Pure Mathematics

1. Algebra and Functions

   • Simplifying expressions

   • Solving equations and inequalities

   • Quadratic functions, completing the square, and the quadratic formula

   • Polynomials and the factor theorem

   • Algebraic manipulation including partial fractions

   • Exponential and logarithmic functions

2. Coordinate Geometry

   • Equations of lines and circles

   • Intersection of lines and circles

   • The distance between two points

3. Sequences and Series

   • Arithmetic sequences and series

   • Geometric sequences and series

   • Sum of finite and infinite series

   • Sigma notation and the binomial theorem

4. Trigonometry

   • Trigonometric functions and their graphs

   • Trigonometric identities and equations

   • Radian measure

   • Sine, cosine, and tangent rules

   • Solving trigonometric equations

5. Calculus

   • Differentiation and its applications

   • Integration and its applications

   • Fundamental theorem of calculus

   • Numerical methods for integration

   • Differential equations

6. Vectors

   • Vector notation and arithmetic

   • Dot product

   • Equations of lines in vector form

Mechanics

1. Kinematics

   • Motion in a straight line

   • Constant acceleration

   • Motion under gravity

   • Velocity-time and displacement-time graphs

2. Dynamics

   • Newton's laws of motion

   • Forces and acceleration

   • Motion of connected particles

   • Projectiles

3. Statics

   • Equilibrium of a particle

   • Moments

4. Work, Energy, and Power

   • Work done by a force

   • Kinetic and potential energy

   • Conservation of energy

5. Impulse and Momentum

   • Momentum and impulse

   • Conservation of momentum

Statistics

1. Statistical Sampling

   • Methods of sampling

   • Bias and representativeness

2. Data Presentation and Interpretation

   • Graphs and charts

   • Measures of central tendency and spread

   • Histograms and cumulative frequency

3. Probability

   • Probability rules

   • Conditional probability

   • Probability distributions

4. Statistical Distributions

   • Binomial distribution

   • Normal distribution

5. Statistical Hypothesis Testing

   • Hypothesis tests for proportions

   • Critical regions

   • Interpreting results in context