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# 2020 HSC Mathematics Extension 1 Marking Guidelines

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Section I Multiple-choice Answer Key Question Answer 1 A 2 C 3 D 4 B 5 C 6 D 7 A 8 C 9 B 10 A Page 1 of 22 NESA 2020 HSC Mathematics Extension 1 Marking Guidelines Section II Qu... estion 11 (a) (i) Criteria Marks • Provides correct solution 1 Sample answer: P 2 ( )2 ( ) = 2 − 13 2 3 + 3 2 ( ) + 6 = 0 Question 11 (a) (ii) Criteria Marks • Provides correct solution 2 • Attempts to divide by x − 2, or equivalent merit 1 Sample answer: x2 + 5x − 3 x − 2 x3 + 3x2 − 13x + 6 x3 − 2x2 5x2 − 13x 5x2 − 10x −3x + 6 −3x + 6 0 ∴ P x ( x − 2 ( 2 ( ) = ) x + 5x − 3) Page 2 of 22 NESA 2020 HSC Mathematics Extension 1 Marking Guidelines Page 3 of 22 Question 11 (b) Criteria Marks • Provides correct solution 3 • Evaluates the dot product and sets it equal to 0, or equivalent value 2 • Writes a dot product = 0, or equivalent merit 1 Sample answer: Since the vectors are perpendicular, ⎛ a ⎞ ⎛ 2a − 3⎞ 0 = ⎜ ⎟ ⋅⎜ ⎟ ⎝ −1⎠ ⎝ 2 ⎠ 0 = 2a2 − 3a − 2 0 = ( ) 2a + 1 ( ) a − 2 1 a = − or 2 2 Question 11 (c) Criteria Marks • Provides correct sketch 3 • Provides a sketch with some correct features 2 • Marks asymptotes at x = −2 or 2, or marks local maximum at or equivalent merit y [Show More]

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