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igcse maths

IGCSE Graph Transformations: Translations & Reflections (H)

“In the Edexcel IGCSE Higher Tier syllabus, Graph Transformations involve modifying a function y=f(x) to change its position or orientation.2 Mastery relies on two fundamental rules: 1) Outside changes (f(x)+a, -f(x)) affect the y-coordinates and follow the expected logic (Vertical Translation, X-axis Reflection); and 2) Inside changes (f(x+a), f(-x)) affect the x-coordinates and behave in the opposite way to what is expected (Horizontal Translation, Y-axis Reflection). Translations are formally described using column vectors.”

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igcse maths

IGCSE Calculus: Differentiation, Gradients & Kinematics (H)

“In the Edexcel IGCSE Higher Tier syllabus, Calculus (Differentiation) allows us to analyze the rate of change of curves. The fundamental rule is: if y = ax^n, then the derivative dy/dx = anx^{n-1}. This technique is used for three main purposes: 1) Finding the Gradient of a curve at a specific point; 2) Locating Turning Points (Maximum/Minimum) by setting dy/dx = 0; and 3) Solving Kinematics problems, where differentiating displacement (s) gives velocity (v), and differentiating velocity gives acceleration (a).”

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