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  • MathJax v3

    This exam uses a theme which uses MathJax v3 to typeset mathematics.

    Exam (1 question) Draft

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    Last modified 09/10/2019 15:35

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  • j's copy of Several variables corresponding to a scenario - Swansea

    by j hopkins and 2 others

    Choose from one of several pre-defined scenarios, and set variables to the corresponding values, defined in lists.

    This question has three variables: city, population, and percent_like_chocolate. These differ for each city. We've defined a list for each variable, with the corresponding values. A variable called scenario picks a random position in the list, so the value of city, for example, is cities[scenario].

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    Last modified 30/09/2019 14:59

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  • Basic Set Theory: power set

    by Picture of Daniel Mansfield Daniel Mansfield and 1 other

    Introductory exercise about power sets.

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    Last modified 29/09/2019 02:45

    • Pure mathematics
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  • Mark the product of two matrices in a mathematical expression part

    A mathematical expression part whose answer is the product of two matrices, $X \times Y$.

    By setting the "variable value generator" option for $X$ and $Y$ to produce random matrices, we can ensure that the order of the factors in the student's answer matters: $X \times Y \neq Y \times X$.

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    Last modified 24/09/2019 15:27

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  • Basic Set Theory: element not in a set

    by Picture of Daniel Mansfield Daniel Mansfield and 1 other

    Introductory exercise about subsets using custom grading code.

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    Last modified 23/09/2019 01:18

    • Pure mathematics
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  • GPUTC C&G 2850-202: Engineering Principles, Test 1 (v2)

    by Mark Jarrett and 3 others

    A set of MCQ designed to help Level 2 Engineering students prepare/practice for the on-line GOLA test that is used to assess the C&G 2850, Level 2 Engineering, Unit 202: Engineering Principles.

    Exam (40 questions) Ready to use

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    Last modified 16/09/2019 13:56

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  • Diff: Quotient rule - differentiate exponential over exponential

    by Timur Zaripov and 1 other

    The derivative of $\displaystyle \frac{a+be^{cx}}{b+ae^{cx}}$ is $\displaystyle \frac{pe^{cx}} {(b+ae^{cx})^2}$. Find $p$.

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    Last modified 11/09/2019 11:56

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  • Andreas's copy of MA100 MT Week 9

    by Andreas Vohns and 1 other

    This is the question for week 9 of the MA100 course at the LSE. It looks at material from chapters 17 and 18.

    Description of variables for part b:
    For part b we want to have four functions such that the derivative of one of them, evaluated at 0, gives 0; but for the rest we do not get 0. We also want two of the ones that do not give 0, to be such that the derivative of their sum, evaluated at 0, gives 0; but when we do this for any other sum of two of our functions, we do not get 0. Ultimately this part of the question will show that even if two functions are not in a vector space (the space of functions with derivate equal to 0 when evaluated at 0), then their sum could nonetheless be in that vector space. We want variables which statisfy:

    a,b,c,d,f,g,h,j,k,l,m,n are variables satisfying

    Function 1: x^2 + ax + b sin(cx)
    Function 2: x^2 + dx + f sin(gx)
    Function 3: x^2 + hx + j sin(kx)
    Function 4: x^2 + lx + m sin(nx)

    u,v,w,r are variables satifying
    u=a+bc
    v=d+fg
    w=h+jk
    r=l+mn

    The derivatives of each function, evaluated at zero, are:
    Function 1: u
    Function 2: v
    Function 3: w
    Function 4: r

    So we will define
    u as random(-5..5 except(0))
    v as -u
    w as 0
    r as random(-5..5 except(0) except(u) except(-u))

    Then the derivative of function 3, evaluated at 0, gives 0. The other functions give non-zero.
    Also, the derivative of function 1 + function 2 gives 0. The other combinations of two functions give nonzero.

    We now take b,c,f,g,j,k,m,n to be defined as \random(-3..3 except(0)).
    We then define a,d,h,l to satisfy
    u=a+bc
    v=d+fg
    w=h+jk
    r=l+mn

    Description for variables of part e:

    Please look at the description of each variable for part e in the variables section, first.
    As described, the vectors V3_1 , V3_2 , V3_3 are linearly independent. We will simply write v1 , v2 , v3 here.
    In part e we ask the student to determine which of the following sets span, are linearly independent, are both, are neither:

    both: v1,v2,v3
    span: v1,v1+v2,v1+v2+v3, v1+v2+v3,2*v1+v2+v3
    lin ind: v1+v2+v3
    neither: v2+v3 , 2*v2 + 2*v3
    neither:v1+v3,v1-2*v3,2*v1-v3
    neither: v1+v2,v1-v2,v1-2*v2,2*v1-v2

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    Last modified 11/09/2019 07:45

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  • Question Draft

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    Last modified 10/09/2019 14:01

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  • James's copy of Descriptive Statistics (P): Median

    Find the medians of two sets of data.

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    Last modified 10/09/2019 13:40

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