This is from a post I made a few years ago. Doing these things helped me get high 90s hsc marks for maths subjects I did.
Often in these subjects people complain that they know the content however keep making silly mistakes. These are some ways to reduce errors;
- practice a lot and write in a note book about common silly mistakes you have done in questions in the past. Read through that before an exam to make sure those things are fresh in your mind
- use the quadratic formula instead of mentally factorising (only 1 source of error from you subbing in, while there is a potential for two errors in factorising as you need to make sure your factorised expression has the sum of the roots and product of roots.
- sub in the value when you solved an equation for example for in x^2=9 you get x=+3 or -3. So by subbing that value you found back into the original equation both sides of the equation should still hold true. A simple example but when you get to cubics and other bigger equations a helpful way to know you have got the correct anwser
- sub a random value into the starting expression and end expression when asked to simplify if the two aren’t equal you have made a mistake along the way, while if they are equal then you have correctly simplified. For example simplify y=(x^2-4)/(x-2) this becomes y=x+2 where x cannot equal -2. So sub in let’s say x=3 to them both for the first one you get 5 and for the second one also 5 so we know we have simplified it correctly
- for differentiation and integration doing the opposite to the answer you have found will give you the a original expression, another way to check you have performed the right calculus
- for graphs to check it’s right you can sub in values into a calculator on either side of the turning points to see which direction the graph continues in
These are just some of the techniques you can use to check errors
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