Hi Mike! For practise test 2, section 3 Q6, how exactly could I use backsolving to solve this? Lets say I start with C and I plug in 8. My gradient of line l is 2/5. If I plug in p as 8, I’m getting gradient of line k as 4/8. Do I now compare the fractions? How do I know if I should try plugging in a bigger or smaller number to get closer towards 2/5 (initial gradient)?


Right, you’re comparing the fractions. (Of course, this requires you to know that parallel lines have the same slope.)

To decide which direction to go, recognize that \dfrac{4}{8}=\dfrac{1}{2} is bigger than \dfrac{2}{5}. You need your fraction to get smaller. Since the value you’re playing with is p, which is in the denominator, you make the fraction smaller by increasing the denominator.

A couple notes:

  1. Generally speaking, don’t spend too much time trying to figure out which answer choice to try next if it’s not obvious. It’s probably faster just to guess at which direction to go and see if you get closer or farther away from where you want to be!
  2. Just because I say a problem CAN be solved by backsolving doesn’t mean I’m saying that backsolving is the best way for that problem. I just want you to train yourself to recognize how often it’s possible to backsolve so that when you encounter a problem that can be backsolved on test day, you’re not blind to the possibility.

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