About the optional questions in N level Mathematics Paper 2

About the optional questions in N level Mathematics Paper 2

This article explores the optional contents, which will appear in the N level Mathematics Paper 2 and how students can exercise their options to score full marks in Section B of Paper 2.
This article aims to help students who are struggling with Math to maximise their time by studying mininal contents in order to get a good grade.
Students who are strong in Mathematics and aspiring to go on to do O levels at Sec 5 should study everything and make sure their foundation is strong to cope with the demands of O levels.

First, let’s look at the Scheme of Assessment in the photo below for the N Level Mathematics Papers.

Notice in section B of Paper 2, students are require to choose only one out of two questions and the two questions are from each of the strands ‘Geometry and Measurement’ and ‘Statistics and Probability’. That is, one question from the ‘Geometry and Measurement’ strand and one from the ‘Statistics and Probability’ strand.

Let’s first take a look at what are the topics under each strands which will appear in Section B.
Underlined portions in the photos taken from the syllabus are the optional contents which will apear in Section B only.

From Geometry and Measurement 

As we can see, the three main optional topics from the Geometry and Measurement strands are

1. Properties of Circles
2. Further Trigonometry – Sine Rule, Cosine Rule, Angle of Elevation and Depression, Bearings.
3. Radian measure of angle

From Statistics and Probability

From the Statistics and Probability strand, the optional topics are

1. analysis and interpretation of cumulative frequency diagrams and  box-and-whisker plots (inlcuding quartiles and percentiles)
2. range, interquartile range and standard deviation as measures of spread for a set of data • (including calculation of the standard deviation for a set of data (grouped and ungrouped))

3. compare two sets of data using the mean and standard deviation

4. probability of combined events (including using possibility diagrams and tree diagrams) and addition and multiplication of probabilities (mutually exclusive events and independent events)

Since each of the 2 questions in Section B will be fully from one strand only and will not involve the other strand, if you are going to give up on one particular part from one strand then you must study the entire part of the other strand. 

For example, if I decided to give up on Properties of circles from the Geometry and Measure strand, I will need to study all of Statistics and Probability. It then makes sense to also give up on Further Trigo and Radian Measure since I’ve given up on Properties of Circles since these will not come out anywhere else on both papers except in the question with Properties of Circles. I must, however, study everything in Statistics and Probability and not give up anything in this strand.

I cannot choose to study probabilties for combined events but give up on quartiles and percentiles because they are going to come out in the same question. Just as I cannot just study Radian Measure and give up on Properties of Circles.

I also cannot just study Probability of Combined Events and Properties of Circles but not study Quartiles, Percentiles, Standard Deviation and Sine Rule, Cosine Rule, Radian Measure. If I do so, I will then only know how to do half of each of the options.  

So to make sure you score the full 7 to 8 marks for Section B of Paper 2, you have to make sure you study the full set – either all of ‘Geometry and Measurement’ or all of ‘Statistics and Probability’.

If you ask me which strand is better, I’ll say it really depends on you. I’d say Statistics and Probability is easier since it’s mostly calculations, which can be easily done on the calculator and comparison of two sets of data is really limited, usually just two things – mean or median and spread. It is also a lot less to learn then the stuff in Geometry and Measure. However, some people just don’t get probability of combined events. So In this case you’ll have to consider Geometry and Measure. On the other hand, some people just don’t get bearings or radian measure so they’ll have to go for Statistics and Probability.

With this, I conclude and wish you all the best in preparing for you N level examinations.


For more about the N level Math syllabus, read https://arielsmathworkshop.blogspot.sg/2016/07/differences-in-new-n-level-emath.html

Differences in new N level EMath syllabus starting from 2016

This post seeks to discuss the differences between the new N Level Elementary Mathematics, Syllabus A (EMath, subject code 4045, examination starting 2016) syllabus from the old syllabus (subject code 4042, last paper 2015).

Both syllabuses can be obtained from https://www.seab.gov.sg

0.     Introduction

“4045 MATHEMATICS SYLLABUS A NORMAL (ACADEMIC) LEVEL (2016) INTRODUCTION


The syllabus is intended to provide students with the fundamental mathematical knowledge and skills. The content is organised into three strands namely,

1. Number and Algebra,
2. Geometry and Measurement, and
3. Statistics and Probability.

Besides conceptual understanding and skills proficiency explicated in the content strands, development of process skills that are involved in the process of acquiring and applying mathematical knowledge is also emphasised. These include

• reasoning,
• communication and connections,
• thinking skills and heuristics, and
• application and modelling;

and are developed based on the three content strands.”


