These are selected revision notes and practice questions. No original exam-year or paper references have been verified; these questions are not presented as authenticated past papers. Use your current textbook and teacher guidance for complete coverage.
1. Essential Algebraic Identities
Identity Vault Must-Memorize Board Identities
- $(x+y)^2 = x^2 + 2xy + y^2$
- $(x-y)^2 = x^2 - 2xy + y^2$
- $x^2 - y^2 = (x+y)(x-y)$
- $(x+a)(x+b) = x^2 + (a+b)x + ab$
- $(x+y+z)^2 = x^2 + y^2 + z^2 + 2xy + 2yz + 2zx$
- $(x+y)^3 = x^3 + y^3 + 3xy(x+y)$
- $x^3 + y^3 + z^3 - 3xyz = (x+y+z)(x^2 + y^2 + z^2 - xy - yz - zx)$
- Special Case: If $x + y + z = 0$, then $x^3 + y^3 + z^3 = 3xyz$
2. Factor Theorem & Middle Term Splitting
Factor Theorem: If $p(x)$ is a polynomial of degree $n \ge 1$ and $a$ is any real number, then $(x-a)$ is a factor of $p(x)$ if $p(a) = 0$.
3. Selected Revision Practice Questions
PRACTICE Q1: Evaluate $(99)^3$ using suitable algebraic identity. (2 Marks)
Solution: Write $99 = 100 - 1$.
$(100 - 1)^3 = 100^3 - 1^3 - 3(100)(1)(100 - 1) = 1000000 - 1 - 300(99) = 1000000 - 1 - 29700 = 970299$.