Module Workbook

Module 12: Mathematics

Trigonometry, surds, indices, and logarithms.

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

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SECTION: MATHEMATICS

MODULE: 12

Part A: Units

1. Further trigonometry

a. Sine rule

b. Cosine rule

c. Area of a triangle using trigonometry

d. Application of sine and cosine rule in problem solving

2. Surds

a. Simplification of surds

b. Rationalisation of denominators

c. Operations with surds

3. Indices and logarithms

a. Laws of indices

b. Simplification using indices

c. Introduction to logarithms

d. Laws of logarithms

e. Use of logarithm tables

Part B: Project

Apply trigonometry, surds, and logarithms to real problems.

Project Title: Trigonometry and Surds Problem Set

Objective: Solve real-life problems using sine rule, cosine rule, surds, and logarithms.

Project Instructions:

1. Solve one triangle using the sine rule and one using the cosine rule.
2. Calculate the area of a triangle using trigonometry.
3. Simplify and rationalise two surd expressions.
4. Solve two problems using laws of indices or logarithms (use tables if available).
5. Consult your coach where necessary.

Evidence to Submit:

• Worked solutions with diagrams.
• Surd simplification steps.
• Logarithm or indices calculations.

Submission

Part C: Training Others

Guide a peer on trigonometry and surds.

Guidance:

• Demonstrate a sine or cosine rule example.
• Show how to simplify a surd and rationalise a denominator.
• Explain one law of indices or logarithms.

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:

• Sine and cosine rules:
• Surds operations:
• Indices and logarithms:

Coach assessment:

• Sine and cosine rules:
• Surds operations:
• Indices and logarithms:

Submission

Ready for the next module?

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

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