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4 Pages

### C4I

Course: MATH c3, Spring 2010
School: Cambridge College
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Word Count: 562

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EDEXCEL GCE FOR Examinations Advanced Subsidiary Core Mathematics C4 Paper I Time: 1 hour 30 minutes Instructions and Information Candidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and / or integration. Full marks may be obtained for answers to ALL questions. Mathematical formulae and statistical tables are available. This paper has seven questions. Advice to...

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Cambridge College - MATH - c3
FOR EDEXCELGCE Examinations Advanced SubsidiaryCore Mathematics C4Paper J Time: 1 hour 30 minutesInstructions and InformationCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and / or integration.
Cambridge College - MATH - c3
FOR EDEXCELGCE Examinations Advanced SubsidiaryCore Mathematics C4Paper K Time: 1 hour 30 minutesInstructions and InformationCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and / or integration.
Cambridge College - MATH - c3
FOR EDEXCELGCE Examinations Advanced SubsidiaryCore Mathematics C4Paper L Time: 1 hour 30 minutesInstructions and InformationCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and / or integration.
Cambridge College - MATH - c3
FOR EDEXCELGCE Examinations Advanced SubsidiaryCore Mathematics C4Paper BMARKING GUIDEThis guide is intended to be as helpful as possible to teachers by providing concise solutions and indicating how marks could be awarded. There are obviously altern
Cambridge College - MATH - c3
FOR EDEXCELGCE Examinations Advanced SubsidiaryCore Mathematics C4Paper CMARKING GUIDEThis guide is intended to be as helpful as possible to teachers by providing concise solutions and indicating how marks could be awarded. There are obviously altern
Cambridge College - MATH - c3
FOR EDEXCELGCE Examinations Advanced SubsidiaryCore Mathematics C4Paper DMARKING GUIDEThis guide is intended to be as helpful as possible to teachers by providing concise solutions and indicating how marks could be awarded. There are obviously altern
Cambridge College - MATH - c3
FOR EDEXCELGCE Examinations Advanced SubsidiaryCore Mathematics C4Paper EMARKING GUIDEThis guide is intended to be as helpful as possible to teachers by providing concise solutions and indicating how marks could be awarded. There are obviously altern
Cambridge College - MATH - c3
FOR EDEXCELGCE Examinations Advanced SubsidiaryCore Mathematics C4Paper FMARKING GUIDEThis guide is intended to be as helpful as possible to teachers by providing concise solutions and indicating how marks could be awarded. There are obviously altern
Cambridge College - MATH - c3
FOR EDEXCELGCE Examinations Advanced SubsidiaryCore Mathematics C4Paper GMARKING GUIDEThis guide is intended to be as helpful as possible to teachers by providing concise solutions and indicating how marks could be awarded. There are obviously altern
Cambridge College - MATH - c3
FOR EDEXCELGCE Examinations Advanced SubsidiaryCore Mathematics C4Paper HMARKING GUIDEThis guide is intended to be as helpful as possible to teachers by providing concise solutions and indicating how marks could be awarded. There are obviously altern
Cambridge College - MATH - c3
FOR EDEXCELGCE Examinations Advanced SubsidiaryCore Mathematics C4Paper IMARKING GUIDEThis guide is intended to be as helpful as possible to teachers by providing concise solutions and indicating how marks could be awarded. There are obviously altern
