Upper Secondary Mathematics
Explore the infinite potential of your child through our excellent Upper Secondary Mathematics programme.
Prepare your child for more complex Mathematics that are essential to our rapidly developing world.
Our Upper Secondary programme will help your child sharpen and hone their Mathematics skills, prepare them for the intense challenges at the 'O' levels or final year IP and guide them on the path to achieving distinctions in Mathematics.
Common Challenges Upper Secondary Students Face
1. Increased Complexity in Topics & Higher-Order Thinking
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The jump from Lower Secondary to Upper Secondary Math is steep, with topics such as trigonometry, differentiation and integration, and advanced algebra (including indices) requiring a deeper conceptual understanding.
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Students must transition from procedural problem-solving to applying mathematical reasoning in unfamiliar contexts
2. Challenging Application & Higher-Difficulty Exam Questions
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Questions are no longer straightforward and often integrate multiple concepts within a single problem.
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Real-world applications demand strong analytical skills to interpret, model, and solve problems effectively.
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Many students struggle with proving mathematical arguments, as topics such as trigonometric proofs and quadratic inequalities require structured reasoning
3. Exam Time Constraints & Rigorous Marking Schemes
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Upper Secondary exams test both speed and accuracy, requiring efficient problem-solving strategies.
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Method marks play a crucial role as losing a single step in calculations can significantly affect the final score.
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Structured and logical answer presentation is essential to avoid unnecessary mark deductions.
How Math Note Prepares Your Child for Success
1. Systematic & Syllabus-Aligned Mastery Learning
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Our lessons follow the MOE curriculum closely, ensuring students stay ahead in school.
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Complex topics such as differentiation, integration, and vectors are broken down into easy-to-follow steps.
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We use real-world examples to illustrate abstract concepts, making learning more intuitive.
2. Strong Focus on Problem-Solving & Critical Thinking
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We teach students how to analyze, strategize, and tackle complex problems with confidence.
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Tutors guide students through different problem-solving techniques to minimize errors and enhance accuracy.
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With guided practice, students develop resilience and the ability to handle unfamiliar exam questions effectively.
3. Essential Exam Techniques to Maximize Scores
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We emphasize proper answer presentation to ensure full method marks are awarded.
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Exam-style practice questions expose students to high-difficulty assessments, preparing them for O-Level and school exams.
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Time management strategies help students complete papers efficiently without compromising accuracy.
Why Parents Trust Math Note: Our Unique Teaching Approach
1. Small Class Sizes for Personalized Support
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Individualized attention ensures students receive the help they need to master difficult topics.
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Tutors track progress closely and provide targeted support to address weak areas.
2. Comprehensive & High-Quality Learning Materials
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Step-by-step Conceptual Notes – Clear, structured explanations tailored to the MOE syllabus.
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Progressive Practice Questions – Strengthens understanding from foundational to advanced levels.
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Exam-Grade & Higher-Order Thinking Questions – Ensures students are fully prepared for challenging assessments.
3. Structured Lessons for Effective Learning
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Each lesson builds from conceptual mastery to guided practice and application in exam-style questions.
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Students learn efficient problem-solving strategies to enhance accuracy and confidence.
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Regular assessments help track progress and reinforce learning for long-term success.
At Math Note, we ensure Upper Secondary students develop the skills, confidence, and strategies to excel in their exams and beyond.
Topic Outlines
Sec 3 Topic Outline (E-Math)
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Indices
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More about Quadratic Equations
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Linear Inequalities
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Conditions of Congruence and similarity
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Coordinate geometry
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Functions and Graphs
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Trigonometry
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Application of Trigonometry
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Arc Lengths, Sector Areas and Radian Measure
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Properties of circles
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Sec 1 and 2 Topics
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Problems in real- world contexts
Sec 4 Topic Outline (E-Math)
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Set Language and Notation
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Data Analysis - Measure of Spread
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Probability
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Matrices
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Vectors in Two Dimensions
Sec 1 to 3 Topics
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Numbers and their Operations
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Ratio and proportion
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Percentage
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Rate and speed
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Algebraic expressions and formulae
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Functions and graphs
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Equations and inequalities
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Set language and notation
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Matrices
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Angles, triangles and polygons
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Congruence and similarity
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Properties of circles
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Pythagoras’ theorem and trigonometry
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Mensuration
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Coordinate geometry
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Vectors in two dimensions
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Data handling and analysis
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Probability
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Problems in real- world contexts
Sec 3 Topic Outline (A-Math)
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Equations and inequalities
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Indices and surds
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Polynomials and Partial Fractions
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Binomial expansions
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Power, Exponential, Logarithmic, and Modulus functions
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Trigonometric functions, identities and equations
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Coordinate geometry in two dimensions
Sec 4 Topic Outline (A-Math)
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Proofs in plane geometry
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Differentiation and integration
Course Contents
Each topic includes:
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Detailed explanation of concepts and principles
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Comprehensive revision notes
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Individualised explanation and support tailored to each student's requirements
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Worksheets encompassing all subtopics within the same chapter
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Practice questions on different level of difficulties.
