中五 · 复习
直线运动学，复习笔记
直线运动学的精要复习笔记，每一项内容标准、考试公式，以及如何复习才能得分。
需要复习什么
本笔记涵盖直线运动学，中五SPM高级数学第8章。本章由4项内容标准构成，下表列出每一项要求你掌握的能力。
逐项复习：理解概念、掌握方法、反复练习直到解题成为本能。由于SPM评分是分析式的，清晰有序的步骤能在最终答案出错时仍保住分数，因此把整洁的排版当作复习的一部分。
内容标准
| 代码 | 内容标准 | 你必须掌握的 |
|---|---|---|
| 8.1 | 位移、速度与加速度作为时间的函数 | Describe and determine instantaneous displacement, instantaneous velocity, instantaneous acceleration of a particle.; Determine the total distance travelled by a particle in a given period of time. The displacement function is limited to linear and quadratic. |
| 8.2 | 直线运动学中的微分 | Relate between displacement function, velocity function and acceleration function.; Determine and interpret instantaneous velocities of a particle from displacement function. Maximum displacement, initial velocity and constant velocity need to be emphasised.; Determine and interpret instantaneous acceleration of a particle from velocity function and displacement function. Maximum velocity, minimum velocity and constant acceleration need to be emphasized. s = f(t) v = g(t) a = h(t) v = dt ds a = dt dv = dt s d v = dt a s = dt v |
| 8.3 | 直线运动学中的积分 | Determine and interpret instantaneous velocity of a particle from accelaration function.; Determine and interpret instantaneous displacement of a particle from velocity function and accelaration function. |
| 8.4 | 直线运动学的应用 | Solve problems of kinematics of linear motion involving differentiation and integration. PERFORMANCE STANDARDS PERFORMANCE LEVEL DESCRIPTOR 1 Demonstrate the basic knowledge of displacement, velocity and acceleration. 2 Demonstrate the understanding of displacement, velocity and acceleration. 3 Apply the understanding of displacement, velocity and acceleration to perform simple tasks. Apply appropriate knowledge and skills of kinematics of linear motion in the context of simple routine problem solving. Apply appropriate knowledge and skills of kinematics of linear motion in the context of complex routine problem solving. Apply appropriate knowledge and skills of kinematics of linear motion in the context of non-routine problem solving in a creative manner. PANEL OF WRITERS 1. 1. Dr. Rusilawati binti Othman Curriculum Development Division 2. 2. Rosita binti Mat Zain Curriculum Development Division 3. 3. Noraida binti Md. Idrus Curriculum Development Division 4. 4. Susilawati binti Ehsan Curriculum Development Division 5. 5. Wong Sui Yong Curriculum Development Division 6. 6. Alyenda binti Ab. Aziz Curriculum Development Division 7. Noor Azura binti Ibrahim Text Book Division 8. Prof. Dr. Zanariah binti Abdul Majid Universiti Putra Malaysia, Selangor 9. 