# Thread: Year 9-10 Maths Discussion & Resources

1. ## Year 9-10 Maths Discussion & Resources

Discuss all your questions for maths related topics for the year 9-10 curriculum here.

If you have any links to past tests, exam papers from your school that would also be nice (if you decided to share).

I also decided to create a poll about what textbook your school uses. (If your school uses more than 1 book , tick the box which you find most relevant or used) I'd be interested in receiving feedback in.

Links
Year 10 Yearly Practice Papers
https://thsconline.github.io/s/yr10/Maths/

2. ## Re: Year 9 & 10 Maths Discussion Thread 2017

Speaking of the Cambridge maths book, there is a slight error in EX 7D Q7.

$\triangle PBR \equiv \triangle FDE is wrong as they are missing the double strike for \triangle FDE in the answer.$

3. ## Re: Year 9 & 10 Maths Discussion Thread 2017

I was a bit confused by the wording of parts (c) and parts (d) and (e).

I also don't get how you can use a compass to see the two points where they can be at two different places. I was thinking it could only be 1 point for each triangle.

Anybody with any tips?

4. ## Re: Year 9 & 10 Maths Discussion Thread 2017

^^^ I have an assumption in this question, they they have done parts (a) and (d) for us already. But if someone wants to correct me, do so.

5. ## Re: Year 9 & 10 Maths Discussion Thread 2017

I know this is a stupid thing to say but when you go back through the Year 9 and 10 NSW maths books, especially with the curriculum here, you pick up and learn little notations, ways of writing of triangles (in relation to congruent triangles) that I thought I may have known before but may have been a bit off. for instance I learnt that the direction of say two parallel lines cannot be used to show that they are the same side. Yep you guessed it all along I've been thinking two parallel lines (the ones with the arrows /direction) could be used as a proof to say that they are the same size. (which clearly the solutions don't mention)

6. ## Re: Year 9 & 10 Maths Discussion Thread 2017

Originally Posted by davidgoes4wce
I know this is a stupid thing to say but when you go back through the Year 9 and 10 NSW maths books, especially with the curriculum here, you pick up and learn little notations, ways of writing of triangles (in relation to congruent triangles) that I thought I may have known before but may have been a bit off. for instance I learnt that the direction of say two parallel lines cannot be used to show that they are the same side. Yep you guessed it all along I've been thinking two parallel lines (the ones with the arrows /direction) could be used as a proof to say that they are the same size. (which clearly the solutions don't mention)
David, I think you have not learnt your triangle congruency well; hence your earlier confusion. Also, nowadays, students have very little experience in use of construction, via straight edges (via set squares - what are these??) and the compass. One's understanding of plane geometry would be greatly helped by some practice of geometrical constructions via these simple devices, like the ancient Greeks did. Of course like handwriting, it is not much taught nowadays. When teaching geometry, I often demonstrate construction of the perpendicular bisector of a line segment, the bisector of an angle, the construction of the circumcircle or the inscribed circle of a given triangle etc etc. Sadly, hardly any of my students adopt the use of set squares; they prefer, as is the practice nowadays, of using free-hand drawing of straight lines and circles etc.

As for part c) of the above question, by means of a compass, construct an arc of a circle of radius 4 cm, centered at B, to intersect AG at 2 points (you were right - 2 different places). This is to show that the specification is insufficient - we can construct 2 different triangles meeting the specs; we have an ambiguity. That's why ASS is not a valid criterion for triangle congruency, unlike SAS, where the A between the 2 S's means the angle is between the 2 said sides, i.e. the included angle.(I hope I have not misread the question or your querry)

7. ## Re: Year 9 & 10 Textbooks, Papers & Links

Thread renamed as Year 9-10 Maths Discussion & Resources, so the conversation will still be relevant for 2018 and future years.

For discussion of Year 9-10 in general, please refer and use this thread
Year 9 & 10 Chat Thread

Edited OP with a link to past papers

And stickied.

8. ## Re: Year 9 & 10 Maths Discussion Thread 2017

Originally Posted by Drongoski
David, I think you have not learnt your triangle congruency well; hence your earlier confusion. Also, nowadays, students have very little experience in use of construction, via straight edges (via set squares - what are these??) and the compass. One's understanding of plane geometry would be greatly helped by some practice of geometrical constructions via these simple devices, like the ancient Greeks did. Of course like handwriting, it is not much taught nowadays. When teaching geometry, I often demonstrate construction of the perpendicular bisector of a line segment, the bisector of an angle, the construction of the circumcircle or the inscribed circle of a given triangle etc etc. Sadly, hardly any of my students adopt the use of set squares; they prefer, as is the preactice nowadays, of using free-hand drawing of straight lines and circles etc.

