SCIENCES STREAM
StudieScope Logbook : Your Personal SPM Study Companion (Beseri Edition) Copyright © 2023 Muhamad Ikmal Arif, All rights reserved. All Rights Reserved. No part of this book may be reproduced in any form or by electronic or mechanical means including photocopying, recording, and information storage and retrieval systems–except in the case of brief quotations embodied in critical articles or reviews–without permission in writing from the author. Written and compiled by: Muhamad Ikmal Arif bin Ahmad Basirun Approved by: Puan Afida binti Abu Bakar Special thanks to: MUAFAKAT MRSM Beseri
Practice self-discipline and growth. Manage your academic studies. Visualize your effort. With this logbook, you may start setting out your goals or targets for SPM and build a study schedule that is personal and comfortable to you. Practice being committed to your own schedule and studies, but never be fearful of losing that commitment. Things happen, and it can deter you away from your academic commitment. Don’t be discouraged; always bring yourself back up and continue moving forward. Remember: improvement is what you desire, not perfection. Without a proper study management system, you may lose track of how much effort you have put into your studies for each subject. With this logbook, you may start managing your studies systematically and see your effort grow from now. Seeing your actual effort being done can be ultimately rewarding. You will feel fulfilled and satisfied due to the visual evidence of the progress tracking that is done by you in this logbook. It can be the reason for you to persist your effort until towards the end of the SPM journey. Section 1
Subject Semester 1 Semester 2 Target Result Target Result BM MARKS GRADE MARKS GRADE MARKS GRADE MARKS GRADE ENG SEJ PAI MATH A.MATH AKAUN PHY CHEM BIO
Semester 3 SPMRSM SPM Target Result Target Result Target MARKS GRADE MARKS GRADE MARKS GRADE MARKS GRADE GRADE
StudyLogbook In this section, you are provided with a complete list of topics for each subject in the SPM KSSM syllabus. Some of the subjects also include Learning Standards. UNDERSTANDING This column assesses your awareness of a particular topic as a whole. ✔ if you feel like you have a general idea of what the topic or LS is about. ✔ ✔ if you feel confident about the topic. ✔ ✔ ✔ if you think you have mastered the topic. NOTES Notes are the most important part of your studies. You will never ace your subjects without comprehensive notes. (You can’t review large textbooks before the day of the exam, duh!) ✔ if you have obtained your notes for a particular subtopic or learning standard. TOPIC LEARNING STANDARD NOTES UNDERSTAN DING STUDY SESSIONS 13.2 The Urinary System Describe the formation of urine: • ultrafiltration • reabsorption • secretion STUDY SESSIONS / PRACTICES You can use the “study sessions” or “practices” columns to track your study progresses. Do so by marking ✔ or putting a date (i.e., 9/3) in the boxes for each topic that you have covered. One column for one study session! You are encouraged to complete all study sessions (in the ‘Study Sessions’ columns) to complete the book. Hopefully, it will help you develop your study habits over time without needing to do much tracking later on. Section 2
What should I do with the Learning Standards? With the learning standards, you are able to use the SMARTS method below: What are Learning Standards (LS)? Learning Standards are concise, written descriptions of what students are expected to know and be able to do at a specific stage of their education. LEARNING STANDARDS (LS) TOPIC LEARNING STANDARDS 1.1 Quadratic Functions and Equations Identify and describe the characteristics of quadratic expressions in one variable. Set goals Measure abilities Assess skills Revise and Practice Tune your studies Seek help Define specific targets you aim to accomplish for each study session. Identify areas of strengths and weaknesses using the LS. Regularly practice questions and revise the topics covered in the LS. Assess whether you are able to achieve the learning standard or not. Use the learning standards as a guide to start your study session. if you have any doubts or need clarification on specific topics or skills outlined in the LS.
TIDAK TIPS ON HOW TO START YOUR STUDY SESSION • Gather all necessary resources before starting your session. For example, reference books, sets of questions, your own notes and the StudieScope Logbook. • Select one topic, concept, or given Learning Standard(s) at a time. Choose an area that you feel requires improvement in your studies. • (Optional) Set a pomodoro timer using any platform available. Be it using the Focus app, online, or using traditional devices such as your clock or watches. Fret not! Take note upon your difficulty in understanding the concept. Jolt down questions in your head and set a reminder to later seek help from friends or teachers. YES NO STUDY COMPLETE • Predict how long the session will take. It can be as short as 2-5 minutes up to 1-1.5 hours. Remember not to burn yourself out! • Choose a study method that suits the subject of your choice. For example, reviewing notes, making recaps, solving practice questions or discussing with friends. Do not abandon your difficulties! You’ll lose your progress and that’ll never make you improve! STUDY COMPLETE! Despite the difficulty, you have put in a lot of effort! Congrats! • Start studying with a ‘santai’ mindset. Learning is about absorbing knowledge. It is difficult to absorb knowledge when you are already exhausted, stressed or mentally filled with a lot of knowledge. Do you find yourself stuck in difficulty?
