Module Workbook

Module 20: Mathematics

Area approximation and integration.

Use this workbook to practice core KCSE communication skills and record evidence of progress.

Module navigation

Move module to module

Use the navigation buttons to move through the workbook in sequence.

Previous subject Next subject Programme overview

SECTION: MATHEMATICS

MODULE: 20

Part A: Units

1. Area approximation

a. Area by counting techniques

b. Trapezium rules

c. Area using trapezium rule

d. Mid ordinates

e. Area by the mid ordinate rule

2. Integration

a. Differentiation

b. Reverse differentiation

c. Integration notation and sum of areas of trapezia

d. Indefinite and definite integrals

e. Area under a curve by integration

f. Application in kinematics

Part B: Project

Estimate area and compare numerical methods with integration.

Project Title: Area and Integration Practice

Objective: Use trapezium and mid-ordinate rules and integrate simple functions.

Project Instructions:

1. Estimate the area of an irregular shape using counting techniques.
2. Apply the trapezium rule to a given table of values.
3. Apply the mid-ordinate rule and compare results.
4. Find the area under a curve by integration.
5. Solve one kinematics problem using integration.
6. Consult your coach where necessary.

Evidence to Submit:

• Area estimates and tables.
• Trapezium and mid-ordinate calculations.
• Integration solution and kinematics example.

Submission

Part C: Training Others

Guide a peer on area approximation and integration.

Guidance:

• Explain the trapezium and mid-ordinate rules.
• Demonstrate reverse differentiation.
• Apply integration to find area under a curve.

Reflection:

• What did the learner understand well?
• Which step needed more explanation?
• What support do you need from your coach?

Submission

Part D: Assessment

Competency Levels:

1 = Expectations not met

2 = Partially met

3 = Satisfactorily met

4 = Excellently met

Coach assessment: Learner completes the self-assessment using the 1-4 scale. The coach prepares a short quiz or conversation (outside the system if needed) and assigns the coach score.

Self-assessment:

• Area approximation methods:
• Integration techniques:
• Area under curve and kinematics:

Coach assessment:

• Area approximation methods:
• Integration techniques:
• Area under curve and kinematics:

Submission

Ready for the next module?

Keep your learning rhythm steady and record your reflections as you progress.

Next subject Back to programme