IB Maths AA HL AA 5.1 Limits and differentiation 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

Easy Medium Hard

Question 1

Paper 1, no calculatorMedium6 marks

In Figure 1, the solid curve is $y=g(x)$ The dashed line is its tangent at $P$ where $x=0$

(a)

Using Figure 1, write down the values of $g(0)$ and $g'(0)$

[2]

(b)

The function $F$ is defined by

F(x)=\frac{e^{g(x)}}{x+2}.

Determine $F'(0)$ giving your answer exactly.

[4]

Question 2

Paper 2, calculatorHard6 marks

Let $n$ be a fixed positive integer and let $f(x)=x^n$ where $x\in\mathbb R$

(a)

Using the definition of the derivative from first principles, show that

f'(x)=nx^{n-1}.

[3]

(b)

For an integer $r$ with $1\le r\le n$ prove that

f^{(r)}(x)=\frac{n!}{(n-r)!}x^{n-r}.

[3]

The best questions are still waiting

Unlock every question in this topic, then type, photograph or draw your answer and have it marked against the markscheme. Find out where you are dropping marks.

Unlock all questions Compare Student and Student Plus