2013 S3-09 Maths Blog: 2013

Monday, 16 September 2013

Find my Centre - Authentic Task

Labels: Circle

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)

mould making process

TASK:
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

centre of the circle
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

Labels: Circle

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

TASK:
Given the object, determine how you would determine the following

centre of the circle
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.

Tuesday, 3 September 2013

Circle - Alternate Segment Theorem

Labels: Circle

source: http://www.onlinemathlearning.com

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.

link to activity

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

Labels: Circle

source: http://www.artofproblemsolving.com/

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

Properties

In cyclic quadrilateral $ABCD$ :

Applicable Theorems/Formulae

The following theorems and formulae apply to cyclic quadrilaterals:

the link

Circle - angles @ centre & angles in same segment

Labels: Circle

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.

link to activity1

link to activity2

Monday, 2 September 2013

Circle - angle properties

Labels: Circle

source: http://www.onlinemathlearning.com/angles-circle.html

source: http://www.bbc.co.uk

Circle - Chord

Labels: Circle

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Sunday, 1 September 2013

Angles in a Circle

Labels: Circle

Angles properties

Saturday, 31 August 2013

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

Labels: ADMIN, ANNOUNCEMENT

(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

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

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 = asin(bx) , y = a sin(x/b + c), y = acos(bx) , y = a cos(x/b + c) and y = 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 = 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

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)