Need help with textbook for 4 unit... (1 Viewer)

[5uMath]

Hello,

I have the Fitzpatrick Mathematics Extension 2 textbook for the new syllabus, however the topic planes is missing from the vectors chapter.
Would anyone using the Cambridge textbook recommend this textbook for the new syllabus? Also, does it cover planes in vectors?

One last question, are cylinders (eg y=z^2) in the 4 unit vectors topic, or is that just extension knowledge at school level?

 

[Drongoski]

But are Planes in 4U? Don't remember seeing them in the syllabus.

 

[5uMath]

But are Planes in 4U? Don't remember seeing ithem in the syllabus.

I dont either. Someone had said they are learning it, and a teacher told me he is teaching it. From what I know, lines were in the syllabus.

 

[5uMath]

Would you recommend cambridge for this syllabus, given its the first year?

 

[ultra908]

Cambridge is v good in my opinion. It covers very little of planes though. Terry Lee's new textbook is the only one i've seen with a focus on planes. The only reference to planes in the syllabus is 'prove geometric results in the plane and construct proofs in 3d' and 'determine when intersecting lines are perpendicular in a plane'

I dont think cylinders, simple paraboloids and stuff are explicitly in our syllabus, but they fall under the general 'vector equations of curves'. So it might just be a 'describe the curve', but we're not expected to know any properties or anything.

 

[5uMath]

Cambridge is v good in my opinion. It covers very little of planes though. Terry Lee's new textbook is the only one i've seen with a focus on planes. The only reference to planes in the syllabus is 'prove geometric results in the plane and construct proofs in 3d' and 'determine when intersecting lines are perpendicular in a plane'

I dont think cylinders, simple paraboloids and stuff are explicitly in our syllabus, but they fall under the general 'vector equations of curves'. So it might just be a 'describe the curve', but we're not expected to know any properties or anything.

Would you say that cambridge covers enough of planes to get through this syllabus successfully?

I think 'prove geometric results in the plane' does not specifically refer to planes in 3D, instead refers to the whole 3D system itself (R3), and constructing proofs would be vector geometric proofs associated with 3D geometry. 'Determine when intersecting lines are perpendicular in a plane' would also refer to the ability to determine whether lines are perpendicular in 3D. I could be wrong, but there is no specific outcome on planes like there are with vectors or lines.

 

[5uMath]

I'm fairly sure 3D planes aren't in the 4u syllabus. The only 3D stuff you do is sphere's and lines.

A teacher that I know is teaching his class planes, and some of my friends are learning planes. Im also fairly sure they are not directly in the syllabus, so could be extension work.

 

[CM_Tutor]

Since there has never been an Extension 2 HSC exam on the new syllabus, we can only express opinions based on the syllabus document itself. Textbook authors have obviously based their content on their interpretations of the syllabus, as will teachers. It follows that there is content that will be universally (or near universally) agreed is examinable, and content that is universally (or near universally) agreed is not examinable. It also follows that there is content where it is unclear whether it is examinable, that will be included in trials at some schools but not others, or be the topic of debate. If you look at the syllabus that has just been replaced, you'll see that there is similar ambiguity and areas of doubt where I would have answered that content was in or out not based on the syllabus but based on the material having (or not having) appeared in HSC exams over the previous 15+ years.

In short, when textbooks and teachers disagree and the material is plausibly within the syllabus, you can't know for sure.

Having said, that, showing that the plane that is perpendicular to the vector and that passes through point P(1, 5, 3) is is pretty simple, and so is not difficult for Extension 2 students to understand.

 

[5uMath]

Since there has never been an Extension 2 HSC exam on the new syllabus, we can only express opinions based on the syllabus document itself. Textbook authors have obviously based their content on their interpretations of the syllabus, as will teachers. It follows that there is content that will be universally (or near universally) agreed is examinable, and content that is universally (or near universally) agreed is not examinable. It also follows that there is content where it is unclear whether it is examinable, that will be included in trials at some schools but not others, or be the topic of debate. If you look at the syllabus that has just been replaced, you'll see that there is similar ambiguity and areas of doubt where I would have answered that content was in or out not based on the syllabus but based on the material having (or not having) appeared in HSC exams over the previous 15+ years.

