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SECONDARY 3 MATHEMATICS PROGRAMMES

Most Secondary Three students face the following challenges with Secondary Elementary and Additional Mathematics:

- Shaky foundation for Lower Secondary Mathematics, especially in Algebra
- Having to learn new topics while trying to grasp old concepts
- Solutions tend to be long and more complex
- Some theorems are isolated and not built on prior topics
- Fall behind due to the fast pace of teaching in school

From our experience…
- Many Secondary Three students are fighting two battles:
       ➝ One, to sort out confusion about Lower Secondary mathematical concepts
       ➝ Two, to understand new topics that are more complex
- Students who are not strong in Mathematics soon begin to panic because Additional Mathematics is a new subject, with new mathematical concepts
- Students are demoralised because solutions are much longer and more complicated with little scaffolding from the questions
- As a result, some students experience a massive drop in grades at Secondary Three

Why your child needs help with Secondary Three Mathematics right now

➡️ While the new Secondary Three mathematical concepts in Elementary and Additional Mathematics may look daunting, clear guidance and tips from a good coach can point students in the right direction.

➡️ Preparing for O Level examinations should start at the beginning of Secondary Three, not Secondary Four.

At Cognitus Academy, we offer weekly regular Mathematics lessons and short intensive programmes to help students at every level of readiness.

Message from our Founder

Dr Daniel Chua

Founder and Director

Greetings, parents! I’m Dr. Daniel Chua, a former Head of Department in the Ministry of Education (MOE), an experienced PSLE exam marker, and a former lecturer at the National Institute of Education (NIE).

During my tenure as an MOE teacher, I had the privilege of instructing highly talented students from the Primary Gifted Education Programme (GEP). However, I also recognised that many of my non-GEP students possessed remarkable but untapped potential.

To address this, I decided to impart some of the critical thinking skills typically taught in the GEP to all my students. To my great satisfaction, these skills enabled them to significantly enhance their English grades.

This forms the foundation of our DEPTH Framework. My team and I employ a ‘gifted’ approach in teaching students of all proficiency levels, ensuring that they too can excel in the subject.

Our Teaching Team

We take pride in helping our students achieve breakthroughs in their results.
We are able to do that because of the strong team that we have built to teach, organise and administer our robust programmes.

At Cognitus Academy, our teachers are the heart and soul of our English programmes. We take great care in selecting our educators, and they go through an intensive 3-month training programme to build their teaching skills.

Our curriculum and teaching methods are always evolving to keep up with changes in the education system. This transformation is led by our curriculum team, which includes ex-MOE teachers, Heads of Department, Senior Teachers, and our experienced Cognitus instructors.

Secondary 3 Regular Mathematics Programme

At Cognitus Academy, our students will get to develop a keen interest in abstract mathematical concepts, learn how to present the solutions coherently and strengthen their skills and techniques in solving the questions efficaciously.

Conquering Mathematics through the DEPTH Framework

Our curriculum methodology provides 5 key elements to help students learn effectively during our Mathematics lessons.
This framework evaluates students’ current ability, helps to clear doubts, and expose students to exam-based questions.

Our curriculum structure includes asking probing questions in class to encourage students to explore, discover and build their confidence in Mathematics.

Deepened Curriculum, Heightened Learning

Apart from what is learnt from the school syllabus, students will develop a deeper insight into the curriculum. Understanding the core concepts deeply will also enhance students’ ability to apply heuristics to handle higher-order thinking questions.

Eliminated Errors and Misconceptions

Drills and practices develop fluency and heighten students’ awareness of their carelessness when solving Mathematics questions. Training students to understand their own tendencies greatly improves the accuracy of their calculations.

Practical and Authentic (Real World) Mathematics Teasers

Learning out of real-world context requires abstract thinking. This requirement stumps some students who need to see concrete examples. Students will learn to link Mathematics to authentic real-world problems, enhancing their number sense and conceptual development.

Think Critically and Mathematically

Thinking critically requires habits of mind and problem-solving skills. Merging critical and mathematical thinking makes the learning of Mathematics exciting and engaging. Learning Mathematics in this way unlocks the fun and challenging aspects of the subject.

Honed Precision


With carefully selected tasks for each lesson, students will learn how to be quick and accurate in their computations. Beyond procedural accuracy, students will also develop structural thinking that provides repeatable steps for analysing non-routine questions.

Hear What Satisfied Parents Have To Say

Developing Concepts in Secondary Three Elementary Mathematics

Our Secondary Three Elementary Mathematics Programme focuses on building foundations for acquiring critical knowledge, sharpening critical thinking skills and applying concepts effectively.

