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mathwithcye

KSSM Additional Mathematics Form 4 • DLP

Chapter 1: Functions 1.1 Functions 📖 TB pp. 2–11
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Cadet Mathematician Class 4 Science 1
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Lesson Progression (PAK-21 Active Learning) 0% Complete
Stage A • Mission Brief

Introduction to Functions (Fungsi)

Mastering relation mappings, vertical line tests, absolute value functions, and domain/range definitions.

🎯 The Vending Machine Paradox

Imagine pressing the button for an iced drink at a smart vending machine:

  • Scenario 1: You press Button #1, and it dispenses a can of green tea every single time.
  • Scenario 2: You press Button #2, and it randomly shoots out either a cola OR a coffee!
  • Scenario 3: You press Button #3, it eats your token, and dispenses nothing!

In which scenario is the machine truly functioning? In mathematics, a relation is a function if and only if every single input maps to one and only one output!

📋 Ministry of Education DSKP Learning Standards:

  • 1.1.1: Explain function using graphical representations and notations (arrow diagrams, Cartesian graphs, vertical line tests, absolute value functions).
  • 1.1.2: Determine domain, codomain, and range of discrete and continuous functions.
  • 1.1.3: Determine the image of a function given the object and vice versa (algebraic, rational, and modulus equations).
SPM Examiner Tip

SPM Paper 1 frequently tests whether students recognize that unmapped elements in the codomain do not invalidate a function, whereas unmapped elements in the domain do!

Stage B • Discovery Lab

Digital Manipulatives & Conceptual Labs

Interact with dynamic digital models before formal mathematical definitions.

Select Relation Type:
The Golden Rule of Functions:

Every element $x \in X$ must map to one and only one element $y \in Y$. Elements in Set Y (Codomain) can be left unmapped, but NO element in Set X may have 0 or $\ge 2$ images!

Choose Test Curve:
Move Vertical Test Line ($x = c$): 1.0

Intersection Points Detected: 1

Coefficient $a$ (Gradient): 2
Constant $b$ (Shift): -1
Test Object $x$: 1.5
Vertex Coordinates:

(0.50, 0)

The dashed line shows the original line $y = ax + b$. The modulus $|ax + b|$ reflects everything below the x-axis upward!

Stage C • Interactive Worked Examples

Official Textbook Worked Examples

Step-by-step interactive breakdown of core textbook questions (Form 4 Add Maths pp. 3–10).

Stage D • Guided Practice

Scaffolded Formative Practice

Direct textbook practice with multi-tier hints and instant feedback (Self Practice 1.1–1.3).

Stage E • Independent Challenge

Tiered Independent Mastery (Intensive Practice 1.1)

Evaluate your mastery with Foundation, Intermediate, and Advanced (KBAT) textbook problems.

Stage F • Exit Ticket & Report

Diagnostic Assessment & Verified Student Report

Complete the 3-question diagnostic assessment to unlock and print your official certificate.