7. Dr. Annie a/p Gorgey Universiti Pendidikan Sultan Idris, Perak 10. Gan Teck Hock IPGK Kota Bharu, Kelantan 11. Asjurinah binti Ayob SMK Raja Muda Musa, Selangor 12. Azizah binti Kamar SBPI Sabak Bernam, Selangor 13. Bibi Kismete Kabul Khan SMK Jelapang Jaya, Perak 14. Oziah binti Othman SMK Puchong Permai, Selangor 15. Rohani binti Md Nor Sekolah Sultan Alam Shah, Putrajaya CONTRIBUTORS 1. Ahmad Afif bin Mohd Nawawi Matriculation Division 2. 8. Norlisa binti Mohamed @ Mohamed Noor Malaysian Examinations Council 3. Prof. Madya Dr. Muhamad Safiih bin Lola Universiti Malaysia Terengganu, Terengganu 4. 9. Prof. Madya Dr. Zailan bin Siri Universiti Malaya, Kuala Lumpur 5. Dr. Dalia binti Aralas Universiti Putra Malaysia, Selangor 6. Dr. Suzieleez Syrene binti Abdul Rahim Universiti Malaya, Kuala Lumpur 7. Dr. Lam Kah Kei IPGK Tengku Ampuan Afzan, Pahang 8. Dr. Najihah binti Mustaffa SM Sains Tapah, Perak 9. Asman bin Ali SMK Kuala Perlis, Perlis 10. Intan Ros Elyza binti Zainol Abidin SM Sains Hulu Selangor, Selangor 11. Masnaini binti Mahmad SMK Bandar Tun Hussein Onn 2, Selangor 12. Nor Haniza binti Abdul Hamid SMK St. John, Kuala Lumpur 13. Nur Aziah binti Nasir SMK Jalan Empat, Selangor 14. Nurbaiti binti Ahmad Zaki SMK Sierramas, Selangor 15. Sabariah binti Samad SM Sains Rembau, Negeri Sembilan 16. Sh. Maisarah binti Syed Mahamud SMK Seberang Jaya, Pulau Pinang 17. Siti Alifah binti Syed Jalal SMK Katholik (M), Selangor 18. Somu a/l Pantinaidu SMK Seksyen 19, Selangor 19. Wan Mohd Suhaimi bin Wan Ibrahim SMK Air Merah, Kedah 20. Zaleha binti Tomijan SMK Syed Ibrahim, Kedah 21. Zefry Hanif bin Burham @ Borhan SM Sains Banting, Selangor PANEL OF TRANSLATORS 1. 10. Dr. Rusilawati binti Othman Curriculum Development Division 2. 11. Rosita binti Mat Zain Curriculum Development Division 3. 12. Noraida binti Md. Idrus Curriculum Development Division 4. 13. Wong Sui Yong Curriculum Development Division 5. 14. Alyenda binti Ab. Aziz Curriculum Development Division 6. Amirah Zayanah binti Asmadi SMK Sungai Manggis, Selangor 7. Faridah binti Abdullah SMK Bandar Baru Bangi, Selangor 8. Gan Fei Ting SMK Seri Bintang Selatan, Kuala Lumpur 9. Hen Li Seong SMK Yok Bin, Melaka 10. Juriah binti Ibrahim SMK Bandar Rinching, Selangor 11. Kong Chung Teck SMK Tengku Ampuan Jemaah, Selangor 12. Krishnan a/l Mookan SMK Telok Datok, Selangor 13. Law Siew Kie SMK Seri Kembangan, Selangor 14. Merah binti Hasan SMK Tinggi Kajang, Selangor 15. Munirah binti Kassim SMK Pauh Jaya, Pulau Pinang 16. Nik Nur Ashikin binti Nik Othman @ Daud SMK Tinggi Port Dickson, Negeri Sembilan 17. Nor Azura binti Mohd. Hashim SMK Seri Bintang Utara, Kuala Lumpur 18. Norhayati binti Zakaria SBPI Temerloh, Pahang 19. Norsushila binti Othman SMK Desa Petaling, Kuala Lumpur 20. Nur Aziah binti Nasir SMK Jalan Empat, Selangor 21. Nurbaiti binti Ahmad Zaki SMK Sierramas, Selangor 22. Nurfariza binti Muhamad Hanafi SMK Tinggi Port Dickson, Negeri Sembilan 23. Premalatha A/P Velu SMK Seremban 2, Negeri