A Level Maths Practise Paper Question

The depth, h metres, of water in a harbour on any particular day can be modelled by the formula, h = 5+3sin (30t) where t is the time in hours after midday.

a) find the maximum depth of water in the harbour using this model (1 mark)

b) The ship can enter the harbour when the depth of water is at least 6.5 metres.
Find the times after mid-day during which the ship can enter the harbour

Reply 1

Notnek

Original post by mumtaz15

What have you tried? Please post your working.

Reply 2

mumtaz15

I haven't known what to do with part a but for part b I substituted h in as 6.5, so 6.5 = 5+3sin(30t), then took the 5 away so 1.5 = 3sin(30t) and divided by 3sin(30) and I got t=1

Original post by Notnek

What have you tried? Please post your working.

Reply 3

Notnek

Original post by mumtaz15

I haven't known what to do with part a but for part b I substituted h in as 6.5, so 6.5 = 5+3sin(30t), then took the 5 away so 1.5 = 3sin(30t) and divided by 3sin(30) and I got t=1

Starting with a):

You need to find the maximum value that h can be. First what's the maximum that sin(30t) can be?

Reply 4

mumtaz15

I don't understand your question, how would I work out the maximum

Original post by Notnek

Starting with a):

You need to find the maximum value that h can be. First what's the maximum that sin(30t) can be?

Reply 5

Notnek

Original post by mumtaz15

I don't understand your question, how would I work out the maximum

You should know from GCSE what the maximum value that sin(x) can be. Think about the graph.

The maximum of sin(30t) is the same as the maximum of the sin(x) graph since t can be any positive value.

Reply 6

mumtaz15

Ohh is it 1?

Original post by Notnek

You should know from GCSE what the maximum value that sin(x) can be. Think about the graph.

The maximum of sin(30t) is the same as the maximum of the sin(x) graph since t can be any positive value.

Reply 7

Notnek

Original post by mumtaz15

Ohh is it 1?

That's right. So what's the maximum of 3sin(30t)? Then what's the maximum of 5 + 3sin(30t)?

Reply 8

Notnek

Original post by mumtaz15

so h = 5 +3sin(30x1)
h= 6.5 metres

Your working is confusing. You know that the maximum of sin(30t) is 1 so what's the maximum of 3sin(30t)? You shouldn't be setting t = 1.

Reply 9

mumtaz15

Omg of course h=8, right?

Original post by Notnek

Your working is confusing. You know that the maximum of sin(30t) is 1 so what's the maximum of 3sin(30t)? You shouldn't be setting t = 1.

Reply 10

Notnek

Original post by mumtaz15

Omg of course h=8, right?

Correct

Are you happy with b) or do you need any help?

Reply 11

mumtaz15

I'd like some help as it says 'times' not 'time' and my working out is giving me 1 answer so I don't think it's right

Original post by Notnek

Correct Are you happy with b) or do you need any help?

Reply 12

Notnek

Original post by mumtaz15

I'd like some help as it says 'times' not 'time' and my working out is giving me 1 answer so I don't think it's right

1.5 = 3\sin (30t)

Dividing by 3 gives

\sin (30t) = 0.5

When you solve this there will be multiple solutions. I'm sure you've done something like this before.

Reply 13

mumtaz15

when I inverse sin then divide by 30 my answer is 1

Original post by Notnek

1.5 = 3\sin (30t)

Dividing by 3 gives

\sin (30t) = 0.5

When you solve this there will be multiple solutions. I'm sure you've done something like this before.

Reply 14

Notnek

Original post by mumtaz15

when I inverse sin then divide by 30 my answer is 1

\sin x = 0.5

. At GCSE there would have been 1 solution to this but at A Level you will have learnt that there are many solutions. t = 1 is only one solution.

Reply 15

Farzxna

yep, to find other solutions, you would've learnt how to use the graph of sine or the CAST diagram if that rings a bell?

Original post by Notnek

\sin x = 0.5

. At GCSE there would have been 1 solution to this but at A Level you will have learnt that there are many solutions. t = 1 is only one solution.

Reply 16

Ahsan Khan

Original post by mumtaz15

do you have the link to this practice paper please?

Reply 17

Aliyu345426

Original post by mumtaz15

Pls can you tell me the name of the paper you found this?

Reply 18

davros

Original post by Aliyu345426

Pls can you tell me the name of the paper you found this?

Please check the dates of threads before you resurrect them - this thread is 2 years old and the OP hasn't logged on for nearly 2 years!

If you're stuck on a particular problem then the best thing to do is to start a new thread of your own with details of any working that you've done :smile:

Reply 19