TI84 Exercise (as completed earlier in term3)

TI84 Exercise

Update on Assessments (i) PT (ii) Paper 3 (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) 

Assessment in Term 4

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!

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 Graph Trigonometric Functions on TI-84+?

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.

MATHEMATICS LESSON 3rd April 2013 1st Period Scribery

MATHEMATICS LESSON
3rd April 2013
1st Period Scribery
Scriber: Harindrar
Special thanks to: Iffah

Exponential:
Equation
y = a^x
Rules
A > 0
A not equal to 1
Asymptote: x-axis
Observations
Bigger the base(a) the closer the line is to the y-axis(Narrower/steeper)

Image: http://www.sosmath.com/algebra/logs/log4/log42/gl01.gif
_______________________________________________________
Logarithm:
What does a logarithm represent? Ans: Power/index
Equation
Y = logax
Rules
A > 0
A not equal to 1
Asymptote: y-axis
Observations
Bigger the base(a) the closer the graph is to the x-axis

Image: http://www.sosmath.com/algebra/logs/log4/log42/gl02.gif
_______________________________________________________
Exponential and Logarithmic relationship:

Image: http://www.regentsprep.org/Regents/math/algtrig/ATP8b/inversegraph.gif

Relationship(With reference to image)
Line through the middle is the line of symmetry.
Inverse relationship between log and exponential.
_______________________________________________________
Modulus:
Equation
Y = a | x |
Possibilities
-x , x < 0
X , x = 0 OR x > 0
Observations
(Linear)
V - Shaped graph.
Line of symmetry is y-axis
Image: http://limchiawei-tennshaun-yongzhen-haoyuan-modulusfunction.wiki.hci.edu.sg/file/view/f%28x%29%3Dabs%28x%29.png/231254306/800x442/f%28x%29%3Dabs%28x%29.png

(Quadratic)
Image: http://limchiawei-tennshaun-yongzhen-haoyuan-modulusfunction.wiki.hci.edu.sg/file/view/quad_graph1.png/238694051/800x567/quad_graph1.png


- Please post any additional notes in the comments section - THANK YOU -

Notes on asymptote.

Sorry for the late post

Summary of points from lesson on 27 March 2013

Graphs of Standard Functions

(Recap)
Functions are relations
- one to one linear graph
- many to one
- one to many (y^2=x)
- many to many (x^2/a^2 + y^2/b^2 =1) eclipse graph

Functions must be
- logical
- reliable
- reasonable
- predictable

How to test for function (graphically)
- vertical line test
cut once: is a function
cut more than once: not a function
--------------------------------------------------------
Linear
- y=kx
- k is the gradient passes through origin
- k>0, sloping up /
- k<0, sloping down \

|k| modulus/ absolute value
- taking the numerical value of k

Quadratic
as |k| increases, the graph becomes narrower

Reciprocal
inverse proportion : y=k/x => xy=k
2 ---(reciprocal)-----> 1/2

when x increase, y decreases
what are values that
x cannot be? -> x≠0
y cannot be? -> y≠0
k cannot be?-> k≠0

At values where x and/or y do not exist, there will be asymptote.

asymptote - a line that continually approaches a given curve but does not meet it at any finite distance.

PERFORMANCE TASK 1

updated on April 2013

updated for clarity

Notes from 7MARCH2013 math class ._.

Reflection type of error (EMAIL TO MRS SIN)

(a) concept
(b) carelessness
(c) lack of practice
 -blank out
 -shortage of time

50 words: what are you going to do?



FIY:
(A-MATH)
Mean: 52.03% ≠16
Median: 53.33% ≠16-17

6th March Lesson Summary - Discriminant (Wed) -Darren

Lesson Summary for 6th March Wednesday - Discriminant

Remember that in the formula:
y = a(x-h)^2 + k

H = to the x-intercept
&
K = to the y-intercept.

And remember the flow chart that if your 'a' must be equal to 1 before u continue the 'completing the square' hence, you must factorise the 'a' first, to put the coefficient outside of the bracket so you could have the remaining of a=1 and carry on the 'completing the square' to solve the equation.

\
Also remember these few important key points in this chapter.













Sorry for the bad quality photos XD Keep practicing the applications of these formulas and ull do well. Just understanding is not enough! Hope this is helpful. All the best for the results for the rest of your tests! :D

5/3 Lesson Summary

HOMEWORK DUE

• Wednesday (6/3): A02d
• Friday (8/3): A02e
– Prepare $12.50 for Math TYS. This will be bought for collectively as a class.
– If you wish to know your A/E-math results for this Level Test, please email Mrs Sin (yeo_chuen_chuen) about it, stating your name, class and index number :)

* Complete pg 154 - 155 of Math notes. You should have finished the graph sketching in class.
Write down the Completed Sq of each graph/function.

Quadratic Equations and Graphs

1. Identifying when to use SUM & PRODUCT of ROOTS (α, β)
- when part of the function has more than two unknowns (refer to pg 153: x^2 +x(2-k)+k = 0), use sum & product of roots.

- find sum (-b/a) > find product (c/a) > form eqn from sum > form eqn from product > solve via simultaneous and quadratics

* refer here.

