Sets And Venn Diagrams Igcse Questions Answers 2r45x

Page 3

Mark Scheme IGCSE - OCT/NOV 2006

Syllabus 0580/0581

Paper 2

SETS AND VENN DIAGRAMS IGCSE QUESTIONS ANSWERS Page 2

Mark Scheme IGCSE – May/June 2006

Syllabus 0580 and 0581

Paper 02

May 2006 Paper 2 Page 3 Mark Scheme Syllabus Paper IGCSE – October/November 2007 0580/0581 02 17 (a) * indicates that it is necessary to2 look in B1the numbers B1 labels working following a wrong answer

1

(a) 4.25957(744…) or 4.25958 (b) 4.3

1 1√

Must have at least 6 figures correct Correct answer or ft from (a)

2

5 x 104 or 50000

2*

3

(b) (a) 4 cao (b) 0

2 1 1

M1 3.6 x 1013 / 7.2 x 108 or M1 8.33…x 10-3 x 6 x 106 B1 numbers B1 labels

x2 , cos x°, x-1

2*

4

5 2 18 w = 30 x = 22 y = 302002 Paper 2 November cao 6 (a) z =0.003 52 x 3000 (10 + 20)2 19 (b) (a)0.01(2xor–1/100 3)(2x + 3) 7

x(b) =2

y = -6– 9) cao x(4x

(c) (4x – 1)(x – 2) November 2006 Paper 2 = –1 c = 8 820 (a)(a) 0.701m cao (b)(b) (-)190

9

p=2

q = -12

Allowzero 0 in or annone intersection of A and B Allow or no symmetry W1 reverse order Numerical values not allowed in answer space

2* M1 25c/35 or 125c/ 175 or 25c = 50 or 125c = 250 or 875c = 1750 oe 1,1 1 f.t. y = w 11 f.t. No w +extra 22 zeros allowed. Accept standard form 11

SC1 for answer 0 if 0 is used for 0.003 in (a)

13*

M1 consistent x and + for x or consistent x and - for y A1A1

2 1,1 1 2*

Allow 0.70, of course, if 0.701 seen in working M1 14020 – 20000 x 0.6915 or reversed

3*

M1 x2 + 2px + p2 (+q) or (x + 2)2 – 4 – 8 A1 A1 If no marks scored give SC1 for p = 2 in answer

2* 1021 170 (a) provided that 22 is not used 7

13*

2 M1 x π x 122 - ½ x π x 62 or ½ x π x (12 or 6) M1 ½ 2 SC2 54π or SC1 π x 12 - π x 62 seen

allow 452…

11 100 November 2007 Paper 2

12

13

1 1 1 1

(a) ø (b) ξ (c) A 28.2

3*

28.6 exact values only

(b)

plane of symmetry

(c)

3

3*

-

113……

M1 M = kr3 A1 k = 0.8 M1 kM = r3 A1 k = 1.25

No brackets allowed. No brackets allowed

Not ε or e

M1 two of 6.05, 6.15, 8.05 or 8.15 seen A1 28.2 or 28.6 in either answer space ©1UCLES 2006 SC2 both correct reversed

1

5 10

38 24.3(0788…) (b) 1

2

M1 for 665/(17 " 18) s.o.i. by 3equivalent M1 5 ×complete 3.5 + 2 × 1.5 method M1 (√) 1.52 + 3.52 1