Cambridge College - MATH - c3
FOR EDEXCELGCE Examinations Advanced SubsidiaryCore Mathematics C4Paper JMARKING GUIDEThis guide is intended to be as helpful as possible to teachers by providing concise solutions and indicating how marks could be awarded. There are obviously altern
Cambridge College - MATH - c3
FOR EDEXCELGCE Examinations Advanced SubsidiaryCore Mathematics C4Paper KMARKING GUIDEThis guide is intended to be as helpful as possible to teachers by providing concise solutions and indicating how marks could be awarded. There are obviously altern
Cambridge College - MATH - c3
FOR EDEXCELGCE Examinations Advanced SubsidiaryCore Mathematics C4Paper LMARKING GUIDEThis guide is intended to be as helpful as possible to teachers by providing concise solutions and indicating how marks could be awarded. There are obviously altern
Cambridge College - MATH - C4
Core Mathematics C4 Advanced LevelPaper A Time: 1 hour 30 minutesInstructions and InformationFor EdexcelCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and/or integration. Full marks may be obtain
Cambridge College - MATH - C4
Core Mathematics C4 Advanced LevelPaper B Time: 1 hour 30 minutesInstructions and InformationFor EdexcelCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and/or integration. Full marks may be obtain
Cambridge College - MATH - C4
Core Mathematics C4 Advanced LevelPaper C Time: 1 hour 30 minutesInstructions and InformationFor EdexcelCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and/or integration. Full marks may be obtain
Cambridge College - MATH - C4
Core Mathematics C4 Advanced LevelPaper D Time: 1 hour 30 minutesInstructions and InformationFor EdexcelCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and/or integration. Full marks may be obtain
Cambridge College - MATH - C4
Core Mathematics C4 Advanced LevelPaper E Time: 1 hour 30 minutesInstructions and InformationFor EdexcelCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and/or integration. Full marks may be obtain
Cambridge College - MATH - C4
Core Mathematics C4 Advanced LevelPaper F Time: 1 hour 30 minutesInstructions and InformationFor EdexcelCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and/or integration. Full marks may be obtain
Cambridge College - MATH - C4
Core Mathematics C4 Advanced LevelPaper G Time: 1 hour 30 minutesInstructions and InformationFor EdexcelCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and/or integration. Full marks may be obtain
Cambridge College - MATH - C4
Core Mathematics C4 Advanced LevelPaper H Time: 1 hour 30 minutesInstructions and InformationFor EdexcelCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and/or integration. Full marks may be obtain
Cambridge College - MATH - C4
Core Mathematics C4 Advanced LevelPaper I Time: 1 hour 30 minutesInstructions and InformationFor EdexcelCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and/or integration. Full marks may be obtain
Cambridge College - MATH - C4
Core Mathematics C4 Advanced LevelPaper J Time: 1 hour 30 minutesInstructions and InformationFor EdexcelCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and/or integration. Full marks may be obtain
Cambridge College - MATH - C4
Core Mathematics C4 Advanced LevelPaper K Time: 1 hour 30 minutesInstructions and InformationFor EdexcelCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and/or integration. Full marks may be obtain
Cambridge College - MATH - C4
