Monday, October 31, 2011
2011 GCE-O Level Additional Mathematics Paper 2
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 and alpha, beta, 1 to 2 questions 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
• relationships between the roots and coefficients of the quadratic equation ax2 + bx + c = 0 (α + β, αβ)
2. Polynomials: (Chapter 1)
(1 question here)
• multiplication and division of polynomials
• use of remainder and factor theorems
• factorisation of polynomials
• solving cubic equations
• sketch graphs of y = a sin(bx) + c, y = a cos(bx) + c, y = a tan(bx)
5. Further Coordinate Geometry (Chapter 11)
• coordinate geometry of the circle (1 question here on equation of circle)
6. Proofs in plane geometry (Chapter 10) (exactly 1 question here, pls refer to elearn portal for solutions for textbook and revision worksheet, if you have time to spare)
7. Differentiation and Integration (Chapter 12 - 18)
(should have around 3 to 4 questions here, be prepared to see quite a fair bit on integration)
• stationary points (maximum and minimum turning points and stationary points of inflexion)
• use of second derivative test to discriminate between maxima and minima
• integration as the reverse of differentiation (differentiate then integrate back)
• definite integral as area under a curve
(NO need to study lo)
1. Indices and surds: (Chapter 4)
• four operations on indices and surds
• rationalising the denominator
• solving equations involving indices and surds
2. Binomial Theorem
3. Modulus Functions
• solving simple equations involving modulus functions
4. Coordinate geometry in two dimensions (Chapters 5)
• condition for two lines to be parallel or perpendicular
• mid-point of line segment
• finding the area of rectilinear figure given its vertices
• transformation of given relationships, including y = axn and y = kbx, to linear form to determine the unknown constants from the straight line graph
5. R-formula
6. Under the topics of Differentiation
• Rate of Change, Increasing and Decreasing Functions, Normal and Tangent
7. 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 chemistry too.
Most important of all:
Do your best and let GOD do the rest.
Yours faithfully,
Mr Ng Song Seng
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 and alpha, beta, 1 to 2 questions 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
• relationships between the roots and coefficients of the quadratic equation ax2 + bx + c = 0 (α + β, αβ)
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. Trigonometric functions
(around 1 to 2 questions here)
• exact values of the trigonometric functions for special angles (30°, 45°, 60°) or pi/6, pi/4, pi/3 (without using calculator)
• coordinate geometry of the circle (1 question on circle equation, be familiar with both the general form and standard)
• amplitude, periodicity and symmetries related to the sine and cosine functions• coordinate geometry of the circle (1 question on circle equation, be familiar with both the general form and standard)
• sketch graphs of y = a sin(bx) + c, y = a cos(bx) + c, y = a tan(bx)
5. Further Coordinate Geometry (Chapter 11)
• coordinate geometry of the circle (1 question here on equation of circle)
6. Proofs in plane geometry (Chapter 10) (exactly 1 question here, pls refer to elearn portal for solutions for textbook and revision worksheet, if you have time to spare)
7. Differentiation and Integration (Chapter 12 - 18)
(should have around 3 to 4 questions here, be prepared to see quite a fair bit on integration)
• stationary points (maximum and minimum turning points and stationary points of inflexion)
• use of second derivative test to discriminate between maxima and minima
• integration as the reverse of differentiation (differentiate then integrate back)
• definite integral as area under a curve
Now the 'maybe' section
1. Matrices
• expressing a pair of linear equations in matrix form and solving the equations by inverse matrix method
2. Logarithm
• solving simple equations involving logarithmic expressions
3. Proofs of trigo identities (do not spend too much time here)
4. Y = mX + C (should be no more but in case because paper 1 only 4 marks so leave it to the last when you really really have spare time)
Next, the topics that you can SKIP completely:
(NO need to study lo)
1. Indices and surds: (Chapter 4)
• four operations on indices and surds
• rationalising the denominator
• solving equations involving indices and surds
2. Binomial Theorem
3. Modulus Functions
• solving simple equations involving modulus functions
4. Coordinate geometry in two dimensions (Chapters 5)
• condition for two lines to be parallel or perpendicular
• mid-point of line segment
• finding the area of rectilinear figure given its vertices
• transformation of given relationships, including y = axn and y = kbx, to linear form to determine the unknown constants from the straight line graph
5. R-formula
6. Under the topics of Differentiation
• Rate of Change, Increasing and Decreasing Functions, Normal and Tangent
7. 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 chemistry too.
Most important of all:
Do your best and let GOD do the rest.
Yours faithfully,
Mr Ng Song Seng
# posted by FaithfullyOnTheRedDot @ 3:43 AM 
