Algebra is the largest strand in IGCSE Maths 0580, covering manipulation of expressions, solving equations, sequences, and functions — essential for progression to A Level.
Simplify by collecting like terms and expanding brackets. Factorise: common factor, grouping, difference of two squares (a² − b² = (a+b)(a−b)), quadratic trinomials. Solve linear equations: isolate the variable. Solve quadratic equations: factorising, quadratic formula x = (−b ± √(b²−4ac)) / 2a, completing the square (Extended).
Simultaneous equations: elimination method or substitution method. One linear + one non-linear (Extended): substitute linear into quadratic. Inequalities: solve like equations but reverse sign when multiplying/dividing by negative. Represent on number lines and regions on graphs.
Linear sequences: nth term = a + (n−1)d. Quadratic sequences (Extended): second differences are constant. Finding nth term of quadratic sequences. Recognising geometric sequences. Fibonacci-type sequences.
Function notation: f(x), g(x). Evaluating f(3). Composite functions: fg(x) = f(g(x)). Inverse functions: f⁻¹(x) — swap x and y, solve. Domain and range. Sketching linear, quadratic, cubic, reciprocal, and exponential graphs. Transformations of graphs (Extended).
Completing the square is on the Extended curriculum only. It is used to: (1) solve quadratic equations, (2) find the vertex of a parabola, and (3) derive the quadratic formula. If you are taking Extended, practice it thoroughly — it appears frequently in Papers 2 and 4.
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