In short, when textbooks and teachers disagree and the material is plausibly within the syllabus, you can't know for sure.

Having said, that, showing that the plane that is perpendicular to the vector and that passes through point P(1, 5, 3) is is pretty simple, and so is not difficult for Extension 2 students to understand.

Wouldnt there then be uncertainty when entering HSC exams as to whether or not you have covered content? There are no explicit outcomes which assess planes or surfaces/cylinders, which therefore implies that is left to calculus 3. Why teach it if you could spend time polishing useful content?

I understand that it is useful to know, but besides that, it is not clearly in the syllabus from when I last checked, and schools which include this in trials are increasing chances for students to lose marks that could have not been lost. Why would authors then include this topic as a formal exercise, for example Terry Lee, when it cannot be assessed?

Clearly this is up to debate, but theres no chance of it showing up in HSC.

 

[CM_Tutor]

Wouldnt there then be uncertainty when entering HSC exams as to whether or not you have covered content?

Yes, that is the case.

There are no explicit outcomes which assess planes or surfaces/cylinders, which therefore implies that is left to calculus 3.

Ok, but the plane that is perpendicular to a given vector through a given point is a straight-forward application of the dot product for vectors in three dimensions. Does the syllabus require vectors in three dimensions? Yes. Does it require the dot product? Yes. I can then argue that finding a plane is examinable. Am I right that it is examinable? I don't know... and nor do you.

Why teach it if you could spend time polishing useful content?

A teacher would only teach what they believe is useful or required... but then what is useful is subjective and what is required is unclear for a new syllabus. When I was doing 4 unit Maths (as then it was), we did much of what is now covered by the "Proof" topic, and it taught us some extremely valuable skills, whether the content was formally HSC-examinable or not.

I understand that it is useful to know, but besides that, it is not clearly in the syllabus from when I last checked, and schools which include this in trials are increasing chances for students to lose marks that could have not been lost. Why would authors then include this topic as a formal exercise, for example Terry Lee, when it cannot be assessed?

Clearly this is up to debate, but theres no chance of it showing up in HSC.

I advise everyone to avoid being certain about what is not examinable unless it is clear that the consensus of teachers / books etc is that it is not examinable. Lee may be wrong... but he may not be, so I would not be comfortable acting on the belief that it is not examinable, and especially in cases where the material in question is not difficult.

We may get formal clarification, or questions like this may become clearer over the coming years based on what the HSCs actually contain.

 

[5uMath]

Yes, that is the case.


Ok, but the plane that is perpendicular to a given vector through a given point is a straight-forward application of the dot product for vectors in three dimensions. Does the syllabus require vectors in three dimensions? Yes. Does it require the dot product? Yes. I can then argue that finding a plane is examinable. Am I right that it is examinable? I don't know... and nor do you.


A teacher would only teach what they believe is useful or required... but then what is useful is subjective and what is required is unclear for a new syllabus. When I was doing 4 unit Maths (as then it was), we did much of what is now covered by the "Proof" topic, and it taught us some extremely valuable skills, whether the content was formally HSC-examinable or not.


I advise everyone to avoid being certain about what is not examinable unless it is clear that the consensus of teachers / books etc is that it is not examinable. Lee may be wrong... but he may not be, so I would not be comfortable acting on the belief that it is not examinable, and especially in cases where the material in question is not difficult.

We may get formal clarification, or questions like this may become clearer over the coming years based on what the HSCs actually contain.

The 4 unit vectors component is titled 'Vectors and Vector Equations of Lines' in the NESA syllabus. This does not say anything about planes, and nor do the subsequent outcomes.

The only condition under which a plane can be examined is when referring to a plane as the equation of 'locus' of vectors which are perpendicular to a particular vector. Further operations with planes cannot technically be assessed unless those particular operations are defined within the exam.

It is then up to a teacher to formally define a plane to a class, in preparation for all possibilities.