北京 景山 学校 数学系
Elective / Pre-Calculus @ MATHEMATICS @ Senior 1+  。2011-12
jiguanglaoshi@gmail.com

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[1] October
[updated : 2011/11/02]
Date
 Activities / Objectives
  Images / Home work / Assignments
 Remarks / Images
 References / Links

Monday

Oct. 10

3:15 -3:55

4:05 -4:45
Introduction to this Elective course :
  • Organisation of work :
    • memos / lectures
    • exercise sheets
    • assignments
    • tests
  • Ch.1:Review of 2° functions :  exercises
    • graphs
    • inequalities
      • one unknown
      • two unknown
  • Review of the Geometric properties of the Parabola (cf. Memo)

  • Review of the Algebraic properties of the 2° functions (cf. Memo)
Parab-up-down.jpg
 Systems of Inequalities : Ass. #1
Senior_1+_2011-12_Ass.1a.png
Syst_Inequ1.png

Senior_1+_2011-12_Ass.1b.png

Syst_Inequ2.png

List of attending Students :
  • Jason
  • Joel
  • Paul
  • Cookie
  • Jacky
  • ...(abs)
  • ...(abs)



paparabola.jpg







Registration Form





Memo / PARABOLA


Assignment #1
Monday

Oct. 17

3:15 -3:55

4:05 -4:45

 Chapter 2
Introduction to Homographic functions.ppt

H_1_5

Review of the algebraic & geometric properties
Generalisation

Exercises in class : see Ass.#2

 Exercises in class : Ass.#2 :
  • Graph of Homographic functions
  • Interception  a Hyperbola and a Parabola
  • system of inequalities associated to the graphs.

    syst.para-Hyper
 List of attending Students :
Jason - Joel - Paul(->Japon) - Cookie - Jacky

  • Parametric problem

Param_hyperb
 Homographic Functions.ppt
(to download)


Memo / Hyperbola

Assignment #2





Monday

Oct. 24

3:15 -3:55

4:05 -4:45
 Chapter 3
Associated Functions
&
Geometric transformations

    Examples  - Equations - Graphs - Exercises
    Use of Mathematical software
a)     f1(x) = - f(x) / Ox Symmetry
b)    f2(x) = f(-x) / Oy Symmetry
c)    f3(x) = - f(-x) / Central Symmetry
d)    f4(x) = f(x - L) + H  / Translation
e)    f5(x) = | f(x) |  partial symmetry / Ox
f)  f6(x) = f( |x| ) partial symmetry / Oy
g) f7(x) = | f(|x|) |

Exercise see  Assignment #3


 Exercises on associated functions
fx_assoc
f1(x) = - f(x) ; f2(x) = f(-x) ;
 f3(x) = - f(-x) ; f4(x) =  f(x-2)+1

Assoc_Parab.jpg


 List of attending Students :
Jason - Joel - Paul(->Japon) -
Cookie (sick)- Jacky

Hx_eq
Transformations :
h1(x) = | h(x) | ; h2(x) = h(|x|) ;
h3(x) = | h(-x) | ; h4(x) = h(x-2)+1

Hoomg_assoc




Assignment #3
Monday

Oct. 31

3:15 -3:55

4:05 -4:45
 		Associated functions
&
General Symmetries
  • EVEN functions :
    Axial Symmetry / (Oy)
            f(- X) = f( X)

  • ODD functions :
    Axial Symmetry / (O)
            f(- X) = - f( X)


  • Axial Symmetry / ∆ (x=a)
            f(a + X) = f(a - X)

  • Central Symmetry / I (a;b)
        f(a + X) + f(a-X) = 2b
Assignment #4

Exercises on Associated functions :

fonct_assoc

f1     f2
f3     f4



 		Exercises on Axial and Central Symmetries

SD2

SI2


Assignment #4


MEMO / Transformations


Ass. #4 ANSWERS