## Thursday, 19 September 2013

## Monday, 16 September 2013

### Update on Assessments (i) PT (ii) Paper 3 (iii) EOY

**(1) Performance Task 2**

This constitutes the Elementary Mathematics component of Assessment.

The performance task focuses on the topic of Geometrical Proof - Circle Properties. (please refer to Blog entry on Mathematics Performance Task 2)

Deadline for submission is

**Term 4 Week 1 (first lesson)**

**(2) Paper 3**

This constitutes the Additional Mathematics component of Assessment.

This will be conducted in

**Term 4**.
Students are expected to familiarise themselves with GC-TI84+.

(please refer to your Math teacher on information on use of GC-TI84+)

**(3) End-of-Year Examination: Mathematics**

Information pertaining to the Maths exam has been communicated to the students in the GoogleSite (as well as the Maths blog).

__Elementary Mathematics paper 1__

Date:

**27 September 2013**(Friday)
Duration: 1 hour 30 minutes

__Elementary Mathematics paper 2__

Date:

**30 September 2013**(Monday)
Duration: 2 hours

__Additional Mathematics__

Date:

**4 October 2013**(Friday)
Duration: 2 hours 30 minutes

**Table of Specification**

__A. Elementary Mathematics__

• Numbers and the four operations (moe 1.1)

• Algebraic representation and formulae (moe 1.5)

• Functions and graphs (moe 1.7)

• Algebraic manipulation (moe 1.6)

• Solutions of equations and inequalities (moe 1.8)

• Properties of circles (moe 2.3)

• Coordinate geometry (moe 2.6)

• Trigonometry

• Mensuration

__B. Additional Mathematics__

**(A1) Equations and inequalities**

**Conditions for a quadratic equation**

Solving

**simultaneous equations**in two variables with at least one linear equation, by substitution
Relationships between the

**roots and coefficients of a quadratic equation**
Solving

**quadratic inequalities**, and representing the solution on the number line**(A2) Indices and surds**

**Four operations**on indices and surds, including rationalising the denominator

**Solving equations**involving indices and surds

**(A3) Polynomials and Partial Fractions**

Multiplication and division of polynomials

Use of

**remainder and factor theorems**
Factorisation of polynomials

**Partial fractions**

**(A4) Binomial Expansions**

**(A5) Power, Exponential, Logarithmic, and Modulus functions**

**(G1)**Trigonometric functions, identities and equations.

- · Six trigonometric functions for angles of any magnitude (in degrees or radians)
- ·
**Principal values**of sin–1x, cos–1x, tan–1x - · Exact values of the trigonometric functions for
**special angles**(30°,45°,60°) or (π/6, π/4, π/3) - ·
**Amplitude, periodicity and symmetries**related to the**sine and cosine**functions - ·
**Graphs**of**y**=**a**sin(**bx**) ,**y**=**a**sin(**x/b + c**),**y**=**a**cos(**bx**) ,**y**=**a**cos(**x/b + c**) and**y**=**a**tan(**bx**) , where a is real, b is a positive integer and c is an integer. - · Use of the following
- ∗ (BASIC TRIG RULES)
- sin A/cos A=tan A,
- cos A/sin A=cot A,
- sin2A+cos2A=1,
- sec2A=1+tan2A,
- cosec2A =1+cot2A
- (DOUBLE ANLES)
- the expansions of sin(A ± B), cos(A ± B) and tan(A ± B)
- the formulae for sin 2A, cos 2A and tan 2A
- (R-FORMULA) - the expression for acosu + bsinu in the form Rcos(u ± a) or R sin (u ± a)
- Simplification of trigonometric expressions
- ·
**Solution of simple trigonometric equations**in a given interval (excluding general solution) - ·
**Proofs**of simple trigonometric identities

**(G2) Coordinate Geometry**

Condition for two lines to be parallel or perpendicular

**(G2) Linear Law**

**Transformation of given relationships, including y = axn and y = kbx, to linear form to determine the unknown constants from a straight line graph**

**Resource and References**

The following would be useful for revision:

- Maths Workbook
- Study notes
- Homework Handouts
- Exam Prep Booklets (that was given since the beginning of the year)
- Ace Learning Portal - where they could attempt practices that are auto-mark
- Past GCEO EM and AM questions (students were recommended to purchase these at the beginning of the year)

**(4) General Consultation and Timed-trial during the school holidays**

**Monday 9 September 2013**(Monday). The focus would be on Additional Mathematics and students are strongly encouraged to attend.

