IB Maths AA SL 5.4 Tangents and normals Question Bank

Practise IB Mathematics SL/HL 5.4 by applying tangents and normals methods to exam-style questions.

Exam points

identify the mathematical structure, variable or representation
select and apply the correct theorem, formula or algorithm
check the result using units, domain, graph or logical reasoning

[Maximum number: 6]

Consider the function $f(x)=\frac{2}{\pi} \sin (3 \pi x)+2$ , where $0 \leq x \leq 2$ . The following diagram shows the graph of f.

Figure for Question SL 5.4—Tangents and normals question 1 — IB Maths AA SL

(a)

Find the gradient of $L_{2}$ .

[ 3 ]

substituting their $m_{L_{1}}$ into $-\frac{1}{m_{L_{1}}}$

\left(m_{L_{2}}=\right)-6

(b)

Hence, or otherwise, find the equation of $L_{2}$ .

The line $L_{1}$ intersects the graph of f at another point B , where the x-coordinate of B is greater than 1.5 . This is shown in the following diagram.

Figure for Question (b) — IB Maths AA SL

[ 3 ]

All question bank results loaded

SL 5.4—Tangents and normals question 1

Question (a)

Question (b)