Core Mathematics C4 Advanced LevelPaper L Time: 1 hour 30 minutesInstructions and InformationFor EdexcelCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and/or integration. Full marks may be obtain
Cambridge College - MATH - C4
Worked Solutions Edexcel C4 Paper A1 2 3x = + (a) (x - 1)(x + 2) x-1 x+233.(a)dy = ex - 3 dx at M ex = 3 x = ln 3ln 3 ln3 3 (ex - 3x)dx = ex - x 2 2 01.(using `cover up' rule)(3)(2)(b)22 1 + dx = ln(x - 1) + 2 ln(x + 2) x-1 x+2 5 4 25 = ln 2
Cambridge College - MATH - C4
Worked Solutions Edexcel C4 Paper B1. (a) xy - 2y + 5x - 10 = 12 x dy dy + y.1 - 2 +5=0 dx dx (b) - 3. 1 1 - 1 2 2 (a) 1 + (8x) + 2 2 1 1 3 - - 2 2 2 (8x)2 + 3.2 (8x)3 + . . . (3) (1)= 1 + 4x - 8x 2 + 32x 3 1 1 &lt;x&lt; 8 8dy (x - 2) = -(y + 5) dx dy y+5 =
Cambridge College - MATH - C4
Worked Solutions Edexcel C4 Paper C1. (a) 5x + 7 2 3 = + (x + 1)(x + 2) x+1 x+2 y = 2(x + 1)-1 + 3(x + 2)-1 dy = -2(x + 1)-2 - 3(x + 2)-2 dx d2 y dx 2 = 4(x + 1)-3 + 6(x + 2)-3 d2 y dx 2 4 6 13 = 3 + 3 = 18 2 3 (3) 4. (3) (b) valid for - 1 1 &lt;x&lt; 2 2 (1)
Cambridge College - MATH - C4
Worked Solutions Edexcel C4 Paper D1. (a)y3.GivendS dr = 640 cm2 s-1 . To find . dt dtS = 4r 2 dS = 8r dr2 xdS dr dS = dt dr dt when r = 5, (2) 640 = 8 5 640 dr = dt 40 = 16 cm s-1 (4) dr dt22 2(b) volume = y 2 dx = (9 - x 2 )dx0 02 1 8 = 9x
Cambridge College - MATH - C4
Worked Solutions Edexcel C4 Paper E3. 1. (a) when y = 1, 4x 2 + 3 = 12 x2 = 9 4 3 2 dy 8x 4x =- =- dx 6y 3y (2) 1 2 cos 2 cos 2 dy 2 = =- (a) dx - sin sin 1 cos 3 = - 2 = -1 at = , gradient = - 1 6 sin 6 2 3 1 1 (b) at = , x = cos = and y = sin = 3. 6 6
Cambridge College - MATH - C4
Worked Solutions Edexcel C4 Paper F1. dx dy = cos t, = 2 + sin t dt dt cos t dy = dr 2 + sin t dy = 0. stationary points where dx 3 , . 2 2 when t = , x = 2 - cos = ; y = 2 2 2 2 i.e. cos t = 0 t = t= 3 , 2 x =2 3 3 - cos = 3; 2 2 y = 1 + sin 3 =0 2 (5)
Cambridge College - MATH - C4
Worked Solutions Edexcel C4 Paper G1. (a) 2 cos t dy = dx - sin t when t = , 2 gradient = 0 (2) (b) (1 + bx) 1 + 6ax + 15a 2 x 2 = 1 + 6ax + 15a 2 x 2 + bx + 6abx 2 we have 6a + b = -9 15a 2 + 6ab = 24 from equation [A] substitute in [B] Hence a = -2, .[
Cambridge College - MATH - C4
Worked Solutions Edexcel C4 Paper Hx 1. (a) 1 1 + e-1 -1 1 1+e 0 1 1+1 1 1 1+ 1 e e = 1 e+1 1+ e 1 2. (a) (i) differentiating implicitly, 1 = ey 1 1 dy = y = dx e x (ii) when y = 0, x = e0 = 1 dy =1 dx dy dx (2)integral 1 e 1 1 + +2 2 1+e e+1 2 (b) (4)
Cambridge College - MATH - C4
Worked Solutions Edexcel C4 Paper I1. (a) dy 1 dx = (- sin ), = 2 cos 2 d (1 + cos ) d dy - sin = dx (1 + cos )2 cos 2 where = , gradient = 6 1 - 1 2 =- 1 3 3 2 2 1+ 1+ 2 2 2 1 (2 - 3) =- =- = 3-2 2+ 3 (2 + 3)(2 - 3) 3. (a) 1 dy + 3x 2 - 2 = 0 y dx dy =
Cambridge College - MATH - C4
Worked Solutions Edexcel C4 Paper J1. (a) We are given that dA = 40 cm2 s-1 dt 3. (a) 3 2 + 2x - 1 x + 2 1 dy = y (using `cover up' rule) (3)(b)after 10 seconds area of circle = 400 cm2 so r 2 = 400 r= (b) A = r 2 dA = 2r dr dA dr dA = dt dr dt when r
Cambridge College - MATH - C4
Worked Solutions Edexcel C4 Paper K1. 4 dV = 4r 2 (a) V = r 3 , 3 dr (b) dV dV dr = dt dr dt given r = 10 and dV dr = 0.1, = 4 102 0.1 dt dt = 40 cm3 s-1 dy 1 dy + ln y + =0 y dx dx (4) 3. (a) at P y = 0. cos t = 0 t= 2. (a) 2x + x dy dx at t = 2 (1) 3x
Cambridge College - MATH - C4
Worked Solutions Edexcel C4 Paper L1. 1 dy = 2x dx y ln y = x 2 + c y = e, x = 1: ln e = 1 + c c=0 ln y = x 2 y=ex23.(a) (, 0) (b) dy = x cos x + sin x dx dy 0.02 when x = 2.02, dx dy -0.03 when x = 2.04, dx (c) Area = x sin x dx =0 0(1)(4) d x (
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