Focus on Locus 1: First Things

Focus on Locus 1: The First Things

Locus is one of the most crucial questions of Math Exam and contributes more than 6% (12 marks) to the final exam score. Candidates ought to take the topic seriously and carefully attempt the question.

There are few major concepts that must be mastered on the topic

1. Learn to construct a 60, 90, and 120 degree angles

These are most common requirements of exam questions. They form the basics of loci and other angles are build upon these angles.
Candidates should be able to construct these angles using compasses and rulers only. Accuracy and visibility of arcs, labels and lines guarantee a higher score.

2. Learn to bisect a line and an angle.
Bisecting an angle means to divide the angle into two equal angles. Bisection gives two or more small, equal angles. It's an important concepts in finding equi-distance between two lines, for instance,finding an equidistance between AB and BC.
Line bisection is finding the midpoint of a line and it's the basic concept of constructing perpendicular lines (90 degrees). This is the equidistance between two points for instance, an equidistance between A and B.

Bisection of an angle helps much in constructing odd angles like 135, 150, 105 and 150.
A 135 angle can be constructed using 90 angle concept and then another bisected 90 angle (45 degree angle). An angle can bisected further into 4, 6 or more equal parts.

Changes to Zimsec Mathematics Paper 2

Mathematics second paper will no longer be answered on separate answer sheets. The paper comes with provided spaces for workings and answers like the first paper. The structure of the paper and the questions have not been changed, the first section remains compulsory and Section B with three options.

We will only comment on the effects of this change to the paper after the exam but the likely effects can be: complexity/simplicity of the questions against the spaces provided, questions either graphs among other items.

Tips for Non Calculator Math Candidates

Although many schools have since adopted a calculator version MATHS syllabus, a significant number of candidates are still registering for a non-calculator version. Many teachers have decided to skip teaching topics that are essential for a non-calculator syllabus.

Many candidates are getting into the exam room without perfect knowledge on how to attempt a non-calculator syllabus. Finishing the second paper is still a challenge for the candidates and they lack skills to calculate complex expressions that are easy on a calculator.

Non-calculator Math Candidate? This blog posts will help you with tips and tricks around the exam.

1. Know how to use logarithms and antilogs.

Don't ignore this topic! Antilogs and logs are used to calculate complex expressions including multiplying sines, cosines and tangents of angle and other decimal fractions. Use of antilogs makes the whole life easy for you in the exam.

2. Use a ruler to look up for a value in the table.

Many candidates make mistakes when looking up a value in the tables and eventually picks a wrong value from the table lists. Make sure you use a ruler to avoid mistakes that might costs you marks.

3. Always use tables to find squares and square roots 

If you try to find squares and square roots using other means, you will obviously not finish the exam. Learn to use tables to find square roots of numbers that are not perfect squares. 

4. Use tables when multiplying decimal fractions

Decimal fractions can eat up half of your exam time if you try to multiply or divide them the traditional way. Learn how to find a solution the shorter way through the use of tables.

5. Identify a reciprocal and use tables

A reciprocal is a decimal value of a fraction whose numerator is 1. Don't stress yourself by trying to find the decimal fraction through division process, it's right there in your reciprocal tables.

These are some of the few tips for a non calculator version. If a non calculator Math candidate understand the use of tables, they are at par with someone who registered a calculator version. 

Algebraic Fractions: What to expect in the Exam!

Algebra Fractions: What to expect in the Exam!

In the previous post I highlighted that Algebra is one of the three major contributors to the Exam. Last year it weighed more than 21% of the total exam. This means it is a critical section of the syllabus and candidates need to master the tested concepts from this section.

In today's post, I will try to explain what is likely to be tested this year in November, referring to previous Exams. 

Let's begin...

1. Algebraic Fractions

Candidates are expected to apply the laws of fractions to algebraic terms. The same concepts of HCF (common denominator) and lowest term (factorisation and division) applies. The concept usually comes in two different forms and can be determined by the structure and length  of the paper.

