Module 11: Mathematics
Quadratics, approximations, and trigonometry.
Use this workbook to practice core KCSE communication skills and record evidence of progress.
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SECTION: MATHEMATICS
MODULE: 11
Part A: Units
1. Quadratic expressions and equations (2)
a. Factorisation of quadratic expressions
b. Perfect squares
c. Completion of square
d. Solution of quadratic equations by completing the square
e. Quadratic formula
i. X = (-b ± √(b² - 4ac)) / 2a
f. Solution of quadratic equations using the formula
g. Formation of quadratic equations and solving them
h. Tables of values for a given quadratic relation
i. Graphs of quadratic equations
j. Simultaneous equations - one linear and one quadratic
k. Application to real life situation
2. Approximations and errors
a. Computing using calculators
b. Estimations and approximations
c. Significant figures
d. Absolute, relative, percentage, round off and truncation errors
e. Propagation of errors from simple calculations
f. Maximum and minimum errors
3. Trigonometry (2)
a. The unit circle
b. Trigonometric ratios from the unit circle
c. Trigonometric ratios of angles greater than 360° and negative angles
d. Use of trigonometric tables
e. Radian measure
f. Simple trigonometric graphs
g. Derivation of sine and cosine rule
Part B: Project
Apply quadratics, approximations, and trigonometry in a mixed task.
Project Title: Quadratics and Trigonometry Practice
Objective: Solve quadratic equations, estimate errors, and apply trigonometric rules.
Project Instructions:
- 1. Solve two quadratic equations using completing the square and the formula.
- 2. Create a table of values and sketch one quadratic graph.
- 3. Solve one problem involving approximations and error bounds.
- 4. Use sine or cosine rule to solve a triangle problem.
- 5. Consult your coach where necessary.
Evidence to Submit:
- • Quadratic solutions and graph.
- • Error calculation notes.
- • Trigonometry solution steps.
Submission
Part C: Training Others
Guide a peer through quadratics and trigonometry tasks.
Guidance:
- • Explain completing the square using an example.
- • Discuss error types and estimation steps.
- • Demonstrate sine or cosine rule on a triangle.
Reflection:
- • What concept did you teach?
- • What was difficult to explain?
- • What did you understand better after teaching?
Submission
Part D: Assessment
Competency Levels:
1 = Expectations not met
2 = Partially met
3 = Satisfactorily met
4 = Excellently met
Self-assessment:
- • Quadratic equations:
- • Approximations and errors:
- • Trigonometry:
Coach assessment:
- • Quadratic equations:
- • Approximations and errors:
- • Trigonometry:
Submission
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