Mathematics Grade-12: Module 1

Description:

The Grade 12 Mathematics curriculum is designed primarily to equip you with the skills necessary for higher education and to enhance your computational abilities for technical training and the workforce. Module 1 of the Grade 12 mathematics program consists of three key units: Sequences and Series, Pre-Calculus, and Statistics.

Within this framework, the principles of calculus are introduced through mechanical and geometrical approaches to differentiation and integration, respectively. This foundation is essential foryou tocontinue your study of calculus at the tertiary level. Important theorems vital to the subject’s development are presented clearly, accompanied by illustrative examples, though proofs are not included. The intention is to enable you to understand the significance of these theorems and to apply them effectively.

Throughout all units, there is a deliberate effort to weave in cross-cutting issues and core competencies, ensuring that you develop a well-rounded understanding of both the theoretical and practical dimensions of mathematics. The integration of technology into mathematical learning is highly encouraged, as it allows youto apply your knowledge to real-life problem-solving scenarios.

Mastery of mathematics is unattainable without substantial practice in problem-solving, which is why it is crucial for you to be motivated and supported in tackling all assigned exercises and problems

Competencies(MLC):

At the end of this module, you will be able to:

• Grasp the concept of sequence and series.         
• Know how to compute any term of sequences from given rule.
• Find out possible rules (formulae) from given terms.
• Understand the types of sequences and series.
• Compute partial and infinite sums of sequences.
• Apply the knowledge of sequence and series to solve practical problems.
• Deduce rate of change of different quantities.
• Know how to calculate rate of change of different quantities.
• Understand gradient of functions at a point.
• Analyze the geometrical and mechanical meaning of derivative.
• Know how to find the derivative of simple functions using gradient method.
• Know how to find area of a region bounded by a function and x-axis on a given interval.
• Understand definite integral
• Know absolute and relative dispersion and their interpretation.
• Deduce specific facts about measurement in statistical data.
• Understand basic concepts about sampling techniques.
• Know how to use statistical application software.

Contents

1. Sequence and Series

Lesson 1: Sequences

Lesson 2: Sigma Notation and Partial Sums

Lesson 3: Infinite Series and Applications

2. Introduction to Pre – Calculus

Lesson 1: Introduction to Derivatives

Lesson 2: Applications of Derivatives

Lesson 3: Introduction to Integrals

3. Statistics

Lesson 1: Measurement of Absolute Dispersion

Lesson 2: Measurement of Relative Dispersion and Sampling

Assessments

Assessment in this module may include:

• Mid Exam
• Quiz and test
• Final Exam
• All assessments consist of automatically graded multiple-choice questions with explanatory feedback. Each question offers four answer choices, marked by small square checkboxes. While the options may not always be labeled A, B, C, or D, you can interpret the checkboxes in that order.

References

1. The new Ethiopian Curriculum
2. Extreme books series
3. Galaxy book series
4. Internet sources