There two forms are 

 i) Express as a single fraction 

Under this concept, two algebraic fractions must be added or subtracted. They usual have a common denominator and can be factorized to identify similar expression. Lowest term is when similar , factorized terms are canceled out to leave the fraction in its simplest/lowest algebraic terms. This is normally a Paper 2 type question usually found on the second question.

 ii) Simplify the fraction:

Simplification of an algebraic fraction can be a tedious task. Candidates are required to simplify or reduce the given algebraic fraction to its lowest terms. There are obviously identical factors both in the denominator and the numerator which must cancelled out yo leave the fraction in its lowest terms . 

This is normally a paper 1 question as observed in other November Past Papers.

 iii) Solve the Equation

The algebraic fractions are also tested as equations that end up in quadratic equations. This can be easiest to some candidates as removing the denominator can be completed by cross multiplication. They usually carry 2 or more marks depending on the complexity of the question. 

NB: These question types can be found in both papers.

In the next series of posts, I will focus on other concepts of Algebra that are likely to be tested in the Exam.

New Tutorials on YouTube

I have uploaded new videos on YouTube on Basic Algebra and Substitution , Number bases, Decimals and percentages, Rate and ratio, Simple interest

You can now watch them on the following link

http://youtu.be/CXrqmGWcBzc
http://youtu.be/LiJ50uA51PY
http://youtu.be/idK50RsjweU
http://youtu.be/J0PCdMFAxFY

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Maths Examination Structure Analysis

Understanding  an Exam structure for any subject is essential in studies and designing an Exam strategy. Candidates ought to be aware of what is expected by the Exam, it's weaknesses and strengths, and how best anyone can score higher marks in every paper.

Exam reports, past papers with answers and textbooks help much in preparing candidates for the Exam. However  it doesn't reveal the major challenge and bias of the exam structure. 

In this blog, I will analyse the Exam Structure of Mathematics, Zimsec syllabus. This analysis will complement Exam reports, Past Paper Revisions and Tutorials. It's premised upon the major strengths of the Exam, topic value, study tips and analysis of the best strategy that should have been adopted by the candidates to score high in the Exam.

The syllabus

Available in booklets and downloadable as PDF, the zimsec syllabus specifies the topics, concepts, and skills that are tested in the final Exam. It's divided into 11 major sections which are 

1. Numbers

2. Sets

3. Consumer Arithmetic 

4. Measures and Mensuration 

5. Graphs and Variation

6. Algebraic Concepts and Techniques

7. Geometric Concepts and Techniques

8. Trigonometry

9. Vectors and Matrices

10. Transformations 

11. Statistics and Probability 

An Ordinary level course should be completed in five school terms, which is less than 2 years. On average, 2 sections and 20% of another section of the syllabus is expected to be full covered. It's advisable to study Mathematics along a syllabus for guidance. 

The Exam Structure 

The piechart above shows the weight of each paper/section as specified in the Syllabus. 

The first paper contributes 50 percent of the total exam Mark. It carries upto 30 questions worth 100 marks and tests almost the whole syllabus. There are no options for the paper and every candidate is expected to attempt all the questions without the use of calculators or tables. 

The second paper is divided into two sections, Section A which is 64% of the paper and has 6 compulsory questions. Section B has 6 questions which carries equal marks and candidates are expected to opt for 3 questions only. This section carries 36% of the paper. 

In total, the second paper contributes 50% to the final Exam Mark, which means Section A contributes 32%, and Section B 18% to the Exam Mark.

Case study: November 2014 paper 1 & 2 

We are going to analyse the structure of November Session 2014 (Not the replacement) Exam. We have chosen the original paper since it was the Zimsec's first choice and reflects the best standards for the Exam. 

The two papers will reveal to us the distribution of topics from the syllabus in 2014 examination, Mark allocation for each topic and the major strengths of the Exam. 

The following sections were tested and Mark allocation for each topic are shown in the table

Table 1: TOTAL QUESTIONS FOR EACH SYLLABUS SECTION

 

The above table shows the total questions for each syllabus sections. The section with highest number of questions for the November 2014 Mathematics Exam was Numbers/Consumer arithmetic, followed by Algebraic Concepts and Techniques and then Geometrical Concepts and Techniques. Many questions were in Paper 1 and the Section which appeared in many questions in Paper 2 was Measurement and Mensuration.

