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SMA 102 Other

SMA 102 • BASIC MATHEMATICS

Canonical syllabus units, structured theorems, lecture notes, and past examination problems.

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Syllabus Units

Curriculum outline, core theorems, and revision problems.
8 Topics
Unit 01

Quadratic Equations and Inequalities

Covers standard quadratic form ax^2 + bx + c = 0, methods of solving quadratic equations (factoring, completing the square, quadratic formula), discriminant b^2 - 4ac, nature of roots, solving quadratic inequalities, and modeling practical problems

Quadratic Equations Methods of Solution Factorization and Completing the Square The Quadratic Formula Nature of Roots and Discriminant Quadratic Inequalities Applications and Word Problems
6 Verified Questions Study Topic →
Unit 02

Remainder and Factor Theorem and their Applications

Focuses on algebra of polynomials, polynomial division, statement and proof of remainder theorem f(c) = R, factor theorem (x - c is a factor iff f(c) = 0), factoring cubics and quartics, and finding roots

Polynomial Functions Polynomial Long Division and Synthetic Division The Remainder Theorem The Factor Theorem Factoring Higher-Degree Polynomials Solving Polynomial Equations
12 Verified Questions Study Topic →
Unit 03

Permutations and Combinations

Theoretical principles of counting and arrangements: fundamental counting principle, permutations nPr, combinations nCr, distinct vs identical objects, circular arrangements, and constrained committee problems

Fundamental Counting Principle Factorial Notation Permutations with and without Repetition Circular Permutations Combinations and Selection Committee Selection Problems Probability Applications
4 Verified Questions Study Topic →
Unit 04

Binomial Theorem and its Applications

Expansion of (a + b)^n using binomial coefficients nCr, properties of coefficients in Pascal triangle, determining specific terms (r-th , independent , middle , and evaluating algebraic approximations

Pascal Triangle Binomial Coefficients and Combinations Binomial Expansion for Positive Integral Index Finding General and Middle Terms Approximations and Fractional Indices
1 Verified Question Study Topic →
Unit 05

Set Theory

Foundational set theory: set builder notation, finite and infinite sets, subsets, power sets, Venn diagrams, cardinality rules, De Morgan laws, and practical survey/voter word problems with multiple overlapping sets

Definitions and Set Notation Subsets and Power Sets Universal Set and Null Set Set Operations: Union, Intersection, Difference, Complement Venn Diagrams and 2/3 Set Problems Laws of Set Algebra (De Morgan Laws) Survey and Cardinality Problems
4 Verified Questions Study Topic →
Unit 06

Logic

Propositional logic, truth values, compound propositions using connectives (~, ^, v, ->, <->), truth table construction, proving logical equivalence, determining tautologies, and negation of conditional statements

Statements and Propositions Logical Connectives: Negation, Conjunction, Disjunction Conditional and Biconditional Statements Truth Tables Tautologies, Contradictions, and Contingencies Logical Equivalence and De Morgan Laws in Logic
1 Verified Question Study Topic →
Unit 07

Method of Proof

Methods of mathematical argumentation: direct proofs, indirect proofs using contrapositive and contradiction, counterexamples, and principle of mathematical induction to prove algebraic summations and divisibility theorems

Structure of Mathematical Proofs Direct Proof Proof by Contradiction (Reductio ad Absurdum) Proof by Contrapositive Principle of Mathematical Induction Base Step and Inductive Hypothesis Counterexamples
2 Verified Questions Study Topic →
Unit 08

Complex Numbers

Introduction to complex numbers z = a + bi, real and imaginary parts, complex arithmetic, conjugate properties, modulus |z|, argument arg(z), representation on Argand plane, conversion between Cartesian and polar forms, and De Moivre theorem

Imaginary Unit i and Powers of i Cartesian Form z = a + bi Arithmetic of Complex Numbers (Addition, Multiplication, Division) Complex Conjugate and Modulus Argand Diagrams Polar Form (Trigonometric Form) De Moivre Theorem and Roots of Complex Numbers
4 Verified Questions Study Topic →