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Year 13 Maths Help Thread

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Original post by vybzkartel
It's GCSE question but I'm in year 13 so, and I need to revise GCSEstyle maths for UKCAT.

"A ford focus holds 13 gallons of petrol, how many litres of petrol can the car hold if 1 gallon is equivalent to 4.5 L? "

I tried two methods of working out, both of which I have used for other questions like this and I can't figure out which one is right since there aren't accessible answers.

Method 1:
1 gallon = 4.5 L
so
13 = 4.5 x 13 L = 58.5

Method 2 :
(1/4.5) x 13 = 2.88

Spoiler



Method 1 is right.

Method two is wrong because you are working out the amount of gallons within 13 Litres, which is the other way around.
Original post by vybzkartel
It's GCSE question but I'm in year 13 so, and I need to revise GCSEstyle maths for UKCAT.

"A ford focus holds 13 gallons of petrol, how many litres of petrol can the car hold if 1 gallon is equivalent to 4.5 L? "

I tried two methods of working out, both of which I have used for other questions like this and I can't figure out which one is right since there aren't accessible answers.

Method 1:
1 gallon = 4.5 L
so
13 = 4.5 x 13 L = 58.5

Method 2 :
(1/4.5) x 13 = 2.88

Spoiler



For the second method you worked out how many gallons were in a litre, and then multiplied it by how many gallons the tank holds. What does that even mean? You get a unit that is gallons2 L−1 \text{gallons}^2\ \text{L}^{-1} .
Original post by RDKGames
Method 1 is right.Method two is wrong because you are working out the amount of gallons within 13 Litres, which is the other way around.



Original post by B_9710
For the second method you worked out how many gallons were in a litre, and then multiplied it by how many gallons the tank holds. What does that even mean? You get a unit that is gallons2 L−1 \text{gallons}^2\ \text{L}^{-1} .


I don't get it.
for example if you do 15/3, that means you're working out many 3's are in 15 right? which =

I did 1/4.5 so Gallon/L, so I thought that meant how many litres were in a gallon or something?! This is so confusing
Original post by vybzkartel
I don't get it.
for example if you do 15/3, that means you're working out many 3's are in 15 right? which =

I did 1/4.5 so Gallon/L, so I thought that meant how many litres were in a gallon or something?! This is so confusing


You're getting confused. Think about what you are doing here. Look at it mathematically.

1G=4.5L1 G = 4.5 L

14.5G=1L\frac{1}{4.5} G = 1 L

(14.5⋅13)G=(1⋅13)L(\frac{1}{4.5} \cdot 13) G = (1 \cdot 13) L

So 134.5G=13L\frac{13}{4.5} G = 13 L which is not what you're looking for.
Original post by RDKGames
You're getting confused. Think about what you are doing here. Look at it mathematically.

1G=4.5L1 G = 4.5 L

14.5G=1L\frac{1}{4.5} G = 1 L

(14.5⋅13)G=(1⋅13)L(\frac{1}{4.5} \cdot 13) G = (1 \cdot 13) L

So 134.5G=13L\frac{13}{4.5} G = 13 L which is not what you're looking for.

thank you :smile:

so if i make the units of whichever side I'm starting off with into 1 then multiply the other side by the value i want to convert it should work right? (or wrong?)

so if it was £5 = $7 "how many pounds can you get from $16?"

make $ side into 1,
5/7 =1
then multiply (5/7) by $16 = ANSWER



can I use that as a general rule?
Original post by vybzkartel
thank you :smile:

so if i make the units of whichever side I'm starting off with into 1 then multiply the other side by the value i want to convert it should work right? (or wrong?)

so if it was £5 = $7 "how many pounds can you get from $16?"

make $ side into 1,
5/7 =1
then multiply (5/7) by $16 = ANSWER



can I use that as a general rule?


Yes, but you're not multiplying it by 16 dollars, you're simply multiplying it by 16. It's easier to see if you lay it out like I did in the post above. Same procedure pretty much all the time.

£5=$7
£5/7 = $1
£5/7 * 16 = $1 * 16
£80/7 = $16

It's just simple equation balancing.
Original post by RDKGames
Yes, but you're not multiplying it by 16 dollars, you're simply multiplying it by 16. It's easier to see if you lay it out like I did in the post above. Same procedure pretty much all the time.

£5=$7
£5/7 = $1
£5/7 * 16 = $1 * 16
£80/7 = $16

It's just simple equation balancing.


oh right I see what you mean, the layout makes it clearer, the exam i'm taking is on screen and you literally have max 40 seconds to answer a question so Ill have to lay it out in my head.. I can't believe simple GCSE stuff confused me so much lol thank you for the help!
Original post by vybzkartel
oh right I see what you mean, the layout makes it clearer, the exam i'm taking is on screen and you literally have max 40 seconds to answer a question so Ill have to lay it out in my head.. I can't believe simple GCSE stuff confused me so much lol thank you for the help!


