Pre-U CIE Mathematics: 2026 Exam Changes and Trends | Pre-U CIE 数学：2026年考试变化与趋势

📚 Pre-U CIE Mathematics: 2026 Exam Changes and Trends | Pre-U CIE 数学：2026年考试变化与趋势

The Cambridge Pre-U Mathematics qualification has long been prized for its depth and academic rigour, preparing students for university-level study. As we approach the 2026 examination series, CIE has announced a series of structural and content refinements designed to keep the course relevant in a rapidly evolving educational landscape. These changes reflect a stronger focus on mathematical modelling, digital literacy in problem-solving, and integrated assessment of pure and applied topics.

剑桥 Pre-U 数学资格证书长期以来因其深度和学术严谨性而备受推崇，为学生进入大学学习做好了充分准备。随着 2026 年考试系列的临近，剑桥国际考试委员会（CIE）宣布了一系列结构与内容上的调整，旨在使课程在快速变化的教育环境中保持前沿性。这些变化体现了对数学建模、解题中的数字素养以及纯数学与应用主题综合评估的更强关注。

This article provides a detailed breakdown of every significant change to the Pre-U Mathematics syllabus and assessment for 2026, offering essential guidance for teachers and students. We will explore new topic allocations, revised assessment objectives, the evolving role of technology, and strategies to excel under the updated framework.

本文详细解析了 2026 年 Pre-U 数学教学大纲与考核的每一项重大变化，为师生提供重要指导。我们将探讨新的主题分配、修订后的评估目标、技术角色的演变，以及在更新后的框架下取得优异成绩的策略。

1. Revised Examination Structure | 考试结构修订

For the 2026 series, the Pre-U Mathematics (9794) examination structure has been streamlined from a four-paper format to three compulsory papers. Paper 1 remains Pure Mathematics, while the former Papers 2 and 3 (Pure Mathematics and Mechanics) have been merged into a single 2.5-hour paper, now designated Paper 2: Pure Mathematics and Mechanics. Probability and Statistics is assessed entirely in Paper 3.

2026 年考试系列中，Pre-U 数学（9794）的考试结构已从四卷简化为三份必修试卷。卷一仍为纯数学，而原卷二与卷三（纯数学与力学）合并为一份时长 2.5 小时的试卷，新编号为卷二：纯数学与力学。概率与统计完全在卷三中进行考核。

This change reduces the total number of assessment hours from 7.5 to 7, easing the overall administrative burden while demanding deeper integration of pure and applied thinking. The weighting of Pure Mathematics now stands at roughly 60% across Papers 1 and 2, with Mechanics constituting 20% and Statistics 20%.

这一变化将总评估时间从 7.5 小时缩减为 7 小时，减轻了整体行政负担，同时要求对纯数学与应用思维进行更深入的融合。纯数学在卷一和卷二中的权重合计约 60%，力学占 20%，统计占 20%。

2. Updated Pure Mathematics Content | 纯数学内容更新

The Pure Mathematics syllabus for 2026 has been expanded to include an explicit section on hyperbolic functions and their inverses, previously reserved for Further Mathematics. Students must now differentiate and integrate hyperbolic and inverse hyperbolic functions, understand logarithmic forms, and solve equations involving sinh x, cosh x, and tanh x. In addition, the topic of differential equations has been deepened to cover second-order linear equations with constant coefficients in both homogeneous and non-homogeneous cases.

2026 年的纯数学大纲新增了双曲函数及其反函数的明确章节，此前这部分内容仅出现在进阶数学中。学生现在必须对双曲函数和反双曲函数进行微分和积分，理解其对数形式，并解含有 sinh x、cosh x 和 tanh x 的方程。此外，微分方程主题得到深化，涵盖了常系数二阶线性方程，包括齐次与非齐次情形。

Complex numbers now explicitly require the ability to find loci in the Argand diagram, such as perpendicular bisectors and half-lines, and to interpret inequalities geometrically. These additions align the Pre-U curriculum more closely with first-year university mathematics.

复数部分现在明确要求能够在阿干特图中找出轨迹，如垂直平分线和射线，并从几何角度解释不等式。这些新增内容使 Pre-U 课程更贴近大学一年级的数学水平。

3. Mechanics Component Rebalancing | 力学部分再平衡

Within the new Paper 2, the mechanics syllabus has been rebalanced to give greater prominence to energy methods and vector kinematics. The work–energy principle, including applications with variable forces, is now a mandatory core topic rather than an optional extension. Students must be proficient in setting up energy balances for inclined planes, springs, and systems with non-constant friction.

在新的卷二内，力学大纲经过再平衡，更加强调能量方法与矢量运动学。功能原理，包括变力作用下的应用，现已成为必修核心主题，而非可选扩展。学生必须熟练掌握斜面上、弹簧及摩擦力非常数系统中能量平衡的建立。

Vector differentiation and integration in 2D kinematics have been elevated, with explicit questions on variable acceleration expressed in vector form. This includes finding position vectors from velocity functions and analysing jerk as a vector quantity. Table 1 summarises the redistribution of mechanics topics.