Acquire Knowledge

➡️ Revise Quadratic and Linear graphs and extend learning to graphs of cubic, reciprocal and exponential functions
➡️ Connect previously learnt topics of Pythagoras Theorem and Trigonometrical ratios to Further Trigonometry and its Applications
➡️ Link geometrical properties of 2-D and 3-D figures to Circular Measure, Area and Volume of Similar Figures and Solids and Geometrical Properties of Circles

Sharpen Skills

➡️ Learn how to integrate existing knowledge from Lower Secondary with Upper Secondary topics in order to tackle questions
➡️ Build a strong foundation in conceptual knowledge
➡️ Hone their presentation skills and answering techniques
➡️ Acquire analytical and communication skills that will enable them to make inferences, draw logical conclusions and evaluate solutions

Apply Concepts

➡️ Read and understand real-world problems and do mathematical modelling with relevant assumptions and simplifications.
➡️ Apply and interpret mathematical solutions in real-world contexts.

Secondary Three Elementary Mathematics Topics

Our Secondary Three Elementary Mathematics programme is modelled closely to the latest MOE syllabus,
covering the following topics in our lessons:

Topics
Quadratic Graphs and Functions
Graphs of Functions
Geometrical Properties of Circles
Further Trigonometry and Application
Arc Length, Area of Sector and Segment
Set Theory
Advanced Probability
Statistics
Vectors

*Lesson schedule may change due to students’ school exam schedules.

Developing Concepts in Secondary Three Additional Mathematics

Our Secondary Three Additional Mathematics Programme focuses on building foundations for acquiring critical knowledge, sharpening critical thinking skills and applying concepts effectively.

Acquire Knowledge

➡️ Learn advanced Algebra topics such as Equations and Inequalities, Indices and Surds, Polynomials and Partial fractions and Binomial expansions
➡️ Gain knowledge of the rules of logarithmic and exponential functions
➡️ Understand the properties and formulae of rectilinear figures and equation of a circle in a Cartesian plane
➡️ See the connections in the long list of trigonometric identities, addition formula, double-angle formula, and R-formula
➡️ Learn the properties of logarithmic, exponential and trigonometric graphs

Sharpen Skills

➡️ Enhance the skills in manipulating symbolic expressions and solutions involving surds, indices as well as logarithmic, exponential and trigonometric functions
➡️ Visualise rectilinear figures and circles in Cartesian plane and solve related questions using a combination of algebraic manipulations, geometrical properties, Midpoint Theorem and Shoelace Method
➡️ Use the list of trigonometric identities, addition formula, double-angle formula, and R-formula to simplify and prove trigonometric expressions, as well as to solve trigonometric equations
➡️ Sketch and transform logarithmic, exponential and trigonometric graphs
➡️ Hone the written communication skills to present solutions logically and coherently

Apply Concepts

➡️ Apply logarithmic and exponential functions to bio-medical fields
➡️ Connect sine and cosine functions to cyclical movements like ferris wheel and sound waves

Secondary Three Additional Mathematics Topics

Topics
Quadratic Functions
Quadratic Inequalities and Nature of Roots
Surds
Polynomial and Partial Fractions
Exponential and Logarithmic Functions
Binomial Theorem
Coordinate Geometry
Circles
Application of Straight Line Graphs
Trigonometric Functions
Trigonometric Identities and Equations
Plane Geometry and Proofs

Secondary 3 Mathematics Power Up Programme

In our experience, many students find A Maths difficult because they are already weak in Algebra and other big topics. Losing confidence for Maths at the start of Sec 3 may spiral downwards to greater fears and worry. Therefore, it is important to level up for A Maths right now and start building towards A1 for the subject.

To support Sec 3 students who need a boost in A Maths, our team of ex-MOE teachers, exam markers and Heads of Department is pleased to launch the Sec 3 A Maths Power Up Programme.

➡️ Conceptual Alignment

Each lesson will focus on the interconnection between related topics. Students will develope clear understanding of the core knowledge within each topic through our concise summary. In addition, students will learn the key skills that help them confidently solve commonly-tested questions and maximise the marks scored through clear presentation. More importantly, students get to consolidate the learning through hands-on practice with the teacher’s coaching.

sec 2 math topics

➡️ Topics Covered

In this 3-day Programme, we will cover the following topics that are foundational to A Maths.
✅ Quadratic Functions, Roots and Inequalities
✅ Polynomials and Partial Fractions
✅ Exponential and Logarithmic Functions and related Graphs

If you are ready...

