📚 IGCSE OCR Further Maths: In-Depth Analysis of Past Papers | IGCSE OCR 进阶数学：历年真题深度解析
For students aiming for top grades in the OCR GCSE Further Mathematics (Level 2 Certificate), working through past papers is not just helpful – it’s essential. This exam tests advanced algebraic manipulation, calculus, vectors, and applied mathematics at a level that bridges the gap between standard GCSE and A Level. Analysing past papers reveals recurring question patterns, examiner expectations, and the precise depth of understanding required. This article provides a comprehensive breakdown of real exam questions from recent series, equipping you with the insights needed to tackle Paper 1 and Paper 2 with confidence.
对于志在 OCR GCSE 进阶数学（Level 2 Certificate）中夺取高分的学生而言，研习历年真题不仅是锦上添花，更是成功的基石。这门考试检验高级代数运算、微积分、向量和应用数学，其深度恰好填补了普通 GCSE 与 A Level 之间的空白。分析历年真题可以揭示反复出现的题型模式、考官期望以及所需理解的精确深度。本文将全面拆解近几次考试中的真实题目，赋予你充足的洞见，以十足信心迎战试卷一和试卷二。
1. Introduction to the Exam | 考试简介
The OCR Level 2 Further Mathematics qualification consists of two equally weighted papers, each lasting 1 hour 45 minutes and carrying 80 marks. Paper 1 focuses primarily on pure mathematics: algebra, functions, graphs, coordinate geometry, vectors, matrices, and calculus. Paper 2 covers mechanics and statistics, though a significant portion still assesses pure content through applied contexts. There is no controlled assessment or coursework; your final grade depends entirely on these two calculator papers. Understanding this structure is the first step towards effective past paper revision.
OCR Level 2 进阶数学资格考试由两份权重相等的试卷组成，每份作答时间为 1 小时 45 分钟，满分均为 80 分。试卷一主要考查纯数学内容：代数、函数、图像、坐标几何、向量、矩阵以及微积分。试卷二涵盖力学与统计，不过仍有相当一部分分值在应用情境下评测纯数能力。该资格没有受控评估或课程作业，最终成绩完全取决于这两份可使用计算器的试卷。理解这一结构是利用好真题复习的第一步。
| Paper | Duration | Marks | Content Focus |
|---|---|---|---|
| Paper 1 | 1h 45m | 80 | Pure Mathematics (no mechanics/statistics) |
| Paper 2 | 1h 45m | 80 | Mechanics, Statistics and contextualised Pure |
2. Breakdown of Past Paper Structure | 真题试卷结构分解
An analysis of papers from 2019 to 2023 shows a remarkably consistent pattern. Paper 1 usually begins with simpler, standalone algebra questions (solving quadratics, indices) worth 4–6 marks, then progresses to longer, multi-step items on calculus and vectors. The final questions frequently involve trigonometric proofs or summation of series, each carrying 8–12 marks. Paper 2 typically opens with a probability or data handling question, moves through kinematics under constant acceleration, and ends with a hybrid question combining differentiation with an area or volume problem. Recognising this map allows you to allocate revision time strategically.
通过对 2019 年至 2023 年真题的分析，可以发现一个非常稳定的出题模式。试卷一通常以较简单的独立代数题（求解二次方程、指数运算）开场，分值为 4–6 分，而后逐步过渡到涉及微积分和向量的多步骤长题。卷末题经常考查三角恒等式证明或级数求和，每题占 8–12 分。试卷二典型开局是一道概率或数据处理题，接着进入匀加速运动学题目，最后以一道结合微分与面积或体积计算的综合题收尾。掌握这张出题地图能让你有策略地分配复习时间。
Moreover, examiners reserve certain topics almost exclusively for high-mark questions. For instance, proof by induction, factor theorem with unknown coefficients, and vector equations of lines have appeared in the last five sitting as 9–11 mark questions. By contrast, topics like basic differentiation, laws of indices, and simple probability distributions tend to appear in the first quarter of each paper. This distribution should influence your practice; aim to secure these foundational marks quickly before tackling the later complexities.
