FaithfullyOnTheRedDot

Dear Visitors to this blog,
Below are the suggestions compiled based on analysis of questions from GCE O-Level Additional Mathematics (4047) Paper 1 that was tested on Friday, 25 Oct 2019.

To help you focus your revision for Paper 2 to be tested on Tuesday, 29 Oct 2019, I am going to start by providing you with a list of topics that you can consider NOT to revise anymore.

Topics that you can LEAVE OUT for paper 2 are:

Topic No.	Topic	Content
Algebra
A1	Equations and inequalities	·     There will be no more standalone question related to Discriminant of a quadratic equation. However, the discriminant concept is still relevant in topic A3 which has yet to be tested
A2	Indices and surds	·     Similarly, there will also be no more standalone question on indices and surds on its own. However, manipulation of surd may still be needed in other topics such as G1 Trigonometry.
A4	Binomial Expansions	·     NO MORE questions on Binomial Theorem
Geometry
G1	Trigonometric functions	·     NO MORE finding amplitude and period, and sketching of sine and cosine curves
G3	Proofs in plane geometry	·     NO MORE Proofs in plane geometry
Calculus
C1	Differentiation and Integration	·     NO MORE rate of change ·     NO MORE Kinematics (displacement, velocity, acceleration)

Next up will be the LIKELY TOPICS to be tested:

Topic No.	Topic	Content
Algebra
A1	Equations and inequalities	·     Relations between the roots and coefficients of a quadratic equation (α + β, αβ)
A3	Polynomials and Partial Fractions	·     Multiplication and division of polynomials ·     Use of remainder and factor theorems ·     Factorisation of polynomial ·     Use of o   a3 + b3 = (a + b)(a2 – ab + b2) o   a3 – b3 = (a – b)(a2 + ab + b2) ·     Solving cubic equations ·     Partial fractions
A5	Power, Exponential, Logarithmic, and Modulus functions	·     Power functions y = axn where n is a simple rational number, and their graphs ·     Exponential and logarithmic functions ax, ex, loga x, ln x and their graphs, including o   laws of lagarithms o   equivalence of y = ax and x = loga y o   change of base of logarithms ·     Modulus functions and their graphs ·     Solving simple equations involving exponential, logarithmic and modulus functions
Geometry and Trigonometry
G1	Trigonometric functions, identities and equations	·     Principal values of sin–1 x, cos–1 x, tan–1 x ·     Exact values of trigonometric functions for special angles ·     Use of o   sin2 A + cos2 A = 1, sec2 A = 1 + tan2 A, cosec2 A = 1 + cot2 A o   the expansion of sin (A ± B), cos (A ± B), tan (A ± B) o   the formulae for sin 2A, cos 2A, tan 2A o   the expression for a cos q + b sin q in the form      R cos (q ± α) or R sin (q ± α) ·     Simplification of trigonometric expressions ·     Solution of simple trigonometric equations in a given interval ·     Proofs of simple trigonometric identities
G2	Coordinate geometry in two dimensions	·     Graphs of parabolas with equations in the form y2 = kx ·     Coordinate geometry of circles in o   Standard form o   General form ·     Transformation of given relationships, including y = axn and       y = kbx, to linear form to determine the unknown constants from a straight line graph
Calculus
C1	Differentiation and integration	·     Increasing and decreasing function ·     Even though there was a question on stationary points and determine their nature in paper 1, there may still be one question on stationary value related question. Likely to be linked to mensuration and to maximise or minimise the measurement. ·     Applying differentiation to gradients, tangents and normal, maxima and minima problems (NO MORE rate of change) ·     Integration as the reverse of differentiation (usually to integrate an expression after differentiating a related expression) ·     Definite integral as area under a curve ·     Evaluation of definite integrals ·     Finding the area of a region bounded by a curve and lines (excluding area of region between two curves) ·     NO MORE Kinematics

All the best to you.

Warmest Regards
Mr Ng Song Seng

Dear Visitors to this Blog,

Below are the suggestions compiled based on analysis of questions from GCE O-Level Maths (4048) Paper 1 which was tested on Monday, 21 Oct 2019. Hope it will help you with your revision for Paper 2 which will be tested on Wednesday, 22 Oct 2019.

To help you focus your revision, I am going to provide you with a list of topics which you need not study anymore. The topics are arranged according to the syllabus document from SEAB for GCE O-Level 2019 Mathematics (4048).

