IB Maths AA HL 1.1 Scientific notation and extreme-scale reasoning Question Bank

Practise IB Maths AA HL 1.1 by analysing scientific notation and precision in multi-step calculations across extreme scales.

Exam points

Combine scientific-notation quantities in a multi-step calculation and retain the requested precision.
Use coefficient bounds and powers of ten to identify the largest or smallest possible product.
Evaluate rounding and significant-figure choices when reporting a result in scientific notation.

[Maximum number: 3]

In this question, you will investigate the maximum product of positive real numbers with a given sum.
Consider the two numbers $x_{1}, x_{2} \in \mathbb{R}^{+}$ , such that $x_{1}+x_{2}=12$ .

Use your answer to part (h) to find the largest possible product of positive numbers whose sum is 100 . Give your answer in the form $a \times 10^{k}$ , where $1 \leq a<10$ and $k \in \mathbb{Z}^{+}$ .

$\frac{100}{\mathrm{e}}=36.8 \quad$ M1
$\left(\frac{100}{36}\right)^{36}=9.3996 \ldots \times 10^{15}$ AND $\left(\frac{100}{37}\right)^{37}=9.47406 \ldots \times 10^{15}$
largest possible product is $9.47 \times 10^{15}\left(9.47406 \ldots \times 10^{15}\right)$

Note: Award A1 independently of the R1 (but not independently of the M1).

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SL 1.1—Scientific notation question 1