Matrix addition, multiplication. Finding inverse. Determinants. Systems of equations.

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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.

Finding the exVAT price

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Finding the cost including VAT

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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.

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

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

Finding probabilities using the Poisson distribution.

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. 

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

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

Find $\displaystyle \int \frac{a}{(bx+c)^n}\;dx$

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

Using simple substitution to find $\lim_{x \to a} bx+c$, $\lim_{x \to a} bx^2+cx+d$ and $\displaystyle \lim_{x \to a} \frac{bx+c}{dx+f}$ where $d\times a+f \neq 0$.

Find $\displaystyle \int \frac{a}{(bx+c)^n}\;dx$

Given two complex numbers, find by inspection the one that is a root of a given quartic real polynomial and hence find the other roots. 

Finding the distance between two complex numbers using the modulus of their difference. Three parts.

Finding the stationary points of a cubic with two turning points

Finding the stationary points of a cubic with two turning points

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

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

Write down the Newton-Raphson formula for finding a numerical solution to the equation $e^{mx}+bx-a=0$. If $x_0=1$ find $x_1$.

Included in the Advice of this question are:

6 iterations of the method.

Graph of the NR process using jsxgraph. Also user interaction allowing change of starting value and its effect on the process.

Write down the Newton-Raphson formula for finding a numerical solution to the equation $e^{mx}+bx-a=0$. If $x_0=1$ find $x_1$.

Included in the Advice of this question are:

6 iterations of the method.

Graph of the NR process using jsxgraph. Also user interaction allowing change of starting value and its effect on the process.

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Finding the confidence interval at either 90%, 95% or 99% for the mean given the mean of a sample. The population variance is given and so the z values are used. Various scenarios are included.