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When are vectors $\boldsymbol{v,\;w}$ orthogonal?

set up x- and y axises.

set linear equations and solve the simulatenous equations.

Calculating particular harmonic components of a Fourier series expansion.

6 questions which introduce the user to the Numbas system.

Manipulation of algebraic fractions

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Fixed base. Chain base. Laspeyres Price and Quantity. Paache Price and Quantity. Interpretation. 

Given vectors $\boldsymbol{A,\;B}$, find $\boldsymbol{A\times B}$

Questions on vector arithmetic and vector operations, including dot and cross product, as well as the vector equations of planes and lines.

Given vectors $\boldsymbol{A,\;B}$, find $\boldsymbol{A\times B}$

Given vectors $\boldsymbol{v}$ and $\boldsymbol{w}$, find their inner product.

Given vectors  $\boldsymbol{v,\;w}$, find the angle between them.

Content: complex arithmetic; argument and modulus of complex numbers; de Moivre's theorem.

This homework counts 10% towards your final Engineering Mathematics mark.

Displacement-time graphs are given and the student should select the correct velocity-time graphs from a list. Includes linear, piecewise linear and quadratic displacement-time functions.

Demonstrates that the marking algorithm for "match text pattern" parts doesn't put quotes around substituted strings any more.

Simplifying algebraic expressions

Solve for $x$: $\displaystyle 2\log_{a}(x+b)- \log_{a}(x+c)=d$. 

Make sure that your choice is a solution by substituting back into the equation.

Solve for $x$: $\displaystyle 2\log_{a}(x+b)- \log_{a}(x+c)=d$. 

Make sure that your choice is a solution by substituting back into the equation.

Find the common ratio of a given geometric sequence, write down the formula for the nth term and use it to calculate a given term in the sequence.

A simultaneous equations question with integers only

Simplifying algebraic expressions

Factorising polynomials using the highest common factor

Multiplication of $2 \times 2$ matrices.

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

Forenkling av algebraiske uttrykk

Questions on manipulating logarithms.

Elementary examples of multiplication and addition of complex numbers. Four parts.

Simplifying expressions such as $b^{\log_b(x)}$ and $b^{\log_b(x)}$.

Questions on manipulating logarithms.