TOPIK NOTA LATIHAN KERTAS 1 LATIHAN KERTAS 2 1 2 3 1 2 3 5 PEMBENTUKAN MALAYSIA 5.1 Konsep Gagasan Malaysia 5.2 Perkembangan Idea dan Usaha Pembentukan Malaysia 11/10 28/10 10/12 5.3 Reaksi Tempatan dan Negara Jiran terhadap Pembentukan Malaysia 5.4 Langkah Pembentukan Malaysia 5.5 Perjanjian Julai 1963 dan Peristiwa Pengisytiharan Malaysia 5.6 Konfrontasi dan Usaha Menangani 6 CABARAN SELEPAS PEMBENTUKAN MALAYSIA 6.1 Cabaran Dalaman Malaysia 6.2 Pemisahan Singapura 6.3 Menangani Ancaman Komunis 6.4 Isu Pembangunan dan Ekonomi 6.5 Tragedi Hubungan antara Kaum ADDITIONAL TIPS FOR YOUR STUDY • Do not get distracted by the thought of wanting to study another topic or concepts when the current one you’re studying isn’t even complete yet. • Treat your homework as study. That way, you won’t have to separate time between doing homework and studying. Both processes involve learning, so make sure that you absorb all knowledge from the homework given to you. Then, you won’t have to study anymore! • Engage in discussions. Active learning is important! • If you start using the logbook section, it should look like the table below.
Bahasa Melayu بهاس ماليو BM Ilmu bukanlah apa yang dihafal akan tetapi yang bermanfaat. J a b a t a n b a h a s a
Format SPM TOPIK NOTA KEFAHAMAN PRAKTIS / LATIHAN 1 2 3 4 5 6 KERTAS 1 1.1 Bahagian A 1.2 Bahagian B KERTAS 2 BHG A: SISTEM & APLIKASI BAHASA 1.1 Morfologi 1.2 Sintaksis 1.3 Kesalahan Bahasa (Penyuntingan) 1.4 Bahasa Melayu Klasik → Bahasa Melayu Standard 1.5 Peribahasa BHG B: PEMAHAMAN 2.1 Petikan Umum 2.2 Sastera 2.3 Novel* BHG C: RUMUSAN 3.1 Rumusan KERTAS 3: UJIAN BERTUTUR KERTAS 4: UJIAN MENDENGAR BM
NOVEL JENDELA MENGHADAP JALAN SONGKET BEBENANG EMAS Permulaan Novel Tema Watak & Perwatakan Persoalan Nilai Pengajaran Klimaks Peristiwa Menarik / Penting Peristiwa Suspens Peristiwa Peleraian Senarai Semak Novel Senarai Semak Sistaksis PENGUASAAN SINTAKSIS AYAT TANYA CERAKINKAN AYAT / GABUNGKAN AYAT SUBJEK DAN PREDIKAT POLA AYAT AYAT SONGSANG JENIS AYAT AYAT PASIF AYAT AKTIF CAKAP AJUK CAKAP PINDAH http://dermagabmk1.blogspot.com /2012/02/nota-tatabahasa.html ✔ jika anda telah membuat nota dan Latihan bagi setiap aspek soalan yang berikut. BM
ENGLISH L A N G U A G E d e p a r t m e n t Believe you can and you’re halfway there. BI
TOPIC NOTE UNDERSTANDING PRACTICES 1 2 3 4 5 6 PAPER 1 (READING AND USE OF ENGLISH) 1.1 Short Texts (MCQ) 1.2 Rational Cloze (MCQ) - Grammar* - Vocabulary 1.3 Extended Text Reading Comprehension (MCQ) 1.4 Gapped Text 1.5 Matching and Information Transfer 1.6 Reading Competency - Understanding - Application - Analysis - Evaluation PAPER 2 (WRITING) 2.1 Short Message - Informal Message 2.2 Guided Writing - Provide details/reasons 2.3 Extended Writing 2.3.1 Articles 2.3.2 Reviews (Book/Movie/Video) 2.3.3 Reports 2.3.4 Formal and Informal Letter 2.3.5 Stories 2.4 Writing Competency - Application - Analysis - Evaluation - Creation SPM Format BI
TOPIC NOTE UNDERSTANDING PRACTICES 1 2 3 4 5 6 PAPER 3 (SPEAKING) 3.1 Speaking and Listening Competency - Understanding - Application - Analysis 3.2 Topics - School life - Home life - Daily routine - Familiar topics * Discussion and decision making PAPER 4 (LISTENING) 4.1 Listening Competency - Understanding - Application 4.2 Tasks - MCQs - Matching - Note completion 4.3 Texts - Short dialogues - Long dialogues - Monologues SPM Format BI
PARTS OF SPEECH Articles Nouns Pronouns Verbs Adverbs Adjectives Conjunctions Prepositions Interjections Tenses TENSES Present Tense Past Tense Future Tense Grammar Checklist https://www.learngrammar.net /english-grammar ADVANCED GRAMMAR Determiners & Quantifiers Punctuation Prefixes & Suffixes Negation Modifiers Clauses Phrases SENTENCE STRUCTURES Independent Clause Dependant Clause Simple Sentences Compound Sentences Complex Sentences Compound-Complex Sentences ✔ if you understood these grammar concepts and how to use them BI
SEJARAH Tingkatan 4 & 5 Kenali asal-usul anda. J a b a t a n s a i n s s o s i a l BM BI ak bio km fz SJ pai MM MT SJ
TOPIK NOTA FAH AM LATIHAN KERTAS 1 LATIHAN KERTAS 2 1 2 3 1 2 3 1 WARISAN NEGARA BANGSA 1.1 Latar Belakang Negara Bangsa Sebelum Kedatangan Barat 1.2 Ciri-ciri Negara Bangsa Kesultanan Melayu Melaka 1.3 Keunggulan Sistem Pentadbiran dan Undang-undang 1.4 Peranan Pemerintah dan Rakyat 2 KEBANGKITAN NASIONALISME 2.1 Maksud Nasionalisme 2.2 Perkembangan Idea Nasionalisme di Barat 2.3 Perkembangan Nasionalisme di Asia 2.4 Perkembangan Nasionalisme di Asia Tenggara 2.5 Kesedaran Nasionalisme di Negara Kita 2.6 Faktor Kemunculan Gerakan Nasionalisme 2.7 Perkembangan Nasionalisme 2.8 Kesan Perkembangan Nasionalisme 3 KONFLIK DUNIA DAN PENDUDUKAN JEPUN DI NEGARA KITA 3.1 Nasionalisme di Negara Kita Sebelum Perang Dunia 3.2 Latar Belakang Perang Dunia 3.3 Perang Dunia Kedua 3.4 Perang Dunia Kedua di Asia Pasifik 3.5 Faktor Kedatangan Jepun ke Negara Kita 3.6 Dasar Pendudukan Jepun ke Negara Kita 3.7 Perjuangan Rakyat Menentang Pendudukan Jepun 3.8 Perkembangan Gerakan Nasionalisme Tempatan dan Pendudukan Jepun 3.9 Keadaan Negara Kita Selepas Kekalahan Jepun T I N G K A T A N 4 SJ
