# 2013 S3-09 Maths Blog

## Wednesday, 29 January 2014

## Thursday, 16 January 2014

### Probability summary

**Probability:**

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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

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Sample space: All the possible outcomes of an experiment

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

Sample point = 1 of the possible outcomes

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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)

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Diagrams:

Probability diagrams:

Used for two independent events

Tree diagram:

Used for two or more events

## 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:**

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

Remember time is a factor so you have to plan your time very well.

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,

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!*## 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:**

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

#### 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.

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*CEA*and 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 angle

*CEA*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

A

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

## Applicable Theorems/Formulae

The following theorems and formulae apply to cyclic quadrilaterals:

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