302 results authored by Christian Lawson-Perfect - search across all users.

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  • Christian's copy of De Moivre's Theorem: $n$th roots of a complex number

    by Picture of Christian Lawson-Perfect Christian Lawson-Perfect and 1 other

    Find modulus and argument of the complex number $z_1$ and find the $n$th roots of $z_1$ where $n=5,\;6$ or $7$.

    Question Draft

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    Last modified 02/04/2019 10:46

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  • Catch malrules

    Identify when the student gives an expected incorrect answer, and give appropriate feedback as well as partial marks.

    Question Draft

    CC BY Published

    Last modified 27/02/2019 13:02

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  • Write a formula based on a word statement and apply it to a given value

    Given a statement in words of a relationship between two variables, write down a corresponding formula. It's marked correct if values satisfying the relationship satisfy the formula, and values not satisfying the relationship don't.

    Then, given a value for one of the variables, work out the value of the other one. They're substituted into the formula given in the first part and marked correct if it's satisfied.

    Both parts use custom marking algorithms.

    Question Draft

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    Last modified 04/02/2019 15:38

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  • Volume of a swimming pool

    Work out the volume of a prism with a trapezium cross-section.

    Question Ready to use

    CC BY Published

    Last modified 28/01/2019 13:49

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  • Find partial derivatives of $f(x,y)$ and identify its stationary points

    by Picture of Christian Lawson-Perfect Christian Lawson-Perfect and 1 other

    Find the stationary points of the function: $f(x,y)=a x ^ 3 + b x ^ 2 y + c y ^ 2 x + dy$ by choosing from a list of points.

    Inputting the values given into the partial derivatives to see if 0 is obtained is tedious! Could ask for the factorisation of equation 1 as the solution uses this. However there is a problem in asking for the input of the stationary points - order of input and also giving that there is two stationary points.

    Question Has some problems

    CC BY Published

    Last modified 16/10/2018 16:39

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    Stage 1

  • Christian's copy of Gauss elimination to solve a system of linear equations

    by Picture of Christian Lawson-Perfect Christian Lawson-Perfect and 1 other

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

    Question Ready to use

    CC BY Published

    Last modified 15/10/2018 20:07

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  • Find gradient of scalar field

    by Picture of Christian Lawson-Perfect Christian Lawson-Perfect and 1 other

    Gradient of $f(x,y,z)$.

    Should include a warning to insert * between multiplied terms

    Question Has some problems

    CC BY Published

    Last modified 15/10/2018 19:32

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  • Find the stationary point of a function on a disk

    Find the coordinates of the stationary point for $f: D \rightarrow \mathbb{R}$: $f(x,y) = a + be^{-(x-c)^2-(y-d)^2}$, $D$ is a disk centre $(c,d)$.

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    Last modified 15/10/2018 19:23

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  • Evaluate double integrals with numerical limits

    Two double integrals with numerical limits

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    Last modified 11/10/2018 16:56

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  • Resolve a double integral

    Calculate a repeated integral of the form $\displaystyle I=\int_0^1\;dx\;\int_0^{x^{m-1}}mf(x^m+a)dy$

    The $y$ integral is trivial, and the $x$ integral is of the form $g'(x)f'(g(x))$, so it straightforwardly integrates to $f(g(x))$.

    Question Ready to use

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    Last modified 11/10/2018 16:45

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