Simon Thomas

Linear combinations of $2 \times 2$ matrices. Three examples.

Cofactors Determinant and inverse of a 3x3 matrix.

Given two 3 dim vectors, find vector equation of line through one vector in the direction of another. Find two such lines and their point of intersection.

Find a unit vector orthogonal to two others.

Uses $\wedge$ for the cross product. The interim calculations should all be displayed to enough dps, not 3,  to ensure accuracy to 3 dps. If the cross product has a negative x component then it is not explained that the negative of the cross product is taken for the unit vector.

Given vectors  $\boldsymbol{v,\;w}$, find the angle between them.

Given vectors $\boldsymbol{a,\;b}$, find $\boldsymbol{a\times b}$

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Find the dot product and the angle between two vectors

angle between two vectors

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Given vectors $\boldsymbol{v}$ and $\boldsymbol{w}$, find their inner product.

Elementary operations on vectors; sum, modulus, unit vector, scalar multiple. 

Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

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Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

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Printing errors in the work produced by a particular film occur randomly at an average rate of p per page.

i.What is the probability that a one page document will contain x1 printing error(s)?

ii.If a n page document is printed, calculate the probability of having more than x2 errors. Assume a Poisson distribution.

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Printing errors in the work produced by a particular film occur randomly at an average rate of p per page.

i.What is the probability that a one page document will contain x1 printing error(s)?

ii.If a n page document is printed, calculate the probability of having more than x2 errors. Assume a Poisson distribution.

It is estimated that 30% of all CIT students cycle to college. If a random sample of eight CIT students is chosen, calculate the probability that...

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$X \sim \operatorname{Binomial}(n,p)$. Find $P(X=a)$, $P(X \leq b)$, $E[X],\;\operatorname{Var}(X)$.

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Calculate the Pearson correlation coefficient on paired data and comment on the significance.

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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.

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Summation Notation

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Scores  in 20 games and frequency given -- calculate mean.

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Scores (including negatives)  in 20 games and frequency given -- calculate mean.

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Algebra word problems using area and perimeter.

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Calculating wages using algebraic equations

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