Algebra

The section that underpins every other part of the qualification.

• An Overview — the big idea, the language, the six core techniques and the common mistakes

The specification statements

• AL1–AL2 · Algebraic Manipulation — vocabulary and notation, algebraic fractions, indices and surds
• AL3–AL4 · Polynomials and the Factor Theorem — adding, multiplying and dividing polynomials; finding linear factors
• AL5 · Completing the Square — the identity ax² + bx + c ≡ a(x + p)² + q, and what it reveals
• AL6 · Setting Up and Solving Equations — linear, quadratic, cubic and simultaneous equations, in and out of context
• AL7–AL8 · Linear and Quadratic Inequalities — manipulating and solving inequalities algebraically and graphically
• AL9 · Inequalities in Two Variables — shading regions, and the groundwork for linear programming
• AL10–AL11 · Recurrence Relationships — sequences defined by the previous term, convergence, and modelling compound interest

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Each page has step-by-step notes, several worked examples, a quick-reference grid and ten practice questions with fully worked solutions.