FaithfullyOnTheRedDot

Topic No.

Topic

Contents

Algebra

A1

Quadratic functions

NO MORE questions on

·       Finding the maximum or minimum value of a quadratic function using the method of completing the square (already tested in Q1 to find the stationary point, it should not be mistaken to be under differentiation)

·     Using quadratic functions as models very unlikely to be tested since quite a lot tested on quadratic functions

·     Conditions for y = ax² + bx + c to be always positive or negative (maybe only, very unlikely to be tested)

A2

Equations and inequalities

NO MORE questions on

·       Solving simultaneous equations in two variables by substitution, with one of the equations being a linear equation

·       questions involving discriminant (very unlikely)

A4

Polynomials and partial fractions

NO MORE questions on

·       Solving cubic equations

·       Partial Fractions

·       Remainder and Factor Theorems (maybe only, very unlikely to be tested again)

A5

Binomial expansions

NO MORE questions on

·       binomial theorem

Geometry and Trigonometry

G1

Trigonometric functions, identities and equations

NO MORE questions on

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

·       no more sketching of sine and cosine curves, if there is any sketching, it shall be y = a tan bx but very unlikely to be tested

G2

Coordinate Geometry in two dimensions

NO MORE questions on

·      linear law

Note:

Paper 1 Q11 tested only a little bit of coordinate geometry so there should still be a possibility of coordinate geometry being tested, most likely tested together with equation of circle.

G3

Proofs in plane geometry

NO MORE questions on

·      proofs in plane geometry

Calculus

C1

Differentiation and integration

NO MORE questions on

·       Increasing and decreasing functions

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

Note: even though the concept of stationary point has been tested in paper 1 Q13, it is still possible for stationary point and nature of stationary points be tested, for example the use of 1st derivative test for stationary point of inflexion.

Topic No.

Topic

Contents

Algebra

A3

Surds

·       Four operations on surds, including rationalising the denominator

·       Solving equations involving surds

[likely 1 question]

A6

Exponential, logarithmic functions

·       Exponential and logarithmic functions

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

-        Laws of logarithms

-        Equivalence of y = a^x and x = log_ay

·       Simplifying expressions and solving simple equations involving exponential and logarithmic functions

[at least 1 question]

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 tan (bx)

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

R cos (q  ± α) or R sin (q  ± α)

·       Proofs of simple trigonometric identities

·       Solution of simple trigonometric equations in a given interval

[2 to 3 questions, 1 on R-formula, 1 on proving of identities and solving equation and possibly together with principal angles]

G2

Coordinate Geometry in two dimensions

·       Conditions for two lines to be parallel or perpendicular

·       Midpoint of line segment

·       Area of rectilinear figure

·       Coordinate geometry of circles

[1 to 2 questions, surely 1 on equation of circle]

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

·       Finding the area of a region bounded by a curve and line(s)

[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]

[ONE question on area of a region bounded by a curve and line(s)]

[Half a question on connected rate of change and some other calculus related question combined together]

 You may still be tested on finding stationary points and determine their nature (max, min or stationary point of inflexion)

Topic No.

Topic

Contents

Number and Algebra 

N5

Algebraic expressions and formulae

·       Recognising and representing patterns/relationships by finding an algebraic expression for the nth term

·       Changing the subject of a formula

·       Addition and subtraction of algebraic fractions with linear or quadratic denominator but this skill is still needed if a question is set to test ‘solving fractional equations that can be reduced to quadratic equations’

N7

Equations and inequalities

Solving simultaneous equations in two variables

N9

Matrices

No more questions on Matrices

Geometry and Measurement

G1

Angles, triangles and polygons

Angle sum of interior and exterior angles of any convex polygon

G2

Congruence and similarity

Determining whether two triangles are congruent

G3

Properties of circles

No more questions on properties of circles

G4

Pythagoras’ Theorem and Trigonometry

·       Extending sine and cosine to obtuse angles

·       Bearings

Statistics and Probability

S1

Data Analysis

Calculation of the standard deviation for a set of data

Topic No.

Topic

Contents

Number and Algebra

N1

Numbers and their operations

·       Approximation and estimation

·       Use of standard form A ×10ⁿ

N2

Ratio and proportion

·       Map scales (distance and area) or scale drawings

·       Direct and inverse proportion

N3

Percentage

·       Percentages greater than 100%

·       Reverse percentages

N5

Algebraic expressions and formulae

·       Factorisation of linear expressions of the form

ax + bx + kay + kby

·       Use of special products

N6

Functions and graphs

·       Graph of a set of ordered pairs as a representation of a relationship between two variables

·       The gradient of a linear graph as the ratio of the vertical change to the horizontal change (positive and negative gradients)

·       Graphs of quadratic functions and their properties

·       Sketching of the graphs of quadratic functions given in the various form

·       Estimating the gradient of a curve by drawing a tangent

Be prepared to be asked what the gradient represent in the real world context

N7

Equations and inequalities

·       Solving simple fractional equations that can be reduced to linear or quadratic equations

·       Solving quadratic equations using the various method: factorisation, complete square or using formula

·       Solving linear inequalities in one variable, and representing the solution on the number line

N8

Set language and notation

·       Use of set language

·       Union and intersection of two sets

·       Venn diagrams

N9

Problems in real-world contexts

·       Solving problems on real-world contexts

·       Interpreting and analysing data from tables and graphs, including distance-time and speed-time graphs

·       Interpreting the solution in the context of the problem

Geometry and Measurement

G1

Angles, triangles and polygons

·       vertically opposite angles, angles on a straight line and angels at a point

·       Angles formed by two parallel lines and a transversal: corresponding, alternate and interior angles

G2

Congruence and similarity

·       enlargement and reduction of a plane figure

·       Scale drawings

·       Ratio of areas of similar plane figures

·       Ratio of volumes of similar solids

·       Solve simple problems involving similarity and congruence

G4

Pythagoras’ theorem and trigonometry

·       Use of Pythagoras’ theorem

·       Determining whether a triangle is right-angled given the lengths of the three sides

·       Use  0.5 ab sin C for the area of any triangle

·       Use of sine and cosine rule for any triangle

·       Problems in two or three dimension including those involving angles of elevation and depression

G5

Mensuration

·       Volume and surface area of cube, cuboid, prism, cylinder, pyramid, cone and sphere

·       Problems involving volume and surface area of composite solids

·       Arc length, sector area and area of a segment of a circle

·       Use radian measures of angle (including conversion between radians and degrees)

G6

Coordinate geometry

·       Finding the gradient of a straight line given the coordinates of two points on it

·       Finding the length of a line segment given the coordinates of its end points

·       Interpreting and finding the equation of a straight line in the form y = mx + c

·       Geometric problems involving the use of coordinates

G7

Vectors in two dimensions

·       Translation by a vector

·       Position vectors

·       Magnitude of a vector

·       Use of sum and difference of two vectors to express given vectors in terms of two coplanar vectors

·       Geometric problems involving the use of vectors

Statistics and probability

S1

Data Analysis

·       analysis and interpretation of the various statistical diagrams

·       purposes and uses, advantages and disadvantages of the different forms of statistical representations

·       Explaining why a given statistical diagram leads to misinterpretation of data

·       Purpose of use of mean, mode and median

·       Quartiles and percentiles

·       Interquartile range as measures of spread for a set of data

·       Using the median and interquartile range to compare two sets of data

S2

Probability

·       Probability of simple combined events (including using possibility diagrams and tree diagrams, where appropriate)

·       Addition and multiplication of probabilities (mutually exclusive events and independent events)

Since paper 1 already tested probability of single event, should there be any question on probability, it will be probability of simple combined events