此外，考官几乎把某些主题专门留给了高分值题目。例如，数学归纳法证明、含未知系数的因式定理，以及直线向量方程，在最近五次考试中均以 9–11 分的题量出现。相比之下，基础微分、指数律以及简单概率分布这类主题，往往出现在每份试卷的前四分之一。这一分布情况应该影响你的练习策略：务必先快速拿下这些基础分，再去攻克后方的复杂题目。
3. Core Pure Topics and Repeated Question Types | 纯数学核心主题与常见题型
Pure mathematics accounts for roughly 65% of the total marks across both papers, making it the backbone of OCR Further Maths. Within pure, three areas dominate past papers: algebraic manipulation (including surds, indices, and binomial expansion), functions and their graphs, and calculus. Questions are rarely purely procedural; examiners often ask you to ‘show that’ a given expression simplifies to a specific form, testing both your accuracy and your ability to present logical steps. For example, a typical Paper 1 question might ask you to express (3+√5)/(1-√5) in the form a+b√5, requiring careful rationalisation.
纯数学在两张试卷中约占 65% 的分数，是 OCR 进阶数学的基石。在纯数范畴内，三大板块统治着历年真题：代数运算（包括根式、指数和二项式展开）、函数及其图像，以及微积分。题目鲜有单纯考查操作步骤的；考官经常要求你“证明”给定的表达式能化简为某种特定形式，既考准确性，又考你呈现逻辑步骤的能力。例如，一道典型的试卷一题目可能要求你将 (3+√5)/(1-√5) 表示为 a+b√5 的形式，这需要细心的分母有理化。
Another heavily tested pure concept is the discriminant of a quadratic. Past papers consistently include questions like ‘Find the set of values of k for which the equation 2x² + kx + 8 = 0 has no real roots.’ The solution requires setting b²-4ac < 0 and solving the resulting inequality. This interleaves quadratic theory with linear inequalities – a hallmark of OCR's approach. Likewise, completing the square to find the vertex of a parabola appears annually, often as part of a larger functions question involving inverse functions or transformations.
另一个高频考查的纯数概念是二次方程的判别式。历年真题始终包含着这样的题目：“求使方程 2x² + kx + 8 = 0 没有实根的 k 值的集合。”解答需要令 b²-4ac < 0 并求解所得的不等式。这巧妙地将二次方程理论与线性不等式交织在一起——这正是 OCR 命题风格的标志。同样，配平方以求抛物线的顶点也是每年必考，通常作为涵盖反函数或图像变换的更大函数问题的一部分出现。
4. Algebra and Functions: Tackling High-Mark Questions | 代数与函数：攻克高分题
High-mark algebra questions in OCR Further Maths frequently involve the remainder and factor theorems. A typical 10-mark question gives a cubic polynomial with two unknown constants, states that (x-2) is a factor and that the remainder upon division by (x+1) is -12, then asks for the values of the constants and the full factorisation. Solving such problems demands setting up simultaneous equations correctly and then factorising completely, often into a linear factor and an irreducible quadratic. Practice from the 2022 Paper 1 shows that many candidates lost marks by failing to write the final fully factorised form explicitly, stopping at the quadratic factor.
OCR 进阶数学中的高分代数题频繁考查余式定理与因式定理。一道典型的 10 分题会给出一个含有两个未知常数的三次多项式，并声明 (x-2) 是其中一个因式，且除以 (x+1) 时所得余数为 -12，然后要求你求出常数的值，并完成完全因式分解。解决这类问题需要正确建立联立方程，再彻底分解因式，通常分解为一个一次因式和一个不可约二次因式。练习 2022 年试卷一的真题后发现，许多考生失分的原因在于没有明确写出最终的完全分解形式，停留在二次因式那一步就止步不前了。
Functions present challenges around domain, range, and inverse functions. Expect questions like ‘Given f(x) = ln(2x-3), find f⁻¹(x) and state its domain.’ You must rearrange y = ln(2x-3) to x = (e^y + 3)/2 and swap variables, but more importantly, determine the domain of the inverse from the range of the original function. The range of f(x) is all real numbers, so the domain of f⁻¹(x) is x ∈ ℝ. However, considering the original domain x > 1.5, the codomain restriction may catch you out. OCR examiners are adept at setting domain traps; careful checking of past mark schemes reveals that stating the domain explicitly can secure those final A-marks.
