TI84 Exercise

Assessment in term 4 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!

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

(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 (first lesson)

(2) Paper 3

This constitutes the Additional Mathematics component of Assessment.

This will be conducted in Term 4.

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
•   Mensuration

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) 

Mathematics Performance Task 2

Due Term 4 Week 1 (first Mathematics Lesson)

the file could be downloaded from google site.

Please fill-up this form once you have submitted the work.

How to Plot Graphs on TI-84+

Scribe for today 12/07

The Sine Rule is not to be confused with Sine = Opposite / Hypotenuse

A/sin a = B/sin b = C/sin c can also be written with flipped numerator and denominator.

It is suggested for the unknown angle/side to be on the upper-left of the equation for easy manipulation.

Semester 2 Update

1. Scheme of Work (Syllabus for Semester 2)

Term 3

Wk 1       (AM)  LINEAR LAW

Wk 2-3    (EM) TRIGONOMETRY

                        - Sine Rule, Cosine Rule, bearings, Angle of Elevation, 3D problems (EM)

Wk 4-6    (AM) TRIGONOMETRY (AM)

Wk 7   (EM) PROPERTIES OF CIRCLES 

Wk 8       (AM) CIRCULAR MEASURE

Wk 9-10  (AM) BINOMIAL THEOREM 

Term 4

Wk 1 Revision

Wk 2 EOY Exam

Self Directed Learning (AM) URVES & CIRCLES

2. Assessment 

Level Test 2 (10%) 

Wk 7-8

format:   1 hour

Marks:    40 marks

Topics

EM

     Coordinate Geometry

     Trigonometry

AM

     Coordinate Geometry

     Trigonometry

     Linear Law

Paper 3 - AM (10%) 

PT2       - EM (10%)

Mathematics Term 2 Practice Paper Answers

AM and EM Assessment Book (GCE O format)

To assist students in their revision and preparation for GCE 'O' Level, the Mathematics Department has made arrangement with the bookshop to order the following 2 books for the students.

The information is as follows:

• Additional Mathematics by topic $7.00
• Mathematics by topic $5.50

Both will include solution booklet

Please make arrangement with your Math teacher on the procedures for purchases.

1 April 2013 

1) domain: x, Range: y

2) Modulus absolute value is the absolute distance from zero.

3) The usage of completing the square depends on the type of question.

4) When the gradient is less, the graph is steeper.

Its Wednesday :D First period of math

Random Scribe Thing

Intersection of curve and line

TOA CAH SOH
⬆ The tangent in TOA is not equal to the graph tangent.
Tangent in graphs represent the gradient in the graph. And also as it is the gradient (Rise/Run)

Eg.
x^2-xy+y^2=1 -----(1)
2x-y=k ---------------(2)
First Step: Solve both equations simultaneously.
From (2),y=2x-k -----(3)
Substitute (3) into (1)
x^2-x(2x-k)+(2x-k)^2=1
x^2 -2x^2+kx+4x^2-4kx+k^2=1
3x^2-3kx+k^2-1=0

If Z is an unknown constant, write it in Zx, not xZ as the constant is in front of the variable.

Edit: Note: Flip the inequality sign when you multiply by negative - .

Friday 15/3/13

Logarithms 

- The power law of logs do not apply if the power affects the whole log. 

Eg. ( log 3) ^2 

Exponential Equations 

-  When an equation seems difficult, simplify it using substitution. 

Eg,  Logarithms , Algebraic 

Notes for 14/3 BY JOVAN

- Use 'discriminant' instead of b^2 - 4ac.

- Question may use terms a, b or c 

- Thus b^2 - 4ac will not equate to the discriminant

- Negative inequalities have to be flipped when both sides are multiplied by negative (exception)

- When question ask for 'show that'

- Find discriminant expression

- Find a range that the discriminant always satisfies

- Link back to question (write 'shown')

- Notes for question 12b

- Expression of discriminant

- Find range of discriminant that is always true

- Link back to question and copy the right question

- Find the range of values by determining the condition of the roots

Performance Task 1

updated on April 2013

updated for clarity

DA STUFF for TODAY (13/03)

The graphic calculator!

ON: (on) duh
OFF: (2nd)(on)

Write your equation for the graph: (y=)

Once the equation is set, you will see your equation by pressing (trace)

ZoomBox = Zoom to certain area that you selected.
You'll see a blinking cursor, set it to where your zoom's upper-left corner is. (Enter) Then set it to where the zoom's lower-right corner is. (Enter) it would zoom to your desired zoom
Alternatively, you can set the max of X and Y axes by pressing (window) and setting to how far of each axis you want to see.

