Welcome to the forum.
Angle BAP = ADP ( see http://www.mathisfunforum.com/viewtopic.php?id=17799 post 7 )
The ratio result then follows from "triangles ABP and DAP are similar".
To tell the truth, I cannot remember exactly what the questions were, just his answer to Q3. It'd be a shame to be unable to tell the story just because of that so I made up Q1 and Q2 both times. It was certainly a set of questions about symmetry and the third question definitely said to draw a picture. And that's the point: The book couldn't give a picture as an answer hence the 'Show your picture.....' answer. Also my memory isn't so great that I remember telling the story more than once. I might have told it three times. Now we have fully analysed the script hopefully you'll forgive me and we can move on.
Would you say the study for the degree was somewhat difficult?
Yes, but I enjoyed it. Up until that level, I can still remember and do the maths I was taught. But most of the university stuff has long since faded from my memory. If someone asks a question here about one of those topics I can sometimes do some research and remind myself, but some of it I never really understood properly. I did get asked to explain stuff by fellow students, so it seems the teaching aspect was beginning to kick in, even then.
When the government decided to give each school its first computer ( a research machine 380 Z ) the school had to have two teachers qualified to use it. Much to his amusement, my head of department was considered qualified as he had done a course ten years before (and forgotten most of it) but I was not. So I had to go to college to learn how to put a floppy disc in a machine to load up an operating system . As I could do stuff like that I was allowed to sit in the corner and write a program in BASIC.
Here's a link to a really useful (free) program for geometry:
Or you could just draw on paper and photograph it.
To put the image onto this site you could join www.imgur.com
Once you have uploaded your image you copy and paste the bbcode into your post.
There are other free sites that allow you to upload images like this.
I have re-worked this and I agree completely with all your answers. No idea what went wrong before. Maybe I only had V or only A. I dislike questions that get you to condense answers like this. If you get one correct but not the other you get no marks instead of half marks. And no clues about what you did wrong. I think it's just a lazy way to use a computer to mark the answers rather than doing it properly.
Anyway, thanks for your contribution.
That's the second time this week. Oh dear! At least I'm getting them right now, so I can dismiss senility. You are not by any chance related to championmathsgirl are you?
All three sciences were compulsory from age 11 to 13. After that you could choose to continue to O level.
I did a three year maths degree and then one year teacher training.
It takes a while to realise that the statement about sarcasm is itself sarcastic.
I am not usually cruel to my pupils but some actions make it necessary. One text book had the answers at the back. The chapter was about line and rotation symmetry. One boy had got (1) 2 lines of symmetry and (2) rotational symmetry order 3 correct. The third question was (3) Draw a shape with rotational symmetry order 2 but no lines of symmetry. His answer was (3) Show your picture to your teacher.
I trained as a maths teacher with science subsidiary. At my first school I also had the opportunity to teach astronomy.
When I started there were no computers in schools! My computing knowledge is all self taught. I played a part in the introduction of computers into the classroom and later taught both computer science and computer studies (analogy: car mechanics and learning to drive).
I was fairly good at mechanics so I may be able to help. Post what you need help with. (probably best to start a new thread or I may miss it).
I tell my class about the sarcasm lessons. It takes a while for the 'penny to drop'.
Welcome to the forum.
This is known as a conditional probability problem. The correct result can catch you out.
Let's say the three white marbles can be told apart in some way. eg. We write 1, 2 and 3 on them. I'll refer to them as W1, W2, and W3. It doesn't matter about the blacks.
Since we know we have a white it could be W1, or W2 or W3.
If it is W1, then the other marble is also white (W2).
If it is W2, then the other marble is also white (W1).
Only if it is W3 is the other marble B.
So there are 2 chances out of 3 of getting a white, not 1 chance in 2. Sorry.
Q17 - 20.
There are six sets here, girl soccer players, girl baseball players and so on.
A diagram showing six sets would be impossibly difficult to deal with. But there is a dodge that makes it simpler. A player cannot be both a boy and a girl. So make three circles, one for soccer, one for baseball and one for tennis. Use two coloured pens, say red for girls and blue for boys. Write information into the regions using the appropriate colour.
I would start with "1 boy played all three sports" and "1 girl played all three sports". You can put a red 1 and a blue 1 in the region where all the sets overlap.
There are a few places where you don't know about the boy/girl split, so you could use a third colour, say green, for these.
I found that there was not enough information to work out every region into blues and reds, but you can answer all the questions anyway.
Q11. I agree with your answer.
Q12. The inverse would be "If it's not a small pinpricks of light in the night sky then it's not a star."
I'm confused by this question. Why has a(n) popped into the question. If we are supposed to accept that the statement is true then it contradicts the original statement which would make it a counter example.
Q13. I cannot find an answer here. A is just a re-statement of the original. B is not a valid conclusion. C may be correct in the real world but in logic theory we cannot think like that. We have to reach conclusions on the basis of what we are told and there's no reason to reach conclusion C. D has nothing to do with the statement at all. E: The inverse would be "If someone is not a baseball player then they are not an athlete." Again we cannot conclude this from the original. F: The converse would be If someone is an athlete then they are a baseball player."
Q14. I've no idea what this question means. Where did q come from?
Hiont for the remaining questions coming up.
Science = 12 so the 4 regions inside the science circle should add up to 12
You have 4 + 3 + 1 + 3 ≠ 12
I've made a new diagram that may help:
You could print a copy or just draw it on a sheet of paper.
There are 8 regions and 8 descriptions. Can you match them?
need to finish this lesson as soon as possible, so can you please help me when you can.
I'm in the UK. I usually check MIF when I get up at about 7 UT.
I'll go quicker but you have got to understand what you are doing or there's no point in me helping.
Good news! Those answers are all correct. So c is 7 and that is letter D in Q16.
When we started you had question 15 correct, so I wanted to work with what you can do first; intending to come back to the 'right_words_in_set_theory questions at the end. I don't think it matters that we have missed them for now. Knowing what those words mean won't help you with Venn diagrams anyway.
Let's practise with another question.
24 pupils are asked about which lessons they like. Altogether 14 say they like maths; 12 like science and 15 like English. 7 say they like both science and maths, of whom 4 like English as well. 1 says he only likes science and 5 say they only like English.
Draw a Venn diagram and enter the information given.
(a) How many like science and English but not maths?
(b) How many like English and maths but not science?
(c) How many like only maths?
As a final check make sure that you have 24 pupils on your diagram.
a cannot be 5. The four numbers in the steak set must add up to 11. You have 3 + 2 + 5 + a = 11.
The answer to b depends on getting a right so I'm surprised you got b correct, but you did. Well done.
So the four numbers for salads must add up to 16. You have 2 + 3 + b + c = 16
Have a look here:
Once you have Q16 right, I'll make up another to practise before we try the rest of the questions set by Compuhigh as they are harder.