Duration: 0800 - 1030 (2 hours 30 minutes)

### Assessment in Term 4

Dear SSTudents,

As mentioned earlier the deadline of the PT2 is 16 September 2013 @ 2359. To date many students have submitted their products with high quality questions and 'proof's. Effective use of ICT tools (google, Blog, Geogebra, Keynote, Powerpoint, Pretzi etc) have further enhanced the final product.

The assessment information will be as follows:

Date:

(Please be punctual and ensure you have a heavier meal in the morning)

Time: 3.00 pm to 4.00 pm

Venue: Auditorium

Note that you are required to sit according to your classes and index numbers. The teachers will supervise you on this.

Logistic:

TI84 Graphic Calculator (or other approved GC model)

(no other calculator will be allowed)

Stationery - pen and ruler

Please refer to your class math blog or google site earlier entries on this.

**1. Performance Task 2 (in lieu of Elementary Mathematics)**As mentioned earlier the deadline of the PT2 is 16 September 2013 @ 2359. To date many students have submitted their products with high quality questions and 'proof's. Effective use of ICT tools (google, Blog, Geogebra, Keynote, Powerpoint, Pretzi etc) have further enhanced the final product.

**2. Paper 3 (in lieu of Additional Mathematics)**The assessment information will be as follows:

Date:

**23 September**2013 (Monday)(Please be punctual and ensure you have a heavier meal in the morning)

Time: 3.00 pm to 4.00 pm

Venue: Auditorium

Note that you are required to sit according to your classes and index numbers. The teachers will supervise you on this.

Logistic:

TI84 Graphic Calculator (or other approved GC model)

(no other calculator will be allowed)

Stationery - pen and ruler

**3. Information on EOY**Please refer to your class math blog or google site earlier entries on this.

*All the best - you can do it because we have faith in you but do you!*## Saturday, 31 August 2013

### Mathematics Performance Task 2

**Due Term 4 Week 1 (first Mathematics Lesson)**

*the file could be downloaded from google site.*

Please fill-up this form once you have submitted the work.

## Friday, 2 August 2013

## Saturday, 6 July 2013

### Semester 2 Update

###
**1. Scheme of Work (Syllabus for Semester 2)**

**Term 3**

Wk 1 (AM) LINEAR LAW

Wk 2-3 (EM) TRIGONOMETRY

- Sine Rule, Cosine Rule, bearings, Angle of Elevation, 3D problems (EM)

Wk 4-6 (AM) TRIGONOMETRY (AM)

Wk 7 (EM) PROPERTIES OF CIRCLES

Wk 8 (AM) CIRCULAR MEASURE

Wk 9-10 (AM) BINOMIAL THEOREM

**Term 4**

Wk 1 Revision

Wk 2 EOY Exam

**Self Directed Learning**(AM) URVES & CIRCLES

###
**2. Assessment **

**Level Test 2 (10%)**

format: 1 hour

Marks: 40 marks
Topics

EM

Coordinate Geometry

Trigonometry

AM

Coordinate Geometry

Trigonometry

Linear Law

**Paper 3 - AM (10%)**

**PT2 - EM (10%)**

## Sunday, 21 April 2013

### AM and EM Assessment Book (GCE O format)

To assist students in their revision and preparation for GCE 'O' Level, the Mathematics Department has made arrangement with the bookshop to order the following 2 books for the students.

The information is as follows:

- Additional Mathematics by topic $7.00
- Mathematics by topic $5.50

Both will include solution booklet

Please make arrangement with your Math teacher on the procedures for purchases.

