IB Maths AA SL 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 calculator Paper 2, calculator

Difficulty

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Question 1

Paper 2, calculatorMedium7 marks

Let $A(x)=(x+1)^2-1$ and $B(x)=x(x+2)$ where $x\in\mathbb{R}$

(a)

Find $A(3)$ and $B(3)$

[2]

(b)

Starting with $A(x)$ show by a chain of algebraic equalities that $A(x)$ has the same value as $B(x)$ for every $x\in\mathbb{R}$

[3]

(c)

Complete each statement using either $=$ or $\equiv$

A(3)\ \square\ B(3)

A(x)\ \square\ B(x),\quad \text{for all }x\in\mathbb{R}

[2]

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