Senior 5

Senior 5 Mathematics Notes and Study Materials

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How to study Senior 5 Mathematics

Start with one Mathematics topic and read its learning points before opening a note. Write down the facts, rules, formulas, or diagrams that you need to remember. Then explain each idea in your own words. This quick check shows what you understand and what needs another careful review.

Study in short sessions and give each session a clear goal. You can learn a definition, practise a calculation, label a diagram, or answer a small group of questions. Mark your work when answers are available. Keep a list of mistakes and return to them after a day or two. Repeated correction builds stronger recall.

For examination preparation, mix new learning with older mathematics topics. Read every question closely, show the important steps, and check units or scientific terms before you finish. Use a timer only after you can answer accurately without rushing. Accuracy should come first; speed improves with steady practice.

You can return to all Senior 5 subjects or use the Senior 5 practice quizzes to check your progress.

Full Senior 5 Mathematics Syllabus Outline

Every topic and subtopic covered in Senior 5 Mathematics.

  • Error Analysis

    • Errors
    • Propagation of errors using simple interval arithmetic method
    • Errors in functions

  • Dynamics I

    • Resultant and Components of forces
    • Friction
    • Connected Particles

  • Descriptive statistics

    • Measure of Dispersion
    • Measure of Relative Position

  • Numerical Concepts

    • Indices
    • Logarithms
    • Surds

  • Equations and Inequalities

    • Linear and Simultaneous equations
    • Quadratic Equations
    • Quadratic Inequalities
    • Polynomials

  • Correlation and Scatter Diagrams

    • Scatter Diagram
    • Correlation

  • Probability Theory

    • Probability Theorems
    • Applications of probability in real life

  • Coordinate Geometry I

    • Straight lines

  • Partial Fractions

    • Linear factor, Quadratic factor, Repeated factor, Improper fraction

  • Random Variables

    • Discrete random variables
    • Continuous random variables

  • Trigonometry

    • Trigonometrical ratios
    • Clockwise and anti-clockwise angles
    • Graphs of sine, cosine,tangent
    • Compound angle formulae and derived identities
    • Solution of triangles

  • Probability Distributions

    • Binomial Distribution
    • Uniform Rectangular distribution
    • Normal Distribution
    • Normal Approximation to binomial distribution for n > 20

  • Differentiation I

    • Gradient of curve, gradient function, composite functions
    • Implicit functions and Parametric functions
    • Chain rule, small changes, Products rule, Quotient rule
    • Nature of turning point and Curve sketching
    • Rates of change
    • Velocity and acceleration

  • Integration I

    • Indefinite and Definite Integral
    • Area enclosed in stated boundaries
    • Volume of solids of Revolution
    • Mean value of a function

  • Permutations and Combinations

    • Permutations and Combinations

  • Series

    • Arithmetic progression (A.P) and Geometric progression (G.P)
    • Proof by Induction
    • Binomial expansion