IBDP Maths AA HL Predicted Paper 2 - IB Maths AA Predicted Papers

Question 1

Let $f(x)=\ln(2x-1)$ and $g(x)=\frac{x}{2}-1$ , with domain $x>\frac12$ .

Part a

[2]

Use your GDC to solve $f(x)=g(x)$ . Give your answer for $x$ to $3$ s.f.

Part b

[2]

Find $f'(x)$ . Hence find the gradient of the tangent to $y=f(x)$ at the solution found in part (a), giving your answer to $3$ s.f.

Part c

[2]

Hence write the equation of this tangent in the form $y=mx+c$ , with $m$ and $c$ to $3$ s.f.

[6]

An Argand diagram shows a filled disk of radius $2$ centred at $3+0i$ . Use it for parts (a)–(c).

Let $C$ be the region shown.

Part a

[1]

Describe $C$ as a set: $C={z\in\mathbb{C}:\dots}$ .

Part b

[2]

From the diagram, state the ranges of $\Re(z)$ and $\Im(z)$ for $z\in C$ .

Part c

[3]

Let $B$ be the boundary circle $|z-3|=2$ . Find $\min_{z\in B}|z|$ and the point(s) where it occurs.

[6]

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