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Cambridge Prelim MX1 Textbook Marathon/Q&A (2 Viewers)

appleibeats

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

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Stuck on part c). Not sure how to use part a) to help.
 

appleibeats

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

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Don't understand what the question is asking me.

Answers says 4 units
 

si2136

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

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Don't understand what the question is asking me.

Answers says 4 units
Not too sure either, but let one of the values be x and the other be x + 4. The distances between them are 4. Now because the midpoint would be x+2, the distances to each side is 2, so because it goes left to x and right to x + 4, the total distance is 4, since 2 + 2 = 4.

Therefore 4 units.
 

InteGrand

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

View attachment 33292

Don't understand what the question is asking me.

Answers says 4 units
It's asking for total distance moved using halving the interval.

E.g. Say we're on the interval [0,4] and we start at 0. Say the root happens to be at 1.245 (but we don't know this).

First we'd move to point 2. Then we'd find we've overshot and we'll go to 1. Then we'll see we're too low and we'll move to 1.5. Then 1.25, then 1.125, and so on.

We're asked to find the total distance we've travelled.

(Note that if the actual root turns out to be either 0, 2, 3 or 1, 3.5 or 1.5, … , then the distance travelled will be less than 4, because we'll land exactly on the root. As an exercise, you may like to try and prove or disprove that such values are the only ones where we'll land exactly on the root after a finite number of steps. :))
 
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leehuan

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Not too sure either, but let one of the values be x and the other be x + 4. The distances between them are 4. Now because the midpoint would be x+2, the distances to each side is 2, so because it goes left to x and right to x + 4, the total distance is 4, since 2 + 2 = 4.

Therefore 4 units.
I am quite positive that it is just a series question that applies the numerical estimation of roots topic to it.
 

InteGrand

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Yes, if we know that the process goes on indefinitely (i.e. the root wasn't 0, or 2, or 3, or 1, or … (exercise: classify exactly which numbers will result in a finite run only)), then the total distance travelled is just the total length of the interval (which is 4 here). This follows from the observation that the length of the step halves each time and the first step is length 2, so the total distance given there is an infinite number of steps is 2 + 1 + 1/2 + 1/4 + … = 4.

In other words, it was mainly just a series and sequences Q. as leehuan has said.
 
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appleibeats

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

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Unsure how to answer part a). I get part b).
 

appleibeats

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

The answer is 1/2^(1/4)
 

appleibeats

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Two bulldozers are sitting in a construction site facing each other. Bulldozer A is at x = 0, and bulldozer B is 36 metres away at x = 36. A bee is sitting on the scoop at the very front of bulldozer A. At 7:00am the workers start up both bulldozers and start them moving towards each other at the same speed V m/s. The bee is disturbed by the commotion and flies at twice the speed of the bulldozers to land on the scoop of bulldozer B.
(a) Show that the bee reaches bulldozer B when it is at x = 24.
(b) Immediately the bee lands, it takes off again and flies back to bulldozer A. Where is
bulldozer A when the two meet?
(c) Assume that the bulldozers keep moving towards each other and the bee keeps flying
between the two, so that the bee will eventually be squashed.
(i) Where will this happen? (ii) How far will the bee have flown?
 

InteGrand

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Two bulldozers are sitting in a construction site facing each other. Bulldozer A is at x = 0, and bulldozer B is 36 metres away at x = 36. A bee is sitting on the scoop at the very front of bulldozer A. At 7:00am the workers start up both bulldozers and start them moving towards each other at the same speed V m/s. The bee is disturbed by the commotion and flies at twice the speed of the bulldozers to land on the scoop of bulldozer B.
(a) Show that the bee reaches bulldozer B when it is at x = 24.
(b) Immediately the bee lands, it takes off again and flies back to bulldozer A. Where is
bulldozer A when the two meet?
(c) Assume that the bulldozers keep moving towards each other and the bee keeps flying
between the two, so that the bee will eventually be squashed.
(i) Where will this happen? (ii) How far will the bee have flown?
We can immediately say the answer to the very last part is just the initial separation between the bulldozers (in this case 36 m) doing essentially no calculation. Can you see why?

Also by symmetry, for c) (i), we conclude with almost no calculation that the bee gets squashed halfway between the bulldozers' starting points, i.e. x = 18.
 
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appleibeats

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Is it something to do with the limiting sum of a GP?? Also I don't get how to answer part a)
 

InteGrand

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Is it something to do with the limiting sum of a GP?? Also I don't get how to answer part a)
Yes the GP method is the other way to do it, and was probably the way the book expected students to do it. But this requires (slightly) tedious calculation, whereas the answer can be obtained with essentially no calculation using the method above.
 

appleibeats

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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

how do you show x = 24 for part a) ??
 

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