Mathematics Syllabus

  • Secondary 1
  • Secondary 2
  • Secondary 3
  • Secondary 4

Numerical Concepts

  • Understand natural numbers, prime factors, multiples, GCD, HCF and LCM
  • Know types of fractions
  • Calculating squares and square roots of numbers Solving problems involving direct and indirect proportion
  • Understand reciprocals of numbers

Commercial Arithmetic

  • Understand profit and loss
  • Understand percentage discount and commission as percentage

  • Calculate length, area and volume of common solids
  • Solving problems involving surface area and volumes of cylinders
  • Calculate Capacity of containers

Geometry

  • 3D Coordinates Angles of plane figures
  • Geometrical constructions
  • Scale drawing and bearing
  • Angles of depression and elevation.
  • Reflection, congruency and rotation.

Trigonometry

Trigonometry (I):

  • Explain relationship between sine, cosine, tangent and special angles

Understand and apply:

  • Simplification, brackets, substitution
  • Factorization and expansion
  • Simultaneous linear equations
  • Formation and solution of inequalities
  • Formulae and equations
  • Functions
  • Relation and mapping
  • Translation as a transformation

Statistics

Statistics (I):

  • Collection of statistical data,
  • construction of frequency tables,
  • understand grouped data average,
  • mode and median,
  • Interpretation and representation of data

Probability

  • Understand probability of events, use of tree diagram

Numerical Concepts

  • Indices (Know rules, evaluating fractional, zero and negative indices)
  • Understand and use surds
  • Explain rational and irrational numbers

Commercial Arithmetic

  • Foreign exchange
  • Simple and compound interest,
  • Compound interest formula,
  • Depreciation and appreciation.
  • Hire purchase and income tax

  • Calculate areas of geometrical figures
  • Surface areas of solids

Geometry

  • Understand and use equations of straight lines.
  • Pythagoras theorem and application of the theorem

Trigonometry

Trigonometry (II):

  • Explain trigonometric ratios from the unit circle,
  • Angle property of circle

Quadratic expressions and equations (1):

  • Expansion,
  • Identification,
  • Factorization

Vectors (I):

  • vectors and scalar quantities,
  • column, position and equivalent vectors,
  • operation on vectors,
  • vector translation

Sets:

  • set notation,
  • Venn diagrams and solving problems up to three sets

Matrices (I):

  • Understand determinant, inverse, transposition of matrices, similarities and enlargement

Functions:

  • Papy gram,
  • functional notation,
  • inverse of simple functions,
  • composite functions and their inverses

Statistics

 

Statistics (II):

  • Understand assumed mean
  • Interpret cumulative frequency tables,
  • Explain ogives, median, quartiles, depression

Probability

  • Calculations involving probability

Numerical Concepts

  • Understand logarithms
  • Know laws of logarithms and apply in calculation
  • Logarithmic equations

 

  • Computation using calculators
  • Estimation and approximation of surface area and volume of irregular objects
  • Understand significant figures

Geometry

  • Three dimensional figures
  • Proof of Pythagoras theorem
  • Understand and use loci
  • Know and understand the equation of a circle is (x-a)2  +  (y-b)2  =  r2

 

Quadratic equations (II):

  • Binomial expansion
  • Compound proportion
  • Mixtures and rate of work

Vectors (II):

  • vector algebra,
  • mid-point of vector in algebraic expression

Sequences and series

  • Explain arithmetic and geometric progression
  • Derivation of the formulae for A.P. and G.P.

Matrices (II):

  • Transformation on the Cartesian plane
  • Identity and inverse;
  • Determinant of matrices, shear and stretch.
  • Isometric and non isometric transformation and their application

Differentiation:

  • gradient of the curve at a point,
  • gradient of y =xn

ADDITIONAL MATHEMATICS OVERVIEW 2013

Functions

  • Domain and range,
  • modulus of a function,
  • inverse (or no inverse] of a function,
  • composite function

Trigonometry

  • Identities,
  • equation with more than one function
  • Addition formulae and the tangents of compound angles (A±B)
  • Derivation of three trigonometrical identitities, secant, cosecant and cotangent
  • The double angle formulae and half angle formulae

