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2013年CIE剑桥国际考试IGCSE数学真题答案(43)


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CAMBRIDGE INTERNATIONAL EXAMINATIONS
International General Certificate of Secondary Education

MARK SCHEME for the May/June 2013 series

/>0580 MATHEMATICS
0580/43 Paper 4 (Extended), maximum raw mark 130

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers.

Cambridge will not enter into discussions about these mark schemes.

Cambridge is publishing the mark schemes for the May/June 2013 series for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components.

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Page 2

Mark Scheme IGCSE – May/June 2013

Syllabus 0580

Paper 43

Abbreviations cao correct answer only cso correct solution only dep dependent ft follow through after error isw ignore subsequent working oe or equivalent SC Special Case www without wrong working art anything rounding to soi seen or implied 1 (a) (b) (c) (i) (ii) (d) 2814 final answer 257.95 final answer 280.5[0] final answer 375 1605.89 or 1605.9[0] 2 2 2 3 3 M1 for 2345 ÷ 5 soi by 469 or ans = 2810 M1 for 2345 × 0.11 oe or ans = 258 M1 for 330 × (1 – 0.15) oe or ans = 281 M2 for 330 ÷ (1 – 0.12) oe Or M1 for 330 = (100 – 12)% oe M2 for 1500 × (1 + 0.023)3 oe soi by 1605.898751 or 1500 × 1.07(05…) Or M1 for 1500 × (1 + 0.023) 2 oe

(e)

23.1 or 23.07 to 23.08

3

325 ? 250 × 100 oe 325 325 ? 250 soi by 0.2307… 3sf or Or M1 for 325 better 250 or × 100 soi by 76.9… 325
M2 for

? Cambridge International Examinations 2013

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Page 3

Mark Scheme IGCSE – May/June 2013 Perpendicular bisector of QR ruled with 2 correct sets of arcs centred Q and R Bisector of angle SPQ ruled with correct arcs. (Marks on PS and PQ and correct pair of arcs) Compass drawn arc centre R with radius 6 cm (±2 mm) Correct region shaded cao 2

Syllabus 0580

Paper 43

2

(a) (i)

B1 for correct bisector ruled

2

B1 for correct angle bisector ruled

B2 1dep 1 2 2 1 1 1 1 1 1 2 2 1dep 2

B1 for any compass drawn arc centre R not used in any construction with no feathering Dependent on all B4 marks for the correct loci

(ii) (b) (i) (ii) 3 (a) (i) (ii) (iii) (b) (c) (i)

217 to 221 6360 or 6361 to 6363 165 or 164.9 to 165 x≥5 y ≥ 11 x + y ≥ 20 4x + 8y ≤ 160 and divide by 4 x = 5 ruled y = 11 ruled x + y = 20 ruled x + 2y = 40 ruled Correct shading of unwanted region

M1 for π × 452 M1 for

210 × 2π × 45 360

–1 once for strict inequalities in (i) to (iii)

If there is a final inequality it must be the given one Must be on correct grid line Must be on correct grid line B1 for one axis intercept correct when extended if necessary but not parallel to an axis B1 for one axis intercept correct when extended if necessary but not parallel to an axis Dependent on 6 marks earned for the boundaries M1 for x + y evaluated where (x, y) is a point in their quadrilateral and x and y are integers

(ii)

29

? Cambridge International Examinations 2013

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Page 4

Mark Scheme IGCSE – May/June 2013 3080 46.2 or 46.18 to 46.2 www 2 4

Syllabus 0580

Paper 43

4

(a) (b)

M1 for ? × 7 × 22 × 40 M3 for 7 2 + 22 2 + 40 2 or M2 for 72 + 222 + 402 soi by 2133 or M1 for correct Pythagoras on one face
7 M2 for sin– 1 their(b) oe
7 oe their(b)

(c)

8.7 or 8.7 to 8.72 www

3

or M1 for sin =

(d)

217

3

4 ×π×1.53 soi by 14.1 to 14.14 3 and M1 dep for their (a) ÷ their 14.14 soi by 218. Dependent on M1 earned
M1 for B1 for 4.55 and 11.05 seen or 25.13875 seen and then spoiled Strict FT their (e)(i) correct to 4s.f. if rounding is possible B1 for each correct value B3FT for 10 correct plots from their (a) B2FT for 8 or 9 correct plots or B1FT for 6 or 7 correct plots and SC1 for two branches not joined

(e) (i) (ii) 5 (a) (b)