T i n g k a t a n 4 TOPIK NOTA FAH AM LATIHAN KERTAS 1 LATIHAN KERTAS 2 1 2 3 1 2 3 4 ERA PERALIHAN KUASA BRITISH DI NEGARA KITA 4.1 British Military Administration 4.2 Gagasan Malayan Union 4.3 Reaksi Penduduk Tempatan terhadap Malayan Union 4.4 Penyerahan Sarawak kepada Kerajaan British 4.5 Reaksi Penduduk Tempatan terhadap Penyerahan Sarawak 4.6 Penyerahan Sabah kepada Kerajaan British 4.7 Reaksi Penduduk Tempatan terhadap Penyerahan Sabah 5 PERSEKUTUAN TANAH MELAYU 1948 5.1 Latar Belakang Penubuhan Persekutuan Tanah Melayu 1948 5.2 Faktor Penubuhan Persekutuan Tanah Melayu 5.3 Ciri-ciri Persekutuan Tanah Melayu 1948 5.4 Kesan Penubuhan Persekutuan Tanah Melayu 1948 6 ANCAMAN KOMUNIS DAN PERISYTIHARAN DARURAT 6.1 Kemasukan Pengaruh Komunis di Negara Kita 6.2 Ancaman Komunis di Negara Kita 6.3 Usaha Menangani Ancaman Komunis 6.4 Kesan Zaman Darurat terhadap Negara Kita 7 USAHA KE ARAH KEMERDEKAAN 7.1 Latar Belakang Idea Negara Merdeka 7.2 Jawatankuasa Hubungan Antara Kaum 7.3 Sistem Ahli 7.4 Sistem Pendidikan Kebangsaan 7.5 Penubuhan Parti Politik SJ
T I N G K A T A N 4 TOPIK NOTA FAH AM LATIHAN KERTAS 1 LATIHAN KERTAS 2 1 2 3 1 2 3 8 PILIHAN RAYA 8.1 Perkembangan Pilihan Raya Umum Pertama 8.2 Proses Pilihan Raya Umum Pertama 8.3 Penubuhan Majlis Perundangan Persekutuan 8.4 Peranan Kabinet Pertama Persekutuan Tanah Melayu 9 PERLEMBAGAAN PERSEKUTUAN TANAH MELAYU 1957 9.1 Usaha Rundingan Kemerdekaan 9.2 Peranan Suruhanjaya Perlembagaan Persekutuan Tanah Melayu 9.3 Langkah Penggubalan Perlembagaan Persekutuan Tanah Melayu yang Merdeka 9.4 Perjanjian Persekutuan Tanah Melayu 10 PEMASYHURAN KEMERDEKAAN 10.1 Pengertian Kemerdekaan 10.2 Persediaan Menyambut Pemasyhuran Kemerdekaan Negara 10.3 Detik Pemasyhuran Kemerdekaan Negara 10.4 Kesan Kemerdekaan terhadap Negara Kita 10.5 Prinsip Kedaulatan Persekutuan Tanah Melayu SJ
T i n g k a t a n 5 TOPIK NOTA FAH AM LATIHAN KERTAS 1 LATIHAN KERTAS 2 1 2 3 1 2 3 1 KEDAULATAN NEGARA 1.1 Konsep Kedaulatan 1.2 Ciri Negara yang Berdaulat 1.3 Kepentingan Mewujudkan Negara Berdaulat 1.4 Langkah Mempertahankan Kedaulatan 2 PERLEMBAGAAN PERSEKUTUAN 2.1 Latar Belakang Sejarah Perlembagaan Persekutuan 2.2 Sejarah Penggubalan Perlembagaan Persekutuan 2.3 Ciri Utama Perlembagaan Persekutuan 2.4 Pindaan Perlembagaan Persekutuan 1963 dan 1965 3 RAJA BERPELEMBAGAAN DAN DEMOKRASI BERPARLIMEN 3.1 Latar Belakang Pemerintahan Beraja dan Demokrasi Berparlimen 3.2 Sejarah dan Kedudukan Institusi Majlis Raja-Raja 3.3 Yang di-Pertuan Agong dan Raja dalam Perlembagaan Persekutuan 3.4 Amalan Demokrasi dan Pengasingan Kuasa 3.5 Keunikan Amalan Demokrasi Berparlimen di Negara Kita 4 SISTEM PERSEKUTUAN 4.1 Latar Belakang Sistem Persekutuan di Negara Kita 4.2 Kuasa Kerajaan Persekutuan dan Kerajaan Negeri 4.3 Kerjasama Kerajaan Persekutuan dan Kerajaan Negeri 4.4 Faktor yang Mengukuhkan Sistem Persekutuan SJ
T i n g k a t a n 5 TOPIK NOTA FAHA M LATIHAN KERTAS 1 LATIHAN KERTAS 2 1 2 3 1 2 3 5 PEMBENTUKAN MALAYSIA 5.1 Konsep Gagasan Malaysia 5.2 Perkembangan Idea dan Usaha Pembentukan Malaysia 5.3 Reaksi Tempatan dan Negara Jiran terhadap Pembentukan Malaysia 5.4 Langkah Pembentukan Malaysia 5.5 Perjanjian Julai 1963 dan Peristiwa Pengisytiharan Malaysia 5.6 Konfrontasi dan Usaha Menangani 6 CABARAN SELEPAS PEMBENTUKAN MALAYSIA 6.1 Cabaran Dalaman Malaysia 6.2 Pemisahan Singapura 6.3 Menangani Ancaman Komunis 6.4 Isu Pembangunan dan Ekonomi 6.5 Tragedi Hubungan antara Kaum 7 MEMBINA KESEJAHTERAAN NEGARA 7.1 Perpaduan dan Integrasi Nasional 7.2 Dasar Pendidikan Kebangsaan 7.3 Bahasa Melayu sebagai Bahasa Ilmu dan Bahasa Perpaduan 7.4 Dasar Kebudayaan Kebangsaan 7.5 Sukan sebagai Alat Perpaduan 7.6 Rukun Negara sebagai Tonggak Kesejahteraan Negar SJ
T I N G K A T A N 5 TOPIK NOTA FAH AM LATIHAN KERTAS 1 LATIHAN KERTAS 2 1 2 3 1 2 3 8 MEMBINA KEMAKMURAN NEGARA 8.1 Pembentukan Dasar Ekonomi Baru (DEB) 8.2 Pelaksaan Dasar Ekonomi Baru (DEB) 8.3 Pembentukan Dasar Pembangunan Nasional (DPN) 8.4 Pelaksanaan Dasar Pembangunan Nasional (DPN) 8.5 Pencapaian DEB dan DPN 9 DASAR LUAR MALAYSIA 9.1 Latar Belakang Dasar Luar 9.2 Asas Penggubalan Dasar Luar 9.3 Malaysia dalam Pertubuhan Bangsa-Bangsa Bersatu (PBB) 9.4 Malaysia dalam Komanwel 9.5 Cabaran Mengukuhkan Dasar Luar 9.6 Malaysia dalam Persatuan Negara-Negara Asia Tenggara (ASEAN) 9.7 Malaysia dalam Pergerakan Negara-negara Tanpa Pihak (NAM) 9.8 Malaysia dalam Pertubuhan Kerjasama Islam (OIC) 10 KECEMERLANGAN MALAYSIA DI PERSADA DUNIA 10.1 Malaysia dalam Isu Global Kontemporari 10.2 Perana Malaysia dalam Hubungan Ekonomi Antarabangsa 10.3 Pelibatan Rakyat dalam Isu Kemanusiaan dan Keamanan 10.4 Usaha Mengekalkan Kelestarian Global 10.5 Wawasan Malaysia Menuju Masa Hadapan SJ
J A B A T A N S A I N S S O S I A L ڤنديديقن اسالم تيڠكتن 4 دان 5 Sentiasalah berniat kerana Allah dalam apa jua perkara. pai
TOPIK NOTA KEFAHAMAN STUDY SESSIONS 1 2 3 4 5 6 AL-QURAN : HAFAZAN 1 Al-An’am: 162-163 2.1 Al-Kahfi: 101-107 2.2 Al-Kahfi: 107-110 AL-QURAN : TAJWID 3 Hukum Tajwid AL-QURAN: KEFAHAMAN 4 Larangan Rasuah 5 Memahami Sunnatullah 6 Larangan Mempersendakan Agama 7 Dakwah Pembawa Kemajuan HADIS 8 Hindari Dosa Besar 9 Kemuliaan Berdikari AKIDAH Allah SWT Maha Pembalas Dan Maha Perkasa 10.1 al-Muntaqim 10.2 al-Jabbar 11 Perkara Yang Membatalkan Iman 12 Hindari Ajaran Sesat FIQAH 13 Haji dan Umrah 14 Sembelihan 15.1 Korban 15.2 Akikah T i n g k a t a n 4 pai
