Exam pattern and priorities
The syllabus states 60 course hours, 30 CCA marks and a 70-mark ESE (2 hours). In the ESE, answer any 5 of 8 two-mark questions, 5 of 8 six-mark questions and 3 of 6 ten-mark questions. The listed counts by module are: Module I (2,2,2), Module II (2,2,1), Module III (2,2,1), Module IV (2,2,2), for Parts A, B and C. This is the distribution printed in the syllabus; it does not guarantee a particular topic.
Truth-table/equivalence problems; set operations and functions; relation properties/equivalence; determinant, inverse and solving systems.
Inference rules, function types, relation representations, symmetric/skew-symmetric matrices.
Definitions, notation, connective meanings, property names and short matrix facts.
Show truth-table columns, set membership, relation checks, matrix operations and substitution checks. A correct result with clear steps is easier to follow.
Recall checklist
10 core concepts: proposition; negation; conjunction; disjunction; conditional; biconditional; truth table; equivalence; premise/conclusion; inference rule.
Key terms: tautology, contradiction, contingency, logical equivalence, valid argument, modus ponens, modus tollens, converse, inverse, contrapositive.
Rules and formulas: p→q≡¬p∨q; De Morgan’s laws; modus ponens and modus tollens patterns.
Common traps: confuse inclusive “or” with exclusive or; forget p→q is false only for T→F; assume converse is equivalent; affirm the consequent.
Recall checklist
10 core concepts: set; element; subset; empty set; universal set; power set; union; intersection; complement/difference; function.
Key terms: Cartesian product, domain, codomain, range, injective, surjective, bijective, image, preimage, inclusion-exclusion.
Formula: |A∪B|=|A|+|B|−|A∩B|. Check each function property using the stated domain and codomain.
Common traps: union vs intersection; codomain vs actual range; function must have exactly one output per input; onto depends on the codomain.
Recall checklist
10 core concepts: Cartesian product; relation; ordered pair; reflexive; symmetric; antisymmetric; transitive; matrix representation; digraph; equivalence class.
Key terms: relation on a set, loop, adjacency matrix, equivalence relation, partition, related elements, property, counterexample.
Core test: equivalence relation = reflexive + symmetric + transitive. Check all elements/pairs; one counterexample disproves a universal property.
Common traps: symmetry is not antisymmetry; relation is relative to its underlying set; proving only two properties is not enough.
Recall checklist
10 core concepts: order; transpose; identity; zero matrix; symmetric; skew-symmetric; matrix operations; determinant; inverse; solution of a non-homogeneous system.
Key terms: square matrix, singular, non-singular, coefficient matrix, constants vector, Cramer’s rule, determinant, inverse, row, column.
Formulas: det([[a,b],[c,d]])=ad−bc; inverse exists when determinant ≠0; AX=B gives X=A⁻¹B when inverse exists; Cramer xᵢ=Dᵢ/D when D≠0.
Common traps: dimensions and order in multiplication; assuming AB=BA; sign errors; using inverse/Cramer when determinant is zero; not checking the solution in original equations.
Expected / Exam-Focused question bank
All prompts below are derived from syllabus topics. They are not represented as past-paper questions.
2-mark questions
- Define a proposition and give an example.
- When is p→q false?
- State one of De Morgan’s laws.
- Define a subset or power set.
- Define an injective function.
- What is a reflexive relation?
- State the three properties of an equivalence relation.
- Define a skew-symmetric matrix.
- When does a 2×2 matrix have an inverse?
- State the condition for Cramer’s rule to give a unique solution.
6-mark questions
- Construct a truth table and determine whether two propositions are equivalent.
- Apply inference rules to decide whether a conclusion follows from given premises.
- Perform set operations and solve a finite set-counting problem.
- Determine whether a given function is one-to-one or onto.
- Test reflexive, symmetric, antisymmetric and transitive properties of a relation.
- Represent a relation by a matrix or digraph and interpret it.
- Find a 2×2 determinant and inverse, showing each step.
- Solve a pair of linear equations using Cramer’s rule.
10-mark questions
- Use truth tables and propositional equivalences to analyse a compound statement and justify the result.
- Analyse a relation for its properties; determine whether it is an equivalence relation and find its classes.
- Carry out matrix operations, find an inverse and solve a non-homogeneous system using the matrix method.
- Solve a suitable system using Cramer’s rule and verify the result.
Model answer structure
2 marks: state the definition or rule accurately, then add one property/example.
6 marks: show definition, method, working (truth table/set/property checks/calculation) and a brief conclusion.
10 marks: introduce the relevant method, show complete organised working, justify each important step, state the answer clearly and verify where possible.
7-day revision plan
| Day | Focus and task |
|---|---|
| 1 | Propositions, connectives and truth tables; complete 3 truth tables. |
| 2 | Equivalences and inference; explain why one invalid argument fails. |
| 3 | Sets and operations; solve one inclusion-exclusion problem and function classification. |
| 4 | Relations and representations; check all properties and equivalence classes. |
| 5 | Matrix types, operations, determinants and inverse calculations. |
| 6 | Systems by inverse matrix and Cramer’s rule; check solutions. |
| 7 | Mixed timed 2-, 6- and 10-mark practice; review errors. |
14-day revision plan
| Day | Focus |
|---|---|
| 1 | Propositions and translating statements into symbols. |
| 2 | Connectives and truth tables. |
| 3 | Logical equivalences and De Morgan’s laws. |
| 4 | Rules of inference and invalid arguments. |
| 5 | Set notation, membership and subsets. |
| 6 | Set operations and counting applications. |
| 7 | Functions: domain, codomain, range and types. |
| 8 | Relations and property checks. |
| 9 | Matrix and digraph representations; equivalence relations. |
| 10 | Matrix definitions, types, transpose and operations. |
| 11 | Determinants and inverse. |
| 12 | System solving by matrix method. |
| 13 | Cramer’s rule and verification. |
| 14 | Mixed timed answers, formula/definition recall and error correction. |
Final 24-hour checklist
If you can do these things, you are exam ready: explain the rule, apply it to a new problem, show enough working for another person to follow, and check the result.