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Create your own Questions for Revision

  1. Sep 12, 2016 #1
    This is an idea I've been thinking of for a while. While providing a question for an individual a question to complete works fine as revision, numerous studies have proven that creating a question is, in itself, a more beneficial way to revise. Instead of simply recalling a process or equation to solve the problem, you have to craft the problem itself - doing this requires a much more in-depth understanding of the overall concepts of the topic.

    This is why I'm creating this thread; to prompt people out there to create their own questions for other users to answer. Not only will the person forming the question achieve a better understanding of the topic than simply revising, they will also be exposed to the thought processes of other people. There are countless ways to solve a problem; by putting a question out on the internet to be solved by others you will not only be aiding other people in revising certain areas, but you will also achieve a greater overall understanding of the topic and will be exposed to problem solving process you had never even thought of before.

    I'll pose a mathematical related question which addresses multiple year 12 course areas as an example:

    Question

    A function, ##f(x)=2ax^3-a^2x## intersects its inverse at the origin, point ##S(-b,f(-b))## and point ##T(b,f(b))##. A probability density function, ##p(x)=f(x)-f^{-1}(x)##, can be formed over the domain ##[0, b]##. Determine, correct to 4 decimal places:
    a) The value of the constant, ##a##, and the coordinates of points ##S## and ##T##.
    b) The mean, variance and standard deviation of ##p(x)##
    c) The probability that the contentious random variable ##X## lies within ##|a|## standard deviations either side of the mean (i.e. ##Pr(μ-|a|σ≤X≤μ+|a|σ)##)

    Answers
    a) ##a=-0.2253, S\left(-1.4515,\ 1.4515\right),\ T\left(1.4515,\ -1.4515\right)##
    b) ##μ=0.6692, Var(X)=0.5673,## ##σ=0.7532##
    c) ##Pr(μ-|a|σ≤X≤μ+|a|σ)=0.3147##
     
  2. jcsd
  3. Sep 13, 2016 #2

    Andy Resnick

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    2016 Award

    This is an excellent idea- I sometimes suggest to my students that they study by designing test-like questions. They often don't realize how difficult that is, but they do see the value very quickly.
     
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