## Tuesday, 2 April 2013

### MATHEMATICS LESSON 3rd April 2013 1st Period Scribery

MATHEMATICS LESSON

3rd April 2013

1st Period Scribery

Scriber: Harindrar

Special thanks to: Iffah

y = a^x

A > 0

A not equal to 1

Asymptote: x-axis

Bigger the base(a) the closer the line is to the y-axis(Narrower/steeper)

Image: http://www.sosmath.com/algebra/logs/log4/log42/gl01.gif

_______________________________________________________

What does a logarithm represent? Ans: Power/index

Y = logax

A > 0

A not equal to 1

Asymptote: y-axis

Bigger the base(a) the closer the graph is to the x-axis

Image: http://www.sosmath.com/algebra/logs/log4/log42/gl02.gif

_______________________________________________________

Image: http://www.regentsprep.org/Regents/math/algtrig/ATP8b/inversegraph.gif

Line through the middle is the line of symmetry.

Inverse relationship between log and exponential.

_______________________________________________________

Y = a | x |

Possibilities

-x , x < 0

X , x = 0 OR x > 0

Observations

(Linear)

V - Shaped graph.

Line of symmetry is y-axis

Image: http://limchiawei-tennshaun-yongzhen-haoyuan-modulusfunction.wiki.hci.edu.sg/file/view/f%28x%29%3Dabs%28x%29.png/231254306/800x442/f%28x%29%3Dabs%28x%29.png

(Quadratic)

Image: http://limchiawei-tennshaun-yongzhen-haoyuan-modulusfunction.wiki.hci.edu.sg/file/view/quad_graph1.png/238694051/800x567/quad_graph1.png

- Please post any additional notes in the comments section - THANK YOU -

3rd April 2013

1st Period Scribery

Scriber: Harindrar

Special thanks to: Iffah

**Exponential:**__Equation__y = a^x

__Rules__A > 0

A not equal to 1

Asymptote: x-axis

__Observations__Bigger the base(a) the closer the line is to the y-axis(Narrower/steeper)

Image: http://www.sosmath.com/algebra/logs/log4/log42/gl01.gif

_______________________________________________________

**Logarithm:**What does a logarithm represent? Ans: Power/index

__Equation__Y = logax

__Rules__A > 0

A not equal to 1

Asymptote: y-axis

__Observations__Bigger the base(a) the closer the graph is to the x-axis

Image: http://www.sosmath.com/algebra/logs/log4/log42/gl02.gif

_______________________________________________________

**Exponential and Logarithmic relationship:**Image: http://www.regentsprep.org/Regents/math/algtrig/ATP8b/inversegraph.gif

__Relationship(With reference to image)__Line through the middle is the line of symmetry.

Inverse relationship between log and exponential.

_______________________________________________________

**Modulus:**__Equation__Y = a | x |

Possibilities

-x , x < 0

X , x = 0 OR x > 0

Observations

(Linear)

V - Shaped graph.

Line of symmetry is y-axis

Image: http://limchiawei-tennshaun-yongzhen-haoyuan-modulusfunction.wiki.hci.edu.sg/file/view/f%28x%29%3Dabs%28x%29.png/231254306/800x442/f%28x%29%3Dabs%28x%29.png

(Quadratic)

Image: http://limchiawei-tennshaun-yongzhen-haoyuan-modulusfunction.wiki.hci.edu.sg/file/view/quad_graph1.png/238694051/800x567/quad_graph1.png

- Please post any additional notes in the comments section - THANK YOU -

## Wednesday, 27 March 2013

### Summary of points from lesson on 27 March 2013

Graphs of Standard Functions

(Recap)

Functions are relations

- one to one linear graph

- many to one

- one to many (y^2=x)

- many to many (x^2/a^2 + y^2/b^2 =1) eclipse graph

Functions must be

- logical

- reliable

- reasonable

- predictable

How to test for function (graphically)

