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所在平台: Udemy |
课程主页: https://www.udemy.com/course/westboundmaths-a-level-pure-maths-course/
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课程名称：10堂课完成A-Level纯数学课程 课程概述： 由两位剑桥大学的应届毕业生创办的Westbound Maths，自2018年以来在北伦敦提供面对面培训，如今已在线上开设课程！我们的课程旨在为考试准备和提高成绩提供支持，已有88%的学生通过课程提高了至少一个等级的最终成绩。 课程内容： Westbound Maths的A-Level纯数学完整课程涵盖了A-Level数学资格考试中，纯数学部分占最终考试权重的三分之二。课程包括10堂课，超过15小时的课堂视频，配有考试风格的家庭作业及详细的评分标准，涉及以下主题： 1. 数列与级数：等差/等比数列与级数 2. 二项展开 3. 三角学第一部分：正弦与余弦定理，三角形的面积，弧度，扇形的弧长和面积 4. 三角学第二部分：三角恒等式、双角公式及解三角函数 5. 代数、函数与参数方程第一部分：因式分解、长除法、部分分式、绝对值函数、指数与对数函数 6. 代数、函数与参数方程第二部分：复合与反函数，图像变换，(x,y)平面中的坐标几何：直线与圆的函数及参数方程 7. 微分第一部分：导数的定义与微分及其图形表示；微分方法包括链式法则、乘积法则、商法则，通过反函数和相关变化率的微分 8. 微分第二部分：如何对三角函数、指数与对数函数、参数方程和隐函数进行微分；静止点的定义、二阶导数和拐点，微分建模问题 9. 积分第一部分：直接积分的记忆项、对三角函数的积分、逆链法则、替换积分及分部积分 10. 积分第二部分：使用部分分式的积分，积分的应用：利用积分找曲线下的面积，解微分方程，以及梯形法则 课程材料的充分利用： - 课堂视频：每节课以主题的关键概念和定义开始，然后直接进入相关的过去考试题，以展示这些概念如何被测试和应用，接着提供考试风格的课堂练习，最后附上详细的解决步骤指南。 - 讲义：每节课都有讲义，总结覆盖的关键概念，考试风格问题的解决示例以及课堂练习的解决方案。 - 考试风格的家庭作业：每节课的家庭作业包含4道考试风格的问题，建议在考试条件下完成，以帮助学生识别知识盲点。 - 错误诊断：利用详细的示例解决方案，帮助学生诊断家庭作业中的错误，这是提高成绩的关键。 此课程充分为学生提供了学习A-Level纯数学所需的所有资源与支持。
Founded by two recent Cambridge graduates, Westbound Maths has been running in-person training for students based in North London since 2018, and now we are online! Our courses are designed for Exam Preparation and Grade Improvement with proven results- 88% of our past students improved their final grades by at least one band from predicted grades!What Complete A-Level Pure Maths Crash Course in 10 Lectures teach:The Westbound Maths Complete A-Level Pure Maths Course covers the entire A-Level pure maths syllabus which represents 2/3 of the final exam weight for A-Level Mathematics qualification. The course consists of 10 lectures with over 15 hours of class videos, accompanying exam- styled homework and detailed mark scheme for the following topics:Sequence and Series: arithmetic/geometric sequence and seriesBinomial expansionTrigonometry part I: sine and cosine rules, area of a triangle, radian, arc length and area of a pie.Trigonometry part II: trigonometric identities, double angle formulae, solving trigonometric functionsAlgebra, Functions and Parametric Equations part I: factorization, long division, partial fractions, modulus functions, exponential and logarithm functions.Algebra, Functions and Parametric Equations part II: composite and inverse functions, transformation of the graph of f(x), coordinate geometry in the (x,y) plane: functions of line and circle, and parametric equations.Differentiation part I: definition of derivative and differentiation, their graphic representation and interpretation; methods of differentiation including chain rule, product rule, quotient rule, differentiation through inverse functions and connected rate of change.Differentiation part II: how to differentiate trigonometric functions, exponential and logarithm functions, parametric equations and implicit functions; the definition of stationary point, second derivative and point of inflection; modelling questions on differentiation.Integration part I: memory items for direct integration, integrating trigonometric functions, reverse chain rules, integration by substitution, and integration by parts.Integration part II: integration using Partial Fractions, application of integration: finding areas under the curve using integration, solving differential equations, and the trapezium RuleHow to fully utilize the course materials:Class video: we always start with the key concepts and definition within a topic, and then jump straight into a past exam question (sourced across major exam boards) to see how these concepts are tested and applied, then you will be given an exam-styled classroom exercise for practice followed by a detailed step-by-step guide on how to solve it.Handouts: every lecture is accompanied with a handout that summarizes key concepts covered, exam- styled question solving examples, and classroom exercise solutions.Homework with exam-styled questions: for each lecture, the homework contains 4 exam-styled questions which should be completed under exam conditions to help students identify any knowledge gap.Mistake Diagnosis: use the detailed sample solution to diagnose any mistake in homework which is the key to grade improvement.
