## Saturday, 31 August 2013

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

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 Day 1 2359

(2) Paper 3
This constitutes the Additional Mathematics component of Assessment.
This will be conducted in Term 4 (23 September 2013).
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

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

(A1) Equations and inequalities
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  = asin(bx) ,      = sin(x/b + c),     = acos(bx) ,      = cos(x/b + c) and          = 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 = axand 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)

Due Term 4 Week 1 (first Mathematics Lesson)

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

## Wednesday, 28 August 2013

### Essential GDC Skills

Essential GDC Skills

View each video carefully and learn these fundamental GDC skills.

1. Basic Graphing Controls
a. Zoom Options

b. Setting the Window

2. Graphing Basics

a. Graph a line and find the table of values:

b. Finding coordinates of turning points of a graph:

c. Finding intersection between two graphs:
(comes with exercises)

d. Finding roots and y-intercept of a graph:

3. PlySmlt2
a. Using PlySmlt2 for Solving Quadratic Equations

b. Using PlySmlt2 to Solve a System of Equations

c. Using PlySmlt2 to Solve Polynomial Equations

## Sunday, 4 August 2013

### TI84 Wave Generator

This activity is walks you through the steps to perform sine regression for a randomly generated data set using the TI-84.

## Step 1: Get some data.

• Go to the Randomized Wave Data Generator and use the form to get some randomly-generated data (check the boxes for more interesting data).
• Your data should be different from every other data set on earth, so copy and paste it to a (spreadsheet or word-processor) file for your later use.

## Step 2: Enter the Data into your Calculator.

1. Press Y= and clear the Y1 function.
2. Press STATPLOT (2nd followed by Y=) and choose Plot1.
3. Under Plot1, select On (press ENTER), after Type select the drawing of disconnected dots, and make sure you have Xlist: L1(2nd followed by 1) and Ylist: L2 (2nd followed by 2).
4. Press STAT. With EDIT highlighted, select 1:Edit…
5. In the table that appears, under L1 type the x values and under L2 type the values of y. Make sure your L1 and L2 lists have the same length. (key in the data obtained from the Randomised Wave Generator)
6. Press ZOOM and choose option 9:ZoomStat to look at a scatter plot of your data.

## Step 3: Find the Sine Wave of Best Fit for the Data.

1. Press STAT. Press the right arrow key to highlight CALC. Then scroll down to select C:SinReg and pressENTER ONCE.
2. In the SinReg screen, choose Iterations:3 Xlist:L1, Ylist:L2 and Store RegEq: Y1 (press VARS, then select Y-VARS , then select FUNCTION, and then select Y1). Then highlight Calculate and press ENTER ONCE.
3. The calculator should now display the values for abc, and d in the function f(x)=asin(bx+c)+dthat best fits the given data set.
4. Press GRAPH to see the sine regression function plotted along with your scatter plot and press Y1 to see the equation of your wave.

## Task: in sub groups of 3s

1. Using the Randomized Wave Data Generator generate a (1) Set of Data.
2. Identify the best fit function f(x)=asin(bx+c)+dthat best fits the given data set
3. Explain the Transformation of your function using f(x)=sin(x) as a bench mark points. Your explanation should be as follows

• Increase in amplitude by a
• period change by ....
• vertical shift by ....