Henrik Skov Midtiby

Solve a pair of linear equations by writing an equivalent matrix equation.

6 questions which introduce the user to the Numbas system.

Questions about complex arithmetic; argument and modulus of complex numbers; complex roots of polynomials; de Moivre's theorem.

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

Find (hyperbolic substitution):
$\displaystyle \int_{b}^{2b} \left(\frac{1}{\sqrt{a^2x^2-b^2}}\right)\;dx$

Solve a system of linear equations using Gaussian elimination.

Two questions on solving systems of simultaneous equations.

Find the determinants of three $2 \times 2$ invertible matrices.

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

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

Questions which rely on knowledge of standard integrals.

Find an integral by choosing a suitable substitution.

Integrate the product of two functions by the method of integration by parts.

Integrate various functions by rewriting them as partial fractions.

Use the quotient rule to differentiate various functions.

Use the product rule to differentiate various functions.

Use the chain rule to differentiate various functions.

Questions on differentiation from first principles, and continuity and differentiability.

Questions about complex arithmetic; argument and modulus of complex numbers; complex roots of polynomials; de Moivre's theorem.

Solve a pair of linear equations by writing an equivalent matrix equation.

5 questions on indefinite integration. Includes integration by parts and integration by substitution.

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