This shows that there are Sections which are the backbone of Paper 1 and others are reserved for Paper 2. Algebra and General Arithmetic appear to be the major topics for the Maths Exam. They contribute significantly to the Exam.

Table 2: TOTAL MARKS FOR EACH SYLLABUS SECTION

The table shows the total marks allocated for each section of the syllabus in the November 2014 Exam. We see that the sections which had many questions also carried more marks for the total exam score. 

Algebra and General Arithmetic weighed more than 40% (combined) of the total exam Mark. Other valuable topics for this Exam were Geometric Concepts and Techniques, Measures and Mensuration and Statistics and Probability.

You can also see that Geometric concept Mark allocation were balanced in both papers and Measurement and Mensuration weighed more in Paper 2.

The graph above reveals that Sets were the least topic in the Exam and those who put much effort in algebra, Numbers and Geometrical concepts were guaranteed of a pass in this Exam...

Recommendations 

We can draw many lessons from the structure of the Exam and mark allocation for each syllabus section.

1. Algebra, Numbers and Geometrical concepts were the major part of the Exam

2. Measures and Mensuration, Transformations and Statistics and Probability are mainly paper 2 questions

3. Paper 1 is the most important since it contributes more to the Exam

4. Section A contributes significantly more than Section B to the total Exam Score

5. Time management for Both papers is essential.

For an in-depth analysis of the Exam, study tips and more recommendations please download a PDF document in the downloads section on this blog.

Mistakes To Avoid During An Exam

Mistakes to avoid in an Examination

A final exam is different from all mock exams that are written in midyears, or end of year exams. A final exam comes with surprises and twisted concepts that requires a new and different approach to the same old topic. 

Midyears and End of year Exams at schools are filled with "standard" questions that taken from from past papers and it's highly likely that you have once met the questions before. A majority of teachers doesn't like to temper with the values and structures of the past questions, thy believe it can distort the standard process of solving typical exam questions. This makes all papers common and easy.

Nevertheless, a Zimsec or Cambridge final exam comes with new, unique questions that test your very mathematical skills rather than sharpness of your memory. You might have met a similar question but not exactly as the one in the final exam.

This exposes you to many mistakes that costs you in the Exam.

Below I have identified few common mistakes and how they can be avoided

1. Don't rush to attempt questions, take your time to study the question

Candidates will be afraid they can't finish the Exam if they delay even for a minute. They rush to work out solutions before fully understand the requirements of the question. They apply methods they are familiar with and doesn't take a breath to think new ways of solving new questions. They later discover that they have provided a wrong solution few seconds before the end. 

Take your time to read and understand the question and its requirements before attempting anything. It's better to omit other questions and correctly answer the few that guarantees a pass.

2. Study the structure of the paper before answering the questions. 

Every candidate at least knows the structure of the paper she or he is going to write and prepares the strategy to the paper. Little do they consider every paper. Although structure can be similar, has its uniqueness that requires a different approach to be successful. 

Mathematics Paper 1 starts with 13 questions that carry 39 marks (39%) and take almost half the length of the paper. The remainder, which is about 12 or 13 questions carry 61% of the paper.  Majority of students don't finish the paper as they try to perfect solutions for the first questions. They eventually fail the exam, they waste time concentrating on less important section of the exam.

3. Carry all Exam requirements even if you don't intent to use them.

A math exam requires pencils, pens, mathematical sets, strings, rulers and calculators. Only few carry all the instruments for the exam and some avoid some of the sections of the exam. In the first paper, candidates don't expect topics like Locus, Transformation, Vector(2) and graphs but to their surprise they meet these questions in the same paper.

Many candidates have to omit the question, skip to return or wait to share the few instruments brought into the exam room. 

NB: calculators are not allowed in Maths Paper 1 exam.

4. Avoid sleeping in an Exam.

Some candidates are faster and accurate and finish the paper in the middle of the Exam. They are tempted to sleep for a few minutes, whilst awaiting collection of papers. This will cost you marks if you happen to omit other questions or inadequately answer a specific question. Take time to ask yourself "Why others are still writing?" 

