H2 Math proof pitfalls: Common mistakes and how to correct them

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H2 Math proof techniques: A checklist for A-Level success

Incorrectly assuming the statement is true for *n* = *k*+1 instead of assuming it’s true for *n* = *k* and then proving it for *n* = *k*+1. Always start by clearly stating your inductive hypothesis.
Ensure each step in your proof is logically sound and clearly justified. State any assumptions you make, and pay close attention to the direction of the inequality. A common error is not considering the sign of a term when multiplying or dividing.
Students often try to work with both sides of the equation simultaneously. Its best to manipulate one side until it matches the other. Choose the more complex side to simplify.
Many students make mistakes by not providing clear diagrams or failing to define their vectors properly. Always draw a clear diagram and label your vectors. State any geometric relationships you are using (e.g., collinearity, perpendicularity).
Forgetting to consider both the real and imaginary parts of a complex number. When equating two complex numbers, make sure you equate both the real parts and the imaginary parts separately.
Not rigorously applying the epsilon-delta definition or incorrectly manipulating inequalities when finding a suitable delta for a given epsilon. Practice applying the definition to various functions.
Assuming matrix multiplication is commutative (AB = BA). It is generally not true. Always be mindful of the order of multiplication.
Confusing the nth term of a sequence with the sum of the first n terms. Use correct notation (u_n vs. S_n) and understand the difference between arithmetic and geometric sequences/series.
Not paying attention to the domain and range of the function. Always consider the domain and range when proving properties like injectivity, surjectivity, or invertibility.
Failing to show that the initial assumption *actually* leads to a contradiction. The contradiction must be a clear and logical consequence of your assumption.

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