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Challenging revision questions
Each term includes:
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Topical revision Papers
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Mock Exam/Test Papers
Students will:
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develop the ability to recognise similar type of questions
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learn the technique to comprehend exam questions and solve accordingly
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acquire the logical reasoning skill to solve questions
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practice good working presentation
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develop good habit of self-checking on incorrect steps
4052 Elementary Mathematics O-level Examination Syllabus
Paper 1
Duration: 2 hours 15 minutes
Number of questions: 26 short answer questions
Candidates are required to answer ALL questions
Marks: 90
Weighting: 50%
Paper 2
Duration: 2 hours 15 minutes
Number of questions: 9-10 questions of varying marks and length. The last question in this paper will focus specifically on applying mathematics to a real-world scenario.
Candidates are required to answer ALL questions
Marks: 90
Weighting: 50%
More information about the GCE O-level examination syllabus can be found here
4049 Additional Mathematics O-level Examination Syllabus
Paper 1
Duration: 2 hours 15 minutes
Number of questions: 12-14 questions of varying marks and length
Candidates are required to answer ALL questions
Marks: 90
Weighting: 50%
Paper 2
Duration: 2 hours 15 minutes
Number of questions: 9-11 questions of varying marks and length, up to 12 marks per question.
Candidates are required to answer ALL questions
Marks: 90
Weighting: 50%
More information about the GCE O-level examination syllabus can be found here
Sample Learning Notes
Elementary Mathematics
Simple and clear diagram to help students to understand the common terms used in exam questions.
Explanation on the mathematical reason behind to derive it instead of just feeding student with formulae
Additional Mathematics
Additional fun facts for the students to induce their critical thinking to handle different type of questions during exam.
Highlight of useful results that are frequently use in the topic to the students.
Present a systematic approach and method to the students to help them solve typical common exam questions
There are more pages to it.
Please join us for lesson to get the complete set of materials for the whole syllabus.
Testimonials
Although elementary mathematics was still my best subject, it was like hell for me learning Additional Mathematics, constantly being behind everyone else and understanding concepts after we have already gone on to the subsequent new ones. As expected, I failed my Additional Mathematics for Mid-Year Examinations. I was downhearted. I had never felt so demoralised and discouraged for any subject before. Hence, this led to my efforts in Additional Mathematics being half-hearted and my confidence in the subject to drop.
I started putting in effort in Additional Mathematics, but it was not enough. When my End-of-Year examination results were released, I felt utterly disappointed and astonished to see that I had failed once again. I told myself that this could not continue any longer, hence I sought for a tuition teacher for Additional Mathematics, and got to know Ms Chua from a friend.
After going through Ms Chua’s lessons, I felt that the extra practice done really helped me to get the hang of new concepts. As such, I went into Secondary 4 feeling prepared for Additional Mathematics. I started to find doing A-Math questions fun as I could understand what I was doing for once, hence doing more practice during my free time. This helped me to improve drastically and I had achieved A1 for Mid-Year Examinations. Receiving my results, I was overjoyed and felt the tears forming in my eyes. I could finally say I have a chance in scoring well for my A-math during O-Levels!
In the end, I received A1 for my O-levels!
Toh Shee Theng, Sec 4
Yishun Town Secondary
One of the challenges I faced when doing Math is not used to new information, thus it is hard to accept the info as it is (e.g. log, binomial), to me they seem so foreign and therefore I feel uncomfortable when learning them, I got help from Miss Chua and her explanations made me understand the topics that I was weak in better.
When I was unable to solve certain problems, I often feel frustrated and irritated, especially after many failed attempts. However after attending Miss Chua’s lesson and when I could solve the questions given to me, I feel a great sense of accomplishment and i become more confident.
My advice to students facing difficulties in Math is one should never give up and have the will to persist. Miss Chua is encouraging and I am grateful for that as it helped me to carry on when I faced difficulties.
He Ningxin, Sec 4
Yishun Town Secondary
"I was not doing well for my Math from Sec 1 to 3. I had quite a few math tuition before I joined Math Note Learning Centre. It didn't work out very well and I kept quitting my tuition because I really couldn't understand. When I received my test result in Sec 4 Term 1, I was very depressed and I thought I needed to do something.
I joined Math Note at the beginning of Term 2 and my results started to improve gradually. I got a B4 for my Mid-year Examination and and A2 for my prelims. I couldn't believe myself that time. At the same time, I was very happy and my confidence in Math increased.
I got an A1 for my actual O-levels! Thank you Miss Chua for your help and guidance!
Keryn Teo, Sec 4
Punggol Secondary School
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