Check if your papers are numbered correctly and labelled. Review your answers before submission and add necessary information that might have been omitted

Mistakes To Avoid During An Exam

Mistakes to avoid in an Examination

A final exam is different from all mock exams that are written in midyears, or end of year exams. A final exam comes with surprises and twisted concepts that requires a new and different approach to the same old topic. 

Midyears and End of year Exams at schools are filled with "standard" questions that taken from from past papers and it's highly likely that you have once met the questions before. A majority of teachers doesn't like to temper with the values and structures of the past questions, thy believe it can distort the standard process of solving typical exam questions. This makes all papers common and easy.

Nevertheless, a Zimsec or Cambridge final exam comes with new, unique questions that test your very mathematical skills rather than sharpness of your memory. You might have met a similar question but not exactly as the one in the final exam.

This exposes you to many mistakes that costs you in the Exam.

Below I have identified few common mistakes and how they can be avoided

1. Don't rush to attempt questions, take your time to study the question

Candidates will be afraid they can't finish the Exam if they delay even for a minute. They rush to work out solutions before fully understand the requirements of the question. They apply methods they are familiar with and doesn't take a breath to think new ways of solving new questions. They later discover that they have provided a wrong solution few seconds before the end. 

Take your time to read and understand the question and its requirements before attempting anything. It's better to omit other questions and correctly answer the few that guarantees a pass.

2. Study the structure of the paper before answering the questions. 

Every candidate at least knows the structure of the paper she or he is going to write and prepares the strategy to the paper. Little do they consider every paper. Although structure can be similar, has its uniqueness that requires a different approach to be successful. 

Mathematics Paper 1 starts with 13 questions that carry 39 marks (39%) and take almost half the length of the paper. The remainder, which is about 12 or 13 questions carry 61% of the paper.  Majority of students don't finish the paper as they try to perfect solutions for the first questions. They eventually fail the exam, they waste time concentrating on less important section of the exam.

3. Carry all Exam requirements even if you don't intent to use them.

A math exam requires pencils, pens, mathematical sets, strings, rulers and calculators. Only few carry all the instruments for the exam and some avoid some of the sections of the exam. In the first paper, candidates don't expect topics like Locus, Transformation, Vector(2) and graphs but to their surprise they meet these questions in the same paper.

Many candidates have to omit the question, skip to return or wait to share the few instruments brought into the exam room. 

NB: calculators are not allowed in Maths Paper 1 exam.

4. Avoid sleeping in an Exam.

Some candidates are faster and accurate and finish the paper in the middle of the Exam. They are tempted to sleep for a few minutes, whilst awaiting collection of papers. This will cost you marks if you happen to omit other questions or inadequately answer a specific question. Take time to ask yourself "Why others are still writing?" 

Check if your papers are numbered correctly and labelled. Review your answers before submission and add necessary information that might have been omitted

5 people who can make you fail or Hate Mathematics.

5 People who can make you fail Mathematics

Mathematics is a unique subject. It needs great attention, higher level of understanding, sharp memory and concentration during learning or a study. Miss a lesson and it will torment you all the days of your live. You can be motivated by your environment and people who hang around with you.

However, they are people who can distract your concentration in mathematics. They will try to convince you that they are more intelligent than you, and if they are not successful in the subject, you will also definitely fail. Someone actions will also discourage you from following recommended path to be successful in the subject.

Let's briefly analyze them

 

1. Your Teacher

A teacher contributes at least 50% to your success in any subject. The remainder is attributed to hardworking, source of information, attitude towards the subject and exam skills. If a teacher discourage you and also claim you are going to fail the subject, it's highly likely you will fail the exam. 

A teacher can simply avoid helping you, or letting you know the source of your errors. Many teachers selects students to concentrate with, and leave the rest to fail. Other teachers believe it's a waste of effort to coach slow learners and below average performers

2. Your Classmate/Schoolmate

Classmates or schoolmates who are challenged by any subject will try to incite others to also hate the subject. They will even statistically prove to you that many students from your school fail the subject and concentrating on it is just a worst of time. This can change your philosophy towards the subject and eventually result in a failure

3. Your Parent, Brother or Sister

When a child fails or succeeds in school, parents and family members try to justify it by now they performed in school. Others will even blame each other for the failure of their children. They believe intelligence is a genetical. You can be discouraged from mathematics through their beliefs and justifications. 