- vertical line test

cut once: is a function

cut more than once: not a function

--------------------------------------------------------

Linear

- y=kx

- k is the gradient passes through origin

- k>0, sloping up /

- k<0, sloping down \

|k| modulus/ absolute value

- taking the numerical value of k

Quadratic

as |k| increases, the graph becomes narrower

Reciprocal

inverse proportion : y=k/x => xy=k

2 ---(reciprocal)-----> 1/2

when x increase, y decreases

what are values that

x cannot be? -> x≠0

y cannot be? -> y≠0

k cannot be?-> k≠0

At values where x and/or y do not exist, there will be asymptote.

asymptote - a line that continually approaches a given curve but does not meet it at any finite distance.

(Recap)

Functions are relations

- one to one linear graph

- many to one

- one to many (y^2=x)

- many to many (x^2/a^2 + y^2/b^2 =1) eclipse graph

Functions must be

- logical

- reliable

- reasonable

- predictable

How to test for function (graphically)

- vertical line test

cut once: is a function

cut more than once: not a function

--------------------------------------------------------

Linear

- y=kx

- k is the gradient passes through origin

- k>0, sloping up /

- k<0, sloping down \

|k| modulus/ absolute value

- taking the numerical value of k

Quadratic

as |k| increases, the graph becomes narrower

Reciprocal

inverse proportion : y=k/x => xy=k

2 ---(reciprocal)-----> 1/2

when x increase, y decreases

what are values that

x cannot be? -> x≠0

y cannot be? -> y≠0

k cannot be?-> k≠0

At values where x and/or y do not exist, there will be asymptote.

asymptote - a line that continually approaches a given curve but does not meet it at any finite distance.

## Wednesday, 13 March 2013

## Wednesday, 6 March 2013

### Notes from 7MARCH2013 math class ._.

Reflection type of error (EMAIL TO MRS SIN)

(a) concept

(b) carelessness

(c) lack of practice

-blank out

-shortage of time

50 words: what are you going to do?

FIY:

(A-MATH)

Mean: 52.03% ≠16

Median: 53.33% ≠16-17

(a) concept

(b) carelessness

(c) lack of practice

-blank out

-shortage of time

50 words: what are you going to do?

FIY:

(A-MATH)

Mean: 52.03% ≠16

Median: 53.33% ≠16-17

### 6th March Lesson Summary - Discriminant (Wed) -Darren

Lesson Summary for 6th March Wednesday - Discriminant

y = a(x-h)^2 + k

H = to the x-intercept

&

K = to the y-intercept.

And remember the flow chart that if your 'a' must be equal to 1 before u continue the 'completing the square' hence, you must factorise the 'a' first, to put the coefficient outside of the bracket so you could have the remaining of a=1 and carry on the 'completing the square' to solve the equation.

\

Also remember these few important key points in this chapter.

Sorry for the bad quality photos XD Keep practicing the applications of these formulas and ull do well. Just understanding is not enough! Hope this is helpful. All the best for the results for the rest of your tests! :D

__Remember that in the formula:__

y = a(x-h)^2 + k

H = to the x-intercept

&

K = to the y-intercept.

And remember the flow chart that if your 'a' must be equal to 1 before u continue the 'completing the square' hence, you must factorise the 'a' first, to put the coefficient outside of the bracket so you could have the remaining of a=1 and carry on the 'completing the square' to solve the equation.

Also remember these few important key points in this chapter.

Sorry for the bad quality photos XD Keep practicing the applications of these formulas and ull do well. Just understanding is not enough! Hope this is helpful. All the best for the results for the rest of your tests! :D

## Monday, 4 March 2013

### 5/3 Lesson Summary

**HOMEWORK DUE**

• Wednesday (6/3): A02d

• Friday (8/3): A02e

– Prepare $12.50 for Math TYS. This will be bought for collectively as a class.

– If you wish to know your A/E-math results for this Level Test, please email Mrs Sin (yeo_chuen_chuen) about it, stating your name, class and index number :)

* Complete pg 154 - 155 of Math notes. You should have finished the graph sketching in class.

Write down the Completed Sq of each graph/function.

