FaithfullyOnTheRedDot

Topic No.

Topic

Contents

Algebra

A1

Equations and inequalities

NO MORE questions on

·       Relationships between the roots and coefficients of a quadratic equation (sum of roots α + β and product of roots αβ)

A3

Polynomials and Partial Fractions

NO MORE questions on

·       Remainder and Factor Theorems

·       Solving cubic equations

·       Partial Fractions

A5

Modulus functions

NO MORE questions on

·       Modulus function | f(x) | and its graph where f(x) is linear

However, modulus functions where f(x) is quadratic or trigonometric may still be tested

Geometry and Trigonometry

G1

Trigonometric functions, identities and equations

NO MORE questions on

·       Proving of trigonometric identities and solving of trigonometric equations

 Very likely also no more special angles, may even not have R-formula

G2

Coordinate Geometry in two dimensions

NO MORE questions on

·       Coordinate geometry of circles

Calculus

C1

Differentiation and integration

NO MORE questions on

·       Increasing and decreasing functions

·       Nature of stationary points using 2nd derivative test

·       Application of differentiation and integration to problems involving Displacement (s), velocity (v) and acceleration (a) of a particle moving in a straight line

·       Area bounded by a curve and lines

 However, you may still be tested on the use of 1st derivative test for stationary point of inflexion (which is quite unlikely but still possible)

Topic No.

Topic

Contents

Algebra

A1

Equations and inequalities

·       Conditions for a quadratic equation to have:

(i)     two real roots

(ii)    two equal roots

(iii)   no real roots

and related conditions for a give 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)

 In short, this sub topic test the use of discriminant

[ONE question]

A2

Indices and surds

·       Four operations on indices and surds, including rationalising the denominator

[ONE question on solving real world context problem using surds]

Note: Green means maybe tested only

A4

Binomial expansions

·       Use of Binomial Theorem for positive integer n

·      Use of the notations n! and nCr

·       Use of the general term

[CONFIRMED ONE question]

A5

Power, Exponential, Logarithmic functions

·       Power functions y = axⁿ where n is a simple rational number, and their graphs

·       Exponential and logarithmic functions

a^x, e^x, log_a x, ln x and their graphs

·       Solving simple equations involving exponential and logarithmic functions

[AT LEAST ONE for exponential and logarithmic functions]

[Maybe   ONE question for power functions, may be together with y² = kx ]

Geometry and Trigonometry

G1

Trigonometric functions, identities and equations

·       Principal values of sin^–1 x, cos^–1 x and tan^–1 x

·       Amplitude, periodicity and symmetries related to sine and cosine functions

·       Graphs of y = a sin (bx) + c, y = a cos (bx) + c and

y = a tan (bx)

·       The expression for a cos q + b sin q in the form

R cos (q  ± α) or R sin (q  ± α)

[ONE question on amplitude, periodicity and symmetries related to sine and cosine functions and their graphs, can also be tan q graph, this question may also include principal values of sin^–1 x, cos^–1 x and tan^–1 x]

[ONE question on R-formula] this is green because paper 1 too many questions on trigonometry but still must study R-formula ok

G2

Coordinate Geometry in two dimensions

·       Conditions for two lines to be parallel or perpendicular

·       Midpoint of line segment

·       Area of rectilinear figure

·       Graphs of parabolas with equations in the form y² = kx

·       Transformation of given relationships, including y = axⁿ and y = kb^x, to linear form to determine the unknown constants from a straight line graph (commonly known as Linear Law)

[ONE question on coordinate geometry involving straight line since geometry of circle has already been tested]

[ONE question on Linear Law]

[ONE question on graphs of y² = kx, may be tested together with power function]

Calculus

C1

Differentiation and integration

·       Derivative as rate of change

·       Using second derivative test to discriminate between maxima and minima (more for real world context problem such as volume of container, area of plot of land etc)

·       Applying differentiation to gradients, tangents and normal, connected rates of change and maxima and minima problems

·       Integration as the reverse of differentiation

·       Evaluation of definite integrals

[ONE question on tangents and normal (because normal already tested in paper 1), this question may also include part of it on connected rates of change or may be two separate question]

[ONE question on maxima and minima for real world context problem]

[ONE question on Integration as the reverse of differentiation, this question requires you to use a previous differentiation to integrate a related expression]

 You may still be tested on using 1st derivative test for stationary point of inflexion (which is quite unlikely but still must study lah)