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| WK | LSN | TOPIC | SUB-TOPIC | OBJECTIVES | T/L ACTIVITIES | T/L AIDS | REFERENCE | REMARKS |
|---|---|---|---|---|---|---|---|---|
| 2 | 1 |
Differentiation
|
Introduction to Rate of Change
|
By the end of the
lesson, the learner
should be able to:
-Understand concept of rate of change in daily life -Distinguish between average and instantaneous rates -Identify examples of changing quantities -Connect rate of change to gradient concepts |
In groups, learners are guided to:
-Discuss speed as rate of change of distance -Examine population growth rates -Analyze temperature change throughout the day -Connect to gradients of lines from coordinate geometry |
Exercise book
-Graph examples |
KLB Secondary Mathematics Form 4, Pages 177-182
|
|
| 2 | 2 |
Differentiation
|
Introduction to Rate of Change
|
By the end of the
lesson, the learner
should be able to:
-Understand concept of rate of change in daily life -Distinguish between average and instantaneous rates -Identify examples of changing quantities -Connect rate of change to gradient concepts |
In groups, learners are guided to:
-Discuss speed as rate of change of distance -Examine population growth rates -Analyze temperature change throughout the day -Connect to gradients of lines from coordinate geometry |
Exercise book
-Graph examples |
KLB Secondary Mathematics Form 4, Pages 177-182
|
|
| 2 | 1 |
Differentiation
|
Introduction to Rate of Change
|
By the end of the
lesson, the learner
should be able to:
-Understand concept of rate of change in daily life -Distinguish between average and instantaneous rates -Identify examples of changing quantities -Connect rate of change to gradient concepts |
In groups, learners are guided to:
-Discuss speed as rate of change of distance -Examine population growth rates -Analyze temperature change throughout the day -Connect to gradients of lines from coordinate geometry |
Exercise book
-Graph examples |
KLB Secondary Mathematics Form 4, Pages 177-182
|
|
| 2 |
Opener exam |
|||||||
| 2 | 5 |
Differentiation
|
Average Rate of Change
|
By the end of the
lesson, the learner
should be able to:
-Calculate average rate of change between two points -Use formula: average rate = Δy/Δx -Apply to distance-time and other practical graphs -Understand limitations of average rate calculations |
In groups, learners are guided to:
-Calculate average speed between two time points -Find average rate of population change -Use coordinate points to find average rates -Compare average rates over different intervals |
Exercise books
-Calculators -Graph paper |
KLB Secondary Mathematics Form 4, Pages 177-182
|
|
| 2 | 6 |
Differentiation
|
Average Rate of Change
|
By the end of the
lesson, the learner
should be able to:
-Calculate average rate of change between two points -Use formula: average rate = Δy/Δx -Apply to distance-time and other practical graphs -Understand limitations of average rate calculations |
In groups, learners are guided to:
-Calculate average speed between two time points -Find average rate of population change -Use coordinate points to find average rates -Compare average rates over different intervals |
Exercise books
-Calculators -Graph paper |
KLB Secondary Mathematics Form 4, Pages 177-182
|
|
| 2 | 7 |
Differentiation
|
Average Rate of Change
|
By the end of the
lesson, the learner
should be able to:
-Calculate average rate of change between two points -Use formula: average rate = Δy/Δx -Apply to distance-time and other practical graphs -Understand limitations of average rate calculations |
In groups, learners are guided to:
-Calculate average speed between two time points -Find average rate of population change -Use coordinate points to find average rates -Compare average rates over different intervals |
Exercise books
-Calculators -Graph paper |
KLB Secondary Mathematics Form 4, Pages 177-182
|
|
| 3 | 1 |
Differentiation
|
Instantaneous Rate of Change
|
By the end of the
lesson, the learner
should be able to:
-Understand concept of instantaneous rate -Recognize instantaneous rate as limit of average rates -Connect to tangent line gradients -Apply to real-world motion problems |
In groups, learners are guided to:
-Demonstrate instantaneous speed using car speedometer -Show limiting process using smaller intervals -Connect to tangent line slopes on curves -Practice with motion and growth examples |