TOPIK NOTA KEFAHAMAN STUDY SESSIONS 1 2 3 4 5 6 FIKAH 16.1 Konsep Muamalat Islam 16.2 Jenis Aqad Dalam Muamalat Islam 17.1 Solat Sunat Dhuha 17.2 Solat Sunat Gerhana SIRAH DAN TAMADUN ISLAM 18 Kerajaan Khulafa’ al-Rasyidin 19 Kerajaan Umaiyah 20 Kerajaan Abbasiah 21 Keunggulan Tokoh Empat Mazhab AKHLAK ISLAMIAH 22 Bersikap Benar Menjauhkan Kemunafikan 23 Khauf dan Raja’ 24.1 Adab Terhadap Orang Sakit 24.2 Abad Terhadap Orang Kurang Upaya 25 Wasatiyyah T i n g k a t a n 4 pai
TOPIK NOTA KEFAHAMAN STUDY SESSIONS 1 2 3 4 5 6 AL-QURAN : HAFAZAN 1 At-Taubah: 128-129 2 Al-Hasyr: 21-24 AL-QURAN : TAJWID 3 Hukum Tajwid AL-QURAN: KEFAHAMAN 4 Ciri-ciri Mukmin Berjaya 5 Memahami Keutamaan dalam Tindakan 6 Kepelbagaian Bangsa dalam Islam HADIS 7 Setiap Orang ialah Pemimpin 8 Tujuh Golongan yang Mendapat Naungan Allah SWT AKIDAH Allah SWT Maha Mengawasi Dan Maha Menyaksikan 9.1 al-Raqib 9.2 al-Syahid 10 Akidah Ahli Sunnah Waljamaah FIKAH 11.1 Solat Sunat Istikharah 11.2 Solat Sunat Tasbih 12.1 Perkahwinan 12.2 Kemahiran Keibubapaan 13 Isu-isu dalam Perkahwinan T i n g k a t a n 5 pai
TOPIK NOTA KEFAHAMAN STUDY SESSIONS 1 2 3 4 5 6 FIKAH Pengurusan Harta Selepas Kematian 14.1 Wasiat dalam Islam 14.2 Faraid dalam Islam 15 Jenayah dalam Islam SIRAH DAN TAMADUN ISLAM 16 Kerajaan Uthmaniyah 17 Keunggulan Tokoh Islam AKHLAK ISLAMIAH 18 Tawaduk Menzahirkan Kesucian Jiwa 19 Istiqamah Jalan Menuju Mujahadah 20 Alam Sekitar Penenang Minda 21 Sifat Mazmumah Meracuni Hati T i n g k a t a n 5 pai
Mathematics Form 4 & 5 M a t h e m a t i c s d e p a r t m e n t Don’t let what you cannot do, interfere what you can do. MM
TOPIC LEARNING STANDARDS UNDERST ANDING STUDY SESSIONS 1 QUADRATIC FUNCTIONS & EQUATIONS IN ONE VARIABLE 1.1 Quadratic Functions and Equations Identify and describe the characteristics of quadratic expressions in one variable. Recognise quadratic function as many-to-one relation, hence, describe the characteristics of quadratic functions Investigate and make generalisation about the effects of changing the values of a, b and c on graphs of quadratic functions, = 2 + + Form quadratic functions based on situations, and hence relate to the quadratic equations. Explain the meaning of roots of a quadratic equation. Determine the roots of a quadratic equation by factorisation method. Solve problems involving quadratic equations. 2 NUMBER BASES 2.1 Number Bases Represent and explain numbers in various bases in terms of numerals, place values, digit values and number values based on the collection process. Convert numbers from one base to another using various methods. Solve problems involving number bases. 3 LOGICAL REASONING 3.1 Statements Explain the meaning of a statement and hence determine the truth value of a statement. Negate a statement. Determine the truth value of a compound statement. Construct and compare the truth value of converse, inverse and contrapositive of an implication. Determine a counter-example to negate the truth of a particular statement. 3.2 Arguments Explain the meaning of an argument and differentiate between deductive and inductive arguments. Determine and justify the validity of a deductive argument and hence determine whether the valid argument is sound. F o r m 4 MM
TOPIC LEARNING STANDARDS UNDERST ANDING STUDY SESSIONS 3.2 Arguments Form a valid deductive argument for a situation. Determine and justify the strength of an inductive argument and hence determine whether the strong argument is cogent. Form a strong inductive argument of a certain situation. Solve problems involving logical reasoning. 4 OPERATIONS ON SETS 4.1 Intersection of Sets Determine and describe the intersection of sets using various representations. Determine the complement of the intersection of sets. Solve problems involving the intersection of sets. 4.2 Union of Sets Determine and describe the union of sets using various representations. Determine the complement of the union of sets. Solve problems involving the union of sets. 4.3 Combined Operations on Sets Determine and describe the combined operations on sets using various representations. Determine the complement of combined operations on sets Solve problems involving combined operations on sets. 5 NETWORK IN GRAPH THEORY 5.1 Network To identify and explain a network as a graph. Compare and contrast: • Directed graphs and undirected graphs • Weighted graphs and unweighted graphs Identify and draw subgraphs and trees. Represent information in the form of networks. Solve problems involving networks. 6 LINEAR INEQUALITIES IN TWO VARIABLES 6.1 Linear Inequalities in Two Variables Represent situations in the form of linear inequalities. Make and verify the conjecture about the points in the region and the solution of certain linear inequalities. Determine and shade the region that satisfies a linear inequality. F o r m 4 MM
