Jingshan Senior 1 November 2009

Date	Activities / Objectives	Images / Home Work	Remarks / Images	References / Links
Monday Nov. 2 14:50 -15:35 15:45 -16:30	Return of Assginment # 5 and # 6 Answer to questions from the students TEST # 1 & 1B Exercise I : Linear programming Exercise II : Graph and intersection of a Parabola and and a Hyperbola. Exercise III : Graph of function associated to elementary functions with absolute value	In the above problem 1 of Test.#1, many students do not really understand why the vertex of the graph defined by the system of contraints yields the maxmum profit.	Corrected Tests and grades have been given to WU Lao Shi on Tuesday Nov.3	Assigment #5 Assigment #6 Test 1 Answers Test 1B Answers
Monday Nov. 9 14:50 -15:35 15:45 -16:30	Questions / Answers about returned Test #1. Study of the transformation of a graph by symmetry through a vertical or horizontal axis and/or through the 1st Bissector (y=x). Application to the transformation of the exponential into the logarithm. Functions associated to the exponential and the logarithm functions, using the usual transformations.	Exercises in Class [ 2nd page of Assigment #7 ] to be continued at home and to be handed back to Wu Lao Shi before Friday 13th at 4:00 pm.	Students who got less than 60% have to make it up for Nov.13	Assigment #7 Erratum : on p.2 §II.2) the transformation required (ommission) is a symmetry through the 1st Bisector.
Monday Nov. 16 14:50 -15:35 15:45 -16:30	Presentation on computers of the Answers expected on assignment #7 (see picture -->) Introduction to Sequences & Series : Examples "in life" : the smiling cow the squares the decimals of Pi Examples of Arithmetic sequences : the Natural numbers The Odd numbers The Even numbers General formula : U_n = U₀ + n.r Examples of Geometric sequences : The powers of 2 the powers of 1/2 General formula : V_n = V₀. qⁿ Properties of a Sequence to be checked : Is the sequence monotonous ? Is the sequence bounded ? Is there an adequate formula ? Is there a limit ?		Video taken by the administration in the presence of WU laoshi. • • • Change of room because of absence of key for connecting laptop computer to the video projector. Question 1 : Supposing that the orignal box cover is a circle of 10cm of diameter, and that the ear rings of the cow are a quater of the size of the box, find how many cow boxes can designed until the size of the earing-box is less than 1mm.... Question 2 : Supposing that the original square side measures 2cm and that the side of each square is 3/4 of the previous square, find the surface that can be covered by all the squares generated.
Monday Nov. 23 14:50 -15:35 15:45 -16:30	Comparison of Arithmetic and Geometric sequences (see document). Exercise on non linear sequences : Sequences defined by an elementary function : Un = √(6+n) Un = (4n -2) / (n+1) Graph of the first terms to examine : Is the sequence monotonous ? Is the sequence bounded ? Is there a limit ?	Assignment # 8 (Sequences)	Change of room because of absence of key for connecting laptop computer to the video projector. Reading the document about the comparaison of arithmetic and geometric sequences made clear that many students don't understand some "ordinary" words like : term, reason, constant, notation, specify, initial, Fibonacci, mean, quadratic, equidistant...	Comparison of Arithmetic & Geometric Sequences Assignment # 8 (Sequences)
Monday Nov. 30 14:50 -15:35 15:45 -16:30	Explain Answers to Assignment # 8 p.1 Example of definition of monotony of a sequence. Example of definition of boudaries of a sequence. Example of definition of the limit of a sequence. finite limit infinite limit Examples of recurrent sequences with elementary functions : v_n+1 = f(v_n) ; v₀ = a (a is a given number) affine homogaphic square root Explain Answers to Assignment # 8 p.2 see picture for the construction of the first terms of the sequence defined by recurrence, using the first bisector. Introducing a geometric sequence to find the limit of a recurrent sequence. Collect Assignment #8 p.1 & 2 Handout Assignment # 9 for Dec.7	Assignment # 8 v₀ = 0 ; ; v₀ = 4 u_n+1 = - 0.5 u_n + 2 ; u₀ = 0	Assignment # 9	Assignment # 9

Date

Activities / Objectives

Images / Home Work

Remarks / Images

References / Links

Monday

Nov. 2

14:50 -15:35

15:45 -16:30

Return of Assginment # 5 and # 6
Answer to questions from the students

TEST # 1 & 1B

Exercise I : Linear programming
Exercise II : Graph and intersection of a Parabola and and a Hyperbola.
Exercise III : Graph of function associated to elementary functions with absolute value

In the above problem 1 of Test.#1, many students do not really understand why the vertex of the graph defined by the system of contraints yields the maxmum profit.

