Friday, October 23, 2015
2015 GCE O-Level Additional Mathematics Paper 2
Additional Mathematics students,
MAYBE ONLY TOPICS (means also must study but after completing blue topics)
ALGEBRA
A1 Equations and inequalities
GEOMETRY AND TRIGONOMETRY
GEOMETRY AND TRIGONOMETRY
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
Monday, October 19, 2015
2015 GCE O-Level Mathematics Paper 2
My dearest Hildans,
I am back! Not to school, not yet. But to this blog for the annual exercise of providing Hildans, like yourself, with suggestions to help you prepare for your mathematics paper 2 exam.
This year, I will be using the GCE O-Level Mathematics syllabus (4016) document to guide the flow of my post. The syllabus is available at
https://www.seab.gov.sg/content/syllabus/olevel/2015Syllabus/4016_2015.pdf
As usual,I will be using the following colour codes:
blue - very likely to be tested
green - maybe only but still must study
red - no need to study liao
May I suggest that you revise the blue topics followed by the green. You may skip the red topics completely.
VERY LIKELY TOPICS
1. NUMBERS AND ALGEBRA
1.6 Algebraic manipulation (Part of a question)
- factorisation of algebraic expression (except by grouping ax+bx+kay+kby)
- multiplication and division of simple algebraic fractions
- addition and subtraction of algebraic fractions (may lead to a question on solving quadratic equation)
1.7 Functions and graphs (One 10-12 marks done on graph paper question and another may be part of a question)
- graphs of quadratic functions and their properties
- sketching of the graphs of quadratic functions
- graphs of y=ax to the power of n where n=-2,-1,0,1,2,3
- graphs of y=ka to the power of x
and yes, the 10 to 12 marks question on graph which requires you to
- plot points and join them with a smooth curve
- estimate gradient by drawing tangents or finding the point on the curve given the gradient of the tangent (for additional maths students, use differentiation to reverse engineer for accuracy)
- add straight lines or curves to the original graph to solve equations and/or inequalities
- find equation of curve (for question in which x- and y-coordinates are given but not the equation)
1.8 Solutions of equations and inequalities (1 question)
- solving quadratic equations in one unknown by factorisation, use of formula, complete the square
- formulating equations to solve problems (usually together with algebraic fractions that leads to a quadratic equation)
- solving simultaneous equation (maybe only)
1.9 Applications of mathematics in practical situations (one or cpart of a question)
- problems derived from practical situations such as utilities bills, hire-purchase, simple interest and compound interest, money exchange, profit and loss, taxation
- distance-time and speed-time graphs
2. GEOMETRY AND MEASUREMENT
2.1 Angles, triangles and polygons (most likely integrated into a question but not a question on its own)
- right, acute, obtuse and reflex angles, complementary and supplementary angles, vertically opposite angles, adjacent angles on a straight line, adjacent angles at a point, interior and exterior angles
- angles formed by two parallel lines and a transversal: corresponding angles, alternate angles, interior angles
2.2 Congruence and similarity (part of a question)
- congruent figures and similar figures
- properties of similar polygons: corresponding angles are equal, corresponding sides are proportional
- determining whether two triangles are congruent or similar
- ratio of areas of similar plane figures
- no more ratio of volumes and total surface area of similar solids
2.3 Properties of circles (part of a question)
- symmetry properties of circles
- angle properties of circles
2.4 Pythagoras' theorem and trigonometry ( 1 to 2 questions)
- use of Pythagoras' theorem
- determining whether a triangle is right-angled given the lengths of three sides
- use of trigonometric ratios (TOA-CAH-SOH) to calculate unkonw sides and angles in right-angled triangles
- extending sine and cosine to obtuse angles
- use of formula 0.5ab sin C for the area of a triangle
- use of sine rule and cosine rule for any triangle
- problems in 2 and 3 dimensions include those involving angles of elevation and depression
2.5 Mensuration (at least one question)
Since cylinder, hemisphere and segment already tested, the question will most probably be involving solids with straight edges such as prism and/or pyramid.
However, radian measure has not been tested. So it may be a small portion that involves radian measure with arc length.
3. STATISTICS AND PROBABILITY
3.2 Data analysis (part of a question)
- interpretation and analysis of dot diagrams, stem-and-leaf diagrams, cumulative frequency diagrams, box-and-whisker plots
- quartiles (lower, upper, interquatile range, median) and percentiles
- calculation of the mean for grouped data together with calculation of the standard deviation for a set of data
Next up are the topics that may also be tested
MAYBE ONLY TOPICS (means also must study but after completing blue topics)
1. NUMBERS AND ALGEBRA
1.1 Numbers and the four operations
- positive, negative, zero and fractional indices
- laws of indices
1.2 Ratio, rate and proportion
- map scales
- direct and inverse proportion
1.4 Speed (this is a more likely one in the category of MAYBE ONLY TOPICS though it is more likely to appear in paper 1 but it did not)
- concepts of speed, uniform speed and average speed
- conversion of units
- problems involving speed, uniform speed and average speed
1.5 Algebraic representation and formula
- recognising and representing number patterns (including finding an algebraic expression for the nth term)
2. GEOMETRY AND MEASURE
2.6 Coordinate geometry
- interpreting and finding equation of a straight line graph in the form y = mx + c
3. STATISTICS AND PROBABILITY
3.3 Probability (Very Unlikely but you never know)
if there is any question on probability it should involve possibility diagram and/or tree diagram
Finally, the topics that you may choose to give little or no attention to:
NO NEED TO STUDY LIAO TOPICS
1. NUMBERS AND ALGEBRA
1.1 Numbers and the four operations
- prime and prime factorisation
- finding HCF and LCM, squares, cubes, square roots and cube roots by prime factorisation
- standard form
1.2 Ratio
1.3 Percentage
1.5 Algebraic representation and formulae
- evaluation of algebraic expressions and formulae
1.6 Algebraic manipulation
- addition and subtraction of linear algebraic expressions
- simplification of linear algebraic expressions
- factorisation by grouping
- changing subject of a formulae
- finding the value of an unknown quantity in a given formula
1.8 Solutions of equations and inequalities
- solving linear inequalities in one unknown
1.10 Set language and notation
1.11 Matrices
2. GEOMETRY AND MEASUREMENT
2.1 Angles, triangles and polygons
- angle sum of interior and exterior angles of any convex polygon
2.2 Congruence and similarity
- ratio of volumes and surface areas of similar solids
2.6 Coordinate geometry
- finding the gradient of a straight line given the coordinates of two points on it
- find the length of a line segment given the coordinates of its end points
2.7 Vectors in two dimensions
3. STATISTICS AND PROBABILITY
3.2 Data analysis
- mean, mode and median as averages
- using the mean and standard deviation to compare two sets of data
Hope this analysis will help you to be more focussed in your revision for the coming Mathematics Paper 2 on Thursday, 22 Oct 2015.
Do your best, let GOD do the rest.
Yours sincerely,
Mr Ng Song Seng
