Algebra (Sec 2) Practice
Master quadratic expressions: expansion using FOIL and special identities (perfect square, difference of two squares), and factorisation. These are the foundation for O-Level quadratic equations and graphing. Sec 2 Algebra is the single most important gateway topic — everything you learn here directly feeds into Sec 3 E-Math, Sec 3 A-Math, and O-Level.
Common Mistakes to Avoid
Forgetting the middle term when expanding: (x + 3)² ≠ x² + 9
Misidentifying difference of two squares: requires a² − b² form, not a² + b²
Incorrect factorisation of trinomials — always verify by expanding back
Dropping the negative sign in the middle term: (x − 3)² = x² − 6x + 9, not x² + 6x + 9
Applying difference of two squares to a sum of squares: x² + 9 cannot be factorised (it is not a difference)
Practice Questions
Try each question. When you're stuck, reveal the Socratic strategy — a guided hint that teaches you how to think, not just what to write.
Expand (x + 3)(x − 2).
Factorise completely: x² − 9.
Expand (2a + 3b)².
Factorise completely: 3x² − 12.
Expand and simplify: (x + 5)(x − 5) − (x − 2)(x + 3).
Factorise: 4y² − 12y + 9.
Parent & Tutor Insight
The three algebraic identities ((a+b)², (a−b)², (a+b)(a−b)) appear constantly in Sec 2 and O-Level exams. Students who have these memorised — not just understood — solve problems significantly faster. A quick 5-minute daily drill on these three identities can boost exam accuracy by 20%.
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Common Questions
What are the three special algebraic identities for Sec 2?
(1) (a + b)² = a² + 2ab + b² — perfect square expansion. (2) (a − b)² = a² − 2ab + b² — perfect square expansion (negative middle term). (3) (a + b)(a − b) = a² − b² — difference of two squares. These three identities appear in nearly every Sec 2 and O-Level algebra question.
How is Sec 2 Algebra different from Sec 1?
Sec 1 algebra deals with linear expressions (highest power = 1). Sec 2 introduces quadratic expressions (highest power = 2), which require new techniques like FOIL, special identities, and trial-and-error factorisation of trinomials.
What is the FOIL method?
FOIL stands for First, Outer, Inner, Last — the four products when expanding two binomials (a + b)(c + d) = ac + ad + bc + bd. It ensures every term is multiplied correctly. After expanding, always combine like terms.
Why is factorisation important for O-Level?
Factorisation is the gateway skill for O-Level E-Math and A-Math. Without fluent factorisation, students cannot solve quadratic equations, simplify algebraic fractions, complete the square, or handle partial fractions in A-Math. It is the single most foundational skill tested across the entire secondary mathematics syllabus.
How do I know which method to use when factorising?
Follow this order: (1) Look for a common factor first — always. (2) Count the terms: 2 terms → check difference of two squares; 3 terms → check perfect square or use cross-factorisation; 4 terms → try grouping. (3) Always verify by expanding back. This systematic approach eliminates guesswork.