Topics that you can LEAVE OUT for paper 2 are:

Topic No.	Topic	Content
Number and Algebra
N1	Numbers and their operations	·     prime and prime factorisation ·     finding HCF, LCM, squares, cubes, square roots and cube roots by prime factorisation ·     law of indices
N2	Ratio and proportion	·     ratios ·     map scales ·     direct and indirect proportions
N4	Rate and speed	·     conversion of units
N5	Algebraic expressions and formulae	·     factorisation (difference of two squares, grouping, ax2 + bx + c) ·     sum and difference of algebraic fractions ·     recognising and representing patterns/relationships by finding an algebraic expression for the nth term (number pattern)
N6	Functions and graphs	·     sketching graphs of quadratic functions
N7	Equations and inequalities	·     solving simultaneous linear equations in two variables ·     solving linear inequalities in one variable
N8	Set language and notation	·     No more questions on Set
N9	Matrices	·     No more questions on Matrices
N10	Problems in real-world contexts	·     Distance-time and speed-time graphs
Geometry and Measurement
G1	Angles, triangles and polygons	·     Construction of simple geometrical figures form given data (including perpendicular bisectors and angle bisectors)
G2	Congruence and similarity	·     No more questions on Congruence and similarity
G6	Coordinate geometry	·     No more questions on coordinate geometry
G7	Vectors in two dimensions	·     translation by a vector ·     magnitude of a vector
G8	Problems in real-world contexts	·     solving problems in real-world contexts (including floor plans etc.) using geometry
Statistics and Probability
S1	Data Analysis	·     histogram ·     cumulative frequency diagram ·     interquartile range
S2	Probability	This topic is very unlikely to be tested again in paper 2. If tested, it will be for combined events using tree/possibility diagram

Next Up will be the likely topics to be tested.

Topic No.	Topic	Content
Number and Algebra
N1	Numbers and their operations	·     use of standard form A × 10n, where n is an interger, and 1 ≤ A < 10
N3	Percentage	·     reverse percentages
N5	Algebraic expressions and formulae	·     evaluation of algebraic expressions and formulae ·     changing the subject of a formula ·     finding the value of an unknown quantity in a given formula ·     expansion of the product of algebraic expressions ·     multiplication and division of simple algebraic fractions ·     translation of simple real-world situations into algebraic expressions
N6	Functions and graphs	·     graphs of power functions of the form y = axn, where n = –2, –1, 0, 1, 2, 3, and simple sums of not more than three of these ·     graphs of exponential functions y = kax, where a is a positive integer ·     estimation of the gradient of a curve by drawing a tangent
N7	Equations and inequalities	·     solving quadratic equations in one unknown by o   use of formula o   completing the square for y = x2 + px + q o   graphical methods ·     solving fractional equations that can be reduced to quadratic equations ·     formulating equations to solve problems
N10	Problems in real-world contexts	·     solving problems based on real-world contexts: o   in everyday life (including travel plans, transport schedules, sports and games, recipes, etc.) o   involving personal and household finance (including simple and compound interest, taxation, instalments, utilities bills, money exchange etc.)
Geometry and Measurement
G1	Angles, triangles and polygons	·     right, acute, obtuse and reflex angles ·     vertically opposite angles, angles on a straight line and angles at a point ·     angles formed by two parallel lines and a transversal: corresponding angles, alternate angles, interior angles ·     properties of triangles, special quadrilaterals and regular polygons (pentagon, hexagon, octagon and decagon), including symmetry properties ·     classifying special quadrilaterals on the basis of their properties ·     angle sum of interior and exterior angles of any convex polygon
G3	Properties of circles	·     symmetry and angle properties of circles
G4	Pythagoras’ theorem and trigonometry	·     all except bearings
G5	Mensuration	·     volume and total surface area of composite solids ·     radian measures (arc length, area of sector and segment, etc)
G7	Vectors in two dimensions	·     use of sum and difference of two vectors to express given vectors in terms of two coplanar vectors ·     multiplication of a vector by a scalar ·     geometric problems involving the use of vectors Focus on parallel vectors (scalar multiple), ratio of areas of triangles
Statistics and Probability
S1	Data Analysis	·     dot diagram ·     stem-and-leaf diagram ·     box-and-whisker plots ·     calculation of the standard deviation for a set of data (grouped or ungrouped) ·     using the mean and standard deviation to compare two sets of data
S2	Probability	This topic very likely NOT to be tested but if tested then it should be the following ·     probability of simple combined events (including using possibility diagram and tree diagrams, where appropriate)

Using the list of the likely topics above, you may want to put more emphasis on

1. Question that involves drawing a graph of power functions on a piece of graph paper and using it to solve equations, find gradient, etc.

2. Trigonometry : sine and cosine rule, finding area of triangles using two sides and an included angle, angle of elevation and depression, etc. (note: no more bearings)

3. Mensuration (see G5)

4. Real-world context problems that involves solving quadratic equations using formula

5. Real-world context problems that involves finance transactions

6. Symmetry and Angle properties of Circles

7. Questions involving standard form, reverse percentage, etc.

8. Angle properties (see G1)

If time permits do some practice on standard form, subject of formulae, simple algebraic manipulations


All the best to you.

Warmest Regards
Mr Ng Song Seng