IBDP Maths AI HL Predicted Paper 1 - IB Maths AI Predicted Papers

Question 1

A geometric sequence has first term $162$ and common ratio $r$ ( $r>0$ ).

Part a

[2]

Find $S_{\infty}$ in terms of $r$ .

Part b

[2]

Given that $S_5=160$ , find $r$ .

Part c

[2]

Hence find $S_{\infty}$ .

[6]

The Argand diagram shows the interior of the circle centred at $3$ on the real axis with radius $2$ .

Let $C_2={,z\in\mathbb{C}:|z-3|\le 2,}$ .

Part a

[2]

Write $C_2$ as an inequality in $x$ and $y$ , where $z=x+iy$ .

Part b

[1]

From the diagram, state the maximum and minimum values of $\mathrm{Re}(z)$ on the boundary.

Part c

[2]

Find the range of $\arg(z-3)$ for points on the boundary above the real axis.

Part d

[2]

A point $w$ lies in $C_2$ with $\arg(w-3)=\pi/6$ and $\mathrm{Im}(w)>0$ . Find the largest possible value of $|w|$ .

[7]

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