Unformatted text preview: e was confusion about the
standard form for a parabola. Some
students made errors when
identifying the point (x,2) on the line
y=2. (x3)^2 was often expanded
unnecessarily, increasing the amount
of work and chance for error. Markers
also reported the usual variety of
algebraic errors. 5. Students usually began by expressing
the left side of the identity in terms of sin
x and cos x. Good use was made of the
identities needed in this question. Some students did not recognize that
1  sin^2 x was cos^2 x. Often 1  sin x
became cos x. Incorrect work with
fractions was also reported (lost
denominators or adding the
denominators together when adding
fractions) Markers also reported poor
notation with missing brackets, no
thetas, and incorrectly writing sin^2 x
as sin x^2. 6. A variety of solutions were used
successfully.
These included similar
triangle proportions, trig, and less
successfully, a system of equations.
Markers reported seeing a good
knowledge of proportions and the
Pythagorean Theorem. The calculation of the slant height
using the Pythagorean Theorem was
as far as some students could get. The
system method often failed due to
poor algebraic skills. Early rounding
led to accuracy deductions, and some
students tried to use area and volume
formulas in this question. 7. Students demonstrated good graphing
skills by showing that they could enter
the function(s), adjust the windows and
find either the zeros or intersection
points. There were very few rounding
errors and most students found both
solutions. Some students did not adjust their
window and therefore found only one
answer. Some answers were
expressed as ordered pairs. Markers
reported that the algebraic "cases"
approach was generally not
successful. A few students listed only
the root 43 when their sketch clearly
showed both zeros. Principles of Mathematics 12 Examination 4 April 2001 Report to Schools 8. Students who recognized that <2 = <BDE
by
the
TangentChord
Theorem
generally completed the proof perfectly.
Both proof methods were used. The key to this proof centered around
studentsâ€™ ability to correctly relate <2
= <7. Often <2 = <7 because AB // DE,
or <2 = <7 by the TangentChord
Theorem, or sometimes the statement
was ignored completely. Other errors
reported
were
using
initials
inappropriately
(ITT, VOA), or
sketching diagrams for reasons. Many
students did not include both givens
in their proof, and the naming of <BDE
was often incorrectly shown as <D,
<5,6 or <56. The markers felt that the overall difficulty level of the exam was appropriate. The examination adequately
represented the Examination Specifications in terms of topic weightings and cognitive levels. Principles of Mathematics 12 Examination 5 April 2001 Report to Schools...
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 Fall '07
 Ms.Boersma
 Math, Pythagorean Theorem, ... ...

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