Mathematical language, notation and argumentAQA A-Level Maths: Mind map

Exam questions on Mathematical language, notation and argument

1. Let $A=\{x\in\mathbb{R}:x^2<9\}$ and $B=\{x\in\mathbb{R}:x\ge1\}$. The universal set is $\mathbb{R}$ and $A'$ denotes the complement of $A$.
   Write down $A'\cap B$ as an inequality, showing how you obtain it.2 marks
2. The function $f$ is defined by $f(x)=x^2-4x+7$ for $x\in\mathbb{R}$, $x\ge2$.
   The domain of $f$ is changed to $x\ge4$. Find the range of $f$ for this new domain, justifying your answer.2 marks
3. A student solves $\sqrt{x+2}=x$ and writes: Line 1: $x+2=x^2$. Line 2: $x^2-x-2=0$. Line 3: $(x-2)(x+1)=0$. Line 4: so $x=2$ or $x=-1$.
   Show that $x=-1$ is not a solution of the original equation, and explain how it arose.3 marks