2. Quadratic Roots Identities – α, β
(α + β) ² = α² + 2αβ + β²
(α – β)² = α² – 2αβ + β²
α²  – β² = (α + β)(α – β)
α²  + β² = (α + β) ² – 2αβ

QUADRATIC EQUATION CAN ALSO BE WRITTEN AS:
x² – (SUM OF ROOTS: b/a) + (PRODUCT OF ROOTS: c/a) = 0

3. Properties of Quadratic Graphs
1. Intersect x-axis at 0, 1, 2 points
2. Symmetrical in the line y=k, where k is the y-coordinate of vertex (turning point)
3. Always has a y-intercept at c.

4.

Sandy (06) to take over tomorrow's lesson summary & math homework updates!

DIS IS IFF
30Point8FM.

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)

Polynomial Diagnostic Test 1B Answers

Common Mistakes of Indices ( Harindrar | Saishwar )

COMMON MISTAKE 1:
Leaving answer in index form even though question does not ask to.
EG: Leaving 216^1/3 as an answer instead of 6

COMMON MISTAKE 2:
Not putting the question into index form, hence getting stuck and being unable to carry on.
EG: 144 = X^2
        144 = 12^2

COMMON MISTAKE 3:
Leaving answer in surd or indices form when the question says otherwise.
EG:
leaving answer as 3^1/2 when question asks for surd form
and
leaving answer as Squareroot(3) when question asks for indices form

Thank you,
Harindrar and Saishwar.

Common Errors

Common Errors
1. Unable to remember all 10 rules.
2. Unable to use multiple rules at once.
3. Careless.


Solutions:
1. Practice more.
2. Try to memorize the 10 rules.
3. Double check work.

Common Errors and Tips (Keming, Isaac, Ying Liang)

Common Errors

1) Confused with how to expand the brackets for indices 

2) Using guess and check to obtain answers

3) Unable to obtain answers for sums with the same indices 

Tips

1) Double check using a calculator and make sure it tallies 

2) Think properly and nicely without getting angry and panic in the process as panicking will only yield useless and marks-reducing results

3) Getting used to the laws of indices

3 Common Errors (Indices) by Imanni and Harriz

Common Errors

1) Confusion of the 10 laws and how they co-relate with each other.

2) Confusion of negative indexes and how they can be solved.

3) Deriving the unknown bases and powers.

Tips

1) Check for errors in calculation whenever you are stuck or skip the question then come back to it to check.

2) Take your time when attempting a question so as to minimize errors during calculation.

3) Revise at home so that you are familiar with what you learnt.

3 Common Errors

1.Negative indices
1 / 2 = 2^-1
2.Squaring negative integers
-3^2=-9
(-3)^2=9

3.Changing the base
9^x=729
(3^2)^x
x=3

3 Common Errors (Indices)

Iffah (05) & Danish (15)

3 Common Errors & How to Avoid Them

1. Splitting up integers to their base+index.

For example, 4^x = 32.
We need to first split up 4 and 32 to their base form, that is 2^2 and 2^5, for 4 and 32 respectively.

Hence, (2)^2x = 2^5
2x = 5
x = 2.5

You can try looking at common bases that both numbers have.

2. Negative indices.

a ^ (-n) = 1 / a^n

Don't get confused! :) Know that for every negative index, you move it either UP or DOWN of the fraction. Like.....

-(3 ^2) x 3 ^(-3)
= -9 [THE SQUARE BELONGS ONLY TO 9, AND NOT TO -9] x 1 / 3^3
= -9 x 1/27
= -9/27
= -1/3
= - (1/3)

You can make sure you follow the BODMAS law first.

3. Multiplication law. a^b x a^c = a ^(b+c)

For example,

3 ^(1/2) x 3 ^(1/2)
= 3 ^ (1/2 + 1/2)
= 3 ^ 1
= 3.

In this case, it is not 1/2 x 1/2, but instead 1/2 + 1/2! Multiplication law (same base!)

BE DETAILED & GOOD LUCK!

PS. Danish didn't do anything omfg

Common Errors of Indices and Tips (Jonathan, Yu Tao, Kenneth)

Common Errors

1) Confusion of multiplication/division and addition of the indices.

2) Distribution of the bracketed index.

3) Conversion of index form into surd form, vice versa.

Tips

1) Double check for arithmetic errors after completing the question or when stuck.

2) Relax, take your time and don't rush when attempting the question.

3) Familiarise yourself with the rules and laws of indices and surds.

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

Page 51

My apologies for the late post.

Classwork for 18 Jan 2013

 Here's a file which you will find helpful in your revision and practice.


Please read page 352 - 355
for an overview of long division, synthetic division, remainder and factor theorems and also a real life application question.

page 356 provides good exercises, both written and mathematical, for revision.

page 366 requires factor theorem, so you are welcome to try it. Do not be too disturbed if you cannot do it for now.

Questions 55 - 62 are untypical questions, and are for those who love a little challenge.

Questions 63 - 65 are relevant for you and you should try them.

Lastly, on page 358, questions 70 - 82 are for those who need revision on the Sec 2 topics (expansion, simplication) and some of you who have been struggling with algebraic manipulation, you should do these.

Regards
Mrs Sin

Page 47

Pg 52, qn 07

Math Page 46