Module Workbook

Module 14: Mathematics

Vectors, matrices, and linear programming.

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

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SECTION: MATHEMATICS

MODULE: 14

Part A: Units

1. Vectors (2)

a. Position vectors

b. Displacement vectors

c. Vector addition using scale diagrams

d. Multiplication of vectors by scalars

e. Applications of vectors

2. Matrices (2)

a. Matrix multiplication

b. Determinant of a 2×2 matrix

c. Inverse of a 2×2 matrix

d. Solution of simultaneous equations using matrices

3. Linear programming

a. Linear inequalities in two variables

b. Graphical representation

c. Feasible region

d. Optimization problems

Part B: Project

Apply vectors, matrices, and linear programming to practical problems.

Project Title: Vectors, Matrices, and Optimization

Objective: Solve applied tasks using vectors, matrices, and linear programming.

Project Instructions:

1. Represent two movements as vectors and add them using a scale diagram.
2. Multiply a vector by a scalar and interpret the result.
3. Solve a 2×2 system using matrices (determinant and inverse).
4. Formulate a linear programming problem and identify the feasible region.
5. Determine an optimum solution from a graph.
6. Consult your coach where necessary.

Evidence to Submit:

• Vector diagrams and calculations.
• Matrix solution steps.
• Linear programming graph and optimum point.

Submission

Part C: Training Others

Guide a peer on vectors, matrices, and optimization.

Guidance:

• Demonstrate vector addition using a scale diagram.
• Solve a 2×2 system using matrix inverse.
• Explain 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:

• Vector representation and operations:
• Matrix operations and inverses:
• Linear programming:

Coach assessment:

• Vector representation and operations:
• Matrix operations and inverses:
• Linear programming:

Submission

Ready for the next module?

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

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