2

2014sin or 3201.3 in ans.and space if 2allowM1 120 evaluated rounding to 2.6 or 3201.25 M1seen one correct move to clear fractions 3 3 M1 second correct better or move to subtract term 2 M1 for 17.5(2.598…) ! 11.5 s.o.i. M1 third correct move2 dividing by 5 May be in any order Mark Scheme Paper 7Page 1 4 < x <63 2 2 SC1 for either one Syllabus , IGCSE , 3EXAMINATIONS – 32JUNE 2– 3,2– 3 M1 correct decimals seen 2005 0580/0581 22 12 M1 15 only in small circle after 0, M1 for 8<2x<12 s.o.i. 2 35 2 M1 10 only in the intersection Q R * indicates to look in the3working following acorrect wrong answer labels A1orall5 correct including +!11 326it is necessary 2 for 4 8 15a4that P 15 –10 !1331 oe 4 2 B1 15a + 32 seen 1 for 2 or 3 correct 40148 196 20– 1 (a) -7 25/32 49 1 3 – 15a 32 + on answer line or SC1 (b) 0.781 (25) 1√ Page 2 Mark Scheme Paper 40 40 Syllabus 13 x = 12 y = –10 3 M1 consistent addition (& mult) for x IGCSE – May/June 2* 2008 M16 sin –4 0580/0581 2 0.276 5° = h/3.17 0.28 may score21 M0 10 17 5 2 2 M1consistent 2 or 2 seen or subtraction (& mult) for y June 2010 Paper 2.2 1 A1Allow 2/125 if method correct 3 9 (a)(a) 0.016 only earned 1 7or 0.16(…..) 1 6 6.4 × 10 2 M1 64 × 1002 × 102 or 64 000 000 oe or 0.17 -2 1√ x 10 essential Syllabus 6 × 10 Page(b)2 1.6 Mark Scheme Paper k ∩ C' or A' ∩ (B ∪ C)' 1 or A' 7 53 3.84 (A B3∪21C)' B' ∩ 114 and∪59 1, 1 independent of each other r M1 y = oe A1 k = 96 or 3 IGCSE – May/June 22007 M1 A0 2other answers 0580 and 0581 0.99 to 1.053 2 4 1(.00) or 0.9 in range 9.5(#) 2 of tan o.e. 3 (b)(A ∪ art C)'25 1M1 for orcorrect A' ∩ xC'use ∩ B ∩ B 11x (a) 3 25 2 61x1 10 x 5 x 8 (a) 433tolines 47 M1 oe fractions −by eye 18 (b) 1+ 10 3 x ! 11 (x $ 3)(xwith " 4)common o.e. denom. not 18M1 for 18 denom. 18 o.e. May 2003 Paper 2 2 4) $2 (x 2(x $ 3) o.e. (to x "68 3)( x ! 4) 6 (a) 645.66 2 for M1234"to +27 4 or 4/sin45 or 4√2 or √32 3 SC1 decimals (b) 2M1 2 (b) 32(.0) 1√ (a) from the answer space 18 © UCLES 2010 cao 3 × 100 M1 figs 1995 M1 39 11 15063.84 integer 2 1 16 or 4 lower 12accept 7 (a) 21.5 22.5(112 / 7) 1,1 M1SC1 correct but reversed 32 × their bound (b) rational 172 1√ (a) least value x8 1 nos. 2.6 accept 0.235 3 1 1cao 4accept 410 (a) x 2870 4/17 forfor each of the four moves completed 8 x == 8P −y1 = 6 3* M13.46 M1 multiplication and subtraction correctly 1 4 2 1 no. oe12 1 Allow n22 + 6n +M1 10,wf(n=+k2 + 1)A1 + 1, (nk–=1 300000 + 4)2 + 1 oe (n +irrational 3)2=+ 300000 9 (b) (a) wf 18 2 1112 (a) (a) 1M1 (b) 10(.0..) 500 1√ for 2p " 3p " 90 = 180 o.e. or /SC1 for245 36 ×or0.94(3...) 54 seen www. 5 $231.13 2 M1 245 1.06 or cao May Paper 2 2 prime 2 count/19 2 2 10 2005 (a) 9.80 8/19 or 0.421 2 M2 their number (b) 30 2Allow3M1 22) or M1 (b) √((a) qM1 " 5q =– 180 o.e. 231,for 231.1, 231.13… for M1PT + 2 = (a) (b) 7/18 or 0.389 1√ 4 or SC1 for 150 seen h 598 399 698 611 2 M1 correct seen M1B1 sinfor 37.1 orcorrect cos 52.9place = oe 2 3 decimals 12 (a) 440 8 in 730 601 401 701 0.99501.... 0.9957(2…) 0.99500… B1 for 2 in correct place 14 7 in correct place First and third B1 mustforbe4toand at least 5sf 730 Accept decimals in answer space 2 theseM1 (b) 3 min 20 sec SC2 3.652 4 8 7 or 2 6 6 7 7 (a) 1045.28 cao 1 −3 ⎞ ⎛ 6 x − 3 ⎞ but not ⎛ 6 x 13 (b)(a)1000 ⎜ 4x + 5⎟ ⎜ 4 x (+)5 ⎟1 Allow2 1.0 × B1 1036x – 3 or B1 4x + 5 in a (2 × 1) matrix on ⎝ ⎠ ⎝ ⎠ 12 (a) 1 4x ⎤ ⎡2 x © University answer lineSyndicate 2003 of Cambridge Local Examinations 2 2 ⎢ ⎥ B1 9 B1 x must be multiplied 8 9x 2 4 x 2 x 2⎣ May 2007 Paper 2 cao⎦ (b) (6x + x + 5) 2 2* M1 any 1 × 21 matrix in answer space ⎡ x + 4x 2 2x 2 + 2x 2 ⎤ 2 2 8 − 5 ⎤ ⎡ 5 x 4 x 1 M1 ⎢ 914 y =(b) x+ 5 ⎢ 3 M1 (m=) (c=) 5of the letter 4 Mark oe theB1 position R (or ⎥the worst ⎥ x 2 + 4 x 2 ⎦⎥ ⎢2 x 2 + 2 x 2 2 2 2 ⎣ 6 − 0 5 x ⎥⎦ unshaded region if R is missing) as follows ⎢⎣4 x or 13 (a) 8, 11, 14 1 M1 A11y – 8 = 1 ( x – 6 ) or y – 5 = 1 ( x – 0 ) (b) 3n + 2 2 2 (c) 182 1√ 1 Allow 3/6 for the 2 (d) 29 1√ integers only 1 A1 y = + 5 or 2y – x = 10 oe x 14 (a) 20% 2* 62000 2 x 100 M1 for 310000 10 r = 18 h = 42 cao www 3 M1 Length scale factor of 6 used or stated Al Al © UCLES 2 20102 May 2008 (b) 400% 2 11 (±) 7.94 Paper 3 M1 212* = (2x) + x2 – 248000 2.2x.x.cos120 oe M1 for x 100 2 62000 M1 441 = 7x 12 2 B1 P and 15 (a) (a) 3/2 oe 1 S not intersecting. Two be labelled (b) y = 3/2x – 7 2*√sets must M1 correct method Three intersecting circles will have P ∩ S empty. 16 3* M1 (x + 2)(x +2) - x2 4( x + 1) oe 2 B1 x + 4x + 4 x ( x + 2) 4w 2 6 02cw −201.25 oe 11 5 June 2010 Paper 2.1

