## 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

• 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

• 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,

### 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

### 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 ij 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

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

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

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