29 results authored by Evi Papadaki - search across all users.

### Refine by Refine by

• #### Topics

• Question

Solving a separable differential equation that describes the rate of decay of radioactive isotopes over time with a known initial condition to calculate the mass of the isotope after a given time and the time taken for the mass to reach $m$ grams.

Decay Constant - Radioactivity - Nuclear Power (nuclear-power.com)

• Natural Sciences
Exam (20 questions)

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

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

Using given information to complete the equation $c= A \cos{ \left( \frac{2 \pi}{P} \left( t-H \right) \right) }+V$ that describes the concentration, $c$, of perscribed drug in a patient's drug over time, $t$. Calculating the maximum concentration and the concentration at a specific time.

• Question

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.

• Question

Using basic derivatives to calculate the gradient function of a hill $y=-e^{x}+b\ln{\left(x\right)+c$, and then substituting values to find the gradient at specific distance from the sea.

• Question

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.

• Question

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.

• Question

Calculating area under curves of the form $ax^2+bx$ and $ax^4+bx^3+cx^2+dx+e$ in a contextualised problem.

• Question

Finding the stationary point (maximum) of a quadratic equation in a contextualised problem.

• Question

Calculating the gradient of a quadratic equation at a specific point and finding the stationary point (maximum) in a contextualised problem.

• Question

The relationship between the frequency of an allele A, $x$, at a genetic locus in a diploid population and the fitness of a population with this frequency of allele A, $w$, is described by the function $w=ax^2+x(b-x)+c(b-x)^2$ . The aims are (a) ti simplify the algebraic expression, (b) calculate the fitness of a population with a given allele A frequency, and (c) calculate the allele A frequency when the fitness of the population is given.

• Question

The proportion of the sodium carbonate, $p$, which has dissolved by time $t$ seconds is given by the formula $p=\frac{bt-at^2}{c}$. The aim is to calculate the proportion of sodium carbonate in a solution at a given time and vice versa.

• Question

Estimating the proportion of sodium carbonate in a solutionat a specific timepoint and vice versa, depicted as a quadratic graph.

• Question

Practicing skills required for sketching line graphs depicting the temperature of a mixture according to time. The question includes: a) choosing the accurate sketch from a list, and b) identifying the initial temperature of the mixture.

• Question

Practicing skills required for sketching line graphs depicting DNA melting temperature according to the percentage of GC content. The question includes: a) identifying the  vertical intercept, b) choosing the accurate sketch from a list, and c) interpreting elements of the sketch in context.

• Question

Interpreting line graphs depicting the melting temperature of DNA depending on the percentage of GC content. Estimating the melting temperature given a GC percentage and vice versa.

• Question

Interpreting line graphs depicting the decrease of temperature in a mixture over time. Estimating the temperature of the mixture at a given time point and vice versa.

• Exam (4 questions)

No description given

• Question

Using the given information to complete the equation $y= A \cos{ \left( \frac{2 \pi}{P} x \right) }+V$ that describes an electromagnetic wave and calculating the smallest angle, $x$, for which $y=y_0$.

• Question

Solving a separable differential equation that describes the population growth over time with a known initial condition to calculate the population after $n$ years.

• Question

Integrating a polynomial functions which describe the rate of change of a population over time to find and use an equation that describes the total population according to time.

• Question

The question includes a quadratic graph depicting the relationship between the frequency of an allele A at a genetic locus in a diploid population and the fitness of a population with this frequency of allele A. The aim is to estimate the maximum and minimum fitness of the population and the corresponding frequency of allele A.

• Trigonometry
Draft
Exam (2 questions)

No description given

Draft
Exam (4 questions)

No description given

• Integration
Draft
Exam (2 questions)

No description given

• Exam (2 questions)

No description given

• Exam (2 questions)

No description given

• Exam (2 questions)

No description given

• Exam (2 questions)

No description given