**Quadratic Equations and Graphs**

__1. Identifying when to use SUM & PRODUCT of ROOTS (α, β)__

- when part of the function has more than two unknowns (refer to pg 153: x^2 +x(2-k)+k = 0), use sum & product of roots.

- find sum (-b/a) > find product (c/a) > form eqn from sum > form eqn from product > solve via simultaneous and quadratics

* refer here.

__2. Quadratic Roots Identities – α, β__

(α + β) ² = α² + 2αβ + β²

(α – β)² = α² – 2αβ + β²

α² – β² = (α + β)(α – β)

α² + β² = (α + β) ² – 2αβ

QUADRATIC EQUATION CAN ALSO BE WRITTEN AS:

**x² –**(SUM OF ROOTS:

**b/a**)

**+**(PRODUCT OF ROOTS:

**c/a**) = 0

__3. Properties of Quadratic Graphs__

1. Intersect x-axis at 0, 1, 2 points

2. Symmetrical in the line y=k, where k is the y-coordinate of vertex (turning point)

3. Always has a y-intercept at c.

__4.__

Sandy (06) to take over tomorrow's lesson summary & math homework updates!

DIS IS IFF

30Point8FM.

## Friday, 15 February 2013

### Answers for Indices A02a and Revision Worksheet (E Math)

Dear all

Here are the answers for your checking for the worksheets.

Here are the answers for your checking for the worksheets.

Indices A02a |

Revision Worksheet (E Math) |

## Thursday, 14 February 2013

## Tuesday, 5 February 2013

### Common Mistakes of Indices ( Harindrar | Saishwar )

COMMON MISTAKE 1:

Leaving answer in index form even though question does not ask to.

EG: Leaving 216^1/3 as an answer instead of 6

COMMON MISTAKE 2:

Not putting the question into index form, hence getting stuck and being unable to carry on.

EG: 144 = X^2

144 = 12^2

COMMON MISTAKE 3:

Leaving answer in surd or indices form when the question says otherwise.

EG:

leaving answer as 3^1/2 when question asks for surd form

and

leaving answer as Squareroot(3) when question asks for indices form

Thank you,

Harindrar and Saishwar.

Leaving answer in index form even though question does not ask to.

EG: Leaving 216^1/3 as an answer instead of 6

COMMON MISTAKE 2:

Not putting the question into index form, hence getting stuck and being unable to carry on.

EG: 144 = X^2

144 = 12^2

COMMON MISTAKE 3:

Leaving answer in surd or indices form when the question says otherwise.

EG:

leaving answer as 3^1/2 when question asks for surd form

and

leaving answer as Squareroot(3) when question asks for indices form

Thank you,

Harindrar and Saishwar.

### Common Errors

Common Errors

1. Unable to remember all 10 rules.

2. Unable to use multiple rules at once.

3. Careless.

Solutions:

1. Practice more.

2. Try to memorize the 10 rules.

3. Double check work.

1. Unable to remember all 10 rules.

2. Unable to use multiple rules at once.

3. Careless.

Solutions:

1. Practice more.

2. Try to memorize the 10 rules.

3. Double check work.

### Common Errors and Tips (Keming, Isaac, Ying Liang)

__Common Errors__

1) Confused with how to expand the brackets for indices

2) Using guess and check to obtain answers

3) Unable to obtain answers for sums with the same indices

__Tips__

1) Double check using a calculator and make sure it tallies

2) Think properly and nicely without getting angry and panic in the process as panicking will only yield useless and marks-reducing results

3) Getting used to the laws of indices

### 3 Common Errors (Indices) by Imanni and Harriz

__Common Errors__

1) Confusion of the 10 laws and how they co-relate with each other.

2) Confusion of negative indexes and how they can be solved.

3) Deriving the unknown bases and powers.

__Tips__

1) Check for errors in calculation whenever you are stuck or skip the question then come back to it to check.

2) Take your time when attempting a question so as to minimize errors during calculation.

3) Revise at home so that you are familiar with what you learnt.