TOPIC LEARNING STANDARDS UNDERST ANDING STUDY SESSIONS 6.2 Systems of Linear Inequalities in Two Variables Represent situations in the form of system of linear inequalities. Make and verify the conjecture about the points in the region and solution of linear inequality system. Determine and shade the region that satisfies a linear inequality system. Solve problems involving systems of linear inequalities in two variables. 7 GRAPHS OF MOTION 7.1 Distance-Time Graphs Draw distance-time graphs. Interpret distance-time graphs and describe the motion based on the graphs. Solve problems involving distance-time graphs. 7.2 Speed-Time Graphs Draw speed-time graphs. Make a relationship between the area under speed-time graph and the distance travelled, and hence determine the distance. Interpret speed-time graphs and describe the movement based on the graphs. Solve problems involving speed-time graphs. 8 MEASURES OF DISPERSION FOR UNGROUPED DATA 8.1 Dispersion Explain the meaning of dispersion. Compare and interpret dispersion of two or more sets of data based on the stem-and-leaf plots and dot plots, and hence make conclusions. 8.2 Measures of Dispersion Determine the range, interquartile range, variance and standard deviation as a measure to describe dispersion of an ungrouped data. Explain the advantages and disadvantages of various measures of dispersion to describe ungrouped data. Construct and interpret the box plot for a set of ungrouped data. Determine the effect of data changes on dispersion based on: • The value of measure of dispersion • Graphical representation Solve problems involving measures of dispersion. F o r m 4 MM
TOPIC LEARNING STANDARDS UNDERST ANDING STUDY SESSIONS 9 PROBABILITY OF COMBINED EVENTS 9.1 Combined Events Determine combined events and list out the possible combined events. 9.2 Dependant Events and Independent Events Determine between dependent and independent events. Make and verify conjecture about the formula of probability of combined events. Determine the probability of combined events for dependent and independent events. 9.3 Mutually Exclusive Events and Non-Mutually Exclusive Events Differentiate between mutually exclusive and non-mutually exclusive events. Verify the formula of probability of combined events for mutually exclusive and non-mutually exclusive events. Determine the probability of combined events for mutually exclusive and non-mutually exclusive events. 9.4 Application of Probability of Combined Events Solve problems involving probability of combined events. 10 CONSUMER MATHEMATICS: FINANCIAL MANAGEMENT 10.1 Financial Planning and Management Describe effective financial management process. Construct and present personal financial plans to achieve short-term and long-term financial goals, and hence evaluate the feasibility of the financial plans. F o r m 4 MM
F o r m 5 TOPIC LEARNING STANDARDS UNDERST ANDING STUDY SESSIONS 1 VARIATION 1.1 Direct Variation Explain the meaning of direct variation. Determine the relation between two variables for a direct variation. Determine the relation between three or more variables for a given joint variation. Solve problems involving direct variation. 1.2 Inverse Variation Explain the meaning of inverse variation. Determine the relation between two variables for an inverse variation. Solve problems involving inverse variation. 1.3 Combined Variation Determine the relation between three or more variables for a combined variation. Solve problems involving combined variation. 2 MATRICES 2.1 Matrices Represent information from real situations in the form of matrices. Determine the order of a matrix, hence identify certain elements in a matrix. Determine whether two matrices are equal. 2.2 Basic Operation on Matrices Add and subtract matrices. Multiply a matrix by a number. Multiply two matrices. Explain the characteristics of identify matrix. Explain the meaning of inverse matrix and hence determine the inverse matrix for a 2 x 2 matrix. Use the matrix method to solve simultaneous linear equations. Solve problems involving matrices. 3 CONSUMER MATHEMATICS: INSURANCE 3.1 Risk and Insurance Coverage Explain the meaning of risk and the importance of insurance coverage, hence determine the types of life insurance and general insurance for protecting a variety of risks. Investigate, interpret and perform calculations involving insurance rates and premiums. Solve problems involving insurance including deductible and co-insurance. MM
F o r m 5 TOPIC LEARNING STANDARDS UNDERST ANDING STUDY SESSIONS 4 CONSUMER MATHEMATICS: TAXATION 4.1 Taxation Explain the purpose of taxation. Describe various taxes, hence the consequences of tax evasion from legal and financial aspects. Investigate, interpret and perform calculations involving various taxes. Solve problems involving taxation. 5 CONGRUENCY, ENLARGEMENT AND COMBINED TRANSFORMATIONS 5.1 Congruency Differentiate between congruent and noncongruent shapes based on sides and angles. Make and verify the conjecture of triangle congruency based on sides and angles. Solve problems involving congruency. 5.2 Enlargement Explain the meaning of similarity of geometric objects. Make a connection between similarity and enlargement, hence describe enlargement using various representations. Determine the image and object of an enlargement. Make and verify conjecture on the relation between area of the image and area of the object of an enlargement. Solve problems involving enlargement. 5.3 Combined Transformations Determine the image and object of a combined transformation. Make and verify conjecture about commutative law in combined transformation. Describe combined transformation. Solve problems involving combined transformation. 5.4 Tessellations Explain the meaning of tessellation. Design tessellation involving isometric transformation. MM