📍 Goldhill Plaza

Programme Run Date and Time
Sec 3 A Maths Power Up
Run 1
20 - 22 Jun

1:30pm – 4pm

*All schedules subject to changes. Classes are usually fully subscribed 1 month in advance. Sign up now to avoid disappointment.

Cognitus 360 to Super-charge your Child's Academic Journey

At Cognitus Academy, we provide your child with comprehension learning through Cognitus 360. This framework accompanies your child at every stage of their learning journey with us, ensuring that all their learning requirements are catered to.

The Cognitus 360 includes a carefully crafted process that addresses your child's diverse needs in conjunction with their weekly lessons!

Schedule a Call

Once you indicate your interest in our programme, our teachers will give you a call. Be prepared to answer their questions about your child's strengths and weaknesses in the relevant subject. This will enable our teachers to further elaborate on addressing your child's weaknesses with our curriculum.

Attend Our Weekly Lessons

Weekly lessons provide guidance and teaching of crucial skills and concepts that will enhance your child’s learning of English.

Through weekly practices and homework assignments, your child will develop mastery and fluency in all important areas of learning.

Past Year Exam Papers for Deeper Diagnosis

We maintain a comprehensive library of past year papers with answer sheets as supplementary resources for students to practice.

Students should identify their areas of weakness from their Mock Exam scorecard and independently work on these areas using the past year papers provided.

Access Lesson Recordings

Our online lesson recordings are shared with students who are unable to attend the lesson live and opted for our Live Online Lessons, providing opportunities for students to engage in self-paced learning before attending the next lesson. Your child will never fall behind!

Holiday Workshops for the Extra Boost

We have a range of additional programmes designed to supplement weekly lessons in order to maximise learning time during school holidays.

Introducing Cognitus 360 Plus

Cognitus YouTube

Uncover instructional films pertinent to your child's needs and encourage them to engage in self-directed learning. 

WhatsApp Support

Parents will be able to keep in touch with our teachers should there be any enquiries anytime.

Additional Materials

We also feature our Students' Works, publish Blog Articles and have a Centre Library for students to browse through our collection of books for reading.

Media Features

You might have seen us here!

Our efforts to always do better for our students have not gone unnoticed!

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Frequently Asked Questions

How is your Secondary Mathematics programme different from other Mathematics tuition programmes?
Cognitus Academy applies the DEPTH Framework where we ensure that learning does not simply come from drill and practice. DEPTH Framework focuses on real-life application of Mathematics and problem-solving skills. We follow a structured lesson plan where students apply their knowledge in bite-size practices and move on to problem sums to build their confidence. Students who are strong in Mathematics will be stretched through practices with non-routine questions.
My child is not doing well in Paper 2 (Problem Sums). How will your programme help him/her?
Our diagnostic process starts from learning the needs of every student. Once we have identified the main cause of the student’s error, we will embark on a remediation plan that runs parallel with our regular lessons. Students often struggle because of conceptual misunderstanding, lack of comprehension for the question, lack of confidence and carelessness. From there, we will focus on the best course of remediation for your child.
How does my child build up his/her foundation in Mathematics?
One key foundation in the DEPTH Framework is the ability to connect mathematical concepts with real-life examples. Starting from the concrete application of Mathematics, your child can then develop understanding in using abstract (numbers and models) forms of presentation for their interpretation and solution of each question. Our experienced teachers will also pace your child towards success by helping them to create small victories that lead to big success in Mathematics.
If my child has Mathematics questions from school that he is unable to solve, can he consult the centre’s teachers?
Certainly! The purpose of conducting a small-class Mathematics tuition is to create a structured, yet individualised learning experience for our students. Please send all your child’s questions from school and individual practices our way.
How is a typical lesson like?
Each lesson runs for 120 minutes.
– For the first 15 minutes, we will go through corrections from previous homework. This step is critical in helping students correct misconceptions.
– The remaining part of the lesson will focus on problem sums where students are taught effective and efficient steps to solve higher-order thinking questions.
What is the difference between IP/IB and O level Mathematics?
90% of the IP/IB Mathematics topics are similar to that of the O level Mathematics. Our programmes are created to teach our students the concepts and to stretch them further to higher order thinking. Hence, IP/IB students will continue to feel engaged during lessons while the O level students’ potential are stretched.

Still can’t decide which Mathematics Programme to enrol in?

We understand that choosing the right programme is an important decision because we have worked with hundreds of parents who are just as concerned as you about their child’s results. If you would like to discuss your needs with one of our curriculum specialists, fill out the form below and we will be in touch with you.