Real numbers $a,\;b,\;c$ and $d$ are such that $a+b+c+d=1$ and for the given vectors $\textbf{v}_1,\;\textbf{v}_2,\;\textbf{v}_3,\;\textbf{v}_4$ $a\textbf{v}_1+b\textbf{v}_2+c\textbf{v}_3+d\textbf{v}_4=\textbf{0}$. Find $a,\;b,\;c,\;d$.

Convert numbers greater than 1 into standard form/scientific notation.

Decide whether statements about square and cube numbers are always true, sometimes true or never true.

German translation of https://numbas.mathcentre.ac.uk/question/22768/always-sometimes-or-never-square-and-cube-numbers/ von Stanislav Duris.

Details on inputting numbers into Numbas. (German translation)

Find the number of people with heights greater then mean plus two times the standard deviation.

This exercise will help you round off decimals to given decimal places.

This exercise will help you round off decimals to given decimal places.

Entering numbers and algebraic symbols  in Numbas. (German translation)

Find the missing whole number power in an equation.

Multiplication and addition of complex numbers. Four parts.

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. 

Given the period of a repeating function, determine the number of repeats in a given amount of time. Part of HELM Book 2.4.

A demo of the number entry part and its options.

Simultaneous equations question. values for the coefficients are generated to be small numbers, random values are generated for the weights and the resultant energies are calculated for the question. Student needs to solve equations to find coefficients. Advice gives solution using method of elimination.

Given some random finite subsets of the natural numbers, perform set operations $\cap,\;\cup$ and complement.

No description given

The number of patients arriving at a dentist’s surgery each afternoon follows
a Poisson distribution, with a mean of four patients per hour.
Calculate the probability that in a particular one-hour period

Application of the Poisson distribution given expected number of events per interval.

Finding probabilities using the Poisson distribution.

rebelmaths

convert large numbers to scientific notation

NC NA Non-calculator and Number and Algebra strand. This number assesses students' ability to add and subtract very simple fractions. Students need two add two fractions (possibly mixed numbers) involving quarters and/or halves, then subtract their answer from a whole number. The answer must be entered in simplest form and will always be less than one.

Several problems involving dividing fractions, with increasingly difficult examples, including mixed numbers and complex fractions. 

This question tests the student's ability to identify equivalent fractions through spotting a fraction which is not equivalent amongst a list of otherwise equivalent fractions. It also tests the students ability to convert mixed numbers into their equivalent improper fractions. It then does the reverse and tests their ability to convert an improper fraction into an equivalent mixed number. 

Add, subtract, multiply of divide two mixed numbers. This question has no advice at this stage.

Several problems involving dividing fractions, with increasingly difficult examples, including mixed numbers and complex fractions. 

Simple questions on square numbers, square roots, cube number, cube roots and prime numbers.

No description given

No description given

No description given

Round random numbers to the closest whole number, 1, 2 or 3 decimals places.