二维运动学中的矢量微分与积分得到提升，明确要求处理矢量形式的变加速度问题。这包括由速度函数求位置矢量，并分析作为矢量的加加速度。表 1 总结了力学主题的重新分配。

Topic	Pre-2026 Status	2026 Status
Work–Energy Principle	Extension only	Core
Variable Force Integration	Optional	Compulsory
Vector Acceleration & Jerk	Not required	Required
Centre of Mass (3D)	Excluded	Introduced

Table 1: Mechanics topic redistribution, 2026 syllabus

4. Probability and Statistics Modernisation | 概率与统计现代化

Probability and Statistics for 2026 embraces data science fundamentals. The syllabus now requires familiarity with large data sets, including the calculation and interpretation of covariance and product-moment correlation coefficients using technology. Hypothesis tests have been extended to cover two-sample t-tests for the difference of means, assuming both equal and unequal variances.

2026 年的概率与统计纳入了数据科学基础。大纲现在要求熟悉大型数据集，包括利用技术计算和解释协方差与积矩相关系数。假设检验扩展到涵盖双样本 t 检验，用于检验均数之差，且需考虑等方差与不等方差两种假设。

There is a new emphasis on interpreting p-values in context and understanding the limitations of statistical conclusions, such as the distinction between practical and statistical significance. Students must also be able to construct confidence intervals for the mean of a Poisson distribution using a normal approximation.

新增了在上下文中解读 p 值并理解统计结论局限性的重点，例如区分实际显著性与统计显著性。学生还必须能够利用正态近似构建泊松分布均值的置信区间。

5. Enhanced Role of Technology and Calculators | 技术及计算器的强化作用

From 2026, the permitted calculator specification has been broadened. Candidates may now use calculators with built-in symbolic algebra, calculus, and matrix manipulation capabilities (CAS calculators) in all papers. This shift acknowledges the increasing digital fluency expected in higher education and professional environments.

自 2026 年起，允许使用的计算器规格放宽。考生现可在所有试卷中使用具备内置符号代数、微积分和矩阵运算功能的计算器（CAS 计算器）。这一变化承认了高等教育及专业环境中日益增强的数字流畅度要求。

Examination questions will be designed to resist trivialisation by technology; they will test strategic application rather than routine computation. For instance, a question might provide CAS output and ask the student to justify an analytical step or to identify when a computational result must be treated with caution due to rounding or domain restrictions.

考题将经过精心设计，以防被技术简化；它们将考查策略性应用而非例行计算。例如，题目可能提供 CAS 输出，要求学生论证一个分析步骤，或指出由于四舍五入或定义域限制而必须谨慎处理计算结果的情形。

6. Assessment Objectives Redefined | 评估目标重新定义

The three CIE assessment objectives (AO1, AO2, AO3) have been recalibrated for 2026. AO1 (Knowledge and understanding) now carries 30% of the total marks, down from 40%. AO2 (Application and analysis) has increased to 45%, and AO3 (Synthesis and evaluation) has risen to 25%. This signals a clear shift towards higher-order thinking skills.

CIE 的三项评估目标（AO1、AO2、AO3）已为 2026 年重新校准。AO1（知识与理解）现占总分的 30%，低于之前的 40%。AO2（应用与分析）提升至 45%，AO3（综合与评价）增至 25%。这明确体现了向高阶思维技能的转移。

AO3 now explicitly includes the ability to evaluate mathematical models, critique given solutions for errors or inefficiencies, and compare alternative approaches. Typical questions may ask, ‘Identify the flaw in the following proof’ or ‘Suggest an improvement to this model given additional data.’

AO3 现明确包括评价数学模型、对给定解法进行错误或低效评判，以及比较不同方法的能力。典型问题可能会问：“指出下列证明中的缺陷”或“根据补充数据提出模型的改进建议”。

7. Increased Emphasis on Proof and Reasoning | 对证明与推理的重视增强

Proof has moved from being an implicit expectation to an explicit syllabus strand. Candidates must now construct rigorous proofs by induction, contradiction, and contrapositive across all topic areas. In addition, they are expected to prove key results such as the irrationality of √2, the divergence of the harmonic series, and the sum formula for geometric series from first principles.

证明已从隐含的要求转变为明确的大纲线索。考生现在必须在所有主题领域中构造严格的归纳证明、反证法证明和逆否命题证明。此外，还应能从基本原理出发证明关键结论，如 √2 的无理性、调和级数的发散性以及几何级数求和公式。

The command word ‘Prove’ will now appear more frequently in structured questions, often with steps pre-arranged to guide candidates through a logical argument. Marks will be explicitly awarded for clarity of logical structure and correct justification of each deductive step.

指令词“证明”现在将更频繁地出现在结构化问题中，通常预设步骤以引导考生通过逻辑论证。评分将明确奖励逻辑结构的清晰度和每个演绎步骤的正确论证。

8. Cross-Topic Integration and Synopticity | 跨主题整合与综合性

One of the most notable trends is the deliberate inclusion of synoptic questions that link pure mathematics with mechanics and statistics within the same item. For example, Paper 2 may present a differential equation derived from a mechanics context, requiring the student to solve it analytically and then interpret the behaviour of the solution in physical terms.

