Module Workbook

Module 17: Mathematics

Probability, statistics, and linear programming.

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

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SECTION: MATHEMATICS

MODULE: 17

Part A: Units

1. Probability (3)

a. Probability of independent events

b. Probability of dependent events

c. Tree diagrams

d. Conditional probability

e. Applications

2. Statistics (3)

a. Grouped data

b. Mean, median and mode for grouped data

c. Histograms

d. Frequency polygons

e. Interpretation of statistical data

3. Linear programming (2)

a. Formulation of linear inequalities

b. Graphical solution of inequalities

c. Feasible region

d. Optimization problems

Part B: Project

Apply probability, statistics, and linear programming to real data.

Project Title: Probability and Data Analysis Practice

Objective: Solve probability and statistics tasks and optimize a simple model.

Project Instructions:

1. Solve one independent and one dependent probability problem.
2. Draw a tree diagram for a simple event and compute conditional probability.
3. Use grouped data to compute mean, median, and mode.
4. Draw a histogram or frequency polygon from the grouped data.
5. Formulate a linear programming problem and find the optimum point.
6. Consult your coach where necessary.

Evidence to Submit:

• Probability solutions and tree diagram.
• Grouped data calculations and chart.
• Linear programming graph and solution.

Submission

Part C: Training Others

Guide a peer on probability, grouped data, and optimization.

Guidance:

• Explain independent vs dependent probability.
• Demonstrate grouped data mean and median.
• Show how to plot a feasible region and optimum point.

Reflection:

• What did the learner understand well?
• What 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:

• Probability and tree diagrams:
• Grouped data and charts:
• Linear programming:

Coach assessment:

• Probability and tree diagrams:
• Grouped data and charts:
• Linear programming:

Submission

Ready for the next module?

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

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