Summary of the big picture:

As with the new O level syllabus, 4048, besides the technicality of solving mathematical problems, the new syllabus 4045 aims to shift the focus to the learning process and application of Mathematical knowledge to real world problems/ context.

A. Scheme of Assessment or Paper format

Duration, total number of marks and weightage of Both paper remains the same.

Changes:

1.     Paper 1 no longer focus test more on fundamentals and Paper 2 on higher order thinking skills but both papers under the new syllabus can test on both fundamentals and higher order thinking skills.

2.     In addition, Paper 2 will now contain one question which “focus specifically on applying mathematics to a real-world scenario.” This real-world scenario question is not limited to financial arithmetic as some have perceived it to be. In both the specimen papers for the New Syllabus O and N level papers, the real-world scenario questions involves volume, density and even weight per unit area in the O level paper.

3.     Section B of Paper 2 will now contain 2 questions in which students have to choose only 1 instead of the previous 3 choose 2.
The 2 questions will be from the two strands
(i)        Geometry and Measurement, and
(ii)       Statistics and Probability.

4.     Consequently, the “Numbers and Algebra” strand will be compulsory. This means the drawing of graph, which many students used to avoid, will no longer be optional.

B. Subject Content / CONTENT OUTLINE

One may scroll thru' the "Subject Content" sections in both syllabuses and conclude that there is little or no change in the subject content. This is not true. Let's just take a closer look.

1.     Removed: Concepts of rounding and Truncation errors, Pre-fixes.

No more needing to memorise Mega, Giga, etc.

Indeed. There wasn’t any questions involving prefixes in the specimen paper with the exception of converting m (metres) to km (kilometres).

I’d think students will also be expected to convert mm, cm, m and km. 

2.     Removed: Sketching of quadratic graphs

Now Compulsory: Graph drawing

As mentioned in the previous section, graphs drawing (on graph paper) is now compulsory. 

3.     Newly added: Solve Numbers and Algebra Problems based on real-world context 

including

·       travel plans,

·       transport schedules,

·       sports and games,

·       recipes,

·       etc

as well as interpret the solution in the context of the problem. 

Removed: drawing of graphs from given data.

Below is a question taken from the specimen paper and one from 2015’s N level paper.

4.     Newly added: Solve Geometrical Problems based on real-world context

 including

·       floor plans,

·       surveying,

·       navigation,

·       etc

as well as interpret the solution in the context of the problem.

In both O level and N level Specimen papers, students are expected to make decision based on their calculations.

Below is an example of this real-world context question from the Specimen Paper.

5.     Newly added: Misleading statistical diagrams.

In the new syllabus 4045, candidates are expected to explain “why a given statistical diagram leads to misinterpretation of data”.

Also, the construction of statistical charts and tables are no longer required. Instead, candidates should focus on analysis and interpretation of data and using them to compare two sets of data.

Below is an example of a misleading statistical chart from the specimen paper.

Conclusion

Some students think the new syllabus is harder. 
This can be true for N level students as there now are more applications, more contextualised questions, comparison and decision making based on calculations. Just memorising steps to solve Math questions mechanically is no longer sufficient.
 
Personally I love it. It makes Math more relevant to real life, more visual and more useful.
As a parent and educator, this is also my aim: to make what my children and students study relevant and useful to them. 

So fellow parents, let's make an conscientious effort to help our kids see Math in our everyday lives and fellow educators, let's include interesting and relevant learning experiences in our lessons and make our questions more authentic. 

click for changes to the new 2016 O level EMath syllabus.

follow me on Facebook where I share more ideas on the teaching and learning Mathematics.http://www.facebook.com/ArielsMathWorkshop

Solutions to N Level 2015 AMath P2 4044/02

Solutions to N Level 2015 Additional Mathematics Paper 2 4044/02

Solutions to N Level 2015 AMath P1 4044/01

Solutions to N Level 2015 Additional Mathematics Paper 1 4044/01

Differences in new O level EMath syllabus starting from 2016

This post seeks to discuss the differences between the new GCE O Level Elementary Mathematics (EMath, subject code 4048, examination starting 2016) syllabus from the current EMath (subject code 4016).

