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Differentiating the natural logarithm

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These questions deal with vector operations and its application in geology.

Application of differentitaion in geology. A projectile problem.

Skills Audit for Maths and Stats for module BIS123 students.

Skills Audit for Maths and Stats for module BIS110 students.

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A portfolio of NUMBAS questions created for first year Natural Sciences students. The questions cover the topics: 

• Linear functions
• Quadratic functions
• Differentiation
• Integration
• Explonatial and logarithms 
• Further differentiation
• Further Integration
• Trigonometric Functions

Knowing the doubling time of a population and the population on day $t$, calculate the initial population and the number of days required for the population to reach a threshold. 

Asked to define a function term, e.g. domain, or x(t). Part of HELM book 2.2.1.

Calculating the rate of change of the temperature during a chemical reaction using the chain rule in a function of the form $T=ate^{-t}$, and finding the maximum temperature of the reaction.

Knowing the half-life of Carbon-14 and the initial mass of Carbon-14 when a tree was cut (a) write an expression that describes the relationship between the remaining mass and time, (b) calculate the remaining mass after $t$ years, and (c) given the remaining mass calculate how many years ago the tree was cut down. 

Asks students to apply laws of logical equivalence to prove the equivalence between two logical statements. The quiz should accept any correct answer (as long as each step is included, with one law per step), and provides detailed feedback on mistakes.

The expected answer involves the logarithm of a negative number, which doesn't have a unique solution.

The part's marking algorithm evaluates the exponential of the student's answer and the expected answer, and compares those.

The expected answer involves the logarithm of a negative number, which doesn't have a unique solution.

The part's marking algorithm checks that the student's answer differs from the expected answer by a multiple of $2\pi$.

Given an equation where x is the base of a log term, the student must solve for x. Hints are included in the question to aid the student as needed.

Given an equation with log terms added together, the student must solve for x. Hints are included in the question to aid the student as needed.

Given an equation with log terms added together, the student must solve for x. Hints are included in the question to aid the student as needed.

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Given a randomised log function select the possible ways of writing the domain of the function.

This question asks students to solve a discrete logarithm problem with Pollard's rho algorithm as exposed in the book "introduction to cryptography with open source software" by McAndrew.

Use laws for addition and subtraction of logarithms to simplify a given logarithmic expression to an arbitrary base.

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Differentiate $\displaystyle \ln((ax+b)^{m})$

Differentiating exponentials and Logs

Solve a logarithmic equation

Questions testing rather basic understanding of the index laws.

Use laws for addition and subtraction of logarithms to simplify a given logarithmic expression to an arbitrary base.