Create your own Questions for Revision

1. Sep 12, 2016

Saracen Rue

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. $Pr(μ-|a|σ≤X≤μ+|a|σ)$)

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. Sep 13, 2016

Andy Resnick

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.