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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How the Exam steals your time

How the Exam Structure Steal your Time. (The First Paper)

Zimsec mathematics exams come in 2 papers, a structured and short questions that test more than 80% of the syllabus (Paper 1) and solid, long questions including a section with choices (Paper 2).

Paper 1 has about 25 - 27 structured short questions that carry a total of 100 marks. It is the most important paper as it has no options and the candidate is forced to attempt every question if he or she is to score higher marks.

The paper contributes 50% percent of the total score, which implies every percent is worth 2 marks. 

The most common comments after the exam is "I didn't finish the paper", "I wasted my time in the middle of the paper", "I don't think it's possible to attempt all the questions,they are just too many for 150 minutes( 1,5 minutes for every mark)", "I lost my concentration just after the easy questions " and so on.

In this post, I will briefly analyze how the paper steal your time and effort and eventually fail you.

MATHS is a tricky exam, without effective exam strategy you are bound to fail.

Let's first look at the structure of the paper:

- 25 up to 27 questions

- more than 35 concepts are tested 

- starts with low value questions (General Arithmetic) that are worth 1 mark

- high value questions are at the end of the paper

Marks Distribution Bias :(Refer June Paper 1, 2013)

- first question carries [3 marks]

- first 13 questions Carry [36 marks]

- from No. 17 up to No. 25 carry [49 marks]

- last three questions carry [20 marks]

- last question carries [8 marks]

Facts of the data:

* first half of the paper is worth 36%

* last third(last 9 questions) of the paper is half of the exam

* last question carries marks that are for three questions in the begin of the paper

The above analysis exhibits that the paper is structured in a way that makes you leave the valuable part of the paper, if you don't finish up. The first questions serves the purpose of tiring you before the real test. You will have to attempt the last part loaded with lots of marks tired, wasted and prone to making silly mistakes. Your motivation for the exam will have been wasted when you reach the last part.

What strategies can be employed to ensure highest score in the exam? Check out the next posts.

We will analyze the second paper in the next post

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Secret to Zimsec Exams (Part 2)

Secret to Zimsec Exams (Part 2) 

Who the Exam favors?

Jungle favors the brave and the tireless, so they say. Mathematics is a unique discipline that has its own approach and learning style. Break the rules, you will pay for it. Religiously follow them and it will handsomely reward you.

The only reason why the same schools continue to dominate Zimsec Rankings is their approaches to the subjects and how they prepare their students for the exam. Their organisational/school culture is cultivated and nurtured in a way that the system will never depend on teachers but on the school and students. 

On My first day at school where I did my A Level, I was surprised to know that 90% of our Math class had 'A's in Maths and majority were former students at the same school. Their first class had 33 students and scored 32 As. The school was under-staffed and they had gone for a full term without a Math Teacher. I learnt that it's only organisational culture backed by study strategies that guaranteed success for the pupils.

Some of the strategies that were employed by students included:

1. Through revision of past papers.

There is need to revise as many past exam papers as can be accessible. The questions may not  be similar but principles, nature and approach to the questions remain the same

2. Memorize what you have practiced 

One day after a Math exam, I overheard a conversation by some of our students saying "No. 4 is exactly No. 7 of paper 1, 1992". If you throughly practice past papers, it likely that you will come across  similar questions in the exam. 

3. Organize Past Papers' Questions in Topics

Those  who study A level Maths know how effective a revision book by "Teo" is. It's only past exam questions organized topically. By concentrating on bulk of questions for a particular topic, you will improve your memory, skills and creativity for the exam. You will easily answer any question for any given topic.

4. Use Red Spots of 1990s

Green_book can be effective in exam preparations but not more than the Cambridge Red Spot. We now know Zimsec derives its questions from Old Cambridge past papers. It's important you familiarize yourself with old Cambridge questions. Using both Greenbook and Redspot is advisable.f.b

5. Groupwork is vital

Different people comes with different strengths and weaknesses. By working in groups we compliment our skills, approaches and resources. Even if you are always busy, find a way to interact with other candidates. Given the wide use of social networks, it's now more easy to share questions, solutions, ebooks, past papers or solution methods.

6. Work with authentic answers and Exam Reports

Study along verified answers. Questions without solutions can be a snare. Ask your colleagues or teachers if answers are not yet available. Exam reports provide answers and common mistakes noticed.

These are some of the approaches that can best prepare you for the Exam. In the next part we will discuss about the secrets to arrangements of questions and how they can fail you.

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Common Elements in Zimsec Examination (Maths)

Zimsec Exam Toolkit 1

" Common Areas "

In the last series of "Secret to Zimsec Exam" posts, we exposed some of the hidden elements of the Exam including structure of the papers and Mark distribution bias. 

In this series of posts, we will concentrate on Specific Topic that will guarantee a pass and how one can effectively plan for the exams.

"Common" Exam Behavior

Most people from all walks of life perceive math as the most challenging of all and chose either to ignore the subject, or the other topics, or the other paper or other questions. They dedicate their time to what they view an effective strategy which does not yield any dividend most of the time. 

"Common" Ignorance

Many candidates and students of mathematics spend the major part of the time working out solutions for specific topics and mathematical problems. They eventually fail the subject or pass with the minimum marks. 

They are ignorant of the exam structure, question structure and value of particular questions. Many don't even have a clear strategy for the exam and spend part of the exam trying to figure out how they can score higher marks that can guarantee a pass.

"Common" Exam Structure

The standard exam structure for Paper 1 is 25-30 simple questions from more than 26 chapters. Many candidates don't attempt the last 5 - 8 questions of the first paper (surprisingly, they carry nearly 36 - 45 marks), which is almost half of the exam. 

The second paper has six compulsory questions in section A and  six questions in Section B where a candidate is required to chose only three. (Surprisingly, many candidates concentrate on section B options and lose most of the marks in section A, which is 64% of the exam)

"Common" Questions in Section A of Paper 2

- Algebraic Fractions and fractional equations

- Percentages, Ratio, Rate and Simple Interest

- Sets

- Circle Geometry

- matrices with vectors

- substitution and triangles involving algebra/similarities 

- locus

"Common" Questions in Section B of Paper 2

- mensuration 

- Vectors (properties of shapes)

- transformation 

- cubic function/ velocity-time curves / quadratic graphs

- linear programming 

- Triangle (sine rule)