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 11 33 5 3 1 1d 2 2 t tt t   −=  ∫∫ (M1) 4 3 1 3 d 2 t = −  (M1)(A1) (C3) 41 42 C =+ + Note: Do not penalise for the absence of + C. [3 marks] 2. 2sin tan xx = 2sin cos sin 0 ⇒− = x (M1) sin (2cos 1) 0 = 1 sin 0, cos 2 ⇒= = (A1)(A1) (C3) 0, or 1.05 (3s.f.) π = ± ± 3 OR (G1)(G1)(G1) (C3) () or 1.05 (3s.f.) π == ± ± 3 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 θθ    tan yx θ = therefore (M1) 4 , 2 0 5 => or 18.4 = ! 0.322 (radians) = The matrix represents reflection in the line (A1) (C3) 1 (or 0.333 , or tan18.4 , or tan0.322) 3 yxy xy x y x == = = ! OR The matrix is of the form , which represents reflection in (M1) tan = therefore , (M1) 3 tan2 , 2 0 4 2 2tan 3 4 1t a n ⇒= , 2 3tan 8tan 3 0 +− = 1 tan 3 The matrix represents reflection in the line (A1) (C3) 1 (or 0.333 , or tan18.4 , or tan0.322) 3 x y x = = ! [3 marks] & 8 & M01/510/H(1)M

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4. 22 34 7 xy += When (since ) (M1) 1, 1 == 0 y > (A1) dd (3 4 7) 6 8 0 y x y xx + = d3 d4 yx ⇒= The gradient where (A1) (C3) 3 1 and 1is 4 OR 7 (M1) 2 73 ,since 0 4 x yy > (A1) 1 2 d 2(7 3 ) x x =− , when (A1) (C3) 3 4 1 x = [3 marks] 5. (a)
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## This note was uploaded on 05/06/2010 for the course MATH 1102 taught by Professor Chang during the Spring '10 term at Savannah State.

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

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