Given the first three terms of a sequence, give a formula for the $n^\text{th}$ term.

In the first sequence, $d$ is positive. In the second sequence, $d$ is negative.

Given sequences with missing terms, find the common difference between terms.

Given the first few terms of an arithmetic sequence, write down its formula, then find a couple of particular terms.

Finding the exVAT price

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Finding the cost including VAT

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Find the exVAT price

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Given the cost and profit, find the selling price

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(Calculating estimate and actual value of temperature using given formulas, and hence finding the percentage error)

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Application of the binomial distribution given probabilities of success of an event.

Finding probabilities using the binomial distribution.

Using trig identities to find solutions to equations

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Given a 3 x 3 matrix, and two eigenvectors find their corresponding eigenvalues. Also fnd the characteristic polynomial and using this find the third eigenvalue and a normalised eigenvector $(x=1)$.

The random variable $X$ has a PDF which involves a parameter $c$. Find the value of $c$. Find the distribution function $F_X(x)$ and $P(a \lt X \lt b)$.

Also find the expectation $\displaystyle \operatorname{E}[X]=\int_{-\infty}^{\infty}xf_X(x)\;dx$.

Finding the coordinates and determining the nature of the stationary points on a polynomial function

Find the dot product and the angle between two vectors

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

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Find the solution of a constant coefficient second order ordinary differential equation of the form $ay''+by'+cy=0$.

Find the determinant and inverse of three $2 \times 2$ invertible matrices.

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

Finding probabilities using the Poisson distribution.

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

Application of the binomial distribution given probabilities of success of an event.

Finding probabilities using the binomial distribution.

Question on the exponential distribution involving a time intervals and arrivals application, finding expectation and variance. Also finding the probability that a time interval between arrivals is less than a given period. All parameters and times randomised. 

Normal distribution $X \sim  N(\mu,\sigma^2)$ given. Find $P(a \lt X \lt b)$. Find expectation, variance, $P(c \lt \overline{X} \lt d)$ for sample mean $\overline{X}$.

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Two ordered data sets, each with 10 numbers. Find the sample standard deviation for each and for their sum.

Two ordered data sets, each with 10 numbers. Find the sample standard deviation for each and for their sum.

Finding unknown sides/angles in right-angled triangles.

Version 1: b,c known

Version 2: a,x known

Version 3: a,y known

Version 4: b,x known

Version 5: b,a known

Version 6: c,a known

Finding unknown sides/angles in right-angled triangles.

Version 1: b,c known

Version 2: a,x known

Version 3: a,y known

Version 4: b,x known

Version 5: b,a known

Version 6: c,a known

Finding unknown sides/angles in right-angled triangles.

Version 1: b,c known

Version 2: a,x known

Version 3: a,y known

Version 4: b,x known

Version 5: b,a known

Version 6: c,a known

Finding unknown sides/angles in right-angled triangles.

Version 1: b,c known

Version 2: a,x known

Version 3: a,y known

Version 4: b,x known

Version 5: b,a known

Version 6: c,a known