# A Comprehensive Study Plan for Additional Mathematics Revision (January to August)

A well-structured study plan can significantly enhance a student’s ability to comprehend and excel in Additional Mathematics (Add Maths). The structured approach of a study plan ensures that the student is organized and prepared for the comprehensive syllabus of Add Maths. Here’s how to use a study plan and the strategies to achieve an A1.

## January – February: ALGEBRA

• Understand the conditions for y = ax2 + bx + c to be always positive or negative.
• Learn to find the maximum or minimum value of a quadratic function using the method of completing the square.
• Practice using quadratic functions as models.
2. Equations and Inequalities:
• Master the conditions for a quadratic equation to have different types of roots and apply it to lines intersecting curves.
• Practice solving simultaneous equations in two variables by substitution.
• Learn to solve quadratic inequalities and represent the solution on the number line.

March: Surds & Polynomials

1. Surds:
• Learn four operations on surds, including rationalising the denominator.
• Practice solving equations involving surds.
2. Polynomials and Partial Fractions:
• Master multiplication and division of polynomials.
• Use the remainder and factor theorems to factorise polynomials and solve cubic equations.
• Understand and apply special forms like a3 + b3 and a3 – b3.
• Practice partial fractions with different types of denominators.

April: Binomial Expansions & Exponential and Logarithmic Functions

1. Binomial Expansions:
• Understand the Binomial Theorem for positive integer n.
• Practice using the general term for binomial expansions.
2. Exponential and Logarithmic Functions:
• Learn the properties of exponential and logarithmic functions.
• Practice simplifying expressions and solving simple equations involving these functions.
• Understand how to use exponential and logarithmic functions as models.

May: GEOMETRY AND TRIGONOMETRY

1. Trigonometric Functions, Identities, and Equations:
• Learn six trigonometric functions for angles of any magnitude.
• Understand principal values of inverse trigonometric functions.
• Master graphs of different trigonometric functions.
• Understand and apply various trigonometric identities and expansions.
• Practice simplifying trigonometric expressions and solving simple trigonometric equations.

June: Coordinate Geometry in Two Dimensions & Proofs in Plane Geometry

1. Coordinate Geometry in Two Dimensions:
• Understand the condition for two lines to be parallel or perpendicular.
• Learn to find the midpoint of a line segment.
• Understand the concept of the area of a rectilinear figure.
• Learn the coordinate geometry of circles.
2. Proofs in Plane Geometry:
• Understand properties of parallel lines cut by a transversal, angle bisectors, triangles, special quadrilaterals, and circles.
• Practice using congruent and similar triangles and the tangent-chord theorem.

July – August: CALCULUS

1. Differentiation and Integration:
• Understand the derivative of f(x) as the gradient of the tangent to the graph of y = f(x) at a point.
• Learn to use derivatives for various functions.
• Understand the concepts of increasing and decreasing functions, stationary points, and application of differentiation.
• Learn integration as the reverse of differentiation and the integrals of various functions.
• Understand the concept of a definite integral as an area under a curve.
• Practice finding the area of a region bounded by a curve and line(s) and the application of differentiation and integration to problems involving displacement, velocity, and acceleration of a particle moving in a straight line.

Throughout the months, regularly work on past year O-Level A-Math papers to familiarize yourself with the exam format and the types of questions. Analyze your mistakes and adjust your study plan as needed. This way, you will reinforce your understanding and ensure you are prepared for the exam.

Here’s the revision study plan in table format:

# September is for the A1

The last month of revision is a crucial period. This is the time to consolidate your knowledge, clarify any remaining doubts, and increase your exam confidence through practice.

Here’s a more detailed breakdown:

1. Evaluate Your Performance: Review the topics you’ve covered over the last eight months. Identify which areas you’re still weak in, as well as which topics you’re strong in. It’s important to know both so that you can allocate your revision time efficiently.
2. Focus on Weak Areas: Dedicate more revision time to the topics you’re struggling with. Go through your notes and practice questions for these topics more thoroughly. Use a variety of resources to aid your understanding, such as textbooks, online tutorials, or study groups.
3. Practice Past Year Papers: Use the GCE O-Level Ten Year Series (TYS) for Additional Mathematics to practice past year papers. This will give you a clear idea of the format of the questions and the type of content that comes up frequently. It also allows you to apply the knowledge you’ve gained from your revision, aiding memorization.
4. Analyze Your Answers: Don’t just correct your workâtry to understand why you made a mistake. Is it a lack of understanding of the concept? Did you misinterpret the question? This analysis will help you avoid making the same mistakes in the real exam.
5. Mock Exams: Simulate real exam conditions at home and time yourself while doing past papers. This will help you manage your time more effectively during the actual examination.
6. Clarify Doubts: Ask your teachers, classmates, or tutors to help you with any questions or doubts that you may have. It’s better to clarify these before going into the examination.
7. Revisit Strong Areas: It’s also essential to revisit the topics you’re good at towards the end of your revision period. This will ensure that these areas remain fresh in your mind for the exam.
8. Rest and Relax: Don’t forget to take care of yourself. Ensure you’re getting enough sleep, eating well, and taking short breaks during your study periods. This will help keep your stress levels down and keep you focused on your studies.

