## Monday, 16 September 2013

### Assessment in Term 4 2013

Dear SSTudents,

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

All the best - you can do it because we have faith in you but do you!

## Saturday, 31 August 2013

### Update on Assessment (i) PT2 (ii) P3 (iii) EOY

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

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

(A1) Equations and inequalities
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  = asin(bx) ,      = sin(x/b + c),     = acos(bx) ,      = cos(x/b + c) and          = atan(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 = axand 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

During the school holidays, there would be a timed-trial on 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)

Due Term 4 Week 1 (first Mathematics Lesson)

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

## Thursday, 29 August 2013

### Essential GC Skills for Paper 3

View each video carefully and learn these fundamental GDC skills.

1. Basic Graphing Controls
a. Zoom Options

b. Setting the Window

2. Graphing Basics

a. Graph a line and find the table of values:

b. Finding coordinates of turning points of a graph:

c. Finding intersection between two graphs:
(comes with exercises)

d. Finding roots and y-intercept of a graph:

3. PlySmlt2
a. Using PlySmlt2 for Solving Quadratic Equations

b. Using PlySmlt2 to Solve a System of Equations

c. Using PlySmlt2 to Solve Polynomial Equations

## Saturday, 13 July 2013

### 5 THINGS WE NEED TO KNOW WHEN DRAWING A GRAPH :D

1) SCALE

Example :
Horizontal axis
8cm: 1 unit

Vertical axis :
2cm to 1 unit

*sometime the scale is given in the question*
_______________________________________________

2) Accuracy
-> How accurate the graph is
eg.
Accuracy =1/2 square
______________________________________________

3) FOR LINEAR LAW
->> Vertical intercept must be shown in the graph

______________________________________________

4) Size of graph
The graph should fill up 2/3 of the graph paper
~ which means we have to choose the scale properly.
> For accuracy purpose
>> Less error

____________________________________________
5) Table of values must be shown
example

## Saturday, 6 July 2013

### 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%)
Wk 7-8
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.

## Wednesday, 13 March 2013

updated on April 2013

updated for clarity

## Tuesday, 5 March 2013

Introduction:

For a quadratic equation $$a{x}^2+bx+c=0$$:

 Discriminant $${b}^2-4ac$$ Nature of roots Characteristics of curve > 0 2 real and distinct roots The curve cuts the x-axis ($$y=0$$) at 2 different points Perfect square 2 real and rational roots Not a perfect square 2 real and irrational roots = 0 2 real and equal roots The curve touches the x-axis at $$x=-\frac { b }{ 2a }$$.  The x-axis is a tangent to the curve. < 0 No real roots The curve does not cut or touch the x-axis. It lies entirely above (a > 0) or below (a < 0) the x-axis.

From the first 2 points, we conclude that

$${ b }^{ 2 }-4ac\ge 0\Longleftrightarrow$$ the roots are real

## Tuesday, 12 February 2013

### Surds: Question Creating

Find the value, in simplest form, of

$$\sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}}$$

Answer:$$\sqrt{8}=2\sqrt{2}$$

### Surds: Question Creating :D

Find the value, in simplest form, of

$$\sqrt{8+3\sqrt{7}}-\sqrt{8-3\sqrt{7}}$$

Answer = $$\sqrt{14}$$
Ming Yi Tay (06)
Find the value, in simplest form, of
$$\sqrt{9+4\sqrt{5}}-\sqrt{9-4\sqrt{5}}$$ .

Dean Ang(00)

## Wednesday, 16 January 2013

### Long Division Method Summary

LONG DIVISION METHOD

Steps

1. The rule of LDM is :

and..

So here is an example:

Step 1

Step 2 Multiply (In this case : x^3(x-3))

Step 3 : Bring down the answer

Step 4 : subtract

Step 5 : Repeat the steps with the other Variables

Step 6 : Repetition of steps 2 -4

Since Dividend = Quotient x Divisor + Remainder

Things to take note of:

Dividend MUST be in descending index form (x^4,x^3,x^2,x,constant)

IF the equation is similar to e.g. x^5-1 / x-3,

then the dividend used in LDM should be

( x^5 + 0x^4 + 0x^3 + 0x^2 + 0x - 1 ) / ( x - 3 )

So that dividend is arranged in descending index form

THATS ALL!!! :D