Hell as algebra

It is both sad and maddening.  If you listen to atheists and even many Christians, God is a homicidal tyrant, ever waiting to damn us to hell, if we don't behave exactly right.
I have been interacting with some atheists as of late and have been trying to clarify the Orthodox position.  And I came up with an analogy.
Imagine you are in high school algebra class.  You are one of those students who sleeps through most classes, never studies and rarely does homework.  Your teacher warns you over and over but you don't listen.  The semester comes to an end, you miserably fall the final exam and you receive a failing grade. Whose fault is it?
So too our earthly life.  We have been born into life, free of charge and we receive instruction, daily. If we choose to pay attention, do what is required to learn and God examines us and finds that we have worked out our salvation, we can come into the glorious presence of God.  If we fail, it's not God's fault.  If we have not prepared our souls for eternity, we have no one to blame but ourselves.
Jesus did his work of freeing us from the power of sin and death, we need to work out our salvation and sanctify our lives, purifying our souls.