Here’s the study plan for September in table format:

## Developing and Using a Study Plan for Add Maths

### 1. Understand the Syllabus:

Begin by familiarizing yourself with the Add Maths syllabus. The syllabus outlines all the topics you need to cover, and understanding it can provide you a comprehensive overview of what to expect.

### 2. Break Down the Syllabus:

Divide the syllabus into smaller, more manageable topics. Allocate specific days or weeks to each topic, ensuring you devote adequate time to each section.

### 3. Create a Timetable:

Formulate a timetable to organize your study hours. Assign slots for each topic as per the breakdown. Ensure you incorporate breaks in between study periods to avoid fatigue and ensure efficient learning.

### 4. Daily Revision:

The key to mastering Add Maths is consistency. Regularly review what you have studied. Include daily revision periods in your study plan.

### 5. Problem-solving:

Add Maths involves a lot of problem-solving. Include plenty of time in your study plan for working on problems related to the topic you are studying.

### 6. Mock Tests:

Allocate time for taking mock tests to evaluate your progress. This also helps familiarize you with the exam pattern and improves time management.

## Customise the study table for yourself

A custom study table can help you optimize your time and resources when studying Additional Mathematics. It ensures you allocate ample time to each topic, considering your proficiency and weaknesses. Here’s how you can create your custom study table from the existing one and address weak areas.

The first step is to evaluate your proficiency in each topic of Additional Mathematics. You might already have an idea about the topics you find challenging and the ones you’re good at. However, this step is about identifying not just your weak areas, but also the areas you are confident in, to avoid over-preparation in those sections.

### 2. Rearrange the Table:

Based on your proficiency, you may want to rearrange the topics in your study table. The topics you find most challenging should be at the top of your table. This ensures you tackle the tough subjects when your energy and focus are at their peak.

### 3. Allocate Time:

Assign more time to difficult topics and less time to those you are confident in. But remember, even the subjects you’re good at need consistent revision.

### 4. Include Revision Slots:

Include regular revision slots for each topic after you complete them. This could be a quick revision at the end of the week or a more comprehensive revision at the end of the month.

### 5. Include Practice Sessions:

Add Maths involves a lot of problem-solving. Make sure to include time for practice sessions in your timetable, particularly for topics you find difficult.

### 6. Include Mock Tests and Past Year Papers:

Schedule time for mock tests and solving past year papers. They are crucial in understanding the exam pattern, improving speed, and testing your understanding.

### 7. Include Breaks:

Don’t forget to include short breaks in your study timetable. They help avoid burnout and improve focus.

### 8. Feedback and Improvement:

Lastly, make your timetable flexible for changes. If you feel a particular topic needs more time or you’ve allocated too much time for a topic, adjust your timetable accordingly. The goal is to make the timetable work for you, not against you.

Improving Weak Areas:

1. Focused Practice: Spend more time practicing problems from your weak areas. The more you practice, the better you understand.
2. Extra Help: Seek help from your teachers or consider getting a tutor for the topics you find especially challenging.
3. Use Different Resources: If you’re struggling with a topic, try studying from different resources. Sometimes, a different explanation or method can make the concept clearer.
4. Break it Down: Break down complex topics into smaller, manageable parts.
5. Consistent Revision: Regularly revise these topics to ensure they stay fresh in your mind.

Remember, a custom study table is not set in stone. It should be a dynamic tool that changes and adapts according to your needs and progress. Make sure to review and adjust your timetable periodically based on your performance and understanding. This will ensure your study plan stays effective and targeted to your needs.

## Strategies for Scoring A1 in Add Maths

### 1. Understand Concepts:

Avoid rote learning. Aim to grasp the underlying concepts, principles, and formulas in Add Maths. Understanding promotes long-term retention and the ability to apply knowledge in various situations.

### 2. Practice Regularly:

The mantra for success in Add Maths is practice. Solve as many problems as possible. Practice helps you become familiar with different types of problems and enhances your problem-solving skills.

### 3. Use Past Year Papers:

Past year papers are an excellent resource for understanding the exam pattern and the type of questions asked. They can also help you gauge the level of your preparedness.

### 4. Work on Weak Areas:

Identify your weak areas and devote more time to them. This can significantly improve your overall performance.

### 5. Stay Consistent:

Adhere to your study plan strictly. Consistent studying aids in better understanding and retention of knowledge.

### 6. Seek Help When Needed:

If you’re struggling with a particular topic or concept, don’t hesitate to seek help. You can ask your teacher, classmates, or even seek help online.

Remember, a study plan serves as a roadmap towards your goal of scoring an A1 in Add Maths. However, it requires dedication, hard work, and consistency to effectively use the study plan. Stick to your plan, keep practicing, and don’t forget to take care of your health as well. Success is sure to follow.

Remember, consistent revision is key to doing well in examinations. As long as you’re dedicated and diligent, you’re on the right path to achieve your desired A1 grade. Good luck!