Exercise books
|
KLB Secondary Mathematics Form 4, Pages 177-182
|
|
| 3 | 2 |
Differentiation
|
Instantaneous Rate of Change
|
By the end of the
lesson, the learner
should be able to:
-Understand concept of instantaneous rate -Recognize instantaneous rate as limit of average rates -Connect to tangent line gradients -Apply to real-world motion problems |
In groups, learners are guided to:
-Demonstrate instantaneous speed using car speedometer -Show limiting process using smaller intervals -Connect to tangent line slopes on curves -Practice with motion and growth examples |
Exercise books
|
KLB Secondary Mathematics Form 4, Pages 177-182
|
|
| 3 | 3 |
Differentiation
|
Instantaneous Rate of Change
|
By the end of the
lesson, the learner
should be able to:
-Understand concept of instantaneous rate -Recognize instantaneous rate as limit of average rates -Connect to tangent line gradients -Apply to real-world motion problems |
In groups, learners are guided to:
-Demonstrate instantaneous speed using car speedometer -Show limiting process using smaller intervals -Connect to tangent line slopes on curves -Practice with motion and growth examples |
Exercise books
|
KLB Secondary Mathematics Form 4, Pages 177-182
|
|
| 3 | 4 |
Differentiation
|
Instantaneous Rate of Change
|
By the end of the
lesson, the learner
should be able to:
-Understand concept of instantaneous rate -Recognize instantaneous rate as limit of average rates -Connect to tangent line gradients -Apply to real-world motion problems |
In groups, learners are guided to:
-Demonstrate instantaneous speed using car speedometer -Show limiting process using smaller intervals -Connect to tangent line slopes on curves -Practice with motion and growth examples |
Exercise books
|
KLB Secondary Mathematics Form 4, Pages 177-182
|
|
| 3 | 5 |
Differentiation
|
Instantaneous Rate of Change
|
By the end of the
lesson, the learner
should be able to:
-Understand concept of instantaneous rate -Recognize instantaneous rate as limit of average rates -Connect to tangent line gradients -Apply to real-world motion problems |
In groups, learners are guided to:
-Demonstrate instantaneous speed using car speedometer -Show limiting process using smaller intervals -Connect to tangent line slopes on curves -Practice with motion and growth examples |
Exercise books
|
KLB Secondary Mathematics Form 4, Pages 177-182
|
|
| 3 | 6 |
Differentiation
|
Instantaneous Rate of Change
|
By the end of the
lesson, the learner
should be able to:
-Understand concept of instantaneous rate -Recognize instantaneous rate as limit of average rates -Connect to tangent line gradients -Apply to real-world motion problems |
In groups, learners are guided to:
-Demonstrate instantaneous speed using car speedometer -Show limiting process using smaller intervals -Connect to tangent line slopes on curves -Practice with motion and growth examples |
Exercise books
|
KLB Secondary Mathematics Form 4, Pages 177-182
|
|
| 3 | 7 |
Differentiation
|
Gradient of Curves at Points
|
By the end of the
lesson, the learner
should be able to:
-Find gradient of curve at specific points -Use tangent line method for gradient estimation -Apply limiting process to find exact gradients -Practice with various curve types |
In groups, learners are guided to:
-Draw tangent lines to curves on manila paper -Estimate gradients using tangent slopes -Use the limiting approach with chord sequences -Practice with parabolas and other curves |
Exercise books
-Rulers -Curve examples |
KLB Secondary Mathematics Form 4, Pages 178-182
|
|
| 4 | 1 |
Differentiation
|
Derivative of y = x^n (Basic Powers)
|
By the end of the
lesson, the learner
should be able to:
-Find derivatives of power functions -Apply the rule d/dx(x^n) = nx^(n-1) -Practice with x², x³, x⁴, etc. -Verify using first principles for simple cases |
In groups, learners are guided to:
-Derive d/dx(x²) = 2x using first principles -Apply power rule to various functions -Practice with x³, x⁴, x⁵ examples -Verify selected results using definition |
Exercise books
|
KLB Secondary Mathematics Form 4, Pages 184-188
|
|
| 4 | 2 |
Differentiation
|
Derivative of y = x^n (Basic Powers)
|
By the end of the
lesson, the learner
should be able to:
-Find derivatives of power functions -Apply the rule d/dx(x^n) = nx^(n-1) -Practice with x², x³, x⁴, etc. -Verify using first principles for simple cases |
In groups, learners are guided to:
-Derive d/dx(x²) = 2x using first principles -Apply power rule to various functions -Practice with x³, x⁴, x⁵ examples -Verify selected results using definition |
Exercise books
|
KLB Secondary Mathematics Form 4, Pages 184-188
|
|
| 4 | 3 |
Differentiation
|
Derivative of y = x^n (Basic Powers)
|
By the end of the
lesson, the learner
should be able to:
-Find derivatives of power functions -Apply the rule d/dx(x^n) = nx^(n-1) -Practice with x², x³, x⁴, etc. -Verify using first principles for simple cases |
In groups, learners are guided to:
-Derive d/dx(x²) = 2x using first principles -Apply power rule to various functions -Practice with x³, x⁴, x⁵ examples -Verify selected results using definition |
Exercise books
|
KLB Secondary Mathematics Form 4, Pages 184-188
|
|
| 4 | 4 |
Differentiation
|
Derivative of y = x^n (Basic Powers)
|
By the end of the
lesson, the learner
should be able to:
-Find derivatives of power functions -Apply the rule d/dx(x^n) = nx^(n-1) -Practice with x², x³, x⁴, etc. -Verify using first principles for simple cases |
In groups, learners are guided to:
-Derive d/dx(x²) = 2x using first principles -Apply power rule to various functions -Practice with x³, x⁴, x⁵ examples -Verify selected results using definition |
Exercise books
|
KLB Secondary Mathematics Form 4, Pages 184-188
|
|
| 4 | 5 |
Differentiation
|
Derivative of y = x^n (Basic Powers)
|
By the end of the
lesson, the learner
should be able to:
-Find derivatives of power functions -Apply the rule d/dx(x^n) = nx^(n-1) -Practice with x², x³, x⁴, etc. -Verify using first principles for simple cases |
In groups, learners are guided to:
-Derive d/dx(x²) = 2x using first principles -Apply power rule to various functions -Practice with x³, x⁴, x⁵ examples -Verify selected results using definition |
Exercise books
|
KLB Secondary Mathematics Form 4, Pages 184-188
|
|
| 4 | 6 |
Differentiation
|
Derivative of y = x^n (Basic Powers)
|
By the end of the
lesson, the learner
should be able to:
-Find derivatives of power functions -Apply the rule d/dx(x^n) = nx^(n-1) -Practice with x², x³, x⁴, etc. -Verify using first principles for simple cases |
In groups, learners are guided to:
-Derive d/dx(x²) = 2x using first principles -Apply power rule to various functions -Practice with x³, x⁴, x⁵ examples -Verify selected results using definition |
Exercise books
|
KLB Secondary Mathematics Form 4, Pages 184-188
|
|
| 4 | 7 |
Differentiation
|
Derivative of Polynomial Functions
|
By the end of the
lesson, the learner
should be able to:
-Find derivatives of polynomial functions -Apply term-by-term differentiation -Practice with various polynomial degrees -Verify results using first principles |
In groups, learners are guided to:
-Differentiate y = x³ + 2x² - 5x + 7 -Apply rule to each term separately -Practice with various polynomial types -Check results using definition for simple cases |
Exercise books
|
KLB Secondary Mathematics Form 4, Pages 184-188
|
|
| 5 | 1 |
Differentiation
|
Applications to Tangent Lines
|
By the end of the
lesson, the learner
should be able to:
-Find equations of tangent lines to curves -Use derivatives to find tangent gradients -Apply point-slope form for tangent equations -Solve problems involving tangent lines |
In groups, learners are guided to:
-Find tangent to y = x² at point (2, 4) -Use derivative to get gradient at specific point -Apply y - y₁ = m(x - x₁) formula -Practice with various curves and points |
Exercise books
|
KLB Secondary Mathematics Form 4, Pages 187-189
|
|
| 5 | 2 |
Differentiation
|
Applications to Tangent Lines
|
By the end of the
lesson, the learner
should be able to:
-Find equations of tangent lines to curves -Use derivatives to find tangent gradients -Apply point-slope form for tangent equations -Solve problems involving tangent lines |
In groups, learners are guided to:
-Find tangent to y = x² at point (2, 4) -Use derivative to get gradient at specific point -Apply y - y₁ = m(x - x₁) formula -Practice with various curves and points |
Exercise books
|
KLB Secondary Mathematics Form 4, Pages 187-189
|
|
| 5 | 3 |
Differentiation
|
Applications to Tangent Lines
|
By the end of the
lesson, the learner
should be able to:
-Find equations of tangent lines to curves -Use derivatives to find tangent gradients -Apply point-slope form for tangent equations -Solve problems involving tangent lines |
In groups, learners are guided to:
-Find tangent to y = x² at point (2, 4) -Use derivative to get gradient at specific point -Apply y - y₁ = m(x - x₁) formula -Practice with various curves and points |
Exercise books
|
KLB Secondary Mathematics Form 4, Pages 187-189
|
|
| 5 | 4 |
Differentiation
|
Applications to Tangent Lines
|
By the end of the
lesson, the learner
should be able to:
-Find equations of tangent lines to curves -Use derivatives to find tangent gradients -Apply point-slope form for tangent equations -Solve problems involving tangent lines |
In groups, learners are guided to:
-Find tangent to y = x² at point (2, 4) -Use derivative to get gradient at specific point -Apply y - y₁ = m(x - x₁) formula -Practice with various curves and points |
Exercise books
|
KLB Secondary Mathematics Form 4, Pages 187-189
|
|
| 5 | 5 |
Differentiation
|
Applications to Tangent Lines
|
By the end of the
lesson, the learner
should be able to:
-Find equations of tangent lines to curves -Use derivatives to find tangent gradients -Apply point-slope form for tangent equations -Solve problems involving tangent lines |
In groups, learners are guided to:
-Find tangent to y = x² at point (2, 4) -Use derivative to get gradient at specific point -Apply y - y₁ = m(x - x₁) formula -Practice with various curves and points |
Exercise books
|
KLB Secondary Mathematics Form 4, Pages 187-189
|
|
| 5 | 6 |
Differentiation
|
Applications to Normal Lines
|
By the end of the
lesson, the learner
should be able to:
-Find equations of normal lines to curves -Use negative reciprocal of tangent gradient -Apply to perpendicular line problems -Practice with normal line calculations |
In groups, learners are guided to:
-Find normal to y = x² at point (2, 4) -Use negative reciprocal relationship -Apply perpendicular line concepts -Practice normal line equation finding |
Exercise books
-Normal line |
KLB Secondary Mathematics Form 4, Pages 187-189
|
|
| 5 | 7 |
Differentiation
|
Applications to Normal Lines
|
By the end of the
lesson, the learner
should be able to:
-Find equations of normal lines to curves -Use negative reciprocal of tangent gradient -Apply to perpendicular line problems -Practice with normal line calculations |
In groups, learners are guided to:
-Find normal to y = x² at point (2, 4) -Use negative reciprocal relationship -Apply perpendicular line concepts -Practice normal line equation finding |
Exercise books
-Normal line |
KLB Secondary Mathematics Form 4, Pages 187-189
|
|
| 6 | 1 |
Differentiation
|
Types of Stationary Points
|
By the end of the
lesson, the learner
should be able to:
-Distinguish between maximum and minimum points -Identify points of inflection -Use first derivative test for classification -Apply gradient analysis around stationary points |
In groups, learners are guided to:
-Analyze gradient changes around stationary points -Use sign analysis of dy/dx -Classify stationary points by gradient behavior -Practice with various function types |
Exercise books
-Classification examples |
KLB Secondary Mathematics Form 4, Pages 189-195
|
|
| 6 | 2 |
Differentiation
|
Types of Stationary Points
|
By the end of the
lesson, the learner
should be able to:
-Distinguish between maximum and minimum points -Identify points of inflection -Use first derivative test for classification -Apply gradient analysis around stationary points |
In groups, learners are guided to:
-Analyze gradient changes around stationary points -Use sign analysis of dy/dx -Classify stationary points by gradient behavior -Practice with various function types |
Exercise books
-Classification examples |
KLB Secondary Mathematics Form 4, Pages 189-195
|
|
| 6 | 3 |
Differentiation
|
Types of Stationary Points
|
By the end of the
lesson, the learner
should be able to:
-Distinguish between maximum and minimum points -Identify points of inflection -Use first derivative test for classification -Apply gradient analysis around stationary points |
In groups, learners are guided to:
-Analyze gradient changes around stationary points -Use sign analysis of dy/dx -Classify stationary points by gradient behavior -Practice with various function types |
Exercise books
-Classification examples |
KLB Secondary Mathematics Form 4, Pages 189-195
|
|
| 6 | 4 |
Differentiation
|
Types of Stationary Points
|
By the end of the
lesson, the learner
should be able to:
-Distinguish between maximum and minimum points -Identify points of inflection -Use first derivative test for classification -Apply gradient analysis around stationary points |
In groups, learners are guided to:
-Analyze gradient changes around stationary points -Use sign analysis of dy/dx -Classify stationary points by gradient behavior -Practice with various function types |
Exercise books
-Classification examples |
KLB Secondary Mathematics Form 4, Pages 189-195
|
|
| 6 | 5 |
Differentiation
|
Types of Stationary Points
|
By the end of the
lesson, the learner
should be able to:
-Distinguish between maximum and minimum points -Identify points of inflection -Use first derivative test for classification -Apply gradient analysis around stationary points |
In groups, learners are guided to:
-Analyze gradient changes around stationary points -Use sign analysis of dy/dx -Classify stationary points by gradient behavior -Practice with various function types |
Exercise books
-Classification examples |
KLB Secondary Mathematics Form 4, Pages 189-195
|
|
| 6 | 6 |
Differentiation
|
Curve Sketching Using Derivatives
|
By the end of the
lesson, the learner
should be able to:
-Use derivatives to sketch accurate curves -Identify key features: intercepts, stationary points -Apply systematic curve sketching method -Combine algebraic and graphical analysis |
In groups, learners are guided to:
-Sketch y = x³ - 3x² + 2 using derivatives -Find intercepts, stationary points, and behavior -Use systematic curve sketching approach -Verify sketches using derivative information |
Exercise book
|
KLB Secondary Mathematics Form 4, Pages 195-197
|
|
| 6 | 7 |
Differentiation
|
Curve Sketching Using Derivatives
|
By the end of the
lesson, the learner
should be able to:
-Use derivatives to sketch accurate curves -Identify key features: intercepts, stationary points -Apply systematic curve sketching method -Combine algebraic and graphical analysis |
In groups, learners are guided to:
-Sketch y = x³ - 3x² + 2 using derivatives -Find intercepts, stationary points, and behavior -Use systematic curve sketching approach -Verify sketches using derivative information |
Exercise book
|
KLB Secondary Mathematics Form 4, Pages 195-197
|
|
| 7 | 1 |
Differentiation
|
Introduction to Kinematics Applications
|
By the end of the
lesson, the learner
should be able to:
-Apply derivatives to displacement-time relationships -Understand velocity as first derivative of displacement -Find velocity functions from displacement functions -Apply to motion problems |
In groups, learners are guided to:
-Find velocity from s = t³ - 2t² + 5t -Apply v = ds/dt to motion problems -Practice with various displacement functions -Connect to real-world motion scenarios |
Exercise books
-r -Motion examples -Kinematics applications |
KLB Secondary Mathematics Form 4, Pages 197-201
|
|
| 7 | 2 |
Differentiation
|
Introduction to Kinematics Applications
|
By the end of the
lesson, the learner
should be able to:
-Apply derivatives to displacement-time relationships -Understand velocity as first derivative of displacement -Find velocity functions from displacement functions -Apply to motion problems |
In groups, learners are guided to:
-Find velocity from s = t³ - 2t² + 5t -Apply v = ds/dt to motion problems -Practice with various displacement functions -Connect to real-world motion scenarios |
Exercise books
-r -Motion examples -Kinematics applications |
KLB Secondary Mathematics Form 4, Pages 197-201
|
|
| 7 | 3 |
Differentiation
|
Introduction to Kinematics Applications
|
By the end of the
lesson, the learner
should be able to:
-Apply derivatives to displacement-time relationships -Understand velocity as first derivative of displacement -Find velocity functions from displacement functions -Apply to motion problems |
In groups, learners are guided to:
-Find velocity from s = t³ - 2t² + 5t -Apply v = ds/dt to motion problems -Practice with various displacement functions -Connect to real-world motion scenarios |
Exercise books
-r -Motion examples -Kinematics applications |
KLB Secondary Mathematics Form 4, Pages 197-201
|
|
| 7 | 4 |
Differentiation
|
Introduction to Kinematics Applications
|
By the end of the
lesson, the learner
should be able to:
-Apply derivatives to displacement-time relationships -Understand velocity as first derivative of displacement -Find velocity functions from displacement functions -Apply to motion problems |
In groups, learners are guided to:
-Find velocity from s = t³ - 2t² + 5t -Apply v = ds/dt to motion problems -Practice with various displacement functions -Connect to real-world motion scenarios |
Exercise books
-r -Motion examples -Kinematics applications |
KLB Secondary Mathematics Form 4, Pages 197-201
|
|
| 7 | 5 |
Differentiation
|
Introduction to Kinematics Applications
|
By the end of the
lesson, the learner
should be able to:
-Apply derivatives to displacement-time relationships -Understand velocity as first derivative of displacement -Find velocity functions from displacement functions -Apply to motion problems |
In groups, learners are guided to:
-Find velocity from s = t³ - 2t² + 5t -Apply v = ds/dt to motion problems -Practice with various displacement functions -Connect to real-world motion scenarios |
Exercise books
-r -Motion examples -Kinematics applications |
KLB Secondary Mathematics Form 4, Pages 197-201
|
|
| 7 | 6 |
Differentiation
|
Acceleration as Second Derivative
|
By the end of the
lesson, the learner
should be able to:
-Understand acceleration as derivative of velocity -Apply a = dv/dt = d²s/dt² notation -Find acceleration functions from displacement -Apply to motion analysis problems |
In groups, learners are guided to:
-Find acceleration from velocity functions -Use second derivative notation -Apply to projectile motion problems -Practice with particle motion scenarios |
Exercise books
-Second derivative examples -Motion analysis |
KLB Secondary Mathematics Form 4, Pages 197-201
|
|
| 7 | 7 |
Differentiation
|
Acceleration as Second Derivative
|
By the end of the
lesson, the learner
should be able to:
-Understand acceleration as derivative of velocity -Apply a = dv/dt = d²s/dt² notation -Find acceleration functions from displacement -Apply to motion analysis problems |
In groups, learners are guided to:
-Find acceleration from velocity functions -Use second derivative notation -Apply to projectile motion problems -Practice with particle motion scenarios |
Exercise books
-Second derivative examples -Motion analysis |
KLB Secondary Mathematics Form 4, Pages 197-201
|
|
| 8 | 1 |
Differentiation
|
Motion Problems and Applications
|
By the end of the
lesson, the learner
should be able to:
-Solve complete motion analysis problems -Find displacement, velocity, acceleration relationships -Apply to real-world motion scenarios -Use derivatives for motion optimization |
In groups, learners are guided to:
-Analyze complete motion of falling object -Find when particle changes direction -Calculate maximum height in projectile motion -Apply to vehicle motion problems |
Exercise books
-Complete motion examples -Real scenarios |
KLB Secondary Mathematics Form 4, Pages 197-201
|
|
| 8 | 2 |
Differentiation
|
Motion Problems and Applications
|
By the end of the
lesson, the learner
should be able to:
-Solve complete motion analysis problems -Find displacement, velocity, acceleration relationships -Apply to real-world motion scenarios -Use derivatives for motion optimization |
In groups, learners are guided to:
-Analyze complete motion of falling object -Find when particle changes direction -Calculate maximum height in projectile motion -Apply to vehicle motion problems |
Exercise books
-Complete motion examples -Real scenarios |
KLB Secondary Mathematics Form 4, Pages 197-201
|
|
| 8 | 3 |
Differentiation
|
Motion Problems and Applications
|
By the end of the
lesson, the learner
should be able to:
-Solve complete motion analysis problems -Find displacement, velocity, acceleration relationships -Apply to real-world motion scenarios -Use derivatives for motion optimization |
In groups, learners are guided to:
-Analyze complete motion of falling object -Find when particle changes direction -Calculate maximum height in projectile motion -Apply to vehicle motion problems |
Exercise books
-Complete motion examples -Real scenarios |
KLB Secondary Mathematics Form 4, Pages 197-201
|
|
| 8 | 4 |
Differentiation
|
Motion Problems and Applications
|
By the end of the
lesson, the learner
should be able to:
-Solve complete motion analysis problems -Find displacement, velocity, acceleration relationships -Apply to real-world motion scenarios -Use derivatives for motion optimization |
In groups, learners are guided to:
-Analyze complete motion of falling object -Find when particle changes direction -Calculate maximum height in projectile motion -Apply to vehicle motion problems |
