311 results authored by Simon Thomas  search across all users.

Question in Simon's workspaceUsing the midordinate rule with 5 ordinates to approximate $\int_a^b{c^x}$

Question in Simon's workspaceUsing the trapezium rule with 6 ordinates to approximate $\int_a^b{c^x}$

Question in Simon's workspaceUsing the trapezium rule with 5 ordinates to approximate $\int_a^b{1/(x^2+c)}$

Question in Rebelmaths and similarCalculate d2y/dx2 for a curve defined parametrically

Question in Rebelmaths and similarFind the equation of the tangent to a curve defined parametrically

Question in Rebelmaths and similarCalculate dy/dx for a curve defined parametrically

Question in Calculus
Find $\displaystyle \frac{d}{dx}\left(\frac{m\sin(ax)+n\cos(ax)}{b\sin(ax)+c\cos(ax)}\right)$. Three part question.

Exam (2 questions) in Rebelmaths and similar
Find the first few terms of the Maclaurin and Taylor series of given functions.

Question in Rebelmaths and similar
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 $\phi$.

Question in Rebelmaths and similar
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 $\phi$.

Question in Rebelmaths and similar
Reduce a 5x6 matrix to row reduced form and using this find rank and nullity.

Question in Rebelmaths and similar
Choose which of 5 matrices are in a) row echelon form but not reduced b) reduced row echelon form c) neither.

Question in Rebelmaths and similar
Given the following three vectors $\textbf{v}_1,\;\textbf{v}_2,\;\textbf{v}_3$ Find out whether they are a linearly independent set are not. Also if linearly dependent find the relationship $\textbf{v}_{r}=p\textbf{v}_{s}+q\textbf{v}_{t}$ for suitable $r,\;s,\;t$ and integers $p,\;q$.

Question in Rebelmaths and similar
Given $5$ vectors in $\mathbb{R^4}$ determine if a spanning set for $\mathbb{R^4}$ or not by looking for any simple dependencies between the vectors.

Question in Rebelmaths and similar
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 $a,\;b,\;c,\;d$.

Question in Rebelmaths and similar
$A$ a $3 \times 3$ matrix. Using row operations on the augmented matrix $\left(A  I_3\right)$ reduce to $\left(I_3  A^{1}\right)$.

Question in Rebelmaths and similar
Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

Question in Rebelmaths and similar
$A,\;B$ $2 \times 2$ matrices. Find eigenvalues and eigenvectors of both. Hence or otherwise, find $B^n$ for largish $n$.

Question in Rebelmaths and similar
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Simon's copy of Pigeonhole principle  greatest number of people with birthdays in the same month, DraftQuestion in Rebelmaths and similar
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Question in Rebelmaths and similar
Rationalise the denominator with increasingly difficult examples involving compound denominators.

Question in Rebelmaths and similar
This question tests the student's understanding of what is and is not a surd, and on their simplification of surds.

Question in Rebelmaths and similar
Manipulate surds and rationalise the denominator of a fraction when it is a surd.

Question in Stats
The human resources department of a large finance company is attempting to determine if an employee’s performance is influenced by their undergraduate degree subject. Personnel ratings are used to judge performance and the task is to use expected frequencies and the chisquared statistic to test the null hypothesis that there is no association.

Question in Simon's workspace
Given two sets of data, sample mean and sample standard deviation, on performance on the same task, make a decision as to whether or not the mean times differ. Population variance not given, so the t test has to be used in conjunction with the pooled sample standard deviation.
Link to use of t tables and pvalues in Show steps.