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# Did report a variety of successful methods as in

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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. (x-3)^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 Tangent-Chord 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 Tangent-Chord 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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