Exercise books
-Complete motion examples -Real scenarios |
KLB Secondary Mathematics Form 4, Pages 197-201
|
|
| 8 | 5 |
Integration
|
Introduction to Reverse Differentiation
|
By the end of the
lesson, the learner
should be able to:
-Define integration as reverse of differentiation -Understand the concept of antiderivative -Recognize the relationship between gradient functions and original functions -Apply reverse thinking to simple differentiation examples |
In groups, learners are guided to:
-Q/A review on differentiation formulas and rules -Demonstration of reverse process using simple examples -Working backwards from derivatives to find original functions -Discussion on why multiple functions can have same derivative -Introduction to integration symbol ∫ |
Graph papers
-Exercise books -Function examples |
KLB Secondary Mathematics Form 4, Pages 221-223
|
|
| 8 | 6 |
Integration
|
Introduction to Reverse Differentiation
|
By the end of the
lesson, the learner
should be able to:
-Define integration as reverse of differentiation -Understand the concept of antiderivative -Recognize the relationship between gradient functions and original functions -Apply reverse thinking to simple differentiation examples |
In groups, learners are guided to:
-Q/A review on differentiation formulas and rules -Demonstration of reverse process using simple examples -Working backwards from derivatives to find original functions -Discussion on why multiple functions can have same derivative -Introduction to integration symbol ∫ |
Graph papers
-Exercise books -Function examples |
KLB Secondary Mathematics Form 4, Pages 221-223
|
|
| 8 | 7 |
Integration
|
Integration of Polynomial Functions
|
By the end of the
lesson, the learner
should be able to:
-Integrate polynomial functions with multiple terms -Apply linearity: ∫[af(x) + bg(x)]dx = a∫f(x)dx + b∫g(x)dx -Handle constant coefficients and addition/subtraction -Solve integration problems requiring algebraic simplification |
In groups, learners are guided to:
-Step-by-step integration of polynomials like 3x² + 5x - 7 -Working with coefficients and constants -Integration of expanded expressions: (x+2)(x-3) -Practice with mixed positive and negative terms -Exercises from textbook Exercise 10.1 |
Calculators
-Polynomial examples -Exercise books |
KLB Secondary Mathematics Form 4, Pages 223-225
|
|
| 9 |
Midterm exam |
|||||||
| 9 |
Midterm break |
|||||||
| 10 | 1 |
Integration
|
Evaluating Definite Integrals
|
By the end of the
lesson, the learner
should be able to:
-Apply Fundamental Theorem of Calculus -Evaluate definite integrals using [F(x)]ₐᵇ = F(b) - F(a) -Understand why constant of integration cancels -Practice numerical evaluation of definite integrals |
In groups, learners are guided to:
-Step-by-step evaluation process demonstration -Multiple worked examples showing limit substitution -Verification that constant c cancels out -Practice with various polynomial and power functions -Exercises from textbook Exercise 10.2 |
Calculators
|
KLB Secondary Mathematics Form 4, Pages 226-230
|
|
| 10 | 2 |
Integration
|
Evaluating Definite Integrals
|
By the end of the
lesson, the learner
should be able to:
-Apply Fundamental Theorem of Calculus -Evaluate definite integrals using [F(x)]ₐᵇ = F(b) - F(a) -Understand why constant of integration cancels -Practice numerical evaluation of definite integrals |
In groups, learners are guided to:
-Step-by-step evaluation process demonstration -Multiple worked examples showing limit substitution -Verification that constant c cancels out -Practice with various polynomial and power functions -Exercises from textbook Exercise 10.2 |
Calculators
|
KLB Secondary Mathematics Form 4, Pages 226-230
|
|
| 10 | 3 |
Integration
|
Evaluating Definite Integrals
|
By the end of the
lesson, the learner
should be able to:
-Apply Fundamental Theorem of Calculus -Evaluate definite integrals using [F(x)]ₐᵇ = F(b) - F(a) -Understand why constant of integration cancels -Practice numerical evaluation of definite integrals |
In groups, learners are guided to:
-Step-by-step evaluation process demonstration -Multiple worked examples showing limit substitution -Verification that constant c cancels out -Practice with various polynomial and power functions -Exercises from textbook Exercise 10.2 |
Calculators
|
KLB Secondary Mathematics Form 4, Pages 226-230
|
|
| 10 | 4 |
Integration
|
Area Under Curves - Single Functions
