IBDP Maths AA HL Predicted Paper 1 sample

Questions

Part 1(a).

[3]

Solve $3^{2x} - 5\cdot 3^x + 6 = 0$ .

Part 1(b).

[2]

Hence find the exact value of $x$ satisfying $9^x = 54$ .

Part 1(c).

[1]

State the range of $f(x) = \log_{3}(x - 1)$ .

Prove by mathematical induction that $\sum_{k=1}^{n} k^{3} = \left[\frac{n(n+1)}{2}\right]^2$ for $n \in \mathbb{N}$ .

[5]

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