25.13875 final answer 25.14 –5.04, 1.75, 0 Fully correct curve

2 1FT 3 5

(c)

–1.6 to – 1.5 –0.4 to –0.3 1.8 to 1.9 –2.6 to –2.5 www –0.4 to –0.3 1 3.25 to 4.25 with correct tangent

1 1 1 1 1 1 3

(d)

After 0 scored, M1 for y = 2x – 2 drawn B1 for correct tangent

(e)

B2 for answer in range dep on close attempt at tangent
rise used with values soi from run tangent, dep on correct or close attempt at tangent

M1dep for [–]

? Cambridge International Examinations 2013

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Page 5

Mark Scheme IGCSE – May/June 2013

Syllabus 0580

Paper 43

6

(a)

3 correctly placed 10 6 3 and correctly placed 9 9 7 2 and correctly placed 9 9 42 21 14 7 or or or 90 45 30 15

1 1

Accept 0.3 Accept 0.667 or better and 0.333 or better

1

Accept 0.778 or better and 0.222 or better

(b)

3

M2 for better

7 3 3 7 × + × soi by 0.467 or 10 9 10 9 7 3 3 7 × or × soi by 0.233 or 10 9 10 9

or M1 for better 7 (a) (i) Triangle at (1, 3) (1, 9) (3, 3) 2

SC1 for correct vertices not joined or triangle(1, 1) (3, 1) (1, 7)

(ii)

?1 0? ? ? ? 0 3? ? ?

2

?1 SC1 for ? ?0 ? ?3 or ? ?0 ?

0? ? , k ≠ ± 1 or 0 k? ? 0? ? 1? ?

(b) (i)

Shear x-axis oe invariant [factor] 2

1 1 1 2FT FT from their 2 in (b)(i) ?1 k ? SC1 for ? ?0 1? ? ,k≠0 ? ?

(ii)

?1 2? ? ? ?0 1? ? ?

0? ? 1 or ? ? ? 2FT 1 ? ? ?
8 (a) (i) (ii) (iii) (b) (i) 27 54 153 59.6 or 59.57… www 1 1 1 4 M2 for 452 + 322 – 2 × 45 × 32 × cos100 or M1 for implicit cos rule and A1 for 3549…. M2 for 324 ÷ (? × 32 × sin67) or M1 for [324 =] ? × 32 × x × sin67 B1 for 22 or (?)2 oe seen or ? × 16 × ? their(b)(ii) × sin67

(ii) (iii)

22.[0] or 21.99… www 81[.0]

3 2

? Cambridge International Examinations 2013

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Page 6

Mark Scheme IGCSE – May/June 2013 14 8 30 – their (ii) 1 1 1FT 2 2 3 SC1 for
69 80

Syllabus 0580

Paper 43

9

(a) (i) (ii) (iii) (b) (c) (d)

11 80
16, 4 18.0625 rot to 3sf or better or 18.1 www Correct widths with no gaps 2nd block w = 5, fd = 2.4 3rd block w = 15 fd = 1.2 4th block w = 10 and fd = 1.6 5th block w = 10 and fd = 0.4

B1 for each correct value M1 for Σmf for m as mid values of 5, 12.5, 22.5, 35 and 45 (= 1445) and M1 dep for Σmf ÷ 80, dep on M1 earned

(e)

1 1 1 1FT 1FT

Strict FT from their (c) Strict FT from their (c) After 0 scored for blocks, SC1 for 4 correct fds soi by correct heights M2 for a complete correct method or M1 for one correct step at any stage. M1 for (x +a)(x +b) where ab = 6 or a + b = - 7 FT their brackets dep on M1 earned After M0 scored SC1 for 1, 6 as answer B1 for 2(3x – 2) + x + 2 = 4×10 oe and B1 for correct multiplication of a bracket and M1 for correct rearrangement of their linear equation without brackets to ax = b + c + d or better B1 for any one of 1 = a + b + 1/6 oe 5 = 8a + 4b + 2/6 oe 14 = 27a + 9b + 3/6 oe 30 = 64a + 16b + 4/6 oe Or any other correct equation and B1 for another of the above equations and M1 for equating one coefficient or correct rearrangement to give a or b as subject and M1 for subtracting to eliminate a or b or correct substitution for their a or their b A1 for a = 1/3 oe or b = 1/2 oe

10 (a) (i) (ii)

4.5 or 4? (x – 6)(x – 1) 1, 6

3 M2 A1FT 4

(iii)

6

(b)

a = 1/3 oe, b = 1/2 oe

6

? Cambridge International Examinations 2013


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