Thursday, October 29, 2009
2009 GCE 'O' Level Additional Mathematics Paper 2
My dearest Sec 4 Express and Sec 5 pupils,
Please focus your attention on the following topics for your revision for Additional Mathematics Paper 2: (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 Tomorrow's paper)
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.
VERY LIKELY TOPICS
1 Algebra
1.1 Quadratic equations and inequalities: (Chapter 2)
• relationships between the roots and coefficients of the quadratic equation (α + β, αβ)
1.4 Simultaneous equations in two unknowns: (Chapter 8)
• expressing a pair of linear equations in matrix form and solving the equations by inverse matrix method (revise conditions for no solution / infinite number of solutions)
1.5 Partial fractions: (Chapter 3)
1.6 Binomial expansions: (Chapter 9)
• term independent of x, coefficients, n!
1.7 modulus functions (Chapters 2)
• solving simple equations involving modulus functions
• sketching
2 Geometry and Trigonometry
2.1 Trigonometric functions, identities and equations (Chapters 6, 7)
• exact values of the trigonometric functions for special angles (30°, 45°, 60°)
• R formula
2.2 Coordinate geometry in two dimensions (Chapters 11)
• coordinate geometry of the circle, (centre, radius, reflection, conditions for touching axes/lines)
2.3 Proofs in plane geometry (Chapter 10)
• do not spend too much time here if you are not too confident, use your knowledge in congruency and similarity to gain some marks here
3 Calculus
3.1 Differentiation and integration
• stationary points (maximum and minimum turning points and stationary points of inflexion), please revise first derivative test as well
• use of second derivative test to discriminate between maxima and minima
• surely one question on Maximum/Minimum
• area under a curve (take note of those regions below the x-axis)
• 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
• surely one question on Kinematics
Next up will be topics that maybe tested too
MAYBE ONLY
1 Algebra
1.2 Indices and surds: (Chapter 4)
• solving equations involving indices
1.7 Exponential and logarithmic functions (Chapter 16)
• functions a^x, e^x, loga x , ln x and their graphs
2 Geometry and Trigonometry
2.1 Trigonometric functions, identities and equations (Chapters 6, 7)
• solution of simple trigonometric equations in a given interval (in degrees)
• proofs of simple trigonometric identities
2.2 Coordinate geometry in two dimensions (Chapter 11)
• graphs of y = ax^n and y^2 = kx
3 Calculus
3.1 Differentiation and integration
• integration as the reverse of differentiation (maybe because only 3 marks for Question 12(iii))
Finally, we have come to the topics that you do not have to give any attention to:
NO NEED TO STUDY LE (a few cheers)
1 Algebra
1.1 Quadratic equations and inequalities (chapter 2)
• 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 (ii) not intersect or (iii) be a tangent to a given curve
• conditions for ax^2 + bx + c to be always positive (or always negative)
1.2 surds (Chapter 4)
1.3 Polynomials: (Chapter 1) (be prepared to see one question because only 4 marks in paper 1)
1.7 Exponential and logarithmic functions (Chapter 16)
• solving simple equations involving logarithmic
2 Geometry
2.1 Trigonometric functions, identities and equations (Chapters 6, 7)
• sketching, amplitude, period
2.2 Coordinate geometry in two dimensions (Chapters 5, 11)
• all except circle and graphs of y = ax^n and y^2 = kx
3 Calculus
3.1 Differentiation and integration
• rate of change (Chapter 14)
• tangent, normal (Chapter 14)
• increasing and decreasing functions (Chapter 13)
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
Please focus your attention on the following topics for your revision for Additional Mathematics Paper 2: (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 Tomorrow's paper)
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.
VERY LIKELY TOPICS
1 Algebra
1.1 Quadratic equations and inequalities: (Chapter 2)
• relationships between the roots and coefficients of the quadratic equation (α + β, αβ)
1.4 Simultaneous equations in two unknowns: (Chapter 8)
• expressing a pair of linear equations in matrix form and solving the equations by inverse matrix method (revise conditions for no solution / infinite number of solutions)
1.5 Partial fractions: (Chapter 3)
1.6 Binomial expansions: (Chapter 9)
• term independent of x, coefficients, n!
