IB Maths AA HL AA 1.3 Proof questions

Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.

Paper
Paper 1, no calculatorPaper 2, calculator
Difficulty
EasyMediumHard

Question 1

Paper 1, no calculatorMedium7 marks
(a)

Show that 33−23=3(2)2+3(2)+13^3-2^3=3(2)^2+3(2)+1

[2]
(b)

For x∈Rx\in\mathbb R prove by starting with the left-hand side and transforming it that (x+1)3−x3(x+1)^3-x^3 simplifies to 3x2+3x+13x^2+3x+1 In your final line, use the appropriate symbol to indicate that this is an identity.

[4]
(c)

Hence determine 213−20321^3-20^3

[1]

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