4. A candidate  next to you in an Exam

Actions of other candidates in an Exam room can affect your performance. At times, it's wise to ignore whatever is happening in an exam and concentrate on your work. Before e-marking was widely adopted, candidates used to write on sheets of paper. You would see others raising their hands for more answer sheets and submitting a booklet of answers, when you have just answered in only 3 or 5 sheets. Others would request graph paper but you haven't located questions that required a graph. 

You can spoil your work by trying to expand what you have already written. Fresh minds have best answers. By trying to revise what have been answered by fresh minds when tired will only guarantee you failure. 

5. Your FRIEND

Friendship is a result of something in common. True friends will try to match their characters and attitudes in everything. Even in the classroom, they will behave the same.if your friend hates the subject, you will eventually buy into it. Friends are greatest threats to our abilities.

10 things to do few months before the Exam

What to do few months before the exam

Ordinary level syllabus takes about 2 years or less to complete but many schools struggle to cover it in stipulated time. They end up "spotting" and concentrating on critical topics that will at least make the pupils successful in an exam.

You are in that situation and still struggles to finish studying textbook principles from cover to cover. At times you are afraid that what you left out in the textbook will be tested and fail you the exam. 

Don't worry there are few things that will guarantee your success in any exam.

1. Study the structure of the Exam.

Don't ever allow yourself to take an Exam without knowledge of its structure. It will confuse you, kill your time and expose you to many mistakes. 

Study the trend of the Exam for the past 3 or 4 years, you will discover the nature of the question, arrangement of the topics and weight of each question type.

2. Estimate maximum time for each question.

Calculate the total time in minutes for the whole exam and divide by the total marks awarded. You will determine stipulated time for each Mark of the Exam. This helps you to finish the exam in time and allow for revision

3. Study Exam Reports, identify errors made by other candidates.

Common mistakes from all candidates are highlighted in the exam report. It's a useful document for both teachers and students. It helps candidates to avoid those mistakes in an exam and guarantees higher marks. Make sure you download or photocopy the exam reports and read them well before the exam

4. Study the marking scheme, how the marks are awarded

The marking scheme shows how marks were allocated to all the questions in the Exam. It helps you know how far you must go to score higher marks. It's also a source for authentic   answers for the past exam papers

5. Practice the questions along correct answers

Practice exam questions with correct answers provided in the marking scheme and greenbooks/reds pots . Don't over depend on your teachers answers, they are also prone to mistakes that costs you in the exam 

6. Attempt the full paper in stipulated time or less

Practice makes perfect. You can identify your weaknesses or strength without putting yourself to test. Make sure you take past papers and practice the whole paper within stipulated time. This exposes you to an exam condition and well prepares you for the Final exam

7. Join study groups and learn new exam skills from others

You can't know everything no matter how intelligent you are. Group world and discussions will open your mind. Helping others also teaches you better methods as you try to make someone understand

8. Identify where major part of the exam lies

Every exam has its core area where a lot of marks are awarded. Identifying these areas will make you successful in an exam. Acquaint yourself with the area and prepare for it.

9. Revise many past papers 

This is an obvious step. We can well prepare the future by looking into the past. It's a rich source of the exam structure. It represent principles that are likely to be tested.

10. Know your strengths and weaknesses 

Identify your strengths and weaknesses. Find solution for your weaknesses and reinforce your strength for better performance

A video lesson on Coordinate Geometry : length of a line

This video lesson will teach you how to calculate length of a line using coordinate geometry principles

A video lesson on coordinate geometry-midpoint.
The video will take you to the basics of coordinate geometry and simple method of calculating a midpoint of two given points or a line.

Build up your Maths skills through simple ways

Building your mathematical skills

Finding a solution for a math problems requires a certain level of skills. Although one can be born with a skill, it needs maintenance, refining and development. In other words a skill is developed by practice and exposure to new challenges. 