### 3 Common Errors

1.Negative indices

1 / 2 = 2^-1

2.Squaring negative integers

-3^2=-9

(-3)^2=9

3.Changing the base

9^x=729

(3^2)^x

x=3

1 / 2 = 2^-1

2.Squaring negative integers

-3^2=-9

(-3)^2=9

3.Changing the base

9^x=729

(3^2)^x

x=3

### 3 Common Errors (Indices)

Iffah (05) & Danish (15)

__3 Common Errors & How to Avoid Them__

**1. Splitting up integers to their base+index.**

For example, 4^x = 32.

We need to first split up 4 and 32 to their base form, that is 2^2 and 2^5, for 4 and 32 respectively.

Hence, (2)^2x = 2^5

2x = 5

x = 2.5

You can try looking at common bases that both numbers have.

**2. Negative indices.**

a ^ (-n) = 1 / a^n

Don't get confused! :) Know that for every negative index, you move it either UP or DOWN of the fraction. Like.....

-(3 ^2) x

**3 ^(-3)**

= -

**9**[THE SQUARE BELONGS ONLY TO 9, AND NOT TO -9] x

**1 / 3^3**

= -

**9**x

**1/27**

= -

**9**/27

= -1/3

= - (1/3)

You can make sure you follow the BODMAS law first.

**3. Multiplication law. a^b x a^c = a ^(b+c)**

For example,

3 ^(1/2) x 3 ^(1/2)

= 3 ^ (1/2 + 1/2)

= 3 ^ 1

= 3.

In this case, it is not 1/2 x 1/2, but instead 1/2 + 1/2! Multiplication law (same base!)

BE DETAILED & GOOD LUCK!

PS. Danish didn't do anything omfg

### Common Errors of Indices and Tips (Jonathan, Yu Tao, Kenneth)

__Common Errors__

1) Confusion of multiplication/division and addition of the indices.

2) Distribution of the bracketed index.

3) Conversion of index form into surd form, vice versa.

__Tips__

1) Double check for arithmetic errors after completing the question or when stuck.

2) Relax, take your time and don't rush when attempting the question.

3) Familiarise yourself with the rules and laws of indices and surds.

## Monday, 4 February 2013

## Tuesday, 22 January 2013

### Uses of Partial Fractions

Some links on the uses of partial fractions.

1. http://www.s-cool.co.uk/a-level/maths/advanced-algebra/revise-it/uses-of-partial-fractions

2. http://www.karlscalculus.org/calc11_5.html

3. http://www.sosmath.com/algebra/pfrac/pfrac.html

## Friday, 18 January 2013

## Thursday, 17 January 2013

### Classwork for 18 Jan 2013

Here's a file which you will find helpful in your revision and practice.

Please read page 352 - 355

for an overview of long division, synthetic division, remainder and factor theorems and also a real life application question.

page 356 provides good exercises, both written and mathematical, for revision.

page 366 requires factor theorem, so you are welcome to try it. Do not be too disturbed if you cannot do it for now.

Questions 55 - 62 are untypical questions, and are for those who love a little challenge.

Questions 63 - 65 are relevant for you and you should try them.

Lastly, on page 358, questions 70 - 82 are for those who need revision on the Sec 2 topics (expansion, simplication) and some of you who have been struggling with algebraic manipulation, you should do these.

Regards

Mrs Sin

Please read page 352 - 355

for an overview of long division, synthetic division, remainder and factor theorems and also a real life application question.

page 356 provides good exercises, both written and mathematical, for revision.

page 366 requires factor theorem, so you are welcome to try it. Do not be too disturbed if you cannot do it for now.

Questions 55 - 62 are untypical questions, and are for those who love a little challenge.

Questions 63 - 65 are relevant for you and you should try them.

Lastly, on page 358, questions 70 - 82 are for those who need revision on the Sec 2 topics (expansion, simplication) and some of you who have been struggling with algebraic manipulation, you should do these.

Regards

Mrs Sin

## Wednesday, 16 January 2013

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