Tuesday, April 22, 2014

April 22nd Math Summary


- If you differentiate the bottom and it is the same as the top, just ln the denominator to integrate it. Or else, you will have to use partial fractions.


General Form:
(a+b) ^n = nCr (a)^(n-r) (b)^r

Answers to worksheet:



Toughest kind of question that will come out for O levels is Question 3. 

Tuesday, February 11, 2014

Lesson Summary for 11th February (Tuesday)

Today we started of with a G+ discussion (LINK HERE) of the differences between a



Where Xintong's explanation was accurate and recommended by Mr Johari.

Conic Sections

A parabola has a line of symmetry, while a Hyperbola has 2 lines of symmetry, the transverse and longitudinal (Vertical and Horizontal)

Equations of Circles



Imaginery Roots


Real and Distinct Roots


Real and Equal Roots

Methods to finding the centre of the circle and the Radius

Method 1 (Completing the Square)

Method 2 (Comparing Coefficients)

General Form of the equation of a circle

Assignment Questions in (Further Coordinate Geometry: Equations of Circles)

Question 5 (Tier B)

Apparently it can intersect with each other 

Question 8 (Tier C)

Closing Note

Homework: Use GeoGebra or any graphing application to test out assumptions

"Your level test is going to hit you like a Meteor" - Mr Johari 2014

Done By Ryan Tan S4-09

Sunday, February 9, 2014

Lesson summary for Wednesday, 5th February

We did a quiz and went revised what standard deviation is.

Standard deviation (σ is the symbol, is a measure of the variance from the mean for a set of data. It is calculated as follows:

x̄ (pronounced as x bar) is the mean of the data set.
n is the number of data in the set.
Σ, or summation, is the addition of all the following datum. In this case, it is (x-x̄)^2.

Showing the proper working during the examples is essential to getting the method mark(s).

For example,

Calculate the mean, median and standard deviation for the following set of data.


mean = (1+2+3)/3
     = 3

Tmedian = (3+1)/2
        = 2
median = 2
standard deviation = √(  (  (1-2)^2  +  (2-2)^2  +  (3-2)^2  ) / 2  )
                   = 1

The standard deviation’s and mean’s working can be in the form of a table containing all the data, and you can just use the values of Σ(x-x̄), n and Σx to calculate your answers.

If there are UNITS in the question, be sure to write them down in your answers as well.

Other reminders:

- Write scale when drawing graphs
- Show ALL the working when calculating the standard deviation, mean and median.

Check out these G+ posts to learn how to use STAT functions in your calculator

p.s. Sorry for the late post!

Wednesday, January 29, 2014

29th Jan Recap

Homework = Statistics (b) Due next friday

Probability summary

(Sorry I just realized I posted this on the old 309 math blog)


Probability: How likely an event can occur

Probability =   The number of ways of achieving desired outcome
                                    Total number of possible outcomes

Event will definitely occur = 1

Event will never occur = 0

Event will not occur = 1 - probability of event occurring

Sample space: All the possible outcomes of an experiment

S = {a, b, c ...}

Sample point = 1 of the possible outcomes

Mutually exclusive: Both events cannot occur at the same time

Probability (A or B) = P(A) + P(B)

Independent events: Both events can occur at the same time; Outcome does not affect probability of outcome of other event

Probability (A and B) = P(A) x P(B)


Probability diagrams:

Used for two independent events

Tree diagram: 

Used for two or more events

Tuesday, January 28, 2014

28th Jan Recap

Math File
Use an orange/red ring file .
1.  Notes                                Earliest at the bottom .
2. Assignments
3. Quizzes    
> Repeat for each topic
Mean , Median and Mode
.They are important for their own purposes depending on the analysis you want to carry out .
. Mean is very subjective as there is an outlier that can severely affect the data .
. Median is the 50% mark , letting you see how the performance of a group is .
. Mode lets you see the most popular set of data and the trends .

Box Plot 

Lower percentile - Underperforming
Upper percentile - Excelling                                > Able to plot data using the 2 points

. Box Plots let you see performances better for evaluation ( Better than Ogive)
- It is easier to see if the data is skewed ( Biased or shifted towards) based on where Q1 , Q2 and Q3 is
- Look at interquartile range and range to determine spread and performance as a whole .

To transfer the box plot into a cumulative frequency against value graph ,
a) Plot it vertically using Q1 , Q2 and Q3 as points
b) Plot it horizontally to see how everyone is performing .