Sembilan 24. Raiha binti Alias SMK Desa Cempaka, Negeri Sembilan 25. Raja Mohd Salihin bin Raja Ariff SMK Putrajaya Presint 14 (1), Putrajaya 26. Razif bin Mohamed Rosli SMS Perempuan Seremban, Negeri Sembilan 27. Rohana binti Dalmen SMK Convent Kajang, Selangor 28. Ruslina binti Abd Rashid SMK Kajang Utama, Selangor 29. Ruzita binti Kamil SMK Jalan Kebun, Selangor 30. Sh. Maisarah binti Syed Mahamud SMK Seberang Jaya, Pulau Pinang 31. Siti Najikhah binti Mohd Isa SAM Tanjong Karang, Selangor 32. Siti Rahimah binti Ahmad SMK Dato' Abu Bakar Baginda, Selangor 33. Somu A/L Pantinaidu SMK Seksyen 19, Selangor 34. Sylviaty binti Norbi SMK Tunku Ampuan Najihah, Negeri Sembilan 35. Yogeswari A/P Punaiyah SMJK Yu Hua, Selangor 36. Zariah binti Zainal SMK Serendah, Selangor 37. Zefry Hanif bin Burham @ Borhan SM Sains Banting, Selangor ACKNOWLEDGEMENT Advisors Dr. Mohamed bin Abu Bakar - Director Datin Dr. Ng Soo Boon - Deputy Director (STEM) Editorial Advisors Dr. Rusilawati binti Othman - Head of Sector Mohamed Zaki bin Abd. Ghani - Head of Sector Haji Naza Idris bin Saadon - Head of Sector Mahyudin bin Ahmad - Head of Sector Mohd Faudzan bin Hamzah - Head of Sector Mohamed Salim bin Taufix Rashidi - Head of Sector Haji Sofian Azmi bin Tajul Arus - Head of Sector Hajah Norashikin binti Hashim - Head of Sector Fazlinah binti Said - Head of Sector Paizah binti Zakaria - Head of Sector Publication Technical and Specification Coordinators Saripah Faridah binti Syed Khalid Nur Fadia binti Mohamed Radzuan Mohamad Zaiful bin Zainal Abidin Graphic Designer Siti Zulikha binti Zelkepli This curriculum document is published in Bahasa Melayu and English language. If there is any conflict or inconsistency between the Bahasa Melayu version and the English version, the Bahasa Melayu version shall, to the extent of the conflict or inconsistency, prevail. |
如何为分数而复习
本章的位置，以及顺序为何重要
直线运动学是中五课程的第8章，而高级数学更青睐按课程顺序复习、而非跳到看起来最难部分的学生。几乎每一章都倚赖中四的代数，移项、处理函数、干净地运算指数与根式，因此若其中任何一项不稳，花一小时把它夯实，会在直线运动学以及之后的一切中都得到回报。
复习本章时，随手记下任何你不得不回查的旧技能：这份笔记就是值得修补的基础地图。稳健的复习计划不是一口气冲完全部4项标准，而是短而规律的多次学习：复习一项标准，几天后自测，只有当你能不看笔记复现方法时才继续下一项。
老师如何帮助直线运动学
笔记与练习能让学生走很远，但直线运动学正是那种"第二双眼睛"能把"大致会"变成"稳定会"的章节。一对一时，老师边做边看你的解题，捕捉出错的确切一步，某处漏了符号、某处忘了条件、公式用对了地方却用错了方法。
这是书本上的标准答案永远做不到的，因为错误发生在动手时，而非阅读时。由于直线运动学建立在前面的章节之上，老师还能发现真正的缺口其实不在直线运动学，而在它默认掌握的某项中四技能，从而先重建它，让新内容终于扎根。
每一堂课的重点都相同：理解概念、展示方法，并把步骤写得足够清晰，即便某天最终答案出错也能得分。课程为一对一在线、以英文进行，老师会围绕孩子在直线运动学上的确切水平来安排每一节，从重建薄弱基础到冲刺A+。
由于老师面对的是一名学生而非三十名，节奏由理解而非教学进度表决定：五分钟就领会的概念不会被拖沓，一时未领会的则会给足所需时间，而不是为了让全班往前赶而被撇下。
这一切都不取代本站的笔记、例题与练习，而是让它们发挥更大的作用。读过直线运动学笔记、做过练习的学生，会带着真实的疑问而非一张白纸走进课堂，而针对这些疑问的一小时教学，远胜于用一小时讲解课本已经写明的内容。
这正是我们希望学生把两者结合使用的方式：在这里学习材料，留意它在何处开始讲不通，然后把那一点带给能够彻底弥合缺口的老师。
获取一对一辅导。
预约试课作者 spmaddmath.com.my 编辑团队.· 最后更新 5 September 2026
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