Module Workbook

Module 19: Mathematics

Linear programming and differentiation.

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

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SECTION: MATHEMATICS

MODULE: 19

Part A: Units

1. Linear programming

a. Formation of linear inequalities

b. Analytical solutions of linear inequalities

c. Solutions of linear inequalities by graphs

d. Optimization (include objective function)

e. Application to real life situations

2. Differentiation

a. Average and instantaneous rates of change

b. Gradient of a curve at a point

c. Gradient of y = x^n (where n is positive)

d. Delta notation (delta)

e. Derivative of a polynomial

f. Equations of tangents and normals to the curve

g. Stationary points

h. Curve sketching

i. Application of differentiation

j. Maxima and minima

Part B: Project

Apply linear programming and differentiation to real problems.

Project Title: Optimization and Differentiation Practice

Objective: Solve constraints, optimize a function, and analyze curves.

Project Instructions:

1. Model a real scenario using linear inequalities.
2. Solve the inequalities analytically and graphically.
3. Use an objective function to find the optimum solution.
4. Differentiate a polynomial and find stationary points.
5. Sketch the curve and identify maxima or minima.
6. Consult your coach where necessary.

Evidence to Submit:

• Linear programming model and graph.
• Optimization results with explanation.
• Differentiation steps and curve sketch.

Submission

Part C: Training Others

Teach a peer about linear programming and differentiation.

Guidance:

• Explain how to form linear inequalities.
• Demonstrate objective functions and optimization.
• Show differentiation and curve sketching steps.

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:

• Linear inequalities and graphs:
• Objective functions and optimization:
• Differentiation and curve sketching:

Coach assessment:

• Linear inequalities and graphs:
• Objective functions and optimization:
• Differentiation and curve sketching:

Submission

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