**(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 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

__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

__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**=**a**sin(**bx**) ,**y**=**a**sin(**x/b + c**),**y**=**a**cos(**bx**) ,**y**=**a**cos(**x/b + c**) and**y**=**a**tan(**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**

**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)

**
**

Duration of Paper: 45 minutes

Total marks: 30

**Date: 22 February 2013
**

Additional Maths Term 1 Level Test 1

**PROCEDURES AND INSTRUCTIONS for COMMON TEST**

· Writing paper will be provided during the Examinations.

· Students are required to bring their own writing and mathematical instruments such as pens, 2B pencils, soft erasers, approved calculators, set-squares, compasses, protractors, rulers and flexible rulers, as required.

· Students sitting mathematics and science papers will be allowed to use

**approved electronic calculators.****Elementary Maths Term 2 Common Test**

**3 May 2013 (Friday)**

**Time: 0750 - 0920 (1 hour 30 minutes)**

**FUNDAMENTAL ALGEBRA**

1. Expressions

a. Expansion

b. Factorisation

c. Algebraic Fractions

2. Indices

3. Equations

a. Solving quadratic equations by (i) factorisation (ii) using formula

b. Word problems

c. Simultaneous Equations"

**FUNCTIONS & GRAPHS (EM)**

1. Graph Sketching of Quadratic Functions

a. Exploring the features of the quadratic graph of the forms:

b. y = ± (x – h)2 + k and

c. y = ± (x – p)(x – q).

2. Graphs of Power Functions and sum of Functions

a. Draw the graph of the function y = axn for n = -2, -1, 0, 1, 2 and 3

b. Draw the graphs of a combination of not more than 3 functions.

3. Graphs of Exponential Functions and Gradients of Curves

a. Draw the graph of an exponential function y = kax, where a is a positive integer

b. Estimate the gradient of a curve by drawing a tangent to the curve

c. Graph Sketching of Linear Functions

4. Equation of a Straight Line

a. Interpret and find the equation of a straight line graph in the form y = mx + c

5. Solve geometric problems involving the use of coordinates

**TRIGONOMETRY**

1. Express trigonometric ratios as ratios of lengths of a right-angled triangle.

2. Solve questions involving angle of elevation and depression.

3. Solve trigonometric equations using the calculator.

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**Additional Maths Term 2 Common Test**

**8 May 2013 (Wednesday)**

**0750 - 0950 (2 hours)**

**01 POLYNOMIAL & PARTIAL FRACTIONS (AM)**

**Polynomial**

1. Add, subtract and multiply polynomials

2. Find the unknown constants in polynomial identities.

3. Divide a polynomial by another polynomial.

**Remainder and Factor Theorem**

4. Apply the Remainder Theorem:

(a) to find the remainder when a polynomial is divided by a linear divisor.

(b) to form and solve equations to find unknown(s).

5. Apply the Factor Theorem.

**Cubic Equations**

6. Solve cubic equations by factorization.

**Partial Fraction**

7. Express a rational expression in partial fractions.

**02 INDICES & SURDS (AM)**

**Surds and Indices**

1. Simplifying surds

2. Use conjugate surds to rationalize the surd denominator of a fraction.

3. Solve simple equations involving surds.

4. Apply the rules of indices to simple problems.

**Indices and Logarithms**

1. Conversion from Index to Log form

2. Application of the laws of logarithm

3. Solving equations involving logarithm

4. Apply the rules of indices and laws of logarithms to solve practical problems"

**03 QUADRATIC EQUATIONS & INEQUALITIES (AM) ^^**

**Roots of Quadratic**

1. State and apply the sum and product of roots of a quadratic equation.

2. Form an equation whose roots are related to the roots of another quadratic equation.

3. Identify the nature of the roots of a quadratic equation by considering the discriminant.

**Discriminant and nature of roots**

4. Apply the relation between the discriminant and the nature of the roots to find the unknown in the quadratic equation.

5. State and apply the conditions for ax2 + bx + c to be always positive or always negative

6. Apply the relation between discriminant and the nature of roots of a quadratic equation to determine whether a line intersects a curve at two distinct points, one point (tangent) or none at all

**Quadratic Inequality**

7. Solve a quadratic inequality using the corresponding quadratic curve

**04 MODULUS FUNCTIONS (AM)**

1. Evaluate or simplify expressions involving absolute values.

2. Solve simple equations involving modulus.

3. Sketch graphs of modulus functions.

**
**

**
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**

Additional Maths Term 1 Level Test 1

Duration of Paper: 45 minutes

Total marks: 30

**Topics:**

**Section 1.2 Polynomials and Identities**

**Section 1.3 Division of Polynomial**

**Section 1.4 Remainder Theorem**

**Section 1.5 Factor Theorem**

**Section 1.6 Cubic Equations**

**Section 1.7 Solving Cubic Equations**

**Section 1.8 Partial Fractions**

**Instructions:**

- All questions must be answered in INK.
- Show all working as it will demonstrates your train of thoughts and understanding on how you arrive at the answers.
- Write neatly.

**What you need to bring:**

- Working Calculator with the approved sticker (please obtain from Mr Johari)
- Ruler & Pencil

**Materials for Preparation:**

- Notes Booklet
- Questions (and answers) to the exercises were discussed in class.
- Homework, Diagnostic Assessments, Quizzes, Summative Assessments
- Ace Learning Portal exercises & video lessons
- Exam Preparation Booklet
- Maths Blog
- Reference Text Book (optional)

**The test results will constitute to your overall Maths results for the year.**

Duration of Paper: 45 minutes

Total marks: 30

**Date: 26 February 2013
**
Elementary Maths Term 1 Level Test 1

Duration of Paper: 45 minutes

Total marks: 30

**Topics:**

Refer to Sec 2 Notes and Exam Preparation Set

Algebraic Fractions

Indices (EM only)

Word Problem involving algebra

Quadratic Expression/Equations

Quadratic Graph plotting

Quadratic and Linear Graphs

**--------------------------------------------------------------------------------------------------------------------------------**

**Solution to Diagnostic Test**

**Diagnostic test (Format)**

- 20 - 30 minutes
- pen and paper exercise based on past knowledge on algebra (refer LO)
- use of approved calculator is allowed

**Objectives**

- Beginning of new topic (to assess prerequisite knowledge and linkages to new knowledge)
- End of topic (to assess level of understanding and competency)

**Expected Outcomes**

- ST will be able to ascertain the competency level of class students and this would enable ST to provide content / product differentiation
- ST will be able to assess the attitude of class students towards the topic
- Students to develop positive work habits in the Mathematics classroom.

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DIAGNOSTIC 2 (CHAPTER 1: POLYNOMIALS, REMAINDER & FACTOR THEOREM)

**
**

- Polynomials
- Dividing Polynomials
- Long Division / Synthetic Division
- Remainder and Factor Theorem
- Factorising Cubic Expressions

**Diagnostic test (Format)20 - 30 minutes**

- pen and paper exercise based on past knowledge on algebra (refer LO)
- use of approved calculator is allowed

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**DIAGNOSTIC 1 (CHAPTER 1: POLYNOMIALS, REMAINDER & FACTOR THEOREM)**

- fundamental of algebra
- manipulation of algebraic functions (including algebraic fractions)
- procedural understanding and demonstration of factorisation and expansion
- solving algebraic equations
- understanding of the concept of division (function, quotient, remainder) of algebraic function. (new knowledge)

**Diagnostic test (Format)**

- 20 - 30 minutes
- pen and paper exercise based on past knowledge on algebra (refer LO)
- use of approved calculator is allowed

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