T1.2

Corrected Tests and grades have been given to
WU Lao Shi
on Tuesday Nov.3

Assigment #5

Assigment #6

Test 1 Answers

Test 1B Answers

Monday

Nov. 9

14:50 -15:35

15:45 -16:30

Questions / Answers about returned Test #1.
Study of the transformation of a graph by symmetry through a vertical or horizontal axis and/or through the 1st Bissector (y=x).
Application to the transformation of the exponential into the logarithm.
Functions associated to the exponential and the logarithm functions, using the usual transformations.

Exercises in Class
[ 2nd page of Assigment #7 ]
to be continued at home and to be handed back to Wu Lao Shi before Friday 13th at 4:00 pm.

Students who got less than 60% have to make it up for Nov.13

Assigment #7
Erratum : on p.2 §II.2)
the transformation required
(ommission) is a symmetry
through the 1st Bisector.

Monday

Nov. 16

14:50 -15:35

15:45 -16:30

Presentation on computers of the Answers expected on assignment #7 (see picture -->)
Introduction to Sequences & Series :

Examples "in life" :

the smiling cow
the squares
the decimals of Pi

Examples of Arithmetic sequences :

the Natural numbers
The Odd numbers
The Even numbers
General formula : U_n = U₀ + n.r

Examples of Geometric sequences :

The powers of 2
the powers of 1/2
General formula : V_n = V₀. qⁿ

Properties of a Sequence to be checked :

Is the sequence monotonous ?
Is the sequence bounded ?
Is there an adequate formula ?
Is there a limit ?

Video taken by the administration in the presence of WU laoshi.
• • •
Change of room because of absence of key for connecting laptop computer to the video projector.

Question 1 :
Supposing that the orignal box cover is a circle of 10cm of diameter, and that the ear rings of the cow are a quater of the size of the box, find how many cow boxes can designed until the size of the earing-box is less than 1mm....

Question 2 :
Supposing that the original square side measures 2cm and that the side of each square is 3/4 of the previous square, find the surface that can be covered by all the squares generated.

Monday

Nov. 23

14:50 -15:35

15:45 -16:30

Comparison of Arithmetic and Geometric sequences (see document).
Exercise on non linear sequences :
Sequences defined by an elementary function :

Un = √(6+n)
Un = (4n -2) / (n+1)
Graph of the first terms to examine :
Is the sequence monotonous ?
Is the sequence bounded ?
Is there a limit ?

Assignment # 8
(Sequences)

un1

Change of room because of absence of key for connecting laptop computer to the video projector.

Reading the document about the comparaison of arithmetic and geometric sequences made clear that many students don't understand some "ordinary" words like : term, reason, constant, notation, specify, initial, Fibonacci, mean, quadratic, equidistant...

Comparison of Arithmetic & Geometric Sequences

Assignment # 8
(Sequences)

Monday

Nov. 30

14:50 -15:35

15:45 -16:30

Explain Answers to Assignment # 8 p.1
Example of definition of monotony of a sequence.
Example of definition of boudaries of a sequence.
Example of definition of the limit of a sequence.

finite limit
infinite limit

Examples of recurrent sequences with elementary functions : v_n+1 = f(v_n) ; v₀ = a
(a is a given number)

affine
homogaphic
square root

Explain Answers to Assignment # 8 p.2
see picture for the construction of the first terms of the sequence defined by recurrence, using the first bisector.
Introducing a geometric sequence to find the limit of a recurrent sequence.
Collect Assignment #8 p.1 & 2
Handout Assignment # 9 for Dec.7

Assignment # 8

REC3b

v₀ = 0 ;

; v₀ = 4

u_n+1 = - 0.5 u_n + 2 ; u₀ = 0

Assignment # 9

Assignment # 9