Both syllabuses can be obtained from https://www.seab.gov.sg

A. Scheme of Assessment or Paper format

In general, the format of Both paper remains the same, i.e. all questions are compulsory, duration, number of questions, total marks and weightage of each paper remain unchanged.
The change is actually in question types. 

1.     Paper 1 no longer focus test more on fundamentals and Paper 2 on higher order thinking skills but both papers under the new syllabus can test on higher order thinking skills. 

2.     In addition, Paper 2 now contains one question which “focus specifically on applying mathematics to a real-world scenario.” This real-world scenario question is not limited to financial arithmetic as some have perceived it to be. In fact, real-world scenario questions for financial arithmetic were already in the current syllabus 4016. 

In both the specimen papers for the New Syllabus O and N level papers, the real-world scenario questions involves volume, density and even weight per unit area in  level paper. 

Let's look at the introduction to the new syllabus:

4048 MATHEMATICS GCE ORDINARY LEVEL (2016)

“INTRODUCTION
The syllabus is intended to provide students with the fundamental mathematical knowledge and skills. The content is organised into three strands namely,

• Number and Algebra,
• Geometry and Measurement, and
• Statistics and Probability.

Besides conceptual understanding and skills proficiency explicated in the content strands, development of process skills that are involved in the process of acquiring and applying mathematical knowledge is also emphasised. These include

• reasoning,
• communication and connections,
• thinking skills and heuristics, and
• application and modelling;

and are developed based on the three content strands.”

so here's my summary of the big picture:
Besides the technicality of solving mathematical problems, the new syllabus 4048 aims to shift the focus to the learning process and application of knowledge to real world problems/ context.

B. Subject Content


One may scroll thru' the "Subject Content" sections in both syllabuses and conclude that there is little or no change in the subject content. This is not entirely true. Let's just take a closer look.



1.     Removed: Concepts of rounding and Truncation errors, Pre-fixes.

No more needing to memorise Mega, Giga, etc.

Indeed. There wasn’t any questions involving prefixes in the specimen paper unlike past year papers from the Current syllabus 4016.

However, I'd think it's still good to know these prefixes. Think they should still be included in O level Physics.

2.     Newly added: Solve Numbers and Algebra Problems based on real-world context including

·       travel plans,

·       transport schedules,

·       sports and games,

·       recipes,

·       etc

as well as interpret the solution in the context of the problem.

Below are some questions taken from the specimen paper.

I remember when I did Q17 with my two Sec 4 students last year, one of them was stumped by this graph. It didn’t make any sense to her. While the other student understood the graph perfectly. Later, I realised that the one who understand the graph, has a family car so she understood that the sudden jump on the graph was because the tank was being filled up.
I’m not saying that we all have to buy a car so that our children can interpret such graphs but as educators and parents, we have to make our children more aware of Mathematics in our daily lives and events. 

For a start, ask if your students / children know what’s the speed limit on the road. From there, when working with questions involving speed, students can get a feel of whether their answers make sense. See question below from Specimen  Paper 2

This question also shows another trend in the new syllabus - the ability to compare using mathematical calculations.

3.    Removed: Scale factor

The term “scale factor” is seldom used even in current syllabus ever since the removal of the topic, Transformation, from the O level Math papers.

Do note that Scale Factor is still relevant in the new N level syllabus, which I’ll discuss in another post.

4.     Newly added: Solve Geometrical Problems based on real-world context including

·       floor plans,

·       surveying,

·       navigation,

·       etc

as well as interpret the solution in the context of the problem.

 

 

Below is an example of this real-world context question

5.     Newly added: Misleading statistical diagrams.

In the new syllabus 4048, candidates are expected to explain “why a given statistical diagram leads to misinterpretation of data”. Also, the construction of statistical charts are no longer required. Instead, candidates should focus on interpretation of data and using them to compare two sets of data.

Some examples below:

 

 

 

It is interesting to note that a similar question actually came out in N level Paper 2, 2011. Will post that question later in the N level syllabus discussion.



Conclusion

Some students think the new syllabus is harder.
I don't agree. It's just more applications and more contextualised.
Personally I love it. It makes Math more relevant to real life, more visual and more useful.
As a parent and educator, this is also my aim: to make what my children and students study relevant and useful to them.

So fellow parents, let's make an conscientious effort to help our kids see Math in our everyday lives and fellow educators, let's include interesting and relevant learning experiences in our lessons and make our questions more authentic.

follow me on Facebook where I share more ideas on the teaching and learning Mathematics. http://www.facebook.com/ArielsMathWorkshop