Friday, October 23, 2015

 

2015 GCE O-Level Additional Mathematics Paper 2

Additional Mathematics students,

Considering past trends, there will be at least one question for each topic taught in the additional mathematics syllabus. (See syllabus from SEAB at https://www.seab.gov.sg/content/syllabus/olevel/2015Syllabus/4047_2015.pdf ) 

Hence, for those topics that have yet to be tested, do be prepared to see them (at least one question) on paper 2 on Monday. For smaller topics such as proofs in plane geometry and modulus functions, if you see them in paper 1 then they will not appear on paper 2 again. However, for major topics such as calculus and trigonometry, they will appear in both paper 1 and paper 2.

As usual, may I suggest that you focus your attention on the topics in blue, followed by those in green and you may pay little or no attention to those in red. Unfortunately, we will not see a long list for the topics in red for this year.

VERY LIKELY TOPICS

ALGEBRA

A1 Equations and inequalities (1 question)
  • Relationships between the roots and coefficients of a quadratic equation (α + β, αβ)
A2 Indices and surds (1 question)
  • Four operations on indices and surds, including rationalising the denominator
  • solving equations involving indices and surds
A3 Polynomials and Partial Fractions (2 questions)
  • use of remainder and factor theorems
  • factorisation of polynomials
  • use of a3 + b3 = (a+b)(a2–ab+b2) and a3 – b 3 = (a – b)(a2+ab+b2)
  • solving cubic equations
  • Partial Fractions
A4 Binomial expansions (1 question)

A5 Power, exponential. logarithmic, and Modulus functions
  • exponential and logarithmic functions and their graphs (no more sketching of logarithmic graph) including laws of logarithms and change of bases
  • solving simple equations involving exponential and logarithmic functions
more likely to be exponential


GEOMETRY AND TRIGONOMETRY

G1 Trigonometric functions, identities and equations (2 more including R-formula)
  • Principal values of sin–1x, cos–1x, tan–1x
  • Exact values of the trigonometric functions for special angles
  • R-formula (die die must learn)
  • proofs of simple trigonometric identities
G2 Coordinate geometry in two dimensions (2 to 3 questions: one on circle equation and one on transformation into a straight line) 
  • conditions for two lines to be parallel or perpendicular
  • midpoint of line segment
  • area of rectilinear figure
  • coordinate geometry of circles (standard and general)
  • transformation of given relationships, including y=axn and y=kbx, to linear form to determine unknown constants from a straight line graph

Calculus

C1 Differentiation and integration (1 question on tangent and normal, 1 question on maxima/minima, 1 on differentiate then integrate back)
  • derivative of f(x) as the gradient of the tangent to the graph of y=f(x) at a point
  • stationary points (still have even though paper 1 already have one question on max amount of water in trough)
  • use of second derivative test to discriminate between maxima and minima
  • applying differentiation to gradients, tangents and normals, maxima and minima problems
  • integration as the reverse of differentiation (differentiate then use the result to integrate)

 MAYBE ONLY TOPICS (means also must study but after completing blue topics)

 ALGEBRA

 A1 Equations and inequalities

  • 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


 GEOMETRY AND TRIGONOMETRY

G1 Trigonometric functions, identities and equations
  • sketching graphs of sine, cosine and tangent functions
  • solution of simple trigonometric equations in a given interval


NO NEED TO STUDY LIAO TOPICS

ALGEBRA

A1 Equations and inequalities
  • conditions for ax2+bx+c to be always positive or always negative
A5 Power, exponential. logarithmic, and Modulus functions
  • graph of modulus functions
  • solving simple equations involving modulus functions

 GEOMETRY AND TRIGONOMETRY

G1 Trigonometric functions, identities and equations
  • amplitude, periodicity related to the sine and cosine functions
G3 Proofs in plane geometry


Calculus

C1 Differentiation and integration
  • rate of change
  • increasing and decreasing functions
  • definite integral as area under a curve
  • applying differentiation and integration to problems involving displacement, velocity and acceleration of a particle moving in a straight line.

Hope this analysis will help you to be more focussed in your revision for the coming Additional Mathematics Paper 2 on Monday, 26 Oct 2015.

Do your best, let GOD do the rest.


Yours sincerely,
Mr Ng Song Seng

# posted by FaithfullyOnTheRedDot @ 11:07 AM
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