函数题在定义域、值域和反函数方面设下重重挑战。你可能会遇到这样的问题：“已知 f(x) = ln(2x-3)，求 f⁻¹(x) 并指明其定义域。”你需要将 y = ln(2x-3) 变形为 x = (e^y + 3)/2 并交换变量，但更重要的是，必须从原函数的值域反推出反函数的定义域。f(x) 的值域为全体实数，所以 f⁻¹(x) 的定义域为 x ∈ ℝ。然而，考虑到原函数的定义域 x > 1.5，值域伴随的限制条件可能会让考生踩坑。OCR 的出卷人擅长设置定义域陷阱；仔细核对过往评分方案后会发现，明确写出定义域往往能锁定最后那几分 A 级关键分。
5. Coordinate Geometry, Vectors, and Matrices | 坐标几何、向量与矩阵
Coordinate geometry questions often involve circles. An archetypal Paper 1 item gives the equation of a circle and a line, asking you to find the points of intersection, then calculate the exact distance between them. You must substitute the line’s equation into the circle’s equation, solve the resulting quadratic, and apply the distance formula. Rephrased, this is a 7-mark question testing simultaneous equations, algebraic accuracy, and surd manipulation. In the 2023 papers, a circle question also required finding the equation of the tangent at a given point, where the gradient of the radius is found first, then the perpendicular gradient is used. This links coordinate geometry with differentiation interchangeably.
坐标几何问题常与圆有关。一道典型的试卷一题目会给出一个圆和一条直线的方程，要求你求出它们的交点，然后计算两点间的精确距离。你需要将直线方程代入圆的方程，求解所得的二次方程，再应用距离公式。换个角度说，这是一道 7 分题，综合考查联立方程、代数运算准确性以及根式处理能力。在 2023 年的真题中，一道圆的相关题目还要求求出给定点的切线方程，这就需要先求得半径所在直线的斜率，再取其负倒数作为切线斜率。这使得坐标几何与微分相互贯通。
Vectors appear predominantly on Paper 1, with questions on finding the vector equation of a line through two points, determining if a point lies on a line, and proving lines are parallel or perpendicular. The vector equation r = a + t(b – a) must be known. A high-mark question might also integrate vectors with area of a triangle: given position vectors of three points, you calculate two side vectors, find their cross product magnitude (in 2D using determinant), and halve it. While cross product is technically beyond GCSE, OCR circumvents this by providing a coordinate method for area using ½|(x₁y₂ – x₂y₁)|, which ties neatly into matrices. Indeed, matrix transformations – rotations, reflections, and enlargements – are tested both standalone and within vector contexts. Past mark schemes insist on clear geometric descriptions for transformations, such as ‘rotation 90° anticlockwise about the origin’.
向量主要出现在试卷一中，题目包括求过两点的直线向量方程、判断某点是否在直线上，以及证明直线平行或垂直。你必须熟记向量方程 r = a + t(b – a)。一道高分值题目还可能将向量与三角形面积相结合：给出三点的位置向量，你计算出两条边向量，求出它们在二维下的叉积模（利用行列式），再取一半。虽然叉积在技术上超出 GCSE 范围，但 OCR 通过提供坐标法计算面积的公式 ½|(x₁y₂ – x₂y₁)| 绕开了这一障碍，这与矩阵联系紧密。事实上，矩阵变换——旋转、反射和位似——既会单独考查，也会嵌套在向量情境中。过往评分方案坚持要求对变换给出清晰的几何描述，比如“绕原点逆时针旋转 90°”。
6. Calculus in Further Maths: Differentiation and Integration | 进阶数学中的微积分：微分与积分
Calculus tops the list of challenging topics for many candidates. Differentiation extends beyond simple polynomials to fractional and negative powers, exponentials, and trigonometric functions. A common Paper 1 question: ‘Find the equation of the normal to the curve y = x²eˣ at the point where x = 1.’ You first differentiate using the product rule, evaluate the gradient, find the normal gradient as -1/m, and then use the line equation. This weaving together of product rule and coordinate geometry exemplifies the multi-skill nature of the exam. In 2022, a question required applying the chain rule to differentiate sin(3x)², with many candidates mistakenly differentiating the outer square without attending to the inner function properly.
