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.
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.
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 |
Termly Assessment
Our students come from a range of different schools with different academic cultures.
Do you know how your child compares with another student from a different school?
We conduct termly assessments for our students to assess their current progress and see where they stand relative to their classmates from different schools.
Our tests comprise of the most challenging questions from past year exams and will be able to diagnose students' weaknesses. From there, we will reinforce Mathematical skills and exam strategies.
Excellent strategies require excellent execution
Our team of experienced teachers and Mathematics specialists are well-versed in the DEPTH Framework and
are fully dedicated to help your child grow and improve.
Mr Stewart Teng
Chief Mathematics Consultant
As an experienced Mathematics educator of more than 20 years, Mr Teng has coached hundreds of Primary and Secondary students towards scoring distinctions for their Maths exams.
It is no surprise that students who apply his methods consistently score distinctions in their Maths exams. In fact, his students’ distinction rates of 88% for PSLE students and 80% for O Level students are way above national averages.
A testament to an illustrious career in the Ministry of Education, Mr Teng has been awarded the prestigious Outstanding Youth in Education (OYEA) Award and made vital contributions to education in his capacity as Head of Department and Vice-Principal (Designate) of one of the top performing schools in Singapore. Throughout his stellar MOE career, Mr Teng’s passion in maths education never wavered.
Mr Joel Chang
Education Consultant / Teacher
Mr Joel Chang teaches Mathematics at the Secondary and Pre-University levels. A Mathematics fanatic since primary school, he deeply enjoys the rigour of learning complex levels of Mathematics, allowing him to consistently ace Mathematics and graduate from NUS with First Class Honours (projected). Learning Mathematics at an advanced level gives Mr Chang the opportunity to combine his passion for mathematical theory and application through his research on machine learning.
Always the enthusiastic Mathematics teacher, Mr Chang has taught Mathematics at various levels of understanding—from high school students to university undergraduates—equipping students to form insightful connections intuitively and propels them to excel academically. Mr Chang finds deep satisfaction in igniting interest in Mathematics among his students, and pushing them to explore concepts beyond the school curriculum.
Our Teaching Team
Cognitus Academy takes 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 Mathematics programmes.
Having been a teacher trainer at the National Institute of Education (NIE), Dr Daniel Chua has not only crafted a solid curriculum for our students, but also an effective training programme for our teachers.
At Cognitus Academy, teachers form the foundation of our Mathematics programmes. Prospective teachers are screened meticulously and undergo a rigorous 3-month training programme to develop core competencies of a teacher. Teaching interns also develop academic and philosophical roots in their pedagogy by studying the relevant materials in-depth and observing senior teachers in action before they enter the classrooms to teach.
After the completion of formal training, new teachers will continue to go through robust training and meet regularly to sharpen their problem-solving skills, explore innovative and effective curriculum for students, and refine teaching methods to enhance the students' mastery of the subject.
Our curriculum and pedagogy are continuously refined and updated in accordance with the changes in the education system by our curriculum team comprising of ex-MOE teachers, Heads of Department, Senior Teachers, PSLE markers and experienced Cognitus teachers.
Here’s what students say after they have attended our Secondary 3 Mathematics Programmes
Highest in Class!
“Emath Paper 1 – 71/80
Emath Paper 2 – 86/100
Amath Paper – 82/90
Amath is highest in class, second highest in cohort!”
Student Hannah
Aced both Math Papers
“I did well for both Math :)) Thank you for all the clear teaching and help for the past 4 years!! It has really allowed me to improve on Math by a lot 😀
FYE
C Math – 91%
A Math – 87%”
Student Josthan
Math - 95, Amath - 93!
“My Math is 95 and my Amath is 93! Also really really wanna thank you for all the help you’ve given me in these close to 8 years, I’ve really grown so much in my confidence towards Math since P3 and I’m really super super thankful for everything you’ve done to help me in my understanding of Math.”
Student Angelica
Interested to find out if Cognitus Academy's Secondary Regular Mathematics Programme fits your child's learning needs?
All new students are offered an immersion session to get a taste of the quality teaching and engagement in our classrooms.
✅ Students should email us their recent test papers in advance for our teachers to look through. A 15-minute pre-lesson diagnostic assessment will be scheduled with the student.
✅ Experience our teachers’ lively and engaging classroom teaching, as they optimise student engagement and provide easily comprehensible instructions in our immersion session.
✅ Evaluation of the student’s learning in class will be given to parents after the immersion session.
Class Size
In order to optimise precious time in every lesson, we have kept our class sizes small. Small class sizes ensure that every student gets the attention from their teachers and have meaningful interaction among classmates and teachers. Such a setting is conducive for clarifying doubts and sharing different points of view.
The DEPTH Framework develops critical thinking and takes time to master. Although some students see improvement right away, most will take 2-3 months to see results.
In order to help your child improve his/her Mathematics results as soon as possible, schedule an immersion session with us today!
Additional support for Members of our Community
Apart from delivering the strongest Mathematics curriculum possible, what else can we do to add value to our students? While we will never stop innovating, we are currently supplementing our Mathematics courses with the following package we like to call Cognitus Plus.
Cognitus Online
Our very own student portal, Cognitus Online, provides supplementary materials and past exam papers for students to practise. This is a portal that not only supports our online students but, also our students attending physical classes.
To learn more about Cognitus Online, click READ MORE.
Blog
Our Blog pages feature study tips, exam techniques and model compositions to support our students and parents.
To learn more about blog, click READ MORE.
Good strategies will only be able to transform students' results if they are motivated
Your child may have been attending Mathematics tuition but has not been seeing improvement.
Why is that so?
The fact is, the lessons your child has been attending are not pitched according to his/her level of readiness.
If students are unable to grasp the lesson, forcing them to finish their Maths assignments demotivates them.
If the lessons are too simple, your child will be bored and unmotivated.
At Cognitus Academy, our programme is crafted to MEET every child’s level of readiness and motivate them to achieve their FULL potential.
Through our own passion for the subject, our trained and experienced teachers ignite students’ LOVE and INTEREST in Mathematics .
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.
➡️ 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.
Frequently Asked Questions
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.
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.
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.
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.
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.