Calculate on the graph: (2nd)(trace)

Value: of Y when X is ____

Maximum: the maximum turning point for a ∩ shaped curve
Minimum: the minimum turning point for a ∪ shaped curve
For use of both the above, find the left and right bounds, where you think the maxi/mini is. Then make a guess on where the maxi/mini point is. The calc will help find it for you afterwards.

:D :D :D :D

Notes for 11/3 BY JOVAN

Quadratic functions:

Ways to express quadratic function:

- f(x) = ax^2 + bx + c (General)

- c is y-intercept

- f(x) = a(x-h)^2 + k (Vertex form)

- coordinates of turning point (h, k)

- f(x) = a(x-p)(x-q) (Factor form)

- roots

- each form gives separate information about the graph

- General to Vertex - Completing the square

- General to Factor - Factorise

- Factor/Vertex to General - Expand

Ways to solve the equations:

- Using quadratic formula

- Completing the square

- Factorise

- Graph

- Sum and product of roots

- Calculator (DUH! =D)

Discriminant:

- b^2 - 4ac

- D > 0

- real and distinct roots (2 intersection on the x-axis)

- D = 0

- real and equal roots (1 intersection on the x-axis)

- D < 0

- imaginary/complex roots

Graphing (Sketching)

- roots, turning point, y-intercept

- shape: symmetrical

- smiley face-curve a > 0

- sad face-curve a < 0

- y-intercept: c

- Roots: solve

Math Summary~ Discriminants (060313)

MATHS SUMMARY - NATURE OF ROOTS OF A QUADRATIC EQUATION (050313)

Ways to solve quadratic equations
1) Factorisation
2) Completing the square
3) General Formula
4) Calculator
5) Graph

The (b^2 - 4ac) within the general formula determines the nature of the roots of an quadratic equation.
If (b^2 - 4ac) = 0, one of the roots is 0, the other root will be a real number. (x will have one value)
If (b^2 - 4ac) < 0, both roots are real (x will have 2 values)
If (b^2 - 4ac) > 0, both roots are imaginary or complex number (x will have no values)

MATH SUMMARY - SUM/PRODUCT OF ROOTS (040313)

Math Quiz ( Logs )

Answers for Indices A02a and Revision Worksheet (E Math)

Dear all

Here are the answers for your checking for the worksheets.

Indices A02a

Revision Worksheet (E Math)

Solutions for Partial Fractions

Uses of Partial Fractions

Some links on the uses of partial fractions.

1. http://www.s-cool.co.uk/a-level/maths/advanced-algebra/revise-it/uses-of-partial-fractions

2. http://www.karlscalculus.org/calc11_5.html

3. http://www.sosmath.com/algebra/pfrac/pfrac.html

Answers for pg 51 - 53 (Long and synthetic division)

The answers are:

Practice 5

quotient = 2x^2-x-12
remainder = 2

Practice 6

quotient = 6x^2 - 4x - 2
remainder = 0

Practice 7

quotient = 2x^4 + 3x^2 + 9
remainder = 0

Practice 8
(a) quotient = 2x^2 - x - 12
     remainder = 0

(b) quotient = 3x^2 -12x + 6
      remainder = 3

Long Division Practice 2

Yes it's very messy and blur sorry ._.

Math Notes Part 1 Answers

Punishment for not knowing which Practice 02 in the math notes as homework :(

Practice 04 - Page 50 of Math Notes Sec 3 Part 1
by Ryan Yeo

Long Division involving polynomials

Polynomials Revision

BY MR JOHARI
source: http://www.regentsprep.org/Regents/math/ALGEBRA 

Attempt the following Quiz and post your score as a comment.
Not to worry about the score - it is non evaluative for CA but would enable me to gauge your understanding and assist you.

Homework for 15 Jan 2013 (Polynomials Worksheet A01B)

Here are the modifications for the homework.

Q3) (b) 3x^2-4x+20 = A(x-2)^2 + B(x+2) + C

  

       (c) 2x^3-x^2 - 7x+C = (2x-3) (x^2 + x - 2) +1

Please complete them by tomorrow.

3 Things Learnt from Today

1. The image of a function is the output
2. f -> x = f(x)
3. Differentiate a function from non-functions.

Yeah!
Try and find what 1/9801 is equal to, the answer is amazing.

