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
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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