Tuesday, January 21, 2014



Please check that the tabulation of marks are correct to date.
Those with R please redo the worksheet as they have either incomplete statement or wrong mathematical notation used.
All the materials must be filed in the following order:
.1 Notes
.2 Assignments
.3 Quizzes (assessments)

according to topic:
.A Financial Matters (Practical Application) - 2 assignments
.B Probability - 4 assignments
.C Statistics - 1 assignment with 1 due in Week 5
.E Geometric Constructions - 1 assignment due in Week 6
.F Equation of Circle - 1 assignment in Week 7
.G Plane Geometry - 1 assignment in Week 7

Should you need assistance in understanding the concept do approach me or your friends.

Marks highlighted in blue indicate excellent to outstanding quality
cell in Pink indicates no submission or work not received (reasons not stated)
R indicates work has to be resubmitted  due to quality or concept
A+ outstanding work submitted

please note the following:
TOPICS covered for Level Test (EM & AM)                                                                      
ensure that you are familiar with the topics to be tested. As secondary 4 is a critical year for assessment you are expected to review past topics covered in secondary 3 and lower secondary. The regular short class quizzes administered by your ST help to review the past and new knowledge and skills.
Ensure that you have the approved scientific calculator (with the SST sticker)
- familiarise yourself with the functions such as the STATs function
Geometrical sets (compass, protractor, rules, eraser, decent pencil)

On Your Own - For Practice, Revision & Acceleration

You would have received an email invite (at your SST account) to sign up as a member of this online portal.

For your information, the Khan Academy comes with a vast collection of video clips on almost all topics (& sub-topics) in our curriculum. It also comes with quizzes that auto-mark and therefore enables you to check your understanding and mastery of the skills. This will complement what we do in class.

Note that the quizzes are largely Multiple Choice Questions or require you to enter numerical values only. You must also keep in mind the importance of writing the working/ steps in a logical manner. Hence, practices on papers should continue.

This is a useful resource that you can use for practice, revision... and for those of you who are would like to accelerate your learning, you may pace yourself accordingly - e.g. pick a topic that would be taught this year and start to learn on your own.

Note of caution: Always check your textbook on the presentation of the mathematical notation.
For example, at secondary level,  4 x 7 should not be written as 4.7 (by inserting a dot between 4 and 7).

You may also invite your parent to sign up an account and invite him/ her as your coach.

Set-up Guide for Parent:

1. Parent to set up an account

2. Student to invite Parent as Coach

3. Parent to login to monitor child's progress

4. Parent can also assign tasks for child to attempt

Wednesday, January 15, 2014

Lesson Summary (15/1/14)

Things to note :
Conditions for drawing histogram
1. Fit graph paper
2. Only use the zig-zag lines if the intercepts are insignificant
3. The zig-zag lines are only used for x-axis not y-axis.
    if used for y-axis, drawing of the bars or curve will be affected.
4. No repeating of the zig-zag lines in an axis.

PS I apologise if this is a disappointing post.


Frequently Asked Questions

1. Who is subjected to the Formula One (F1) Cess?
All tourist hotels are subject to the F1 Cess. Tourist hotels include all hotels previously gazetted for purposes of collecting Cess under the Singapore Tourism (Cess Collection) Act.  New hotels deemed to be tourist hotels will also be required to make a contribution via the F1 Cess.

2. Do I need to register my hotel for the F1 Cess? How do I register for the F1 Cess?
You are automatically registered for F1 Cess, once your hotel is gazetted under the Singapore Tourism (Cess Collection) Act. Accordingly, thereupon as a gazetted hotel, you are required to pay the F1 Cess.
3. Are there any forms that I need to submit? How do I submit my forms?
You are required to submit the F1 Cess Payment Form to STB. To download the form, please click here.
4. What is the submission deadline for the F1 Cess Payment Form and payment?
The F1 Cess Payment Form and F1 Cess payment are to be submitted within two months after the end of the F1 event i.e. by 22 November 2013.
5. How do I pay the F1 Cess? Who do I pay the F1 Cess to?
Kindly issue a crossed cheque payable to Singapore Tourism Board, and write the name of your hotel and Cess Reference Number on the reverse side of the cheque.
The cheque accompanied by your F1 Cess Payment Form should be sent to:
Singapore Tourism Board
1 Orchard Spring Lane
Tourism Court
Singapore 247729
Attn: Financial Operations Department – AR Section (F1 Cess)
Please note that STB does not accept post-dated cheques. No receipt will be issued for cheque payment. Do ensure that your cheques reach us by the due date to avoid a late payment penalty.
6. What is the penalty for paying late or not paying F1 Cess?
A penalty equal to 5% of the F1 Cess shall be payable after 22 November 2013.  If the F1 Cess outstanding is not paid within 60 days of the imposition of the penalty, an additional penalty of 2% of the F1 Cess shall be payable for each completed month that the F1 Cess remains unpaid commencing 22 November 2013. The total additional penalty shall not exceed 50% of the amount of F1 Cess outstanding.
Rates of F1 Cess

7. How many room nights does the F1 Cess cover and for which period?
The F1 Cess is applied on a period of four days – from Thursday, 19 September to Sunday, 22 September 2013, both dates inclusive.
8. What are the F1 Cess rates? Why are there different levels of contribution for different hotels?
The F1 Cess rates are 30% of the total room revenues for trackside tourist hotels, and 20% of the total room revenues for all other tourist hotels.

