papers imitate real exam phrasing closely, they are excellent at exposing the typical errors that cost students grades. These are the ones that appear again and again.
由于 Delphis 试卷高度模仿真题措辞，它们非常擅长暴露那些真正让学生丢分的典型错误。以下是最常见、反复出现的一批。
- Forgetting to square the units when converting variance: 1 cm² = 100 mm², not 10 mm². | 换算方差时忘记平方单位：1 cm² = 100 mm²，而不是 10 mm²。
- Using σ instead of σ² when a question asks for variance, or the reverse. | 题目要方差时用了 σ，或反过来。
- Treating a normal distribution question as if it were discrete. | 把正态分布题当作离散分布来处理。
- Failing to apply the continuity correction when a continuous distribution approximates a discrete one. | 用连续分布近似离散分布时忘记做连续性修正。
- Confusing P(A | B) with P(B | A) in conditional probability. | 在条件概率中把 P(A | B) 与 P(B | A) 搞混。
- Calculating the regression line of y on x but then using it to predict x. | 求的是 y 对 x 的回归直线，却用它来预测 x。
- Not using the "given that" information and thereby treating dependent events as independent. | 忽略 "given that" 条件，把相关事件当作独立事件。
Print these in your error log and check each one before every timed paper you sit.
把这些写进错题本首页，每次限时做卷前都对照检查一遍。
10. Answering Statistics Questions: Technique Rules | 统计题的作答技巧规则
Statistics marking is heavily method-based, but the method marks are only awarded if the examiner can follow your work. Presentation is therefore worth marks in S1 in a way it rarely is in pure maths.
统计阅卷非常看重过程分，但只有当阅卷人跟得上你的思路时，方法分才会给。因此 S1 中的书写呈现本身就是得分点，这在纯数里很少见。
- Define your random variable in words before using it: "Let X be the number of ..." | 使用随机变量前先用文字定义："设 X 为……的数量"
- State the distribution you are using, with parameters: X ~ B(20, 0.3). | 明确写出所用分布及其参数：X ~ B(20, 0.3)
- Show the standardising step explicitly when using the normal distribution. | 使用正态分布时，显式写出标准化这一步。
- Quote probabilities to at least 3 significant figures, or 4 for intermediate work. | 概率至少保留 3 位有效数字，中间步骤建议 4 位。
- Write a sentence of context at the end of a worded question, not just a number. | 文字题结尾要写一句结合情境的结论，不能只给数字。
- Draw the scatter diagram, box plot or tree diagram when it is asked for. | 题目要求画散点图、箱线图或树形图时一定要画。
Examiners mark positively: they look for what you have shown, not what you have omitted. Showing an explicit step never costs you marks, whereas omitting one often does.
阅卷是加分制：阅卷人看你写出了什么，而不是你没写什么。多写一步显式过程不会扣分，少写一步却常常会丢分。
11. S1 in the Wider Modular Mathematics Picture | S1 在模块化数学整体中的位置
For many students S1 is taken alongside C1 and C2 in the first year, or alongside C3 and C4 in the second. Some take it as an AS-only unit and stop there; others carry it forward for a full A Level.
很多学生在第一年把 S1 与 C1、C2 一起考，或在第二年与 C3、C4 一起考。有人只把它当 AS 单元考完就结束，也有人把它算进完整 A Level。
Whichever route you take, S1 tends to be the module where consistent practice pays off fastest, because the question types are finite and highly repetitive. A student who has genuinely worked through ten full papers usually outperforms a student who has read the textbook twice.
无论走哪条路线，S1 往往都是"持续刷题见效最快"的模块，因为题型有限且重复度高。真正做完十套整卷的学生，通常成绩会好过把教材读两遍的学生。
12. How to Plan the Ten Papers Before the Exam | 考前如何安排这十套卷
Ten papers is a comfortable number to plan around. The table below suggests a sensible distribution with roughly six weeks to go. Adjust the pace to your own schedule, but keep the principle: earlier papers for learning, later ones for timing.
十套卷是一个很好安排的数目。下表给出考前约六周的合理分配方案。你可以按自己的时间调整节奏，但保持这个原则：前面的卷子用来学习，后面的卷子用来练时间。
| Weeks to Exam | 距考试周数 | Papers | 试卷 | Focus | 重点 |
|---|---|---|
| 6-5 | Delphis 01-03 | Untimed, notes open, topic gaps | 不限时、可查笔记、补主题漏洞 |
| 4-3 | Delphis 04-07 | Timed, full marking, error log | 限时、完整批改、错题本 |
| 2-1 | Delphis 08-10 | Exam conditions, no notes, review log | 严格考试条件、不查笔记、复习错题本 |
Always keep the last two days before the exam free of new papers. Use them only to re-read your error log and the formula list above.
考前两天一定不要再做新卷子，只用来重读错题本和上面的公式清单。
Download the papers, print them, and treat each one as a genuine exam rather than a reading exercise. Combined with the Delphis mark schemes, these ten S1 papers give you a complete and realistic preparation cycle, whatever your target grade.
把试卷下载并打印出来，把每一套都当成真正的考试而不是阅读材料。配合 Delphis 评分标准，这十套 S1 试卷构成一个完整而贴近实战的备考循环，无论你的目标分数是多少都适用。
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