FaithfullyOnTheRedDot

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)

• 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

• 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)

• 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)

• 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

• symmetry properties of circles
• angle properties of circles

• 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

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

• map scales
• direct and inverse proportion

• concepts of speed, uniform speed and average speed
• conversion of units
• problems involving speed, uniform speed and average speed

• recognising and representing number patterns (including finding an algebraic expression for the nth term)

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

1.3 Percentage

1.5 Algebraic representation and formulae

• evaluation of algebraic expressions and formulae

• 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

• solving linear inequalities in one unknown

2. GEOMETRY AND MEASUREMENT

2.1 Angles, triangles and polygons

• angle sum of interior and exterior angles of any convex polygon

• ratio of volumes and surface areas of similar solids

• 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

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