Hotels at different locations are likely to benefit to varying extents. For instance, hotels that have a view of or are in close proximity to the race track should be able to command a much higher room rate than the other hotels. Hence, it is deemed reasonable for these trackside hotels to make a contribution towards the staging of the race.

9. Will the Cess be imposed on rooms that have been sold during this period but have not yet been paid for? What about pre-collected room revenues, for e.g. in the event of “no shows”?
Yes, all rooms sold during this period are subjected to the F1 Cess.

This includes
1) Rooms that have not been paid for (e.g., on credit terms),
2) Rooms where payment was pre-collected, and
3) Rooms where an amount was charged for cancellation or “no-show”.

Thus, all room revenues collected or are accruable to rooms sold during this period must be reported as paid lettings. 

10. Will the hotels be taxed for early check-in and late check-out?
Only rooms sold during the F1 Cess period (i.e. 19 – 22 September 2013) will be subjected to the F1 Cess and this includes early check-in and late check-out during this period. However, early check-in and late check-out which falls outside the period will not be subjected to the F1 Cess.

11. Will the F1 Cess payment be refunded to the hotels if there are cancellations of room bookings? What is the validity period for refunds? Who do I submit the refund request to?
Yes, refunds will be made with proper documentation evidence. The window period for refunds is up to one year of the end of the event i.e. by 22 September 2014. Please submit any refund request to STB.

For example, non trackside tourist hotel cost S$100 per room night excluding GST. If the cancellation entitles the hotel to charge the guest 40%, the amount that can be refunded to hotel is S$100 x 60% x 20% = S$$12.

12. Why is there a need to provide information for 16, 17, 18, 23 & 24 September 2013 since F1 Cess is not levied on the revenue earned on these days? [Note: Race days are from Friday to Sunday, 20 to 22 September 2013.  But F1 levy period for 2013 will start from Thursday, 19 September 2013 for 4 nights, ie. 19 to 22 September2013 inclusive.]
Although 2013 F1 hotel levy takes effect from Thursday, 19 September 2013 to Sunday, 22September 2013, the information collected for a broader timeframe will allow for more comprehensive pre- and post-race visitor trends

Mechanics of F1 Cess

13. How is the F1 Cess calculated?
The F1 Cess is based on the total room revenues during the stipulated period. Using the below official invoices to illustrate, if the room charge is S$100 (excluding ancillary charges), the F1 Cess will be $30 for trackside tourist hotels and S$20 for all other tourist hotels.

(A) Room Charge

S$ 100.00

(B) Breakfast

S$   40.00


S$   10.00

Total (A+B+C)

S$ 150.00

Service Charge 10%
S$   15.00
GST  7%
S$   11.55
Total Reflected on Guest’s Bill
S$ 176.55

F1 Cess collected from trackside tourist hotel @ 30%    è       S$ 30.00
                                                                                    (30% of S$ 100)

F1 Cess collected from all other tourist hotel @ 20%     è       S$ 20.00
                                                                                    (20% of S$ 100)

The breakdown between the room revenue and other revenue components in the “F1 CESS PAYMENT FORM” should tally against the  invoice to hotel guest.

If the invoice the hotel guest is reflected as a package price, without breakdown into room and non-room components, the F1 Cess will be calculated based on the package price.

Package Price

S$ 500.00

Service Charge 10%
S$   50.00
GST  7%
S$   38.50
Total Reflected on Guest’s Bill
S$ 588.50

F1 Cess collected from trackside tourist hotel @ 30%    è      S$ 150.00
                                                                                    (30% of S$ 500)

F1 Cess collected from all other tourist hotel @ 20%     è      S$ 100.00
                                                                                    (20% of S$ 500)
* The above illustration uses official invoice as the source document for the F1 Cess payment submission. You may use other source of supporting document, for example, system printed revenue distribution, on condition that the submission figure can be audited. The onus of declaring accurate and complete information remains the responsibility with the Hotel.

14. Are hotels required to reflect the F1 Cess as a separate item on the bill of hotel guests?
No, the F1 Cess should not be reflected on guests’ bills as a separate item. The levy is considered a business tax (i.e. more like corporate tax), as opposed to a consumer tax (i.e. the previous 1% cess and 7% GST).