对于很多考生来说，微积分位居最具挑战性的主题榜首。微分从简单的多项式扩展到分式和负指数、指数函数以及三角函数。一道常见的试卷一题目是：“求曲线 y = x²eˣ 在 x = 1 处的法线方程。”你需要先用乘积法则求导，算出梯度值，再求出法线斜率 -1/m，最后利用直线方程得出结论。这种将乘积法则与坐标几何交织在一起的考法，体现出考试对多重技能整合的要求。在 2022 年的试卷中，有一道题要求运用链式法则对 sin(3x)² 进行求导，许多考生错误地对二次方求导，却没有恰当处理内层函数。
Integration in Further Maths goes a step beyond standard GCSE: candidates must integrate functions like (2x+3)⁴, 1/(2x-1), e^(3x), and cos(2x). Reverse differentiation is the key. You will regularly be asked to find the area under a curve between two x-coordinates or the volume of revolution around the x-axis. A typical 8-mark question from Paper 2 integrates finding the volume when a region bounded by y = √x, the x-axis, and x = 4 is rotated 360° about the x-axis. The volume formula V = π∫y² dx is used, leading to π∫₀⁴ x dx = 8π. Candidates often lose marks by forgetting the π multiplier or mishandling limits. Analysing examiners’ reports shows that precision in writing the limits and final unit is crucial.
进阶数学中的积分比普通 GCSE 更进一步：考生必须掌握对 (2x+3)⁴、1/(2x-1)、e^(3x) 以及 cos(2x) 这类函数进行积分。反向求导是其中的关键。你经常会被要求求出两条 x 坐标线之间的曲线下方面积，或是绕 x 轴旋转的体积。一道典型的试卷二 8 分题会整合如下内容：将由 y = √x、x 轴和 x = 4 所围成的区域绕 x 轴旋转 360°，求所得体积。使用体积公式 V = π∫y² dx，得到 π∫₀⁴ x dx = 8π。考生常常因遗忘 π 的乘数或因积分限处理不当而丢分。分析考官报告后可知，精确写出积分限和最终单位至关重要。
7. Trigonometry: Identities and Equations in Past Papers | 三角学：恒等式与方程在真题中的应用
Trigonometry is examined in depth. You need fluency in the sine and cosine rules, area of a triangle formula ½ab sinC, and the two key identities: sin²θ + cos²θ ≡ 1 and tanθ ≡ sinθ/cosθ. Past papers show that solving trig equations within a given range, such as 0° ≤ θ ≤ 360°, is a staple. In the 2023 Paper 1, a question asked: ‘Solve 2sin²θ + 3cosθ = 3 for 0 ≤ θ ≤ 2π.’ The approach involves using sin²θ = 1 – cos²θ to form a quadratic in cosθ, solving it, and then finding all values of θ that satisfy it, including those found using the CAST diagram or periodic properties. Missing solutions in the specified range remains the top error.
三角学被深度考查。你需要熟练掌握正弦定理和余弦定理、三角形面积公式 ½ab sinC，以及两个重要恒等式：sin²θ + cos²θ ≡ 1 和 tanθ ≡ sinθ/cosθ。历年真题显示，在给定区间内（如 0° ≤ θ ≤ 360°）求解三角方程是必考题型。在 2023 年试卷一中，一道题这样问道：“在 0 ≤ θ ≤ 2π 范围内，解方程 2sin²θ + 3cosθ = 3。”解法涉及用 sin²θ = 1 – cos²θ 替换，构建出一个关于 cosθ 的二次方程，求解后找出所有满足条件的 θ 值，包括通过 CAST 图或周期性求得的值。漏掉指定区间内的解，依然是首要失分点。
Trigonometric graph transformations also feature. You might be asked to sketch y = 2cos(θ – 30°) for 0° ≤ θ ≤ 360°, labelling intercepts. The amplitude, period, and phase shift must be clearly shown. Examiner reports emphasise that merely plotting a vague cosine shape without key coordinates results in only partial credit. Use the standard 30°, 45°, 60° values accurately; recall that transformations inside the argument shift the graph horizontally in the opposite direction. Tying this to real past questions, a 2021 paper required stating the coordinates of the maximum point of y = 4sin(2θ) + 1, which is (45°, 5) when considering the period halving.
