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IB Maths AI HL Sl 1 5 Integer Exponents and Logarithms Questions

Practise IB Maths AI HL 1.5 through questions that extend logarithms to parameters, exponential models, thresholds and multi-step reasoning.

Syllabus
First assessment 2021
Course
Mathematics: applications and interpretation HL
Level
HL

Exam points

  • Apply laws of integer exponents and logarithms to simplify, rearrange or compare expressions, including equivalent base-10 and natural-log forms.
  • Solve exponential and logarithmic equations, selecting valid bases, domains and parameter values.
  • Use logarithmic scales or inverse exponentials in contextual calculations such as pH, sound, brightness, information or decay.
  • Interpret the numerical solution, checking domain, units, scale and whether the model’s condition is satisfied.

IB Maths AI HL Sl 1 5 Integer Exponents and Logarithms Questions question 1

[Maximum number: 1]

This question is about applying ideas from logarithms, calculus and probability to an unfamiliar mathematical theory called information theory.
Claude Shannon developed a mathematical theory called information theory to measure the information gained when random events occur. He defined the information, I, that is gained when an event with probability p occurs as

I=−ln⁡pI=-\ln p

where 0<p≤10<p \leq 1. For example, no information is gained ( I=0 ) when an event is certain to occur⁡(p=1)\operatorname{occur}(p=1).

When a coin is flipped, the outcome is either heads or tails. The coin may be biased. Let p be the probability of the outcome being heads.

Find, in terms of p, the information gained when the outcome is tails.

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