Answers for practice 2,3,4,5

Edited for better viewing!! :)

Gotfried Wilheim Leibniz: Contribution as Mathematician

Leibniz was the first to employ function to denote any of several geometric concepts derived from a curve, such as abscissa, ordinate, tangent, chord, and the perpendicular. In the 18th century, "function" lost these geometrical associations. Leibniz was the first to see that the coefficients of a system of linear equations could be arranged into an array, now called a matrix, which can be manipulated to find the solution of the system, if any. This method was later called Gaussian elimination.

Daniel Bernouli: Bernouli's principle

In fluid dynamics, Bernoulli's principle states that for an inviscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy. Bernoulli's principle is named after the Swiss scientist Daniel Bernoulli who published his principle in his book Hydrodynamica in 1738.

Leonhard Euler

He is a Swiss mathmetician and physicist.

He is the one responsible for the "e" you see in your calculators. It is a constant that is approximately equal to 2.71828.
Basically it means this:

The base of the natural logarithm.

From "e" he derived "Exponential Function" from f(x) = e^x. It is used to model a relationship in which a constant change in the independent variable gives the same proportional change (i.e. percentage increase or decrease) in the dependent variable. 

http://www.mathsisfun.com/numbers/e-eulers-number.html

WANNA SHARE:

I've found this nice math video that is got to do with youtube:

FUNCTION (GRAPHICAL PERSPECTIVES)

by Mr Johari

The previous activities explicated the definitions of Relation and Function.

In the following task you have to use a suitable graphing tool to identify the graph and equation of

(1)  a FUNCTION 

(2)  a Non FUNCTION 

The graph below is an example.

graph from GEOGEBRA
The above shows a FUNCTION (property one to one)
equation y = x

GCP - ITALY

Please complete this by 13 January 2013

What can you tell about these machines?

Coffee Making Machine

Chocolate wrapping Machine

Popcorn making machine

Tidbits vending machine

In groups of 2's or 3's, discuss and post your observation in this thread.

Math Olympiad and Math Italy Trip

Here are two programmes for your consideration. 

 1. Math Olympiad 

     - Saturday Morning for 15 weeks 

      

     Please send me an email before this Friday, 11 Jan 2013, if you are interested.

2. Math Italy Trip

    - Mr Ingham has briefed you on the trip last year.

    - June or Oct (not confirmed yet)

    Please send me an email before this Friday, 11 Jan 2013, if you are interested. More information may be obtained from Mr Ingham.

Thank you.

Mutual Swap between Math and SS & Chem

Dear students

 As I will be away on course this Friday, 11 Jan 2013, your SS and Chemistry teachers have kindly agreed to swap their lesson with me.

11 Jan (Fri) Math 08 55 - 09 45 --> SS
11 Jan (Fri) Math 0945 - 1035 --> Chemistry
14 Jan (Mon) 10 45 - 11 35 Chemistry --> Math
15 Jan (Tues) 1155 - 1245 SS --> Math Thank you.

Sec 3 Scheme of Work

BEGIN WITH THE END IN MIND

by Mr Johari

Welcome to an exciting year 2013
Success comes with adequate preparation and as a start do take note of the following.

1. Know your Syllabus for 2013.
    Elementary Mathematics 4016 (SEAB site)
    Additional Mathematics 4038 (SEAB site)

2. Right Resources.
    SST Maths Note (Sec 3 term 1)
    Optional Reference Book
    Calculator (with approved SST seal)
    SST Foolscap paper and graph papers (for assignments)
    ICT Resources (Class Maths Blog, ACE Learning, graphing tools etc)

3. Assessment for 2013
    Term 1   Level Test 1 + Authentic Assessment         10% + 10%
    Term 2   Common Test 1                                         20%
    Term 3   Level Test 2 + Authentic Assessment         10% + 10%
    Term 4   End of Year Summative Assessment          40%
  
4. Diagnostic Test will be conducted as Follows:
    Beginning of new topic
       - to assess prerequisite knowledge and linkages to new knowledge
    End of topic
       - to assess level of understanding and competency
    duration - 20 -30 minutes

5. Daily learning and monitoring platforms
    Class work -  in the form of activities and practice questions
    Assignment - to be done on SST foolscap papers
                         (or SST exercise books - pending style of teacher)
    all classwork to be completed within designated time

6. Character is Destiny
    Your destiny should begin with your daily routines
    A.   Be Present
    B.   Listen without Prejudice
    C.   Be Socially Aware (we are after all living in a gregarious community)
    D.   Manage your impulses
    E.   Know that the choice that you have chosen has its own consequences