-
Finished your HSC? Check out our University Discussion, Non-School forums or help out next year's HSC students! -
YOU can help the next generation of students in the community! Share your trial papers and notes on our Notes & Resources page
CSSA 2023 (1 Viewer)
- Thread starter Unovan
- Start date
Pretty easy. I put my solutions here: https://4unitmaths.com/cssa2023e1-tywebb.pdf
Note in 14a for the extension 1 I used the regularised incomplete beta function, which although outside the syllabus, gets the answer much quicker.
Furthermore use of the complementary error function instead of the table gives a more accurate answer.
Note in 14a for the extension 1 I used the regularised incomplete beta function, which although outside the syllabus, gets the answer much quicker.
Furthermore use of the complementary error function instead of the table gives a more accurate answer.
Alternative method for 14a with a major caveat
In 1998 a review was undertaken in which it was recommended that rigour be maintained in any syllabus development.
Stacey, K, Dowsey, J, McCrae, B & Stephens, M 1998, Review of Senior Secondary Mathematics Curriculum, Board of Studies NSW, Sydney.
This became referred to as "The Stacey Review".
This recommendation was subsequently accepted in a government white paper.
The current syllabus says in the most cryptic way possible to "understand and use the normal approximation to the distribution of the sample proportion and its limitations" - page 61
It is a very sloppy non-rigorous aspect in some textbooks applying the Central Limit Theorem without any justification - in clear breach of the Stacey Review.
For example in the Year 12 Cambridge textbook we see the abomination: "We cannot in this course give theoretical arguments why such approximations work — we can only look at the pictures and confirm the results." on page 797.
Such sloppy non-rigorous abrogations of proper mathematical development should be avoided.
One must uphold the Stacey Review recommendation to maintain rigour at all times.
Having said that there is an alternative method to 14a but I also include a justification and references - such rigour is entirely absent in the CSSA solutions of course - again in breach of the Stacey Review.
 to ascertain appropriateness of the Central Limit Theorem we see that})
}{\sqrt{25\times0.6915\times0.3085}}\right)\approx P(z<2.07).)
https://en.wikipedia.org/wiki/Binomial_distribution
In 1998 a review was undertaken in which it was recommended that rigour be maintained in any syllabus development.
Stacey, K, Dowsey, J, McCrae, B & Stephens, M 1998, Review of Senior Secondary Mathematics Curriculum, Board of Studies NSW, Sydney.
This became referred to as "The Stacey Review".
This recommendation was subsequently accepted in a government white paper.
The current syllabus says in the most cryptic way possible to "understand and use the normal approximation to the distribution of the sample proportion and its limitations" - page 61
It is a very sloppy non-rigorous aspect in some textbooks applying the Central Limit Theorem without any justification - in clear breach of the Stacey Review.
For example in the Year 12 Cambridge textbook we see the abomination: "We cannot in this course give theoretical arguments why such approximations work — we can only look at the pictures and confirm the results." on page 797.
Such sloppy non-rigorous abrogations of proper mathematical development should be avoided.
One must uphold the Stacey Review recommendation to maintain rigour at all times.
Having said that there is an alternative method to 14a but I also include a justification and references - such rigour is entirely absent in the CSSA solutions of course - again in breach of the Stacey Review.
Last edited: