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Mathematics HL - May 2001 - P1 \$

# Mathematics HL - May 2001 - P1 \$ - INTERNATIONAL...

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MARKSCHEME May 2001 MATHEMATICS Higher Level Paper 1 14 pages M01/510/H(1)M INTERNATIONAL BACCALAUREATE BACCALAUR°AT INTERNATIONAL BACHILLERATO INTERNACIONAL

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1. 5 3 1 1 3 3 5 3 1 1 d 1 d 2 2 t t t t t t = (M1) 4 3 1 3 d 2 t t t = (M1)(A1) (C3) 4 1 3 3 3 3 4 2 t t C = + + Note: Do not penalise for the absence of + C. [3 marks] 2. 2sin tan x x = 2sin cos sin 0 = x x x (M1) sin (2cos 1) 0 = x x 1 sin 0, cos 2 = = x x (A1)(A1) (C3) 0, or 1.05 (3 s. f.) π = = ± ± 3 x x OR (G1)(G1)(G1) (C3) ( ) 0, or 1.05 (3s.f.) π = = ± ± 3 x x Note: Award (G2) for . 0, 60 = ± ! x [3 marks] ± 7 ± M01/510/H(1)M
3. The matrix is of the form , which represents reflection in (M1) cos2 sin2 sin 2 cos2 θ θ θ θ tan y x θ = therefore (M1) 4 cos2 , 2 0 5 θ θ = > or 18.4 θ = ! 0.322 (radians) = θ The matrix represents reflection in the line (A1) (C3) 1 (or 0.333 , or tan18.4 , or tan0.322) 3 y x y x y x y x = = = = ! OR The matrix is of the form , which represents reflection in (M1) cos2 sin2 sin 2 cos2 θ θ θ θ tan y x θ = therefore , (M1) 3 tan2 , 2 0 4 θ θ = > 2 2tan 3 4 1 tan θ θ = , 2 3tan 8tan 3 0 θ θ + = 1 tan 3 θ = The matrix represents reflection in the line (A1) (C3) 1 (or 0.333 , or tan18.4 , or tan0.322) 3 y x y x y x y x = = = = !

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Mathematics HL - May 2001 - P1 \$ - INTERNATIONAL...

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