# A Level Maths Practise Paper Question

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#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
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
0
#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)
0
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?
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#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
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
#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
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
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
#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
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?
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#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
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 Dividing by 3 gives When you solve this there will be multiple solutions. I'm sure you've done something like this before.
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#14
when I inverse sin then divide by 30 my answer is 1

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1 year ago
#15
(Original post by mumtaz15)
when I inverse sin then divide by 30 my answer is 1 . 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.
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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) . 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
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
0
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