15. Are hotels required to keep records for audit purposes?
Yes, hotels are required to retain relevant and sufficient records for a minimum period of 2 years for audit purposes.

Last updated on 13 August 2013

Tuesday, January 14, 2014

Lesson summary 14/1/14 (Crystal)

When there are a lot of datas to analyse like the examples given, it's easier to classify the datas into groups for analysis.
The class limits are composed of the lower class limit and the upper class limit. Each class has a respective set of class limits. 

When making a histogram, there should be no gaps between the bars. Therefore, the midpoints between the upper class limit of a class and the lower class limit of the next class in the sequence are calculated to be the class boundaries.

Class interval is the difference between two adjacent class boundaries.

02 STATISTICS: Class Limits, Boundaries And Intervals


Class Limits, Boundaries And Intervals

Class Limits
Class limits are the smallest and largest observations (data, events etc) in each class. Therefore, each class has two limits: a lower and upper.
200 – 29912
300 – 39919
400 – 4996
500 – 5992
600 – 69911
700 – 7997
800 – 8993
Total Frequency60
Using the frequency table above, what are the lower and upper class limits for the first three classes?
For the first class, 200 – 299
The lower class limit is 200
The upper class limit is 299
For the second class, 300 – 399
The lower class limit is 300
The upper class limit is 399
For the third class, 400 – 499
The lower class limit is 400
The upper class limit is 499
Class Boundaries
Class Boundaries are the midpoints between the upper class limit of a class and the lower class limit of the next class in the sequence. Therefore, each class has an upper and lower class boundary.
200 – 29912
300 – 39919
400 – 4996
500 – 5992
600 – 69911
700 – 7997
800 – 8993
Total Frequency60
Using the frequency table above, determine the class boundaries of the first three classes.
For the first class, 200 – 299
The lower class boundary is the midpoint between 199 and 200, that is 199.5
The upper class boundary is the midpoint between 299 and 300, that is 299.5
For the second class, 300 – 399
The lower class boundary is the midpoint between 299 and 300, that is 299.5
The upper class boundary is the midpoint between 399 and 400, that is 399.5
For the third class, 400 – 499
The lower class boundary is the midpoint between 399 and 400, that is 399.5
The upper class boundary is the midpoint between 499 and 500, that is 499.5
Class Intervals
Class interval is the difference between the upper and lower class boundaries of any class.
200 – 29912
300 – 39919
400 – 4996
500 – 5992
600 – 69911
700 – 7997
800 – 8993
Total Frequency60
Using the table above, determine the class intervals for the first class.
For the first class, 200 – 299
The class interval = Upper class boundary – lower class boundary
Upper class boundary = 299.5
Lower class boundary = 199.5
Therefore, the class interval = 299.5 – 199.5 = 100


class interval

Class Interval
Definition of Class Interval 
While arranging large amount of data (in statistics), they are grouped into different classes to get an idea of the distribution, and the range of such class of data is called the Class Interval.
More about Class Interval
  • Class intervals are generally equal in width and are mutually exclusive.
  • The ends of a class interval are called class limits, and the middle of an interval is called a class mark.
  • Class interval is generally used to draw histogram.
Example of Class Interval
  • In the table above, heights of 20 students of a class are divided into classes with the size of each class interval being 5.
Solved Example on Class Interval
Plant scientists developed different varieties of corns that have a rich content of lysine which is a nutritious animal feed. A group of chicks were given this food to test the quality. Weight gains (in grams) of these chicks after 21 days are as recorded: 380, 321, 366, 356, 349, 337, 399, 384, 410, 329, 350, 340, 324, 396, 412, 420, 382, 318, 344, 438. By constructing a frequency distribution table for 7 classes, find the class interval in which the weight increase is maximum.
A. 426 - 443
B. 335 - 351
C. 318 - 438
D. 336 - 353
Correct Answer: D
Step 1: Range of the data = higher value - lower value = 438 - 318 = 120
Step 2: Width = Range/number of classes = 120/7 = 17.14 ˜ 18
[Round to the higher value.]
Step 3: Construct the class limits (weight gains) with width 18, so that the least and the highest values are included.
Step 4: The class limits, boundaries, tally marks and the frequency for each class (number of tally marks) are shown in the table.
Step 5: 
Step 6: The class interval in which the weight increase maximum is 336 - 353. [Frequency is more for the class 336 - 353.]

Comment on the following:
.1 What are the key differences between class limits, class boundaries and class intervals ?
.2 How will these differences impact the accuracy of the analysis?