(b) 4 13

2

1√ 1

from the number of elements in the shaded area

x < −23 2 or –23.5 © University of Cambridge 3 M1 2International moves completed correctly2005 Examinations M1 2 more moves completed correctly

7

7 3200

3 (a)

06 41

8

3.23

17 ⎝ 3 ⎠

M1 R = kv2 M1 k = 2 Note 2400 scores M0

3*

1

$204 May(b) 2009 Paper 2

1

Allow 6.41(am). 6:41 and 06:41 2* figs 4 figs 128 − figs 124 Not 6h41m or M1 or 641h or 6.41pm figs 124 figs 124

Note 3.13 is M0 4

9

(a) 71 (b) 7n + 1 (c) 37

1, 1

Page 2

10

2

M1 sin 12 = h/864 their–“180” M1 det M1 A or586 |A| or+ 5×–2 4×–3 = 2 or B1 cos78 − 3 ⎞– if one a bin ⎛ 5 M1 ⎛error ⎞ formula M2 or 1 ⎜rule ⎜ ⎟ sine ⎟ seen or 2 ⎝c d⎠ ⎝ 4 − 2⎠ 2

A2

(a) 145

B1 7

B sin Q A sin 41 × 10 or 62.225 or 55 6.2225 2 (ii) 62225000 o.e. = million cao 45 48 15 14 43 47 sin Q =

49

46 2

40 42 44

www4

The numbers must be completely

inside the M1 9.5(million) andcorrect 6.55 seenregion M1 3sf not appropriate for UB and not allowed for 2 marks M1

15 sin 55 14

(4,61.4 2)

7

4

(RS ) = 169–2/2 in matrix A1 for –3/2, Allow 2* 5/2, B1 One4/2, region correct

13

6

0580/0581

3*

53 (a) (i) 60 1 ⎛⎜ 5 − 3 ⎞⎟ or ⎛⎜ 2.5 − 1.5 ⎞⎟ 2 − 2 2 Paper November 42004 (ii) 2 ⎝(RS ⎠ 60 ) = 7⎠ + 15 2⎝−22 ×27 ×−151cos

(b)(i)

Allow 7 x n + 1 Their part (b) = 260 correctly solved Syllabus Paper

Mark Scheme IGCSE – NOVEMBER 2005

766

11

1 1 1√

Implies previous method

2+6 −5+9 A1 oe M1 www3 and 2 2 or a drawing used correctly

(iii) (R =) 63.6

B1

(b) 2 14 sin'63.6' (PQ ) =

Count the numbers in the region

1√ their sin(180 – 55 – b(ii)). Could be explicit M1 between A and equivalent cosine ruleB

sin 55

Not 45, 49 15.3

A1

1 7 b.215+sin' 5 60'+ 12 .15.'15.3'. sin 55

12 (c)

www3

3* M1M1 for acorrect correct operation M2 for one triangle area in working (45.466 + 93.998) M1 for a second correct operation

c =2

3

November 2005 Paper 4 139 or 140 www

A2

A1 for 139.4 to 139.5

www4 [16]

© UCLES 2009

4 (a) (i) (ii)

12

B1

3

B1

© University of Cambridge International Examinations 2005 (iii) 21

B1

(iv) 2

B1

(v)

14

B1

o.e

Accept probabilities as fractions/decimals/%

24

Page 7

Mark Scheme

(vi) 122008 B1 o.e. Paper 4 November 19 IGCSE – October/November 2008 (b)(i)

12 22

132 (q =) 12 cao o.e. (0.286) 462

(r =) 1 ft (ii)

10 22

× 12

240

cao o.e.(0.519) 462

(c) (i) 26

B1 Accept in correct order if no labels A1 www2 B1 2/7 in simplest form B1ft ft for r = 18 – their p – their q provided r not negative M1

21

(b) (i) 17 10 cao 12 their × × 2 o.e. 22 21 (ii) 12

Paper 04

M1

× 11 21

(p =) 5 cao,

9 (a)

Syllabus 0580/0581

cao

B1 M1 B1 A1

40/77 in simplest form

www3

B1 [11]

(ii) 57 (d) (i)

ft

B1ft

ft 45 + their q

B1

8 oe isw

100 (ii)

B1

45 oe isw

100 © University of Cambridge International Examinations 2005