Search - Numbas at mathcentre.ac.uk

1076 results for "number".

Find point when a sequence becomes strictly decreasing
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

$x_n=n^k t^n$ where $k$ is a positive integer and $t$ a real number with $0 < t<1$ . Find the smallest integer $N$ such that $(m+1)^k t^{m+1} \leq m^k t^m$ for all $m \geq N$ .
Input 1 PSY
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Entering numbers in Numbas, Part 1.
Input 2 PSY
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Details on inputting numbers into Numbas.
Approximate the integral of a quadratic by Riemann sums,
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Approximating integral of a quadratic by Riemann sums . Includes an interactive graph in Advice showing the approximations given by the upper and lower sums and how they vary as we increase the number of intervals.
Calculate probabilities from frequency table
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Simple probability question. Counting number of occurences of an event in a sample space with given size and finding the probability of the event.
Calculate relative percentage frequencies from table of data
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Given a table of the number of days in which sales were between £x1000 and £(x+1)1000 find the relative percentage frequencies of these volume of sales.
Compute Riemann sums of a linear function,
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Approximating integral of a linear function by Riemann sums . Includes an interactive graph in Advice showing the approximations given by the upper and lower sums and how they vary as we increase the number of intervals.
Compute Riemann sums of a linear function,
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Approximating integral of a linear function by Riemann sums . Includes an interactive graph in Advice showing the approximations given by the upper and lower sums and how they vary as we increase the number of intervals.
Construct stem and leaf plot
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Given random set of data (between 13 and 23 numbers all less than 100), find their stem-and-leaf plot.
Decide whether pairs of events are independent,
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Independent events in probability. Choose whether given three given pairs of events are independent or not.
Find and use linear regression equation for a small sample
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find a regression equation.
Factorise four numbers
Doesn't work
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

Pick four numbers from $1900\dots 2015$ and ask the student to factorise them.

Custom marking scripts make sure the student has entered a complete factorisation.
Factorise numbers into products of prime powers
Doesn't work
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Factorising 5 to 7 digit numbers into a product of prime powers.

Uses the marking algorithms from question 1 of this CBA
Find $\mu(n)$ , $\sigma(n)$ , $\tau(n)$ , $\phi(n)$
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Number Theory.

Given $n \in \mathbb{N}$ find $\mu(n),\;\tau(n),\;\sigma(n),\;\phi(n).$
Find all numbers with given value of $\phi(n)$
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Given $\frac{a}{b} \in \mathbb{Q}$ for suitable choices of $a$ and $b$ , find all $n \in \mathbb{N}$ such that $\phi(n)=\frac{a}{b}n$ .
Find n such that $\sigma(n)$ is the given number
Needs to be tested
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

Given $m \in \mathbb{N}$ , find values of $n\in \mathbb{N}$ such that $\sigma(n)=m$ .

There are at most two such solutions in this question.
Find the smallest $n$ with given number of divisors
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Given $m \in \mathbb{N}$ , find the smallest natural number $n \in \mathbb{N}$ with $\tau(n)=m$ divisors.
Find sample standard deviations of two samples
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Two ordered data sets, each with 10 numbers. Find the sample standard deviation for each and for their sum.
Multiple and partial correlation(old)
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Multiple correlation question. Given the correlation coefficent of $Y$ with $X_1$ is $r_{01}$ , the correlation coefficent of $Y$ with $X_2$ is $r_{02}$ and the correlation coefficent of $X_1$ with $X_2$ is $r_{12}$ then explain the proportion of variablity of $Y$ . Also find the partial corr coeff between $Y$ and $X_2$ after fitting $X_1$ and find how much of the remaining variability in $Y$ is explained by $X_2$ after fitting $X_1$ .
Multiply 2x2 matrices
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Multiplication of $2 \times 2$ matrices.
Probability - draw without replacement
Doesn't work
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

A box contains $n$ balls, $m$ of these are red the rest white.

$r$ are drawn without replacement.

What is the probability that at least one of the $r$ is red?
Probability - sum of two numbers drawn without replacement
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Two numbers are drawn at random without replacement from the numbers m to n.

Find the probability that both are odd given their sum is even.
Sample standard deviation
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Two ordered data sets, each with 10 numbers. Find the sample standard deviation for each and for their sum.
Number theory and cryptography
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Exam (18 questions) in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Questions used in a university course titled "Number theory and cryptography"
Find expected profit of gambles,
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Given a large number of gambles, find the expected profit.
Maclaurin series (three terms)
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find the first 3 terms in the MacLaurin series for $f(x)=(a+bx)^{1/n}$ i.e. up to and including terms in $x^2$ .
Represent a linear map as a matrix given a basis
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Let $P_n$ denote the vector space over the reals of polynomials $p(x)$ of degree $n$ with coefficients in the real numbers. Let the linear map $\phi: P_4 \rightarrow P_4$ be defined by: $\phi(p(x))=p(a)+p(bx+c).$ Using the standard basis for range and domain find the matrix given by $\phi$ .
Represent a linear map as a matrix with a given basis
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Let $P_n$ denote the vector space over the reals of polynomials $p(x)$ of degree $n$ with coefficients in the real numbers.

Let the linear map $\phi: P_4 \rightarrow P_4$ be defined by:

$\phi(p(x))=ap(x) + (bx + c)p'(x) + (x ^ 2 + dx + f)p''(x)$

Using the standard basis for range and domain find the matrix given by $\phi$ .
Indefinite integration using standard integrals
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Integrate $f(x) = ae ^ {bx} + c\sin(dx) + px^q$ . Must input $C$ as the constant of integration.
Integration: Indefinite integral
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find $\displaystyle \int ax ^ m+ bx^{c/n}\;dx$ .

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