Many students think Mathematics is for those born with brains that are comfortable digesting a mathematical solution for any given problem. They don't understand that a skill can be a acquired through simple hacks. Anyone can be successful in Mathematics if the rules of the discipline are religiously followed.

In this blog posts I will look into easy and fastest ways of acquiring a problem-solving skill for mathematical problems. These tricks can sharpen your mind and ignite a passion for the subject in a short of period of time, if correctly applied.

1. Know the basics

Many students think if they ignored or dodged maths lessons in primary school or at any level of Education, they can get away with it. The ghost will continue to haunt you until the end of your academic journey. 

Understanding the basics is the first rule in mathematics. Go back to primary level principles, study the basic operations of mathematics including the "long division" concept. Understand the nature of fractions, volumes and mass, basic geometrical calculations like area. 

2. Test your level of understanding 

When studying, measuring your skill level is one of the most effective ways to grasp concepts. By just letting your eyes pass through a passage or a formula without writing something or test if you have understood the concept, you are digging your own academic grave. You can test your skills through answering basic questions, referring to standard questions for that level and attempting questions from your colleagues.

3. Join a study group

A group work is a proven way that increases your level of understanding. Joining others to study mathematics through discussions, mock questions and school assignment improves your problem solving skill. A group study can facilitate exchange of ideas, new skills, skill development and passion development.

4. Participate in class or in group works

Participation builds confidence and passion. It shows you have at least a background for the concepts. It drives you to study the concepts earlier in preparation for the lesson or discussion. When a teacher or a colleague revisits the concepts you already attempted, it becomes easy and clear. It guarantees your success and corrects  your mistakes earlier. 

There are many hacks for mathematics but these are the simple and fastest ways to learn mathematics. 

How to choose your A' Level Combination

Choosing an A Level Combination

A level is an important stage in our academic ladder and determines our careers and future. Many students start to make decisions when Ordinary Level results are out or during the course of Advanced Level itself. This might be attributed to different reasons ranging from lack of knowledge to Ordinary level subjects passes.

Few students plan for their future while in the early stages of secondary education. Some are guided in their academic and professional decisions by their parents, guardians, brothers and sisters and some by their relatives or friends. There is really need for carrier guidance for a successful academic route everyone takes.

However, following your passion seems to be the best determinant of whatever we eventually pursue in life. Relatives and Friends who advices have their own passions and ability different from ours. Their strengths and weaknesses might be totally different from ours.

Whilst there is no correct formula to determine our passions or ability, there are other obvious ways to identify our successful route. The process of identifying ourselves can start as early as primary school education or early secondary stage.

1. Identify your strength and weaknesses 

It's easy to identify that we perform better in particular subjects than in other subjects. This can be either mathematics, history or english literature. At primary level, you can be doing best in Mathematics and English language. Knowing your strengths helps you determine your academic route earlier. 

2. Know your passion.

When you enjoy doing something, then it ceases to be your job but becomes your passion. Follow your passion and success will follow you, goes the adage. If you want to live happier and healthier, know and follow your passion. At school, our friends might encourage us to pursue a certain profession because someone did this and become successful in life. If it's not your passion, you will never enjoy your job nor your studies. 

3. Acquaint yourself with the next academic stages

Many students proceed to the next academic stage without any plans. About 90% of A level students didn't have their own choices for their combination but were either allocated by the school or followed the crowd. 

Looking for information on the careers you wish to pursue is vital in choosing both your O' and A' level subjects. Those who had a passion for medicine didn't know you need to focus on pure sciences, those who wanted to be lawyer never knew the requirements of the discipline at the University level. It's important to know about the academic requirements for your passion and ideal job. 

Transformation : Tips and Tricks

Transformation: Tips and Tricks

Although perceived as the most challenging option in Section B of Paper 2, the topic has the easiest questions in the paper. The first question doesn't need you to know the concept of transformation but the Cartesian plane. Let's analyse possible question structure on transformation:

Part (a) this question usually requires candidate to identify the coordinates of the shape and draw it on the Cartesian plane. The normal value of the question is 2 marks

(b) usually translation T - you will be given a column matrix (column vector) to translate the shape drawn in (a). You are required to calculate the new coordinates and then draw the translated shape. Value of the question is 4 marks

(c) Rotation/Reflection - these are slightly challenging questions to few candidates who attempts this question. The textbook and teachers usually restrict the concepts to Origin/y-axis/x-axis but the questions in this section provides you with a different line of reflection or point of rotation(invariant) and requires you to calculate new coordinates and draw the reflected/rotated shape. 