1.7 modulus functions (Chapters 2)
• solving simple equations involving modulus functions
• sketching
2 Geometry and Trigonometry
2.1 Trigonometric functions, identities and equations (Chapters 6, 7)
• exact values of the trigonometric functions for special angles (30°, 45°, 60°)
• R formula
2.2 Coordinate geometry in two dimensions (Chapters 11)
• coordinate geometry of the circle, (centre, radius, reflection, conditions for touching axes/lines)
2.3 Proofs in plane geometry (Chapter 10)
• do not spend too much time here if you are not too confident, use your knowledge in congruency and similarity to gain some marks here
3 Calculus
3.1 Differentiation and integration
• stationary points (maximum and minimum turning points and stationary points of inflexion), please revise first derivative test as well
• use of second derivative test to discriminate between maxima and minima
• surely one question on Maximum/Minimum
• area under a curve (take note of those regions below the x-axis)
• 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
• surely one question on Kinematics
Next up will be topics that maybe tested too
MAYBE ONLY
1 Algebra
1.2 Indices and surds: (Chapter 4)
• solving equations involving indices
1.7 Exponential and logarithmic functions (Chapter 16)
• functions a^x, e^x, loga x , ln x and their graphs
2 Geometry and Trigonometry
2.1 Trigonometric functions, identities and equations (Chapters 6, 7)
• solution of simple trigonometric equations in a given interval (in degrees)
• proofs of simple trigonometric identities
2.2 Coordinate geometry in two dimensions (Chapter 11)
• graphs of y = ax^n and y^2 = kx
3 Calculus
3.1 Differentiation and integration
• integration as the reverse of differentiation (maybe because only 3 marks for Question 12(iii))
Finally, we have come to the topics that you do not have to give any attention to:
NO NEED TO STUDY LE (a few cheers)
1 Algebra
1.1 Quadratic equations and inequalities (chapter 2)
• 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 (ii) not intersect or (iii) be a tangent to a given curve
• conditions for ax^2 + bx + c to be always positive (or always negative)
1.2 surds (Chapter 4)
1.3 Polynomials: (Chapter 1) (be prepared to see one question because only 4 marks in paper 1)
1.7 Exponential and logarithmic functions (Chapter 16)
• solving simple equations involving logarithmic
2 Geometry
2.1 Trigonometric functions, identities and equations (Chapters 6, 7)
• sketching, amplitude, period
2.2 Coordinate geometry in two dimensions (Chapters 5, 11)
• all except circle and graphs of y = ax^n and y^2 = kx
3 Calculus
3.1 Differentiation and integration
• rate of change (Chapter 14)
• tangent, normal (Chapter 14)
• increasing and decreasing functions (Chapter 13)
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
Tuesday, October 27, 2009
GCE 'O' Level Mathematics Paper 2 (2009)
My dearest Sec 4 Express, Sec 4NA pupils and Sec 5 pupils,
Please focus your attention on the following topics for your revision for Paper 2: (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 Tomorrow's paper)
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.
VERY LIKELY TOPICS
Numbers & Algebra
1. Graph
• plotting of points & drawing of curves
• estimation of gradients by drawing tangents, finding the point given the gradient (for addition 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 (maybe only) and compound interest (no need study compound interest)
• money exchange
• taxation
3. Formulating equation to solve problem. Algebraic fractions, simple fractional equations that can be reduced to quadratic or linear equation
4. Variation (proportional and inversely proportional type of questions, y = k/x)
5. Set language and notation: Venn diagram, shading and writing down in set notation to represent shaded region in Venn diagram
6. Matrices: problems involving the product and sum of two matrices, interpreting the data in a given matrix and product of a scalar quantity and a matrix
Geometry
7. Angle properties
• circle properties
• parallel lines
8. 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)
9. Mensuration
• total surface area (very likely)
• cuboid, pyramid, cylinder (unlikely cone, sphere)
10. Statistics
• dot diagram, stem & leave, box-and-whisker plots, histogram
• mean and standard deviation
• comparing spread (consistency based on standard deviation)
• comparing performance (based on mean (more likely) or median)
11. Probability (must study)
Next up are the topics that may also be tested
MAYBE ONLY
Algebra
1. Number Pattern
2. Sketching of graphs: quadratic (x - 3)(x + 4) = 0, (x + a)^2 + b = 0, solving quadratic equation like (x + a)^2 + b = 0.