As for part c) of the above question, by means of a compass, construct an arc of a circle of radius 4 cm, centered at B, to intersect AG at 2 points (you were right - 2 different places). This is to show that the specification is insufficient - we can construct 2 different triangles meeting the specs; we have an ambiguity. That's why ASS is not a valid criterion for triangle congruency, unlike SAS, where the A between the 2 S's means the angle is between the 2 said sides, i.e. the included angle.(I hope I have not misread the question or your querry)
I didn't see much congruency of triangles in IB maths so I am slightly behind in that aspect. I was having a quick look at the SL and HL textbooks, they don't have many congruency triangles and/or circle geometry. Like with any topic you have to put a good amount of time to cover it. I am making sure that I go through this topic more thoroughly. I think from memory I have only gone through a Yr 9-10 (5.3) study guide worth of questions (which isn't enough time as you miss some of the basics). Think if you are learning any topic , putting time into anything is of importance.

I like the way they explain congruency of triangles in Cambridge over New Century. (just a personal preference). A question came up like this last night

in (f) , I said AB = DE (Given). I admit that was wrong, it's not something that I have seen alot. The big learning lesson for me, and this will stick with me forever now, is that it's only the 'marked sides' (or dashed sides or marked lines) that you can relate to when comparing side lengths. (not the direction)

But anyway this was the answer at the back of the book to that part in (f) :

$AC=EC (given)$

$\angle CAB=\angle CED ( alternate angles, AB||DE)$

$\angle ACB=\angle ECD (Vertically opposite )$

$\therefore \triangle ABC \equiv \triangle EDC (AAS)$

I guess just want to clear it up, would I be wrong if I wrote the letters in reverse order? The book doesn't really mention it and I have tried Googling it and it doesn't really come up with a clear answer e.g

$CA=CB (given)$

$\angle BAC=\angle DEC (alternate angles, AB||DE)$

$\angle BCA=\angle CED (alternate angles, AB||DE)$ ?

9. ## Re: Year 9 & 10 Maths Discussion Thread 2017

Originally Posted by davidgoes4wce
I didn't see much congruency of triangles in IB maths so I am slightly behind in that aspect. I was having a quick look at the SL and HL textbooks, they don't have many congruency triangles and/or circle geometry. Like with any topic you have to put a good amount of time to cover it. I am making sure that I go through this topic more thoroughly. I think from memory I have only gone through a Yr 9-10 (5.3) study guide worth of questions (which isn't enough time as you miss some of the basics). Think if you are learning any topic , putting time into anything is of importance.

I like the way they explain congruency of triangles in Cambridge over New Century. (just a personal preference). A question came up like this last night

$CA=CB (given)$

$\angle BAC=\angle DEC (alternate angles, AB||DE)$

$\angle BCA=\angle CED (alternate angles, AB||DE)$ ?

Did you mean:

CA = CE (given)

angl BAC = angl DEC

angl ABC = angl CDE

???

Also don't understand what you mean by "if I wrote the letter in reverse order"?

angl BAC can equally well be written as angl CAB.

10. ## Re: Year 9-10 Maths Discussion & Resources

My bad , I should have said CA=CE (given)

angle ABC= angle EDC (alternate angles, AB||DE)

11. ## Re: Year 9-10 Maths Discussion & Resources

After going through all the majority of the chapter, on "Properties of Geometrical figures" in Cambridge for 5.3 Year 9 , I will look to do one of a similar chapters in Signpost or New Century.It's the only topic that I need more brushing up on. (plus I also enjoy it)

12. ## Re: Year 9-10 Maths Discussion & Resources

I'm in WA and our school uses the ICE-EM books.

13. ## Re: Year 9-10 Maths Discussion & Resources

Originally Posted by Mongose528
I'm in WA and our school uses the ICE-EM books.
I brought over a couple of A.J Sadler books from WA to NSW. Love the good old Sadler books but sadly the standards of those books are alot lower compared to the ones in NSW. ( Just used to hate the Rossmoyne kids bragging about how they had good resources/the best teachers in the state there. Those kids had a real arrogance which showed in their competitive spirit) O.T Lee was not too bad though (which was the best book in WA) but thats about 2nd or 3rd best over here. I heard there is now a 3rd or 4th competitor over there? Will definitely head to the bookstore in Scarborough (on Scarborough Beach Road) if I get the chance. (Think that store was still there, last visited there mid year in 2016)

I've used ICM-EM before and it ticks off the syllabus points of the national curriculum well. But a slight criticism is some of the questions are a bit repetitive?

14. ## Re: Year 9-10 Maths Discussion & Resources

I was also surprised to know that there is a Campion bookstore franchise here in NSW, its based in Artarmon.

I thought Campion was a WA based company only having operations over there.

15. ## Re: Year 9-10 Maths Discussion & Resources

Question 7B

OK with this question tonight, I thought for the life of me it was an alternate angle reasoning.

