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# Maths year 11

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1. (Original post by RDKGames)
Correct. Though uhh... you said that 0.12/12=1/100 then on the next line you proceeded to work out 3/300 through manipulation? Why? You know that 3/300=1/100 right?

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2. (Original post by RDKGames)
Correct.
What do I do on the one above?its still a decimal.

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3. (Original post by z_o_e)
What do I do on the one above?its still a decimal.

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Multiply top and bottom by 10 once more. Come on you've done these types of conversions yesterday :P
4. (Original post by RDKGames)
Multiply top and bottom by 10 once more. Come on you've done these types of conversions yesterday :P
Oh I'd rather times it by 1000

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5. (Original post by z_o_e)
Oh I'd rather times it by 1000

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Exactly. If in doubt just keep multiplying top and bottom by 10 until you have integers on both.
6. (Original post by RDKGames)
Multiply top and bottom by 10 once more. Come on you've done these types of conversions yesterday :P

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7. Correct.
8. (Original post by RDKGames)
Correct.

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9. Yep.
10. (Original post by RDKGames)
Yep.
Did this.
Can you do something on bounds please

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11. (Original post by z_o_e)
Did this.
Can you do something on bounds please

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Apologies for the delay, I was dealing with some uni stuff.

Anyhow, that's correct. If you give me an example of a bounds question I'll be able to help you as I forgot what bounds are like at GCSE level.
12. (Original post by RDKGames)
Apologies for the delay, I was dealing with some uni stuff.

Anyhow, that's correct. If you give me an example of a bounds question I'll be able to help you as I forgot what bounds are like at GCSE level.

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13. (Original post by RDKGames)
Apologies for the delay, I was dealing with some uni stuff.

Anyhow, that's correct. If you give me an example of a bounds question I'll be able to help you as I forgot what bounds are like at GCSE level.

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14. (Original post by RDKGames)
Apologies for the delay, I was dealing with some uni stuff.

Anyhow, that's correct. If you give me an example of a bounds question I'll be able to help you as I forgot what bounds are like at GCSE level.
Here

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15. Sorry my tsr froze before!

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16. (Original post by z_o_e)
Sorry my tsr froze before!

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Think of bounds like two extreme cases of a particular value; one will be the lowest possible one, and the other will be the highest possible one. All the numbers between the two will make up a range of values that will round to that particular value.

Explanation, bear with me as I can find this difficult to explain in any simpler terms:
Spoiler:
Show
You know how 0.5 rounds UP to 1 and 1.4 rounds DOWN to 1? Finding the bounds would be kinda like working backwards from this. Although bounds are LIMITS, which is a term not worked with at GCSE and I'm unsure how to explain it otherwise. Here's an example.

Finding the bounds of 1 to 1d.p.
- Lower bounds: these are very simple to understand. For 1 this would be 0.5 because 0.5 rounds up to 1. Anything less than 0.5 would make the number round down to 0 instead. Now the lower limit (also known as the lower bound) is 0.5. Therefore the lower bound of 1 is 0.5.

- Upper bounds: these require more thinking in order to understand and I'll try my best to make sure you do. We know that 1.5 would NOT round down to 1, therefore we cannot simply say that the upper bound is 1.5 based on that argument. However we use a trick around this. Let's start with 1.4. We know this will round down to 1. What about 1.49? This will also round down to 1. And 1.499? ALSO rounds down to 1. 1.4999? 1.49999? Yes and yes. This is because they are all LESS than 1.5. However with observation, we can notice that the more digits of 9 we add onto the end, the number will approach 1.5 closer and closer while still being less than 1.5 itself. So what is the limit? The limit is the number that 1.4999... approaches as you keep adding digits of 9 onto the end. We can see that the more you add, the closer and closer it will get to 1.5 BUT it will never reach it. Therefore this limit is 1.5, hence the upper bound being 1.5.

Here is an inequality portaying this explanation that you might find useful: and anything in that range will indeed round to 1. The two numbers on the side are the LIMITS, hence they are the lower and upper bounds respectively.

The two bounds of the first one would be 1.5cm (lower bound) and 2.5cm (upper bound). So the maximum length would be 2.5cm.
17. (Original post by RDKGames)
Think of bounds like two extreme cases of a particular value; one will be the lowest possible one, and the other will be the highest possible one. All the numbers between the two will make up a range of values that will round to that particular value.

Explanation, bear with me as I can find this difficult to explain in any simpler terms:
Spoiler:
Show
You know how 0.5 rounds UP to 1 and 1.4 rounds DOWN to 1? Finding the bounds would be kinda like working backwards from this. Although bounds are LIMITS, which is a term not worked with at GCSE and I'm unsure how to explain it otherwise. Here's an example.

Finding the bounds of 1 to 1d.p.
- Lower bounds: these are very simple to understand. For 1 this would be 0.5 because 0.5 rounds up to 1. Anything less than 0.5 would make the number round down to 0 instead. Now the lower limit (also known as the lower bound) is 0.5. Therefore the lower bound of 1 is 0.5.

- Upper bounds: these require more thinking in order to understand and I'll try my best to make sure you do. We know that 1.5 would NOT round down to 1, therefore we cannot simply say that the upper bound is 1.5 based on that argument. However we use a trick around this. Let's start with 1.4. We know this will round down to 1. What about 1.49? This will also round down to 1. And 1.499? ALSO rounds down to 1. 1.4999? 1.49999? Yes and yes. This is because they are all LESS than 1.5. However with observation, we can notice that the more digits of 9 we add onto the end, the number will approach 1.5 closer and closer while still being less than 1.5 itself. So what is the limit? The limit is the number that 1.4999... approaches as you keep adding digits of 9 onto the end. We can see that the more you add, the closer and closer it will get to 1.5 BUT it will never reach it. Therefore this limit is 1.5, hence the upper bound being 1.5.

Here is an inequality portaying this explanation that you might find useful: and anything in that range will indeed round to 1. The two numbers on the side are the LIMITS, hence they are the lower and upper bounds respectively.

The two bounds of the first one would be 1.5cm (lower bound) and 2.5cm (upper bound). So the maximum length would be 2.5cm.
Thank you so much.

Can you do the first question on paper please and how you'd lay it out.

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18. (Original post by RDKGames)
Apologies for the delay, I was dealing with some uni stuff.

Anyhow, that's correct. If you give me an example of a bounds question I'll be able to help you as I forgot what bounds are like at GCSE level.
I tried the first question myself.

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19. (Original post by z_o_e)
I tried the first question myself.

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That's good. No need to show the progression with the increasing 9s though. A simple inequality would suffice.
20. (Original post by RDKGames)
That's good. No need to show the progression with the increasing 9s though. A simple inequality would suffice.
How do I do Q2?

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