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Find the first few terms of the Maclaurin and Taylor series of given functions.

Multiple choice question. Given a randomised polynomial select the possible ways of writing the domain of the function.

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

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

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Find the first 3 terms in the Taylor series at $x=c$ for $f(x)=(a+bx)^{1/n}$ i.e. up to and including terms in $x^2$.

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Find the determinant of a $4 \times 4$ matrix.

Find the determinant of a $3 \times 3$ matrix.

Calculating the work done by 1 mole of an ideal gas at constant temperature.

Q12 from Thermochemistry revision sheet

Use the specific heat capacity of an object and the heat released to calculate the final temperature.

Custom marking used to allow for partial credit for common errors (mal rules)

Thermochemistry Revision Sheet Q7

Question steps student through the process of finding the molar heat of dissolution.

Adaptive marking and partial credit used

Thermochemistry Revision Sheet Q3

Basic rules of derivatives

Given a randomised log function select the possible ways of writing the domain of the function.

Rearranging equations to change the subject

Find the inverse of a composite function by finding the inverses of two functions and then the composite of these; and by finding the composite of two functions then finding the inverse. The question then concludes by asking students to compare their two answers and verify they're equivalent.

A few simple functions are provided of the form ax, x+b and cx+d. Values of the functions, inverses and compositions are asked for. Most are numerical but the last few questions are algebraic.

Substitute values into formulae for the area or volume of various geometric objects.

Given a randomised square root function select the possible ways of writing the domain of the function.

Given a randomised rational function select the possible ways of writing the domain of the function.

Multiple choice question. Given a randomised polynomial select the possibe ways of writing the domain of the function.

A graphical introduction to the concept of even functions a symmery

A graphical introduction to the concept of even functions a symmery

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