FaithfullyOnTheRedDot

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) [1 question 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

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. Modulus Functions (Chapter 2) [1 question here]
• solving simple equations involving modulus functions
• sketch graphs involving modulus functions

5. Trigonometry (Chapter 7) [1 – 2 questions here of which 1 is on R-Formula]
• R-Formula
• Proving identities (maybe)
• Solving Trigo equations in degree (maybe)

6. Coordinate geometry in two dimensions (Chapters 5) [1 question here]
• condition for two lines to be parallel or perpendicular
• mid-point of line segment
• finding the area of rectilinear figure given its vertices

7. Proofs in plane geometry (Chapter 10) [exactly 1 question here, if you have time to spare]

8. Differentiation and Integration (Chapter 12 - 18)
[should have a number of questions here]
• Increasing and Decreasing Functions
• Applying Differentiation to Gradient, Normal and Tangent
• Definite integral as area under a curve
• General differentiation and integration involving Trigonometric Functions, Exponential Functions


For students who have time to revise Proofs in Plane Geometry, please refer to ASKnLearn portal for worksheet and solutions. I have reloaded the solutions as you have difficulty opening the PDF file containing the solutions. Please take a look at the summary for questions 2, 3 and 4. It will help you to zero in to the properties you need for your proofs. Please also look at the solutions for Geometrical Proofs for 2008, 2009, 2010 and 2011.


Now the 'maybe' section

1. Logarithm
• solving simple equations involving logarithmic expressions

2. Trigonometry
• Proofs of trigo identities
• solving trigo equation in degree
3. Differentiation
• use of second derivative test to discriminate between maxima and minima (should be problem involving maxima value of volume or area kind but not be nature of stationary point)



Next, the topics that you can SKIP completely:
(NO need to study lo)

1. Matrices (Chapter 8)
• expressing a pair of linear equations in matrix form and solving the equations by inverse matrix method

2. Quadratic Equation (Chapter 2)
• relationships between the roots and coefficients of the quadratic equation ax2 + bx + c = 0 (α + β, αβ)

3. Indices and surds: (Chapter 4)
• four operations on indices and surds
• rationalising the denominator
• solving equations involving indices and surds

4. Binomial Theorem (Chapter 9)

5. Trigonometric functions (Chapter 6)
• exact values of the trigonometric functions for special angles
• amplitude, periodicity and symmetries related to the sine and cosine functions
• sketch graphs of y = a sin(bx) + c, y = a cos(bx) + c, y = a tan(bx)

6. Further Coordinate Geometry (Chapter 11)
• coordinate geometry of the circle

7. Coordinate geometry in two dimensions (Chapters 5)
• transformation of given relationships, including y = axn and y = kbx, to linear form (Y= mX + c) to determine the unknown constants from the straight line graph

8. Under the topics of Differentiation
• connected rate of change
• stationary points (maximum and minimum turning points and stationary points of inflexion)
• integration as the reverse of differentiation (differentiate then integrate back)

9. 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 science paper too.



Most important of all:

Do your best and let GOD do the rest.



Yours faithfully,

Mr Ng Song Seng

My dearest Sec 4 Express, Sec 4NA and Sec 5 pupils,

Please focus your attention on the following topics for your revision for Paper 2:

To help you further, I will be using the following colour codes: blue - very likely topic, green - maybe only, red - no need to study le.

You should study blue topic then green. You may want to skip red completely.


VERY LIKELY TOPICS

Under the topic of Numbers and Algebra


1. Functions and Graphs
(a) 12-mark question on graph
• plotting of points; drawing of curves
• estimation of gradients by drawing tangents, finding the point given the gradient (for additional maths pupils, please use differentiation to check your answers)
• add lines or curves to the original graph to solve equations, inequalities
• find equation of curve (for questions in which points are given but equation not given)

(b) sketching of quadratic graphs

2. Problems derived from practical situations
• utilities bills
• hire-purchase
• simple interest and compound interest
• money exchange
• profit and loss
• taxation

3. Formulating equation to solve problem. The type of question that asks you to form an equation and reduced to the form ax^2 + bx + c = 0 then solve using formula.

4. Algebra: complete square then use it to solve quadratic equation (if don’t have formulating equation to solve problem then this one sure have), factorization by difference of two squares, changing subject of a formula, simultaneous equations

5. Numbers and the Four Operations – very large and very small numbers such as Mega, Giga, Tera, Million, Billion, Trillion, micro, nano and pico and use of standard form

6. Set language and notation [combined with another topic]

7. Matrices – please practise those long long type problems like 2009 Q5 where you need to state what the elements of the matrix represent


Under the topic of Geometry and Measurement

8. Trigonometry
• sine rule, cosine rule
• pythagoras theorem, toa-cah-soh, ½ ab sin C
• 2- and 3- dimension problems (angle of elevation, depression, shortest distance, largest angle of elevation and depression, no more bearings, yeah)

9. Mensuration
• total surface area and volume of all sorts of solids
• perimeter and area of all sorts of plane figures


Under the topic of Statistics and Probability

10. Statistics
• cumulative frequency curve, box-and-whisker plots, histogram,
• median, lower quartile, upper quartile and interquartile range
• comparing spread (consistency based on interquartile range)
• comparing performance (based on median)


Next up are the topics that may also be tested

MAYBE ONLY

Number and Algebra

1. Percentages greater than 100% and problems involving percentages

Geometry

2. Angle properties – corresponding angles, alternate angles, interior angles, properties of triangles and special quadrilaterals

3. maybe congruency, ratio of volumes of similar solids, determining whether two triangles are congruent, pray hard it is not like 2007 Q3


Finally, the topics that you may choose to give little or no attention to:

NO NEED TO STUDY LE

Numbers and Algebra

1. H.C.F. and L.C.M.
2. Indices
3. Scale and Map
4. direct and inverse proportion
5. Speed and all the distance-time, speed-time and acceleration-time graphs
6. Algebraic fraction
7. factorisation of x^2+bx+c, by grouping
8. solving inequalities and number line
9. Number Pattern

Geometry
10. Similarity
11. angle properties of polygons
12. Radian measure (area of sector, arc length)
13. Yeah, no more circle properties
14. No more bearings
15. Coordinate Geometry (y = mx + c, length of line segment joining two points, etc)
16. NO more vectors

Statistics
17. Stem-and-Leaf
18. standard deviation
19. Probability

Hope that this analysis will help you to be more focussed in your revision.

Do your best, let GOD do the rest.


Yours sincerely,
Mr Ng Song Seng