F o r m 5 TOPIC LEARNING STANDARDS UNDERST ANDING STUDY SESSIONS 6 RATIOS AND GRAPHS OF TRIGONOMETRY FUNCTIONS 6.1 The Value of Sine, Cosine and Tangent for Angle θ, 0° < θ < 360° Make and verify conjecture about the value of sine, cosine and tangent for angles in quadrants II, III and IV with the corresponding reference angle. Determine the value of sine, cosine and tangent for angles in quadrants II, III and IV based on the corresponding reference angle. Determine the angle when the value of sine, cosine and tangent are given. Solve problems involving sine, cosine and tangent. 6.2 The Graphs of Sine, Cosine and Tangent Functions Draw graphs of trigonometric functions, = sin , = cos and = tan for 0 ° ≤ ≤ 360° , hence compare and contrast the characteristics of the graphs. Investigate and make generalisations about the effects of changes in constants , and on the graphs of trigonometric functions: (i) y = a sin bx + c (ii) y = a cos bx + c (iii) y = a tan bx + c For > 0, > 0. Solve problems involving graphs of sine, cosine and tangent functions. 7 MEASURES OF DISPERSION FOR GROUPED DATA 7.1 Dispersion Construct histogram and frequency polygon for a set of grouped data. Compare and interpret the dispersions of two or more sets of grouped data based on histogram and frequency polygon, hence make conclusion. Construct an ogive for a set of grouped data and determine the quartiles. 7.2 Measures of Dispersion Determine range, interquartile range, variance and standard deviation as a measure to describe dispersion for grouped data. Construct and interpret a box plot for a set of grouped data. Compare and interpret two or more sets of grouped data, based on measures of dispersion hence make conclusion. Solve problems involving measures of dispersion for grouped data. MM
F o r m 5 TOPIC LEARNING STANDARDS UNDERST ANDING STUDY SESSIONS 7.2 Measures of Dispersion Design and conduct a mini-project involving statistical investigations based on measures of central tendency and measures of dispersion and hence interpret and communicate research findings. 8 MATHEMATICAL MODELING 8.1 Mathematical Modeling Explain mathematical modeling. Solve real life problems through mathematical modeling which involves the following functions: (i) Linear (ii) Quadratic (iii) Exponential And communicate the mathematical modeling process implemented. MM
Mathematics ADDITIONAL Form 4 & 5 M a t h e m a t i c s d e p a r t m e n t There’ll always be another way. MT
TOPIC LEARNING STANDARDS UNDERS TANDIN G 1 2 3 1 FUNCTION 1.1 Function Explain function using graphical representations and notations. Determine domain and range of a function. Determine the image of a function when the object is given and vice versa. 1.2 Composite Functions Describe the outcome of composition of two functions. Determine the composite functions. Determine the image of composite functions given the object and vice versa. Determine a related function given composite function and another function. Solve problems involving composite functions. 1.3 Inverse Functions Describe inverse of a function. Make and verify conjectures related to properties of inverse functions. Determine the inverse functions. 2 QUADRATIC FUNCTIONS 2.1 Quadratic Equations and Inequalities Solve quadratic equations using the method of completing the square and formula. Form quadratic equations from given roots. Solve quadratic inequalities. 2.2 Types of Roots of Quadratic Equations Relate types of roots of quadratic equations to the discriminant value. Solve problems involving types of roots of quadratic equations. 2.3 Quadratic Functions Analyse and make generalisation about the effects of changes of a, b and c in = 2 + + towards the shape and position of the graph. Relate the position of the graph of quadratic functions with type of roots. Relate the vertex form of quadratic functions, () = – ℎ 2 + with other forms of quadratic functions. Analyse and make generalisation about the effects of changes of a, h and k in quadratic functions () = – ℎ 2 + towards the shape and position of the graphs. Sketch graphs of quadratic functions. Solve problems involving quadratic functions. F o r m 4 MT