The books answer is:

$\angle EAB=\angle DCB (corresponding angles in congruent triangles )$

$\therefore AE || CD (alternate angles equal)$

I understand the last line but in the 1st line , I thought it was:

$\angle EAB=\angle DCB ( alternate angles , AE||CD)$

I don't quite understand why they used the words 'corresponding angles' in the first line. Maybe I am overthinking things?

16. ## Re: Year 9-10 Maths Discussion & Resources

My thinking is if they say 'Hence, prove AE||CD' , if they use those words specifically , you have to refer to 'corresponding angles' in your answer.

17. ## Re: Year 9-10 Maths Discussion & Resources

Ha Ha!

This is a case of confusion in the meaning of the word "corresponding". In our day to day usage, "corresponding" refers to another object, situation or whatever in a matching or equivalent position or location. This is the usage in the 1st line. It is not the usage of "corresponding" referring to the relative location of 2 angles usually concerning 2 angles positioned in a pair of parallel lines and a transversal.

In fact when teaching this area, I have often cautioned my students that this "corresponding" is a technical usage; not our every day usage.

People of my vintage have spent lots more time on plane geometry.

18. ## Re: Year 9-10 Maths Discussion & Resources

Originally Posted by davidgoes4wce
Question 7B

OK with this question tonight, I thought for the life of me it was an alternate angle reasoning.

The books answer is:

$\angle EAB=\angle DCB (corresponding angles in congruent triangles )$

$\therefore AE || CD (alternate angles equal)$

I understand the last line but in the 1st line , I thought it was:

$\angle EAB=\angle DCB ( alternate angles , AE||CD)$

I don't quite understand why they used the words 'corresponding angles' in the first line. Maybe I am overthinking things?
In the context of congruent triangles, corresponding angles refers to 'matching angles' in the congruent triangles (i.e. if you moved one of the congruent triangles so that it lies on top of the other (which is possible since they are congruent), corresponding angles are the ones that would match up).

E.g. see the picture here: https://en.wikipedia.org/wiki/CPCTC . Angles A and D would be corresponding angles. (They match up if we placed one triangle over the other.) Similarly we can also have 'corresponding sides' in congruent triangles, they are sides that would match up if we placed the triangles one on top of the other.

19. ## Re: Year 9-10 Maths Discussion & Resources

Confirming there is a mistake with this question for Cambridge Year 10 EX 1D Q8.

$(a) Area= 66m^{2}$

$(b) Two bags of cement = 5m^{2}$

$\frac{2 \ bags \ of \ cement}{x}=\frac{5}{66}$

$x=26.4 bags$

$I then rounded the answer up to 27 bags, as the required amount for purchase of the job$

The answer at the back of the book for part(b) has 14 bags. Could anyone confirm if this is a mistake?

20. ## Re: Year 9-10 Maths Discussion & Resources

Just a bit of a left field question, do the high schools in NSW teach the students to spend much time on drawing out Circles , in circle geometry? Personally, think it would be a great learning tool in learning Geogebra or the equivalent circle geometry software and enhancing that learning at the same time.

From what I see the New Century teaches the student step by step in order to draw the circles etc

Even though I have used Geogebra in the past by no means am I an expert on it.

21. ## Re: Year 9-10 Maths Discussion & Resources

What other Circle Geometry programs are there ? Or ones that the NSW curriculum encourage students to use?

Geogebra is one.

Efofex is one that is used in WA (but I never touched much on that subject in the past), so rarely touched it

Are there maybe other ones that are used?

22. ## Re: Year 9-10 Maths Discussion & Resources

I came across this question in the Cambridge year 10 maths book and it got me thinking this early morning. This chapter was part of the Geometrical figures and circle geometry. (I haven't looked at the answer yet)

Q. Are these statements true or false?

" All circles are similar"

I think it's FALSE

When comparing different circles, they may the same shape and of a different size.

But there are no corresponding angles to compare against. However, the can very in proportion (or ratio)

23. ## Re: Year 9-10 Maths Discussion & Resources

Originally Posted by davidgoes4wce
I came across this question in the Cambridge year 10 maths book and it got me thinking this early morning. This chapter was part of the Geometrical figures and circle geometry. (I haven't looked at the answer yet)

Q. Are these statements true or false?

" All circles are similar"

I think it's FALSE

When comparing different circles, they may the same shape and of a different size.

But there are no corresponding angles to compare against. However, the can very in proportion (or ratio)
The answer is 'true'.

24. ## Re: Year 9-10 Maths Discussion & Resources

Don't need angles. You can see the definition of similarity here: https://en.wikipedia.org/wiki/Similarity_(geometry) .

25. ## Re: Year 9-10 Maths Discussion & Resources

Now everybody on the forum can have a laugh at me now !

And the answer was True

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