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 and alpha, beta, 1 to 2 questions 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
• relationships between the roots and coefficients of the quadratic equation ax2 + bx + c = 0 (α + β, αβ)

2.  Polynomials: (Chapter 1)
(1 question here)

• multiplication and division of polynomials
• use of remainder and factor theorems
• factorisation of polynomials
• solving cubic equations


• 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)

5. Further Coordinate Geometry (Chapter 11)
• coordinate geometry of the circle (1 question here on equation of circle)

6. Proofs in plane geometry (Chapter 10) (exactly 1 question here, pls refer to elearn portal for solutions for textbook and revision worksheet, if you have time to spare)

7. Differentiation and Integration (Chapter 12 - 18)
(should have around 3 to 4 questions here, be prepared to see quite a fair bit on integration)
• stationary points (maximum and minimum turning points and stationary points of inflexion)
• use of second derivative test to discriminate between maxima and minima

• integration as the reverse of differentiation (differentiate then integrate back)
• definite integral as area under a curve

(NO need to study lo)

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

2. Binomial Theorem

3. Modulus Functions
• solving simple equations involving modulus functions

4. Coordinate geometry in two dimensions (Chapters 5)
• condition for two lines to be parallel or perpendicular
• mid-point of line segment
• finding the area of rectilinear figure given its vertices
• transformation of given relationships, including y = axn and y = kbx, to linear form to determine the unknown constants from the straight line graph


5. R-formula

6. Under the topics of Differentiation
• Rate of Change, Increasing and Decreasing Functions, Normal and Tangent

7. 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 chemistry 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 colour topic then green. You may want to skip red completely.



VERY LIKELY TOPICS






Under the topic of Numbers and Algebra






1. Functions and Graphs


• 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)






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 grouping, algrabraic fractions, should have no more simultaneoues equations






Under the topic of Geometry and Measurement






5. Trigonometry


• sine rule, cosine rule


• pythagoras theorem, toa-cah-soh


• 2- and 3- dimension problems (angle of elevation, depression, shortest distance, largest angle of elevation and depression, bearings)






6. Mensuration


• total surface area and volume of all sorts of solids


• perimeter and area of all sorts of plane figures


• most likely to be objects with straight edges such as pyramid and cuboid






7. Vectors in two dimensions


• position vectors


• magnitude


• parallel vectors


• triangle law of vectors addition






Under the topic of Statistics and Probability






8. Statistics


• stem and leaf diagram, box-and-whisker plots, histogram,


• mean and standard deviation


• comparing spread (consistency based on standard deviation)


• comparing performance (based on mean)






9. PROBABILITY



Next up are the topics that may also be tested



MAYBE ONLY


Number and Algebra


1. Number Pattern (quite like too)

2. Direct and Inverse Proportion






Algebra


3. Solving inequalities


4. factorisation by grouping






Geometry


4. Angle properties of polygon

5. Circle Properties (quite likely)

6. maybe congruency



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. Very large and very small numbers (Mega, Giga, Nano, Pico, etc), standard form


3. Indices


4. Matrices


5. Scale and map


6. Sets (Venn Diagram, union, intersection, empty set, subset)






Algebra


7. Simultaneous equations


8. Sketching graphs involving filling up container, Distance-time and Speed-time graphs






Geometry


9. Similarity


10. Construction


11. Radian measure (area of sector, arc length)


12. Coordinate Geometry (y = mx + c)






Statistics


13. cumulative frequency, upper and lower quartile, interquartile range





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

My dearest 4C and 4D pupils,

Please focus your attention to the following topics:

(Note: this is just a guide to help you to be more focussed in your revision. It is in no way a guarantee match of Thursday's paper)


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

VERY LIKELY TOPICS


1. Prime factorisation, H.C.F. and L.C.M.

2. Very large and very small numbers such as mega/million, giga/billion, tera/trillion, micro, nano, pico.

3. Map scales.

4. Functions and Graphs – graphs of quadratic functions and their properties, sketching quadratic graphs including maximum/minimum point, line of symmetry, where the graphs cut the x an y axes, AND for sure one big question on drawing graph on graph paper and finding information from the graph for example estimation of gradient of the curve by drawing a tangent, etc.


5. Simultaneous equations.


6. Properties of a circle – angle and symmetry properties of circles


7. Pythagoras’ Theorem and Trigonometry – use of Pythagoras’ Theorem, sine and cosine rules, bearings, angle of elevation/depression, area of triangle = half a b sin C


8. Mensuration – area and volume, most likely the object is circular such as cylinder, cone, sphere, etc., use of radian measure of angle
9. Statistics – cumulative frequency, range, lower quartile, upper quartile, interquartile range, box-and-whisker plots, mean and standard deviation, histogram



NO NEED TO STUDY LE
Below are the topics that you do not have to study anymore:
1. indices

2. direct and indirect proportion: y = kx where k is a constant type of question

3. speed, distance, time.


4. Algebraic fractions i.e. fractions involving algebra.

5. Number patterns.

6. Change subject of a formula.

7. Coordinate Geometry : y = mx + c

8. simple interest and compound interest.

9. Angle Properties of Polygons: sum of interior angles = (n-2)180 degrees, sum of exterior angles = 360 degrees.

10. Constructions.


11. arc length and sector area.

12. stem & leaf diagram, median and mode.




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