FaithfullyOnTheRedDot

My Dearest Additional Mathematics Students,

Please focus your attention to the following topics.

As usual, please spend more time on topics that are highlighted in blue, followed by those in green. You may skip those highlighted in red.


Most Likely Topics are:

1. Quadratic equations and inequalities (chapter 2)
(b squared minus 4ac) [1 question here]
• conditions for a quadratic equation to have:
(i) two real roots
(ii) two equal roots
(iii) no real roots

and related conditions for a given line to:
(i) intersect a given curve
(ii) be a tangent to a given curve
(iii) not intersect a given curve
• conditions for ax2 + bx + c to be always positive (or always negative)
• solution of quadratic inequalities, and the representation of the solution set on the number line

2. Polynomials: (Chapter 1)
[1 question here]
• multiplication and division of polynomials
• use of remainder and factor theorems
• factorisation of polynomials
• solving cubic equations

3. Partial fractions (Chapter 3) [1 question here, usually together with differentiation or integration]

4. Modulus Functions (Chapter 2) [1 question here]
• solving simple equations involving modulus functions
• sketch graphs involving modulus functions

5. Trigonometry (Chapter 7) [1 – 2 questions here of which 1 is on R-Formula]
• R-Formula
• Proving identities (maybe)
• Solving Trigo equations in degree (maybe)

6. Coordinate geometry in two dimensions (Chapters 5) [1 question here]
• condition for two lines to be parallel or perpendicular
• mid-point of line segment
• finding the area of rectilinear figure given its vertices

7. Proofs in plane geometry (Chapter 10) [exactly 1 question here, if you have time to spare]

8. Differentiation and Integration (Chapter 12 - 18)
[should have a number of questions here]
• Increasing and Decreasing Functions
• Applying Differentiation to Gradient, Normal and Tangent
• Definite integral as area under a curve
• General differentiation and integration involving Trigonometric Functions, Exponential Functions


For students who have time to revise Proofs in Plane Geometry, please refer to ASKnLearn portal for worksheet and solutions. I have reloaded the solutions as you have difficulty opening the PDF file containing the solutions. Please take a look at the summary for questions 2, 3 and 4. It will help you to zero in to the properties you need for your proofs. Please also look at the solutions for Geometrical Proofs for 2008, 2009, 2010 and 2011.


Now the 'maybe' section

1. Logarithm
• solving simple equations involving logarithmic expressions

2. Trigonometry
• Proofs of trigo identities
• solving trigo equation in degree
3. Differentiation
• use of second derivative test to discriminate between maxima and minima (should be problem involving maxima value of volume or area kind but not be nature of stationary point)



Next, the topics that you can SKIP completely:
(NO need to study lo)

1. Matrices (Chapter 8)
• expressing a pair of linear equations in matrix form and solving the equations by inverse matrix method

2. Quadratic Equation (Chapter 2)
• relationships between the roots and coefficients of the quadratic equation ax2 + bx + c = 0 (α + β, αβ)

3. Indices and surds: (Chapter 4)
• four operations on indices and surds
• rationalising the denominator
• solving equations involving indices and surds

4. Binomial Theorem (Chapter 9)

5. Trigonometric functions (Chapter 6)
• exact values of the trigonometric functions for special angles
• amplitude, periodicity and symmetries related to the sine and cosine functions
• sketch graphs of y = a sin(bx) + c, y = a cos(bx) + c, y = a tan(bx)

6. Further Coordinate Geometry (Chapter 11)
• coordinate geometry of the circle

7. Coordinate geometry in two dimensions (Chapters 5)
• transformation of given relationships, including y = axn and y = kbx, to linear form (Y= mX + c) to determine the unknown constants from the straight line graph

8. Under the topics of Differentiation
• connected rate of change
• stationary points (maximum and minimum turning points and stationary points of inflexion)
• integration as the reverse of differentiation (differentiate then integrate back)

9. Kinematics
• application of differentiation and integration to problems involving displacement, velocity and acceleration of a particle moving in a straight line with variable or constant acceleration


Hopefully this will help you to complete your revision earlier tonight.

Remember, do NOT exhaust yourself out. Have enough rest for tomorrow's paper.

Please do NOT forget to revise for your science paper too.



Most important of all:

Do your best and let GOD do the rest.



Yours faithfully,

Mr Ng Song Seng