need help in reading and writing in math

Question

how to solve these type of question . please solve atleast one then i will try to solve remaining

Answer 1

1. After the first cut and pile the total thickness will be 0.02mm. On the second cut we double this to 0.04mm; then 0.08, 0.16, 0.32, 0.64, 1.28, 2.56, 5.12, 10.24. So the final thickness is 10.24mm=1.024cm.
2. Day 1, 50 people, Day 2, 78, Day 3, 106; the increase is 28 per day. We have to get from 50 to 200 people, so that's an increase of 150 from Day 1. 150/28=5 and then some. So after 6 days we have 6*28=168 extra people, making 168+50=218.
3. One way of working this out is to pick a triangle of a particular shape and size and write down how many of that size there are; then pick a different sized triangle and do the same for that. The answer is likely to be a multiple of 5. I can see more than 20 triangles. How many can you see?
4. 0.4*0.4*0.4*0.4=0.0256. So the height after 4 bounces is 0.0256*2.3=0.05888m=5.888cm. Two more bounces takes us to just under 1cm.
5. Add all the areas together. Take the area of each lake and divide by the total then multiply by 100 to get the percentage.
6. Time how fast you breathe in normally. Let's suppose this is 4 seconds. Remember that you breathe slower when asleep. If you're very energetic you may breathe faster on average. There are 60*60*24=86,400 seconds in a day, so that's 21,600 breaths a day. Multiply by 365.25 to find how many breaths in a year=7,889,400 breaths a year. Now multiply by your age. You can round the figures of course. It's only a fun exercise.
7. a) 1/10 b) 7/10 c) 5/10 d) 7/10 The probability is simply the ratio of the marbles you are counting to the total number of marbles, 10.

You may have to write in your words what the answers are. I hope this helps.

Comments

in the left side of page they mention some strategies , what are they ? should i uses these or can write your answers ?

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A strategy is a sort of tool that helps you to visualise the problem better and hence help you to work it out. If you had to undo a few screws to remove a panel to get to the inside of something you suspected of not working properly, you wouldn't look for a hammer or saw or knife to remove the panel, you would look for a suitable screwdriver, wouldn't you? In the same way, the strategy you use to solve a problem in mathematics would need to suit the problem. So a strategy is a method to help you solve the problem.

I've used all sorts of strategies, including looking at the problem from a different angle, drawing a picture or graph, solving a simpler but similar problem, making a rough guess or estimate, using logical reasoning, etc. Take Q3, for example, I would do as I suggested in my answer and count how many triangles of a particular shape there are. Do this for all the shapes there are and then add up the counts. This avoids losing count, or counting something twice, or missing something out, and it's easier to check one of the counts instead of starting all over again from scratch. You could say this method is compiling an organised list.

So it's entirely up to you. You can even make models. In Q7 you could use actual marbles or some other object to represent a marble. Actually handling something material can help a lot in converting the abstract mathematics into something practical.

For Q4 you could draw a picture or graph showing the diminishing height of each bounce.

You don't always need a strategy because you're able to solve the problem directly.

When you look at my answers, make sure you understand them, and then you will be able to explain in your own words how YOU arrived at the answers. I've indicated to a certain extent how you might do this. But you need to make absolutely sure you understand the answers.

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ok got it thanks a lot