Antiderivatives

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Finding the stationary points of a cubic with two turning points

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Critical points, absolute minimum, local maximum and minimum points, increasing and decreasing, concavity

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Differentiating the natural logarithm

Some questions which use JSXGraph to create interactive graphics.

$A$ a $3 \times 3$ matrix. Using row operations on the augmented matrix $\left(A | I_3\right)$ reduce to $\left(I_3 | A^{-1}\right)$.

$A$ a $3 \times 3$ matrix. Using row operations on the augmented matrix $\left(A | I_3\right)$ reduce to $\left(I_3 | A^{-1}\right)$.

Differentiating the natural logarithm

Differentiating further exponentials

Questions on integration using various methods such as parts, substitution, trig identities and partial fractions.

This is a set of questions designed to help you practice adding, subtracting, multiplying and dividing fractions.

All of these can be done without a calculator.

Given a graph, the student is asked to determine the quadratic function.

Testing addition, multiplication and division involving negative numbers.

Show one of several blocks of text depending on the value of a question variable.

As well as a simple check for the value of a variable, the condition to display a block of text can be a complex expression in any of the question variables - in this example, depending on the discriminant of the generated quadratic.

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

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

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

aij  notation and definition of the order of a matrix.

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

Let $x_n=\frac{an+b}{cn+d},\;\;n=1,\;2\ldots$. Find  $\lim_{x \to\infty} x_n=L$ and find least $N$ such that $|x_n-L| \le 10^{-r},\;n \geq N,\;r \in \{2,\;3,\;4\}$.

Questions on differentiating with the chain rule and product rule.

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

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5 questions on definite integrals - integrate polynomials, trig functions and exponentials; find the area under a graph; find volumes of revolution.

Find $\displaystyle \int \frac{2ax + b}{ax ^ 2 + bx + c}\;dx$

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Express $f(z)$ in real-imaginary form, given that $z=x+iy$, where $f(z)$ involves hyperbolic functions.

Express $f(z)$ in real-imaginary form, given that $z=x+iy$.