## Monday, 16 September 2013

### Find my Centre - Authentic Task

ACTIVITY 3

Objective:
This is a collaborative activity to consolidate the learning of angles in a circle viz a viz APPLIED LEARNING MODE.

ICT tools:
your choice (Geogebra, Geometer Sketch Pad etc)

You are a mechanical engineer that is supervising a mould making process. You have just been tasked to replicate a circular object in your production line. The products must be precise (congruent of the highest degree) and must be mass produced efficiently at the shortest possible time with minuscule margin of error.

The first task is to produce a mould by which all the objects will be replicated from.

To facilitate the process, you are required to first determine how you would determine the following
1. centre of the circle
2. radius of the circle / sphere
For the above activity, you are required to use the angles properties discovered in the topic.
Do provide the logical reasoning in your answer.
Post your solution in blog page assigned to you.
Remember time is a factor so you have to plan your time very well.

### Assessment 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
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!

## Sunday, 15 September 2013

### Angles in a Circle - SELF DIRECTED

ACTIVITY 1

Objective:
This is a self directed activity to consolidate the learning of angles in a circle.

ICT tools:
Math Blog for activity specifications
TI-Nspire CAS
tns file will be given at the beginning of session

ACTIVITY 2

Objective:
This is a collaborative activity to consolidate the learning of angles in a circle viz a viz formative assessment.
Error analysis will follow the assessment.

ICT tools:
TI-Nspire CAS
tns -based poll will be used to assess learning.

ACTIVITY 3

Objective:
This is a collaborative activity to consolidate the learning of angles in a circle viz a viz APPLIED LEARNING MODE.

ICT tools:
TI-Nspire CAS

Given the object, determine how you would determine the following
1. centre of the circle
2. radius of the circle / sphere
For the above activity, you are required to use the angles properties discovered in the topic. Do provide the logical reasoning in your answer.

## The Alternate Segment theorem states

An angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.

Recall that a chord is any straight line drawn across a circle, beginning and ending on the curve of the circle.
In the following diagram, the chord CE divides the circle into 2 segments. Angle CEAand angle CDE are angles in alternate segments because they are in opposite segments.

The alternate segment theorem states that an angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment
In terms of the above diagram, the alternate segment theorem tells us that angleCEA and angle CDE are equal.

Example:
In the following diagram, MN is a tangent to the circle at the point of contact A.Identify the angle that is equal to x

Solution:
We need to find the angle that is in alternate segment to x.
x is the angle between the tangent MN and the chord AB.
We look at the chord AB and find that it subtends angle ACB in the opposite segment.

So, angle ACB is equal to x.

### Circle - Cyclic Quadrilateral

cyclic quadrilateral is a quadrilateral that can be inscribed in a circle. They have a number of interesting properties.

## Applicable Theorems/Formulae

The following theorems and formulae apply to cyclic quadrilaterals:

## Class based activity:

Objectives:
to proof the validity of the following theorems through geometrical manipulations using Geogebra.
Theorem 1: Angle at the centre theorem
Theorem 2: Angle in a semi circle theorem
Theorem 3: Angles in the same segment

Activity 1:
Using the attached links explore the following:
a. the various permutations of Angle at the centre theorem
b. the relationship between Angle at the centre theorem and Angle in a semi circle theorem

Activity 2:
Using the attached links explore the limitations of Angles in the same segment theorem.

## Monday, 2 September 2013

### Circle - Chord

========================================================================

## Sunday, 1 September 2013

### Angles in a Circle

Angles properties

## Saturday, 31 August 2013

### Update on Assessment (i) PT2 (ii) P3 (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 Day 1 2359

(2) Paper 3
This constitutes the Additional Mathematics component of Assessment.
This will be conducted in Term 4 (23 September 2013).
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

(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  = 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)

### Mathematics Performance Task 2

Due Term 4 Week 1 (first Mathematics Lesson)

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

## Wednesday, 28 August 2013

### Essential GDC Skills

Essential GDC Skills

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