最值得注意的趋势之一是，有意设置综合性试题，在同一题目内将纯数学与力学、统计联系起来。例如，卷二可能给出一个源自力学情境的微分方程，要求学生进行解析求解，然后用物理语言解释解的行为。

Example: ‘A particle moves with acceleration a = e⁻ᵗ. Find its velocity as a function of time, sketch the velocity–time graph, and discuss the long-term implications for energy dissipation.’

示例：“一质点以加速度 a = e⁻ᵗ 运动。求其速度作为时间的函数，绘制速度-时间图，并讨论对能量耗散的长期影响。”

Such questions demand fluency in calculus, graphical interpretation, and mechanical principles, making compartmentalised study insufficient.

此类问题要求学生熟练掌握微积分、图形解读和力学原理，使分模块式的学习方式难以满足需求。

9. Changes to Marking Schemes and Grade Thresholds | 评分方案及等级门槛变化

Mark schemes from 2026 onward will apply a ‘best-fit’ approach to holistic judgements for AO3 criteria, allowing examiners to credit partially valid reasoning even if a final solution is incomplete. There is also a stronger use of ‘B’ marks for independent reasoning steps, decoupled from method marks (M marks).

自 2026 年起，评分方案将对 AO3 准则采用“最佳匹配”的整体判断方法，即使最终答案不完整，考官亦可对部分有效的推理给予分数。同时，会更多地使用独立的推理步骤分（B 分），使其与方法分（M 分）解耦。

Grade thresholds are expected to shift modestly upwards as students and teachers adapt to the new CAS allowance and integrated assessments. CIE’s published statistics suggest the A boundary in Paper 1 may rise by 2–3 raw marks compared to pre-2026 series.

随着学生和教师适应新的 CAS 许可和综合评估，等级门槛预计将小幅上升。CIE 公布的统计数据显示，与 2026 年前的系列相比，卷一的 A 等级分数线可能上升 2–3 个原始分。

10. Strategies for Success in 2026 | 2026 年成功策略

To excel under the new structure, students should treat proof as a standalone skill and practise constructing arguments from definitions. They must become fluent with CAS calculators, using them to verify analytical work, explore cases, and accelerate statistical computation, but not as a substitute for understanding.

要在新结构下取得优异成绩，学生应将证明作为一项独立技能，并练习从定义出发构建论证。他们必须熟练使用 CAS 计算器，用以验证分析工作、探索案例并加速统计计算，但不可将其作为理解的替代品。

Regular engagement with synoptic practice material is essential. Students should create topic matrices, linking pure topics like integration or differential equations to their occurrences in mechanics and statistics contexts. Teachers are advised to incorporate modelling projects that require critical evaluation and refinement.

经常接触综合性练习材料至关重要。学生应制作主题矩阵，将积分或微分方程等纯数学主题与它们在力学和统计背景中的应用联系起来。建议教师纳入需要批判性评估和改进的建模项目。

11. Resource and Textbook Updates | 资源与教材更新

All major publishers have issued revised editions aligned with the 2026 syllabus. Core texts now include dedicated ‘Proof Corner’ features and CAS exploratory activities. CIE’s online Teacher Support hub provides specimen papers, scheme of work planners, and CAS-ready teaching units free of charge.

所有主要出版社均已推出与 2026 年大纲对应的修订版。核心教材现附有专门的“证明角”专栏和 CAS 探索活动。CIE 的在线教师支持中心免费提供样卷、教学计划编制工具和适配 CAS 的教学单元。

A dedicated formula booklet update has been released, removing some previously given standard integrals (now expected to be derived or computed) and adding the hyperbolic identities. Students should memorise the new booklet layout well before the exam.

已发布更新的公式手册，移除了部分之前给出的标准积分（现要求推导或计算），并增加了双曲恒等式。学生应在考试前熟记新版手册的布局。

12. Future Outlook Beyond 2026 | 2026 年后的未来展望

Looking ahead, CIE has signalled that the 2026 changes serve as a bridge towards a possible fully digital assessment mode. Trials of on-screen examinations for selected Pre-U subjects are underway, with mathematics being a strong candidate due to the integration of dynamic geometry software and live CAS environments.

展望未来，CIE 已表明 2026 年的变化是迈向可能的全数字化评估模式的桥梁。正在对部分 Pre-U 科目进行机考试点，由于集成了动态几何软件和实时 CAS 环境，数学成为强有力的候选科目。

Furthermore, the growing emphasis on data science may lead to the introduction of machine learning concepts or Bayesian inference in later revisions. Students who develop a deep conceptual understanding and computational agility now will be best prepared for these ongoing developments.

此外，对数据科学的日益重视可能在后续修订中引入机器学习概念或贝叶斯推断。现在培养出深刻概念理解和计算敏捷性的学生，将为这些持续发展做好最充分的准备。

Published by TutorHao | Mathematics Revision Series | aleveler.com

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