If you're allowed a piece of paper it literally takes 10 seconds to jot it all down, but I'm not sure how effective you'd find this. No problem. :smile:
Original post by RDKGames
If you're allowed a piece of paper it literally takes 10 seconds to jot it all down, but I'm not sure how effective you'd find this. No problem. :smile:


1:

21m/h into km/m

21/1000 so it's into kilometres, and then divide by 60? = 0.00035 km/m
I don't get why you divide and don't multiply?

also 2:

I have no idea how to answer this, please help
(its so huge cause i copy and pasted it from the quiz i was doing but won't let me access the answers)
Original post by vybzkartel
1:

21m/h into km/m

21/1000 so it's into kilometres, and then divide by 60? = 0.00035 km/m
I don't get why you divide and don't multiply?

also 2:

I have no idea how to answer this, please help
(its so huge cause i copy and pasted it from the quiz i was doing but won't let me access the answers)

Do you mean 21 metres per hour to kilometres per minute? Sorry I'm getting confused by the 'm's

If so if you travel 21 metres in an hour, you will travel 21/60 metres per minute, and then when you convert to km it would become 21/60000 kilometres per minute
Original post by vybzkartel
...


1. Literally just use the same idea as before just slightly differently. There's no multiplication because the measurements are going down, so to speak. Like from m into km you divide, and from hours into mins you multiply, but divide the numerator. I'll show you:

21metres1hour→0.021kilometres60minutes\displaystyle \frac{21 \text{metres}}{1 \text{hour}} \rightarrow \frac{0.021 \text{kilometres}}{60 \text{minutes}}

at this stage just divide top and bottom by 60 which gets you:

0.00035kilometres1minute\displaystyle \frac{0.00035 \text{kilometres}}{1 \text{minute}} therefore 0.00035km per minute.

2. 1 ft = 30 cm and 30cm = 0.03m

1 square ft = 0.32 square metres
1000 square ft = 1000 * 0.09 square m
1000 square ft = 90 square m

It's been a while since I've done this type of question so I don't even trust myself, but it makes sense to me. Happy for anyone to verify/correct me.
Original post by RDKGames
1. Literally just use the same idea as before just slightly differently. There's no multiplication because the measurements are going down, so to speak. Like from m into km you divide, and from hours into mins you multiply, but divide the numerator. I'll show you:

21metres1hour→0.021kilometres60minutes\displaystyle \frac{21 \text{metres}}{1 \text{hour}} \rightarrow \frac{0.021 \text{kilometres}}{60 \text{minutes}}

at this stage just divide top and bottom by 60 which gets you:

0.00035kilometres1minute\displaystyle \frac{0.00035 \text{kilometres}}{1 \text{minute}} therefore 0.00035km per minute.

2. 1 ft = 30 cm and 30cm = 0.03m

1 square ft = 0.32 square metres
1000 square ft = 1000 * 0.09 square m
1000 square ft = 90 square m

It's been a while since I've done this type of question so I don't even trust myself, but it makes sense to me. Happy for anyone to verify/correct me.

??
Original post by B_9710
??


Original post by RDKGames

It's been a while since I've done this type of question so I don't even trust myself, but it makes sense to me. Happy for anyone to verify/correct me.


I just visually imagined creating squares then scaled it up. :smile:
(edited 7 years ago)
Original post by metrize
Do you mean 21 metres per hour to kilometres per minute? Sorry I'm getting confused by the 'm's

If so if you travel 21 metres in an hour, you will travel 21/60 metres per minute, and then when you convert to km it would become 21/60000 kilometres per minute


yes i do

Original post by RDKGames
1. Literally just use the same idea as before just slightly differently. There's no multiplication because the measurements are going down, so to speak. Like from m into km you divide, and from hours into mins you multiply, but divide the numerator. I'll show you:

21metres1hour→0.021kilometres60minutes\displaystyle \frac{21 \text{metres}}{1 \text{hour}} \rightarrow \frac{0.021 \text{kilometres}}{60 \text{minutes}}

at this stage just divide top and bottom by 60 which gets you:

0.00035kilometres1minute\displaystyle \frac{0.00035 \text{kilometres}}{1 \text{minute}} therefore 0.00035km per minute.

2. 1 ft = 30 cm and 30cm = 0.03m

1 square ft = 0.32 square metres
1000 square ft = 1000 * 0.09 square m
1000 square ft = 90 square m

It's been a while since I've done this type of question so I don't even trust myself, but it makes sense to me. Happy for anyone to verify/correct me.


I understand them when I see it visually laid out like that, thank you sm


idk about the counting squares thing... did you seriously count up like 10 000 squares lol?


Original post by B_9710
??


؟؟
Original post by vybzkartel


idk about the counting squares thing... did you seriously count up like 10 000 squares lol?



What? Why on earth would I do that? I scaled it, didn't count it.
Original post by RDKGames
What? Why on earth would I do that? I scaled it, didn't count it.


idk what that means cause im **** at this kinda maths, aka real life math
Original post by vybzkartel
idk what that means cause im **** at this kinda maths, aka real life math


I just visually created a square of length's 1 ft, so the area is 1ft squared. Scaled this area up by 1000 by multiplying it.
Reply 557
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Palette
OP
14
After hours of missing the obvious, I did the first part of STEP I 2007 Q5- will see if I can do the second part too.
This website has some nice resources
http://www.mathcentre.ac.uk/students/topics/
Reply 559
Avatar for Palette
Palette
OP
14
Managed to finish STEP I 2007 Q5 :smile:!

One area of maths which I'm particularly weak at is recurrence relations, particularly the types of questions which define un+1u_{n+1} in terms of unu_n and then ask you to define unu_n in terms of nn.

What are some good questions that I can do to practice?

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