3. scale and map
Geometry
4. area of sector, segment
5. Construction (very slim chance)
Statistics
6. Mean, mode, median (quite unlikely but if it appears, will be test on finding possible values of x such that the median/mode comes from a particular group)
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)
3. Indices
4. Factorisation and expansion of quadratic expressions except difference of two squares
5. Solving inequalities
6. Simultaneous equations
7. compound interest
8. Distance-time and Speed-time graphs
Geometry
9. congruency, similarity (maybe)
10. Properties of polygons ((n-2) x 180 degrees, sum of ext angles = 360 degrees, etc)
11. Coordinate geometry (y = mx + c)
12. Vectors
Statistics
13. cumulative frequency.
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
Please focus your attention on the following topics for your revision for Paper 2: (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 Tomorrow's paper)
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.
VERY LIKELY TOPICS
Numbers & Algebra
1. Graph
• plotting of points & drawing of curves
• estimation of gradients by drawing tangents, finding the point given the gradient (for addition 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 (maybe only) and compound interest (no need study compound interest)
• money exchange
• taxation
3. Formulating equation to solve problem. Algebraic fractions, simple fractional equations that can be reduced to quadratic or linear equation
4. Variation (proportional and inversely proportional type of questions, y = k/x)
5. Set language and notation: Venn diagram, shading and writing down in set notation to represent shaded region in Venn diagram
6. Matrices: problems involving the product and sum of two matrices, interpreting the data in a given matrix and product of a scalar quantity and a matrix
Geometry
7. Angle properties
• circle properties
• parallel lines
8. 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)
9. Mensuration
• total surface area (very likely)
• cuboid, pyramid, cylinder (unlikely cone, sphere)
10. Statistics
• dot diagram, stem & leave, box-and-whisker plots, histogram
• mean and standard deviation
• comparing spread (consistency based on standard deviation)
• comparing performance (based on mean (more likely) or median)
11. Probability (must study)
Next up are the topics that may also be tested
MAYBE ONLY
Algebra
1. Number Pattern
2. Sketching of graphs: quadratic (x - 3)(x + 4) = 0, (x + a)^2 + b = 0, solving quadratic equation like (x + a)^2 + b = 0.
3. scale and map
Geometry
4. area of sector, segment
5. Construction (very slim chance)
Statistics
6. Mean, mode, median (quite unlikely but if it appears, will be test on finding possible values of x such that the median/mode comes from a particular group)
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)
3. Indices
4. Factorisation and expansion of quadratic expressions except difference of two squares
5. Solving inequalities
6. Simultaneous equations
7. compound interest
8. Distance-time and Speed-time graphs
Geometry
9. congruency, similarity (maybe)
10. Properties of polygons ((n-2) x 180 degrees, sum of ext angles = 360 degrees, etc)
11. Coordinate geometry (y = mx + c)
12. Vectors
Statistics
13. cumulative frequency.
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
Wednesday, October 07, 2009
Sec 4NA Maths Paper 2 2009
My dear Sec 4NA pupils,
Please focus on the following topics for Maths Paper 2:
Algebra: make subject, factorise, solve equations
Mensuration: Cone, Sphere, Cylinder
Probability
Indices
Variation: Direct and inverse proportion
Angle properties of polygon: interior and exterior angles of polygon
Circle Properties
Statistics: box plot, histogram
Graph: One big question on finding values in the table then plot points and join them with a smooth curve then use graph to find gradient, other x and y values etc.
Good Luck
Please focus on the following topics for Maths Paper 2:
Algebra: make subject, factorise, solve equations
Mensuration: Cone, Sphere, Cylinder
Probability
Indices
Variation: Direct and inverse proportion
Angle properties of polygon: interior and exterior angles of polygon
Circle Properties
Statistics: box plot, histogram
Graph: One big question on finding values in the table then plot points and join them with a smooth curve then use graph to find gradient, other x and y values etc.
Good Luck