三角函数的图像变换同样会出现。你可能会被要求画出 y = 2cos(θ – 30°) 在 0° ≤ θ ≤ 360° 上的草图，并标注截距。振幅、周期和相位平移必须清晰呈现。考官报告强调，仅仅画出一个模糊的余弦形状，却未标出关键坐标，只会得到部分分数。要准确运用 30°、45°、60° 的常用三角值；记住，函数自变量内部的变换会使图像沿水平方向朝相反方向移动。回顾真实考题，2021 年某份试卷曾要求写出 y = 4sin(2θ) + 1 最大值点的坐标，考虑到周期减半，该点为 (45°, 5)。
8. Probability and Statistics: Understanding the Data Questions | 概率与统计：理解数据题
Paper 2 statistics questions often incorporate conditional probability, tree diagrams, and summary statistics. A favourite examiners’ twist is to present a two-way table and ask for the probability of A given B. For instance: ‘In a survey, 60% of students study French, 45% study German, and 25% study both. Find the probability that a student studies French given they study German.’ Using the formula P(F|G) = P(F∩G)/P(G) = 0.25/0.45 = 5/9. Always express final probabilities as simplified fractions unless specified otherwise. Past papers reveal that many candidates fail to differentiate between P(A∩B) and P(A|B), leading to mark loss.
试卷二的统计题目经常融入条件概率、树形图和概括性统计量。考官偏爱的一个巧妙变化是给出双向表格，要求计算在 B 发生的条件下 A 的概率。例如：“一项调查显示，60% 的学生学习法语，45% 学习德语，25% 两者都学。求一名学生学习德语条件下学习法语的概率。”利用公式 P(F|G) = P(F∩G)/P(G) = 0.25/0.45 = 5/9。除非另有要求，最终概率都应以最简分数形式给出。历年真题表明，许多考生难以区分 P(A∩B) 与 P(A|B)，这成为失分的一大原因。
Histograms and cumulative frequency diagrams also appear. A standard question provides grouped data and asks to estimate the mean or median, and to construct a histogram with unequal class widths. You must remember that frequency density = frequency / class width. Examiners frequently test the ability to identify the modal class from a histogram and to interpolate the median from a cumulative frequency graph. These questions are often deemed ‘easier’ but carry significant utility marks; neatness in drawing and accurate reading of scales can prevent careless errors.
直方图和累积频率图也会出现。标准的题目会给出分组数据，要求估算均值或中位数，并绘制组距不等的直方图。你必须牢记，频率密度 = 频率 / 组距。考官频繁考查的是从直方图中识别众数所在区间，以及根据累积频率图内插求中位数的能力。这类题目通常被视为“容易题”，但却带有重要的实用分值；绘图整洁、读数精确，能够防止粗心导致的错误。
9. Mechanics Applications: Kinematics and Forces | 力学应用：运动学与力
Mechanics questions are confined to Paper 2 and draw on the constant acceleration equations (SUVAT). A typical 7-mark problem: ‘A particle moves from rest with constant acceleration 0.8 m/s² for T seconds, covering 100 m. Find T and the final velocity.’ You select s = ut + ½at², giving 100 = 0 + ½ × 0.8 × T², so T = 15.8 s (3 s.f.), then v = u + at = 12.6 m/s. Familiarity with choosing the correct SUVAT equation is essential, and past papers show that mixing up ‘u’ and ‘v’, or using ‘v = s/t’ for non-uniform motion, are classic blunders.
力学问题仅限于试卷二，并依赖匀加速运动方程（SUVAT）。一道典型的 7 分问题为：“一质点由静止出发，以恒定加速度 0.8 m/s² 运动 T 秒，通过的距离为 100 m。求 T 和末速度。”你选择 s = ut + ½at²，得到 100 = 0 + ½ × 0.8 × T²，因此 T = 15.8 s（保留三位有效数字），然后利用 v = u + at 得 12.6 m/s。熟练选出正确的 SUVAT 方程至关重要，历年真题表明，混淆“u”和“v”，或对非匀变速运动使用“v = s/t”，是考生屡犯的典型错误。
Force and motion are modelled using Newton’s second law in simple contexts. Expect questions involving tension in a string connecting two masses, or a particle on a smooth inclined plane. These require resolving forces parallel to the slope. For example: ‘A 5 kg block on a smooth slope inclined at 30° is attached by a light string over a pulley to a 3 kg hanging mass. Find the acceleration of the system.’ You set up simultaneous equations from the two free-body force diagrams. Past mark schemes award method marks for clear diagrams and correct resolution, even if the final acceleration is wrong. Thus, always draw and label forces.