Calculus 1

  • Derivatives of a polynomials
  • The composite (combined) function
  • The 2nd derivative coefficient
  • Application of differentiations
  • Tangent, normal, maximum, minimum, velocity and acceleration
  • Small increments: Approximate changes-connected rates of change

Calculus II

  • Definition of integration
  • Integration as opposite of differentiation
  • Indefinite integration
  • Integration by substitution and by parts

Algebra

  • 3x3 Matrices
  • Determinants
  • Crammer's rule

Complex numbers

  • Concepts (introduction) and definition.
  • Addition and subtraction of complex number
  • Multiplication and division of complex numbers

The Circle

  • Equation of the circle at the origin
  • General form of equation of the circle
  • Equation of a circle that satisfies special condition:
      • Equations of the circle passing 3 points,
      • Equation of a circle when ends of diameter in it are given
      • Equation of a circle passing through two points and its centers lies on a given straight line
      • The equation of tangent to a circle at a point on it
      • Length of tangent drawn to a circle from an external point

Kinematics

  • Graph: Area under velocity -time graph
  • Straight line motion with constant acceleration
  • Vertical motion under gravity

Velocity

  • Composition of velocities
  • Resolution of velocities

Force

  • Unit of force
  • Types of forces-weight, reaction, tension, friction, thrust
  • Composition of two forces
  • Resolution of forces
  • Co-planar forces acting on a point
  • Equilibrium of a particle
  • Triangle of forces; 
  • Lemi's theorem;
  • polygons of forces

Momentum

  • Understand the conservation of momentum

Numerical Concepts

  • Complex numbers,
  • Operations on complex numbers,
  • graphical representation of complex numbers,
  • polar form of complex numbers

  • Approximation of area of irregular object by counting
  • Use of trapezium rule, mid- ordinate rule

Geometry

 

The circle:

  • explain the equation of a circle passing through two points touching x-axis

Trigonometry

 

Trigonometry (III):

  • Plot graphs of trigonometrical ratios

 

Forming inequalities

  • find maximum and minimum values of linear inequalities and apply linear programming.

Permutation and combination,

  • definition
  • Ways of arrangement of objects,
  • factorial notation and its application

Vectors (III):

  • Understand coordinates in two and three dimension systems,
  • column and position vectors in three dimensions

  • Derivative of polynomial,
  • equations of tangents and normals,
  • maxima and minima points,
  • application of differentiation to kinematics.

Integration:

  • application of integration,
  • integration of polynomials,
  • finding area under a curve

ADDITIONAL MATHEMATICS OVERVIEW 2013

Functions

  • Limits (rational numbers)

Trigonometry

  • Simplification of trigonometrical ratios and solutions of trigonometrical equations
  • Sum and differences of two angles (A±B)
  • Functions, a cos θ + b sin θ
  • The equation, a cos θ + b sin θ = c

Calculus 1

  • Differentiation of product of two functions, quotient and implicit function
  • Differential of trigonometric functions sin x, cos x and tan x

Calculus II

  • Application of integration - Area under the curve Integration of powers of linear function  Ax + b
  • Integration of trigonometric functions

Algebra

Partial fractions.

  • Introduction, identify denomination or with only linear factors, with quadratic factors and with repeated factors
  • Vectors in terms of i,  j and k,
  • Application of vector method in geometry

Complex numbers

  • Graphical representation and polar form of complex numbers
  • The powers and De-Moivres's theorem
  • The roots of complex numbers and solution of quadratic equation in complex numbers

Projectiles

  • Velocity components,
  • coordinates,
  • greatest height,
  • time of flight and
  • horizontal range

Force

  • Explain why friction is a force,
  • calculations of friction

Laws of Motion

  • Understand Newton’s laws of motion
  • Explain the difference between mass and weight
  • Connected particles

Work, Power and Energy

  • Explain kinetic energy, potential energy, work and power

Biology Syllabus

  • Secondary 1
  • Secondary 2
  • Secondary 3
  • Secondary 4

Chemistry Syllabus

  • Secondary 1
  • Secondary 2
  • Secondary 3
  • Secondary 4

Physics Syllabus

  • Secondary 1
  • Secondary 2
  • Secondary 3
  • Secondary 4