Sec 4 Math Syllabus: Complete Overview for Parents (2026)

Secondary 4 is the final and most important year before O-Levels. The syllabus is the integration of all Sec 1-3 concepts — algebra, graphs, trigonometry, geometry, and equations.

Sec 4 will also introduce new topics like, Set Notation, Matrices, and Vectors that connect mathematics to real world uses in science, computing and advanced levels.

This is your child’s last chance to master everything before O-Levels. Our secondary math tuition ensures students have the foundational skills to master abstract concepts while providing proven exam strategies to build confidence and achieve O-Level excellence.

Consider downloading this revision note as a PDF for printing or reading. It will be delivered to your email inbox.

$secondary math revision notes$

✅ Key Topics Covered in Sec 4

1. Set Language and Notation

Students learn how to work with sets using:

Set notation (e.g. ∪, ∩, ⊂, ∅)
Venn diagrams
Complements, unions, and intersections

Set theory introduces basic logic and is commonly used in probability, computer science, and databases.

2. Data Analysis – Measures of Spread

This topic goes deeper into statistics. Students explore:

Cumulative frequency diagrams
Range, quartiles, interquartile range, and percentiles
Box-and-whisker plots
Standard deviation for both ungrouped and grouped data

These tools help students better describe and compare data sets.

3. Probability (Advanced)

Expanding from Sec 2 probability, students now learn to calculate:

Combined events
Mutually exclusive events using the addition rule
Independent events using the multiplication rule

They solve problems involving tree diagrams, lists, and real-world applications.

4. Matrices

Matrices are rectangular arrays of numbers used in many advanced fields. Students learn:

Matrix notation and equality
Addition, subtraction, and multiplication of matrices
Applications such as solving systems of equations or representing transformations

5. Vectors in Two Dimensions

Vectors are used to represent direction and movement. Students will:

Represent vectors with arrows or coordinates
Perform vector addition, subtraction, and scalar multiplication
Work with position vectors and parallel vectors
Apply vectors in geometry and real-world problems

Recap of Topics from Sec 1–3

Students will also revise and be tested on:

Algebra (simplification, expansion, factorisation, algebraic fractions)
Quadratic inequalities and graphs
Coordinate and function graphs
Trigonometry and applications
Congruence, similarity, geometry, and circle properties
Indices, standard form, speed, proportion, and data interpretation

Common Challenges Faced by Sec 4 Students

1. Managing Revision and Learning New Topics

Many students feel overwhelmed because they have to revise 3 years’ worth of content while also learning new Sec 4 topics like matrices and standard deviation. Without good time management, they may fall behind. Our teachers will guide students on how to balance their time between practicing old concepts and grasping new ones.

2. Confusing Sets and Venn Diagrams

Students often mix up symbols or misread shaded areas in Venn diagrams. Set notation and logical relationships (like union and intersection) are also new concepts that require consistent practice and proper understanding.

3. Probability Rules

The difference between mutually exclusive and independent events — and when to use addition or multiplication — can be confusing to many students.

4. Matrices and Vectors

These are completely new topics for most students. Many find it hard to follow the rules of matrix multiplication or differentiate similar properties between parallel vectors and collinear points

5. Understanding Spread and Standard Deviation

Calculating range is easy, but concepts like quartiles, interquartile range, and standard deviation are more abstract. Students must understand what the numbers mean to interpret the data correctly.

Before you go, download this entire revision note in PDF format for printing or reading. It will be delivered to your email inbox.

$secondary math revision notes$

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