|
By the end of the
lesson, the learner
should be able to:
-Understand integration as area calculation tool -Calculate area between curve and x-axis -Handle regions bounded by curves and vertical lines -Apply definite integrals to find exact areas |
In groups, learners are guided to:
-Geometric demonstration of area under curves -Drawing and shading regions on graph paper -Working examples: area under y = x², y = 2x + 3, etc. -Comparison with approximation methods from Chapter 9 -Practice finding areas of various regions |
Graph papers
-Curve sketching |
KLB Secondary Mathematics Form 4, Pages 230-233
|
|
| 10 | 5 |
Integration
|
Area Under Curves - Single Functions
|
By the end of the
lesson, the learner
should be able to:
-Understand integration as area calculation tool -Calculate area between curve and x-axis -Handle regions bounded by curves and vertical lines -Apply definite integrals to find exact areas |
In groups, learners are guided to:
-Geometric demonstration of area under curves -Drawing and shading regions on graph paper -Working examples: area under y = x², y = 2x + 3, etc. -Comparison with approximation methods from Chapter 9 -Practice finding areas of various regions |
Graph papers
-Curve sketching |
KLB Secondary Mathematics Form 4, Pages 230-233
|
|
| 10 | 6 |
Area Approximation
|
Area Approximation - Deriving the trapezium rule
|
By the end of the
lesson, the learner
should be able to:
- recall the formula for area of a trapezium - derive the trapezium rule A = (h/2)[y₀ + yₙ + 2(y₁ + … + yₙ₋₁)] - identify ordinates and the strip width h |
In groups, learners are guided to:
- Review of trapezium area formula - Step-by-step derivation by dividing a region into strips and summing areas - Guided drawing of strips under a sample curve |
Graph paper,r, rulers, chalkboard
|
KLB Sec. Maths Form 4, pg. 210
|
|
| 10 | 7 |
Area Approximation
|
Area Approximation - Deriving the trapezium rule
|
By the end of the
lesson, the learner
should be able to:
- recall the formula for area of a trapezium - derive the trapezium rule A = (h/2)[y₀ + yₙ + 2(y₁ + … + yₙ₋₁)] - identify ordinates and the strip width h |
In groups, learners are guided to:
- Review of trapezium area formula - Step-by-step derivation by dividing a region into strips and summing areas - Guided drawing of strips under a sample curve |
Graph paper,r, rulers, chalkboard
|
KLB Sec. Maths Form 4, pg. 210
|
|
| 11 | 1 |
Area Approximation
|
Area Approximation - Estimating area under a curve using the trapezium rule
|
By the end of the
lesson, the learner
should be able to:
- construct a table of values for a given function y = f(x) - apply the trapezium rule to estimate area between a curve and the x-axis - discuss how the number of strips affects accuracy |
- Worked example: area under y = x² + 1 from x = 0 to x = 4 using 4 then 8 strips
- Learners construct tables of values and compute areas - Discussion linking the rule to definite integration |
Graph paper, calculators, chalkboard
|
KLB Sec. Maths Form 4, pg. 215
|
|
| 11 | 2 |
Area Approximation
|
Area Approximation - Deriving and applying the mid-ordinate rule
|
By the end of the
lesson, the learner
should be able to:
- distinguish between an ordinate and a mid-ordinate - derive the mid-ordinate rule A = h(y₁ + y₂ + … + yₙ) - apply the rule to estimate area under a curve |
In groups, learners are guided to:
- Step-by-step derivation treating each strip as a rectangle - Worked example computing mid-ordinates for y = x² + x from x = 2 to x = 3 - Pair work on a textbook example |
Graph paper, calculators, chalkboard
|
KLB Sec. Maths Form 4, pg. 217
|
|
| 11 | 3 |
Area Approximation
|
Area Approximation - Deriving and applying the mid-ordinate rule
|
By the end of the
lesson, the learner
should be able to:
- distinguish between an ordinate and a mid-ordinate - derive the mid-ordinate rule A = h(y₁ + y₂ + … + yₙ) - apply the rule to estimate area under a curve |
In groups, learners are guided to:
- Step-by-step derivation treating each strip as a rectangle - Worked example computing mid-ordinates for y = x² + x from x = 2 to x = 3 - Pair work on a textbook example |
Graph paper, calculators, chalkboard
|
KLB Sec. Maths Form 4, pg. 217
|
|
| 12-13 |
End term exam |
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| 14 |
Report making and school closure |
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