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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.
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Last modified 04/02/2019 15:38
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Last modified 28/01/2019 13:49
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Find partial derivatives of $f(x,y)$ and identify its stationary points
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
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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
Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.
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Last modified 15/10/2018 20:07
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Find gradient of scalar field
Gradient of $f(x,y,z)$.
Should include a warning to insert * between multiplied terms
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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 $f: D \rightarrow \mathbb{R}$: $f(x,y) = a + be^{(xc)^2(yd)^2}$, $D$ is a disk centre $(c,d)$.
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Last modified 15/10/2018 19:23
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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 $\displaystyle I=\int_0^1\;dx\;\int_0^{x^{m1}}mf(x^m+a)dy$
The $y$ integral is trivial, and the $x$ integral is of the form $g'(x)f'(g(x))$, so it straightforwardly integrates to $f(g(x))$.
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Last modified 11/10/2018 16:45
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Double integral  limit is a polynomial
3 Repeated integrals of the form $\int_a^b\;dx\;\int_c^{f(x)}g(x,y)\;dy$ where $g(x,y)$ is a polynomial in $x,\;y$ and $f(x)$ is a degree 0, 1 or 2 polynomial in $x$.
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Last modified 11/10/2018 16:34
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Student must pick all correct choices, and gets nothing otherwise
A "match choices with answers" part where the student either gets all the marks or none. Any incorrect choice is penalised with a huge negative mark, so they end up with the minimum mark of 0.