GSP ENRICHMENT

Enrichment objectives:
a. You will learn how to use the various features in the GSP software.
b. You will use the GSP to investigate the various properties of circle.

PART 1

INTRODUCTION

a. What is GSP?
b. Why do we use GSP?

HOW TO USE GSP

a. How to use GSP? (Video)
b. How to measure object using GSP? (Video)

PRACTICE

Learn to do all of the items on the following list of basic Sketchpad commands:

a. Construct points, segments, lines, circles.
b. Label an object. Change the name of the object.
c. Construct a segment, line, or ray through two specified points.
d. Construct a circle given its center and a point on it.
e. Construct a circle given its center and radius.
f. Construct the intersection of two objects.
g. Construct the midpoint of a segment.
h. Given a line j and a point A, construct lines perpendicular and parallel to j through A.
i. Any three noncollinear points lie on a circle.
j. Measure angle between 2 line segments.
k. Measure distance between 2 points.

EXAMPLE OF GSP

Refer to file: bubble.gsp in folder (GSP).

TASK 1

a. Sketch these figures using GSP.

POST YOUR PICTURES HERE

Post all your work at this wiki.

Click HERE.

Open either:
301 - GSP TASK 1
302 - GSP TASK 2
303 - GSP TASK 3

PART 2

PARTS OF CIRCLE





Using the GSP software, describe these parts of a circle.

a. radius of circle
b. diameter of circle
c. circumference of circle
d. chord
e. minor segment
f. major segment
g. arc
h. tangent

PROPERTIES OF CIRCLES

Using the worksheets given and files in the folder (GSP), we are going to learn about the properties of circles through exploration and inducton techniques.

These are 4 properties of circles that you will be learning in this lesson.
a. Angle at the centre
b. Angle in a semicircle
c. Angle in same segment
d. Angle in opposite segment

EXPLORATION

Click HERE to explore about thee properties.

INDUCTION

Now refer to the worksheet given to you. Follow the tasks that are listed in the worksheets.

a. Recognise the angle at the centre (Open GSP file: angle at centre.gsp)
b. Recognise an angle in a semicircle (Open GSP file: angle in semicircle.gsp)
c. Recognise the angles in the opposite segment and same segments (Open GSP file: angle in opposite segment)

REFLECTION

List 3 things that you have learnt today.
List 2 things that you like about today's lesson.
List 1 thing that on how we can improve today's lesson.

Survey for GSP Enrichment

Thank you for attending this enrichment. We hope that the enrichment was enriching and fun. Pls complete this SURVEY.

June Holiday Assignments

Hi everyone,

Please refer to the following information for your June holiday assignments.

1. Add Maths (402 & 511)
Nov 2006 Paper 1 (402 students, pls omit Q1, 4, 5, 7i)
Nov 2006 Paper 2 (402 students, pls omit Q1, 4, 8, 10, 12Either)

511A students, there will be no omission of questions.

2. Elem. Maths (402)
Nov 2004 Paper 1 (Pls omit Q24, 25)
Nov 2004 Paper 2

All papers need to be submitted to me on the 4th week of your vacation. I would expect full attendance during my holiday classes.

Have a good break!!

Binomial Expansion

1. (i) Calculate the coefficient of in the expansion of . [2]

(ii) Obtain the expansions of and in ascending powers of x. Hence or otherwise, find the coefficient of x, x² and x³ in the expansion of . [4]

2. (a)

(i) Find the first three terms in the expansion, in ascending powers of x, of . [2]

(ii) Hence find the value of p such that the coefficient of in the expansion of is . [3]

(b) Find the term independent of x in the expansion of . [3]

3. Write down and simplify the first four terms in the expansion, in

ascending powers of x, of . [2]

Use this expansion to

1. estimate the value of , correct to 3 decimal places, [2]

2. find the coefficient of in the expansion

. [2]

4. (a)

(i) Obtain the expansion, in ascending powers of x, of . [3]

(ii) Hence find the coefficient of in the expansion of [2]

(b) Find the term independent of x in the expansion of . [3]

5. (a) Find the term independent of x in the expansion of . [4]

2. Expand up to the term in x³. [ 4 ]

Solution to Binomial Exercises

Binomial Assignment

To all my A-Maths students,

Wishing all of you a Happy Chinese New Year!!

Your ang pow is attached. Pls submit by Monday, 11/2/2008.

Have a good holidays.

Any problems with probability?

Hi everyone, we have completed the topic on probability. I do hope that all of you are able to understand and cope with the topic.

Now, if you have any difficulty or queiries with the topic, do drop me with your comment. Remember to sign out with your name.

Thanks.

Post Lesson Task on Angle of Elevation

Hi eveyone,

After learning about angle of elevation, you are now given an assignment to:

- Create a question that make use of the principle of angle of elevation through the use of clinometer.

Limit your question to a maximum of 70 words. Deadline by Monday, 20th August 2007. This assignment will be graded.

Good luck.

Miss Yong

Trigonometry Assignment for 302

In Trigonometry, you have learnt about SINE Rule. In using SINE rule to solve some problems, there is a situation in which the solution becomes AMBIGUOUS.

Task:
1. When does a problem becomes AMBIGUOUS when you apply SINE rule?
2. Craft a question with its solution demonstrating AMBIGUOUS case when you apply SINE rule.

Total marks: 10
Due date: Friday, 3rd August 2007

PS: No copying of example given in textbook.

Solution to Find the Mistakes

After reading all your entries, I do realise that many of you have difficulty with completing the square method. I will re-explain the concept to you again in class one of these days.

The mistakes in the example given is not solely due to the completing square method. There are some mistakes committed due to incorrect algebraic manipulation.

Hint: To know where are the mistakes, TRY to do the algebraic manipulation steps by yourself.

Question: Coordinate Geometry (A-Maths)

To all my 302A students, pls solve this question by Friday 20/7/2007. Submit your solution to Chiu Rong. This is to prepare you for your test on Monday, 23/7/2007.

Question:
The coordinates of the points P and Q are P(-1,10) and Q(2,4).
a. Find the equation of the perpendicular bisector of the line joining P and Q.
b. If the perpendicular bisector of PQ cuts x and y-axes at points H and K, calculate the length of HK, giving your answer correct to 1d.p.

Find the mistakes.

Hi everyone,

I need you to find the mistakes of this solution given by a student. You just need to describe

i) where is the mistake

ii) what is the correct solution.

Lastly,

iii) what is the difficulty that you find in this chapter?

Remember to sign off your name.

Post Lesson Review - Human Plotter

To all my students, I will need all of you to answer these simple questions. Pls remember to sign off with your correct name. Thanks.

3. Give 3 words to describe the activity.
2. List 2 things that you have learnt.
1. Give 1 suggestion to make the activity better.