Learning Objectives
What You Should Be Able To Do
Interactive Study Tools
These tools are here to help students slow down and think about the method before rushing to an answer.
Tool 1
Study Planner
Use this to break a topic into small study sessions.
Plan: A clear breakdown will appear here.
Tool 2
Method Reminder
This quick guide reminds students what to do when they feel stuck.
- Read the story: what is the question really asking?
- Choose the method: identify the correct idea before calculating.
- Show the reason: do not skip the logic.
- Check the answer: make sure it fits the situation.
1. The Derivative (Differentiation)
Simple explanation: This section is about change. It explains how calculus helps us measure how quickly something is increasing or decreasing.
Differentiation measures the rate of change of a function. Geometrically, it is the slope of the tangent line at any point.
If f(x) = xⁿ, then f'(x) = nxⁿ⁻¹
2. Applications of Differentiation
Simple explanation: This section is about change. It explains how calculus helps us measure how quickly something is increasing or decreasing.
- Maxima/Minima: Find where the derivative equals zero (f'(x) = 0).
- Curve Sketching: Use derivatives to find where the graph is increasing (f'(x) > 0) or decreasing (f'(x) < 0).
- Kinematics: Velocity is the derivative of position; Acceleration is the derivative of velocity.
Examiner Tip
💡 Examiner Tip: Always state your units! If you are asked to find the rate of change of volume with respect to time, your answer must be in cm³/s.📝 Exam Style Questions
Simple explanation: This section explains the main idea in simple English first, then builds toward the formal method used in exam questions.
Easy Q1: Find the derivative of f(x) = x³ + 4x² - 5.
Medium Q2: Find the stationary points of f(x) = x² - 4x.
A1: f'(x) = 3x² + 8x.
A2: Set f'(x) = 2x - 4 = 0. So x = 2. Plug in: f(2) = 4 - 8 = -4. Stationary point: (2, -4).