A Level Maths Practise Paper Question

Watch
mumtaz15
Badges: 7
Rep:
?
#1
Report Thread starter 1 year ago
#1
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
0
reply
Sir Cumference
  • Study Helper
Badges: 20
Rep:
?
#2
Report 1 year ago
#2
(Original post by mumtaz15)
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
What have you tried? Please post your working.
0
reply
mumtaz15
Badges: 7
Rep:
?
#3
Report Thread starter 1 year ago
#3
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.
0
reply
Sir Cumference
  • Study Helper
Badges: 20
Rep:
?
#4
Report 1 year ago
#4
(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?
0
reply
mumtaz15
Badges: 7
Rep:
?
#5
Report Thread starter 1 year ago
#5
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?
0
reply
Sir Cumference
  • Study Helper
Badges: 20
Rep:
?
#6
Report 1 year ago
#6
(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.
0
reply
mumtaz15
Badges: 7
Rep:
?
#7
Report Thread starter 1 year ago
#7
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.
0
reply
Sir Cumference
  • Study Helper
Badges: 20
Rep:
?
#8
Report 1 year ago
#8
(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)?
0
reply
Sir Cumference
  • Study Helper
Badges: 20
Rep:
?
#9
Report 1 year ago
#9
(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.
0
reply
mumtaz15
Badges: 7
Rep:
?
#10
Report Thread starter 1 year ago
#10
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.
0
reply
Sir Cumference
  • Study Helper
Badges: 20
Rep:
?
#11
Report 1 year ago
#11
(Original post by mumtaz15)
Omg of course h=8, right?
Correct Are you happy with b) or do you need any help?
0
reply
mumtaz15
Badges: 7
Rep:
?
#12
Report Thread starter 1 year ago
#12
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?
0
reply
Sir Cumference
  • Study Helper
Badges: 20
Rep:
?
#13
Report 1 year ago
#13
(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.
0
reply
mumtaz15
Badges: 7
Rep:
?
#14
Report Thread starter 1 year ago
#14
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.
0
reply
Sir Cumference
  • Study Helper
Badges: 20
Rep:
?
#15
Report 1 year ago
#15
(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.
0
reply
Farzxna
Badges: 6
Rep:
?
#16
Report 1 year ago
#16
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.
0
reply
Ahsan Khan
Badges: 2
Rep:
?
#17
Report 1 year ago
#17
(Original post by mumtaz15)
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
do you have the link to this practice paper please?
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Back
to top
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

With no certainty that exams next year wil take place, how does this make you feel?

More motivated (48)
24.49%
Less motivated (148)
75.51%

Watched Threads

View All
Latest
My Feed