TOPIC LEARNING STANDARDS UNDER STANDING 1 2 3 3 SYSTEMS OF EQUATIONS 3.1 Systems of Linear Equation in Three Variables Describe systems of linear equations in three variables. Solve systems of linear equations in three variables. Solve problems involving systems of linear equations in three variables. 3.2 Simultaneous Equations involving One Linear and One Non-Linear Equation Solve simultaneous equations involving one linear equation and one non-linear equation. Solve problems involving simultaneous equations; one linear equation and one non- linear equation. 4 INDICES, SURDS AND LOGARITHMS 4.1 Laws of Indices Simplify algebraic expressions involving indices using the laws of indices. Solve problems involving indices. 4.2 Laws of Surds Compare rational numbers and irrational numbers, and hence relate surds to irrational numbers. Make and verify conjectures on (i) × (ii) ÷ and hence make generalisation. Simplify expressions involving surds. Simplify expressions involving surds by rationalising the denominators. Solve problems involving surds. 4.3 Laws of Logarithms Relate equations in the form of indices and logarithms, and hence determine the logarithm of a number. Prove laws of logarithms. Simplify algebraic expressions using the laws of logarithms. Prove log = log log and use the relationship to determine the logarithm of a number. Solve problems involving the laws of logarithms. 4.4 Applications of Indices, Surds and Logarithms Solve problems involving indices, surds and logarithms. F o r m 4 MT
TOPIC LEARNING STANDARDS UNDERSTANDING 1 2 3 5 PROGRESSION 5.1 Arithmetic Progressions Identify a sequence as an arithmetic progression and provide justification. Derive the formula of the th term, , of arithmetic progressions, and hence use the formula in various situations. Derive the formula of sum of the first terms, , of arithmetic progressions, and hence use the formula in various situations. Solve problems involving arithmetic progressions. 5.2 Geometric Progressions Identify a sequence as a geometric progression and provide justification. Derive the formula of the nth term, , of geometric progressions, and hence use the formula in various situations. Derive the formula of sum of the first n terms, , of geometric progressions, and hence use the formula in various situations. Determine the sum to infinity of geometric progressions, ∞ and hence use the formula in various situations. Solve problems involving geometric progressions. 6 LINEAR LAW 6.1 Linear and Non-Linear Relations Differentiate between linear and non-linear relations based on tables of data and graphs. Draw lines of best fit for graph of linear relations with and without the use of digital technology. Form equations of lines of best fit. Interpret information based on lines of best fit. 6.2 Linear Law and Non-Linear Relations Apply linear law to non-linear relations. 6.3 Applications of Linear Law Solve problems involving linear law. 7 COORDINATE GEOMETRY 7.1 Divisor of a Line Segment Relate the position of a point that divides a line segment with the related ratio. Derive the formula for divisor of a line segment on a Cartesian plane, and hence use the formula in various situations Solve problems involving divisor of a line segment. F o r m 4 MT
TOPIC LEARNING STANDARDS UNDERST ANDING 1 2 3 7.2 Parallel Lines and Perpendicular Lines Make and verify conjectures about gradient of: (i) parallel lines, (ii) perpendicular lines and hence, make generalisations. Solve problems involving equations of parallel and perpendicular lines. 7.3 Areas of Polygons Derive the formula of area of triangles when the coordinates of each vertex are known. Determine the area of triangles by using the formula. Determine the area of quadrilaterals by using the formula. Make generalisation about the formula of area of polygons when the coordinates of each vertex are known, and hence use the formula to determine the area of polygons. Solve problems involving areas of polygons. 7.4 Equations of Loci Represent graphically, the locus that satisfies these conditions: i. the distance of a moving point from a fixed point is constant, ii. the ratio of a moving point from two fixed points is constant, and hence determine the equation of the locus. Solve problems involving equations of loci. 8 VECTORS 8.1 Vectors Compare and contrast between vectors and scalars, and hence identify whether a quantity is a vector or a scalar by providing justifications. Represent vectors by using directed line segments and vector notations, and hence determine the magnitude and direction of vectors. Make and verify conjectures about the properties of scalar multiplication on vectors. Make and verify conjectures about parallel vectors. 8.2 Addition and Subtraction of Vectors Perform addition and subtraction involving two or more vectors to obtain a resultant vector. Solve problems involving vectors. F o r m 4 MT
TOPIC LEARNING STANDARDS UNDERST ANDING 1 2 3 8.3 Vectors in a Cartesian Plane Represent vectors and determine the magnitude of the vectors in the Cartesian plane. Describe and determine the unit vector in the direction of a vector. Perform arithmetic operations onto two or more vectors. Solve problems involving vectors. 9 SOLUTION OF TRIANGLE 9.1 Sine Rule Make and verify conjectures on the relationship between the ratio of length of sides of a triangle with the sine of the opposite angles, and hence define the sine rule. Solve triangles involving sine rule. Determine the existence of ambiguous case of a triangle, and hence identify the conditions for such cases. Solve triangles involving ambiguous cases. Solve problems related to triangles using the sine rule. 9.2 Cosine Rule Verify the cosine rule. Solve triangles involving the cosine rule. Solve problems involving the cosine rule. 9.3 Area of A Triangle Derive the formula for area of triangles, and hence determine the area of a triangle. Determine the area of a triangle using the Heron’s formula. Solve problems involving areas of triangles. 9.4 Application of Sine Rule, Cosine Rule and Area of a Triangle Solve problems involving triangles. 10 INDEX NUMBER 10.1 Index Numbers Define index numbers and describe the use of it. Determine and interpret index numbers. Solve problems involving index numbers. 10.2 Composite Index Determine and interpret composite index with and without the weightage. Solve problems involving index numbers and composite index. F o r m 4 MT