力与运动通过简单情境下的牛顿第二定律进行建模。你可能会遇到涉及连接两个物体的绳子张力，或光滑斜面上质点的题目。这要求沿斜面方向进行力的分解。例如：“一个 5 kg 的滑块置于倾角 30° 的光滑斜面上，通过轻绳经滑轮与一个 3 kg 的悬挂物相连。求系统的加速度。”你需要根据两个受力图建立联立方程。过往评分方案会对清晰的受力图和正确的分解方式给予方法分，即使最终加速度计算错误。因此，务必画出并标识各力。
10. Common Mistakes and Examiner Reports Insights | 常见错误与考官报告洞见
OCR examiner reports repeatedly highlight five main error categories. First, algebraic slip-ups: misapplying the distributive law with negative numbers, or incorrectly expanding brackets like (x-3)² as x²-9 instead of x²-6x+9. Second, missing the second case when solving absolute value equations or modulus inequalities. For |2x-1| > 5, both 2x-1 > 5 and 2x-1 < -5 must be considered; writing just one range halves the marks. Third, degrees/radian confusion: in calculus with trig functions, the argument must be in radians when differentiating sin and cos. OCR expects radian mode unless degrees are explicitly stated, and forgetting this turns correct derivatives into nonsense.
OCR 考官报告反复强调五大类错误。其一，代数计算粗心：对含负数的分配律使用不当，或错误展开如 (x-3)² 这样的括号，得出 x²-9 而非 x²-6x+9。其二，解绝对值方程或模不等式时遗漏第二种情况。对于 |2x-1| > 5，必须同时考虑 2x-1 > 5 和 2x-1 < -5；只写出一个区间，得分直接减半。其三，角度与弧度混淆：在进行含三角函数的微积分时，对 sin 和 cos 求导时必须使用弧度制。OCR 要求采用弧度制，除非试题中明确注明“角度”，忘记这一点会把正确的导数变得毫无意义。
Fourth, notation errors, especially with vectors and functions. When stating inverse functions, writing f⁻¹(x) = … and then forgetting to replace y with x, or failing to use correct vector notation (bold or underlined) can lose precision marks. Fifth, missing units in mechanics answers. A final velocity without ‘m/s’ or a time without ‘s’ is penalised. In statistics, drawing graphs without labelling axes or using incorrect scales are common avoidable errors. Past papers show that up to 5% of raw marks are lost to such communication issues. Practice under timed conditions and review mark schemes with a focus on these presentation details.
其四，符号书写错误，尤其是向量与函数方面。写出 f⁻¹(x) = … 之后忘记将 y 替换为 x，或未使用正确的向量符号（粗体或下划线），都会丢掉精确分。其五，力学答案中遗漏单位。末速度未带“m/s”或时间不带“s”都会被扣分。在统计部分，绘制图表却不标注坐标轴或使用错误比例也是常见的可避免错误。历年真题显示，有多达 5% 的原始分因这类表达问题而白白流失。在计时条件下练习，并重点针对这些呈现细节审视评分方案，将大有裨益。
11. A Deep Dive into a 2023 Paper | 2023年真题深度剖析
Let’s dissect a question from the OCR Further Maths June 2023 Paper 1 (question 10, 11 marks): ‘The polynomial P(x) = 2x³ + ax² + bx – 6 has a factor of (x+2). When P(x) is divided by (x-1), the remainder is -12. Find a and b, and hence factorise P(x) completely.’ Using the factor theorem, P(-2) = 0 gives -16 + 4a – 2b – 6 = 0 leading to 4a – 2b = 22, or 2a – b = 11. By the remainder theorem, P(1) = -12 gives 2 + a + b – 6 = -12, so a + b = -8. Solving the simultaneous equations yields a = 1, b = -9. Many candidates stopped here, but full factorisation requires dividing P(x) by (x+2) to obtain a quadratic quotient 2x² – 3x – 3, which does not factorise over rational numbers. The final answer: (x+2)(2x² – 3x – 3). The examiners’ report noted that some incorrectly tried to further factor the quadratic, while others omitted the intermediate division step entirely.
让我们来剖析 OCR 进阶数学 2023 年 6 月试卷一的一道题目（第 10 题，11 分）：“多项式 P(x) = 2x³ + ax² + bx – 6 含有因式 (x+2)。当 P(x) 除以 (x-1) 时，余式为 -12。求 a 和 b，并由此将 P(x) 彻底分解因式。”由因
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