📐 Algebra & Equations

Algebra is the highest-weightage topic in E-Math, appearing in both papers and forming the foundation for many other topics including graphs, trigonometry, and statistics. You must master algebraic manipulation, factorisation, quadratic equations, simultaneous equations, algebraic fractions, and inequalities. This chapter provides comprehensive coverage with multiple worked examples for every key technique.

Algebraic fluency is what separates A1 students from the rest. Many students understand the concepts but lose marks because they make errors during manipulation. The key to mastery is practice — work through every example in this chapter, then attempt past paper questions until the techniques become second nature.

Algebraic Expansion & Identities

Expansion means removing brackets by multiplying each term inside the bracket by the term outside. For two binomials, use the FOIL method (First, Outer, Inner, Last) or the grid method. However, the three special algebraic identities below are so commonly used that you should memorise them and apply them directly — this saves time and reduces errors.

The most common mistake with perfect squares is forgetting the middle term. Students write (a + b)^2 = a^2 + b^2, which is WRONG. The correct expansion always has the middle term 2ab. Always check your expansion by counting terms: a perfect square expansion should have 3 terms.