(d) Combined transformation - the question either gives you coordinates of another shape or just illustrate the shape on a diagram. The common concepts tested are enlargement with rotation or reflection, shear with translation or anyway. In recent years  the questions have not been testing Shear and stretch but enlargement.

(e) description- the question requires you to observe and fully describe the transformation on the given diagrams illustrated on a Cartesian plane. They want you to identify the movement, direction and change to the original shape using either observation or calculation by matrices.

Tips

Translation- remember to add each set of coordinates by a given translation column vector T to find the position of a new shape.

Reflection - identify the mirror line and its equation, by observing similar sides and points. You can find the line of reflection by calculation it can be in the y or x-axis or along y=x line. The matrix is usually rep by N. 

Rotation - center of rotation (invariant point) will be a major theme of the question. Remember to identify the 90 degrees (clockwise/anti clockwise) and 180 degree rotation as stipulated by the syllabus. Rotation matrix is usually rep by R

Enlargement- scale factor and center of enlargement are major demands of the question. Remember to to find factor by factoring out common terms out of the enlargement matrix.

Invariant - means unchanging point or line in transformation.

For demonstrations and further explanation, register for our Facebook Class on Vectors, Matrices and Transformation. The learning materials includes Video tutorials, worksheets, tutorial notes and exercises, 

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Basics of Transformation

Transformation: Fundamentals

Transformation is one of the few topics avoided by majority of both candidates and Teachers. They discourage each other to attempt any question that has elements tied to transformation.

However, the topic has been a regular in section B of the second paper and Zimsec has recently introduced part of the topic in Paper 1 and Section A of Paper 2. This has however made it necessary to at least appreciate its fundamentals even to those who will avoid it in the second paper

Pre-requests of the Topic:

- position vectors 

- matrices operations

- knowledge of the Cartesian plane

- Congruence 

- basic knowledge of plane shapes

Before attempting to study the topic, make sure you are good at the above topics. That way your life will be easy.

 

Elements of the Topic:

> congruence elements: Translation, Reflection and Rotation

These are the areas mainly tested in the first paper and section A of Paper 2. It's imperative to know the basic principles of these areas.

> further elements: Enlargement, Stretch and shear (stretch and shear is not part of Cambridge)

> Use of matrices and vector elements in calculations 

In the next posts we will look at tricks and tips of all these areas.

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Do you Trust your Textbook?

Textbooks: the Good and the Evil

'O' Level Math Bible (New General Mathematics) arrange the topics strategically and psychologically. The authors designed it in a way that ensure candidates will have a bit of everything. They randomly distributed the topics and separated similar concepts in different topics. They bore in mind that for many, it's not possible to  cover all the topics of the syllabus.

The main aim is to allow candidates:

- gradually acquire knowledge and skills in every topic

- to cover parts of all topics in a year

- to carefully study and practice every concept of every topic

- break from a challenging topic and refresh with new concepts.

Many teacher religiously follow the topic arrangement until they finish the two books. Some skip other topics to return to them later. The learning path is hugely determined by the Teacher who designs a school syllabus. 

On the other hand, The arrangement of the "sub-topics" has its drawbacks as far as completing a study of all principles is concerned.

The major concern of this are:

- what if you do not cover all topics in the textbook?

- does topic breaks positively contributes to students' understanding?

- will every one follow the arrangement of the topic for two years?

- doesn't the arrangement hide other major topic principles?

Only a few cover all the topics and use other textbooks due to limited learning and preparation time. Many candidates will have to face the exam with limited options. Given this scenario, if they miss the last 8 questions of Paper 1, the lose 49 marks.

What are your strategies to cover all the concepts?

Do you really have enough time to cover the whole syllabus?

For those who are retaking the Math exam, what's is the best method to prepare for the exam?

Next posts will focus on study skills

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