HSC Stuff > HSC Mathematics Advanced
Year 11 Revision
jakesilove:
--- Quote from: jamonwindeyer on July 17, 2016, 02:22:59 pm ---Hey!! No worries at all, it's a clever method that works the same every time.
So let us put x equal to the recurring decimal. Then, let us also consider 100x, you'll see why:
What we see here is that the recurring decimals actually line up with each other!! In general, we always consider x, and then x multiplied by 10 once for every recurring decimal. This has two, so we consider 100x. If it were 4, we'd consider 10,000x. That just guarantees the repeats will line up. Now, we subtract the first equation from the second, because everything after the decimal point cancels:
Basically, we've been clever and allowed subtraction to cancel out the recurrence!! From there we just simplify.
Edit: Rui gave a method as I finished typing this, but this sort of explains the methodology behind it ;)
--- End quote ---
Also; pro tip. You can just type a bunch of decimal places into you calculator and hit equals. Then, there is usually a decimal --> fraction converting button. Hit that and, if you're calculator is good enough, it will literally give you the answer. Maybe you use this to check your answer, maybe you use it to get the answer, up to you! Always cheat whenever you can.
Jake
jamonwindeyer:
--- Quote from: jakesilove on July 17, 2016, 03:42:15 pm ---Also; pro tip. You can just type a bunch of decimal places into you calculator and hit equals. Then, there is usually a decimal --> fraction converting button. Hit that and, if you're calculator is good enough, it will literally give you the answer. Maybe you use this to check your answer, maybe you use it to get the answer, up to you! Always cheat whenever you can.
Jake
--- End quote ---
OMG no way!! Awesome. Although you'd probably need working out for marks ;)
mfjw:
Thanks so much for all your explanations! It's really helpful and easy to understand :)
I'm having trouble understanding Difference of Two Squares and Perfect Squares? My Maths teacher says it's vital that I understand it to get a good mark in the HSC.
Syndicate:
--- Quote from: mfjw on July 17, 2016, 03:54:52 pm ---Thanks so much for all your explanations! It's really helpful and easy to understand :)
I'm having trouble understanding Difference of Two Squares and Perfect Squares? My Maths teacher says it's vital that I understand it to get a good mark in the HSC.
--- End quote ---
Different of two squares occurs where two brackes have the opposite signs:
For example:
perfect squares occurs where you basically multiply the bracket by itself:
Both of them (perfect squares and diffences of two squares) involves expanding the brackets via FOIL
jamonwindeyer:
--- Quote from: mfjw on July 17, 2016, 03:54:52 pm ---Thanks so much for all your explanations! It's really helpful and easy to understand :)
I'm having trouble understanding Difference of Two Squares and Perfect Squares? My Maths teacher says it's vital that I understand it to get a good mark in the HSC.
--- End quote ---
Just to add to Syndicate's response above, a shortcut for the perfect squares in words (without needing the formula, perhaps a little easier) is this:
- Square the first, plus
- Square the last, plus
- Double the Product
The first two bits are always positive, the last bit can be either positive or negative depending on the signs involved ;D for example:
Might be a bit nicer to think about without the pro numerals, I know that was my preference ;D Basically, both are just algebraic shortcuts, but both are seriously important if you want to get through Mathematics questions quickly, because they show up a lot ;D
Navigation
[0] Message Index
[#] Next page
[*] Previous page
Go to full version