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Mathematics (AS)

Mathematics (AS)

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AS Mathematics builds strong foundations in algebra, geometry, trigonometry, and calculus, while also introducing statistics, probability, and mechanics. Students practice problem-solving through functions, sequences, differentiation, integration, and data analysis. The course develops logical reasoning, precision, and the ability to apply mathematics to real-life and scientific contexts.

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Topics

Unit 1: Pure Mathematics (Core Concepts)

Sub-Unit 1.1: Algebra

  • Laws of indices & surds
  • Factorization (quadratics, cubics)
  • Rational expressions & simplification
  • Partial fractions

Sub-Unit 1.2: Functions

  • Definition of a function, domain & range
  • Composite & inverse functions
  • Graphs of functions (quadratic, exponential, logarithmic, modulus, transformations)

Sub-Unit 1.3: Quadratics & Inequalities

  • Solving quadratic equations
  • Discriminant and nature of roots
  • Simultaneous equations (linear/quadratic)
  • Linear & quadratic inequalities

Sub-Unit 1.4: Sequences & Series

  • Arithmetic progressions (AP)
  • Geometric progressions (GP)
  • Sums of finite series
  • Convergence of infinite GPs

Unit 2: Trigonometry

Sub-Unit 2.1: Trigonometric Ratios & Identities

  • Sine, cosine, tangent graphs
  • Reciprocal trig functions (cosec, sec, cot)
  • Standard identities:
    • sin⁡2x+cos⁡2x=1\sin^2 x + \cos^2 x = 1
    • Double-angle & compound-angle formulae

Sub-Unit 2.2: Equations & Applications

  • Solving trig equations (general solutions)
  • Applications in geometry & modeling

Unit 3: Calculus (Differentiation & Integration)

Sub-Unit 3.1: Differentiation

  • First principles
  • Derivatives of polynomials, trig, exponential, logarithmic functions
  • Product, quotient & chain rules
  • Stationary points & curve sketching
  • Applications (rates of change, optimization problems)

Sub-Unit 3.2: Integration

  • Indefinite integration (reverse of differentiation)
  • Definite integrals (area under curve)
  • Substitution & integration by parts (intro in P3)
  • Applications (area between curves, kinematics)

Unit 4: Coordinate Geometry

Sub-Unit 4.1: Straight Lines

  • Gradient & equation of a line
  • Midpoint & distance formulae
  • Parallel & perpendicular lines

Sub-Unit 4.2: Circles

  • Equation of a circle
  • Tangents & normals
  • Geometrical interpretation

Unit 5: Statistics (S1)

Sub-Unit 5.1: Representation of Data

  • Histograms, bar charts, cumulative frequency, box plots
  • Measures of central tendency (mean, median, mode)
  • Measures of spread (range, variance, standard deviation)

Sub-Unit 5.2: Probability

  • Basic probability laws
  • Mutually exclusive & independent events
  • Tree diagrams & Venn diagrams

Sub-Unit 5.3: Discrete Random Variables

  • Probability distributions
  • Expected value (mean), variance
  • Binomial distribution

Sub-Unit 5.4: Normal Distribution

  • Properties of normal curve
  • Standardization (Z-scores)
  • Approximations using normal distribution

Unit 6: Mechanics (M1)

Sub-Unit 6.1: Forces & Equilibrium

  • Vectors in 2D
  • Forces, moments, equilibrium conditions

Sub-Unit 6.2: Kinematics

  • Motion in a straight line
  • Displacement, velocity, acceleration
  • Equations of motion (SUVAT)

Sub-Unit 6.3: Newton’s Laws

  • First, Second & Third Laws
  • Applications (particles, connected bodies, friction)

Sub-Unit 6.4: Work, Energy & Power

  • Work done by a force
  • Kinetic & potential energy
  • Power = work/time or force × velocity

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