Lesson Notes By Weeks and Term v4 - SHS 1
PRINCIPLES OF CALCULUS
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PRINCIPLES OF CALCULUS
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Subject: Additional Mathematics
Class: SHS 1
Term: 2nd Term
Week: 10
Grade code: 1.3.1.LI.4
Strand code: 3
Sub-strand code: 1
Content standard code: 1.3.1.CS.1
Indicator code: 1.3.1.LI.4
Theme: CALCULUS
Subtheme: PRINCIPLES OF CALCULUS
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This lesson introduces the fundamental concept of the derivative. We will move from a simple idea we already know—the gradient (or slope) of a straight line—to a powerful new idea: the gradient of a curve at a single point. This is the heart of differential calculus. Imagine a tro-tro driver accelerating from a bus stop. Their speed is not constant; it's changing every second. How can we find their exact speed at the 3-second mark? This lesson will give us the mathematical tool to answer such questions. We will learn that the derivative is simply the instantaneous rate of change, and we will discover how to find it using the concept of limits.
Materials: Whiteboard/Chalkboard, Markers/Chalk, Graph paper (optional), Calculators.
Teacher's Note: This topic bridges algebra and calculus. Ensure learners are comfortable with algebraic expansion (e.g., `(x+h)²`) and simplification before proceeding. Part A: From Average Rate of Change to Instantaneous Rate of Change (The Big Idea)
Let's start with a familiar situation. Imagine you are travelling from Accra to Kumasi, a distance of about 250 km. If the journey takes 5 hours, what is your average speed? Average Speed = Total Distance / Total Time = 250 km / 5 hours = 50 km/h.
But was your speed *exactly* 50 km/h for the entire journey? Of course not! You slowed down in towns like Nsawam and sped up on open stretches of the motorway. 50 km/h is the average rate of change of your position.