TOPIC LEARNING STANDARDS UNDERST ANDING 1 2 3 1 CIRCULAR MEASURE 1.1 Radian Relate angle measurement in radian and degree. 1.2 Arc Length of a Circle Determine i. arc length, ii. radius, and iii. angle subtended at the centre of a circle. Determine perimeter of segment of a circle. Solve problems involving arc length. 1.3 Area of Sector of a Circle Determine i. area of sector, ii. radius, and iii. angle subtended at the centre of a circle. Determine the area of segment of a circle. Solve problems involving areas of sectors. 1.4 Application of Circular Measures Solve problems involving circular measures. 2 DIFFERENTIATION 2.1 Limit and its Relation to Differentiation Investigate and determine the value of limit of a function when its variable approaches zero. Determine the first derivative of a function () by using the first principle. 2.2 The First Derivative Derive the formula of first derivative inductively for the function = , is a constant and is an integer. Determine the first derivative of an algebraic function. Determine the first derivative of composite functions. Determine the first derivative of a function involving product and quotient of algebraic expressions. 2.3 The Second Derivative Determine the second derivative of an algebraic function. 2.4 Application of Differentiation Interpret gradient of tangent to a curve at different points. Determine equation of tangent and normal to a curve at a point. Solve problems involving tangent and normal. Determine the turning points and their nature. F o r m 5 MT
TOPIC LEARNING STANDARDS UNDERST ANDING 1 2 3 2.4 Application of Differentiation Solve problems involving maximum and minimum values and interpret the solutions. Interpret and determine rates of change for related quantities. Solve problems involving rates of change for related quantities and interpret the solutions. Interpret and determine small changes and approximations of certain quantities. Solve problems involving small changes and approximations of certain quantities. 3 INTEGRATION 3.1 Integration as the Inverse of Differentiation Explain the relation between differentiation and integration. 3.2 Indefinite Integral Derive the indefinite integral formula inductively. Determine indefinite integral for algebraic functions. Determine indefinite integral for functions in the form of + , where a and b are constants, n is an integer and ≠ −1. Determine the equation of curve from its gradient function. 3.3 Definite Integral Determine the value of definite integral for algebraic functions. Investigate and explain the relation between the limit of the sum of areas of rectangles and the area under a curve. Determine the area of a region. Investigate and explain the relation between the limits of the sum of volumes of cylinders and the generated volume by revolving a region. Determine the generated volume of a region revolved at the x-axis or the y-axis. 3.4 Application of Integral Investigate and explain the relation between the limit of the sum of areas of rectangles and the area under a curve. F o r m 5 MT
TOPIC LEARNING STANDARDS UNDERST ANDING 1 2 3 4 PERMUTATION AND COMBINATION 4.1 Permutation Investigate and make generalisation about multiplication rule. Determine the number of permutations for: (i) different objects. (ii) different objects taken r at a time. (iii) objects involving identical objects. Solve problems involving permutations with certain conditions. 4.2 Combination Compare and contrast permutation and combination. Determine the number of combinations of objects chosen from different objects at a time. Solve problems involving combinations with certain conditions. 5 PROBABILITY DISTRIBUTION 5.1 Random Variable Describe the meaning of random variable. Compare and contrast discrete random variable and continuous random variable. Describe the meaning of probability distribution for discrete random variables. Construct table and draw graph of probability distribution for discrete random variable. 5.2 Binomial Distribution Describe the meaning of binomial distribution. Determine the probability of an event for binomial distribution. Interpret information, construct table and draw graph of binomial distribution. Determine and describe the value of mean, variance and standard deviation for a binomial distribution. Solve problems involving binomial distributions. 5.3 Normal Distribution Investigate and describe the properties of normal distribution graph. Describe the meaning of standard normal distribution. Determine and interpret standard score, . F o r m 5 MT