IGCSE Mathematics 0580 / 4

IGCSE Mathematics 0580 / 4 June 1999 Mark Scheme

QUESTION ANSWER MARK

12 M1 for x48790 or equivalent 1 (a) 83640 2 7 SC1 for 83600 or 34850 given as answer 14760 FT M1 for x100 (b) 15% to 15.01% 2 14760  (a) SC1 for 17.6% or 85% did vote 48790 M1 for x100 14760  (a) (c) No 3 A1 for 49.5 to 49.6 or 0.495 to 0.496 A1 for ‘No’ – only if previous A1 awarded 2 (a) 40 years 1 B1 for 50 seen or implied (b) 7.95cm to 7.96cm 3 2.5x20 M1 for or equivalent 2

(c)(i) 19.5cm to 19.6cm 2 M1 for 1200  

(c)(ii) 49 years 2 FT M1 for 2π x (a) ÷ 2.5 B3 for 125 or 126 seen (d) 2093 or 2094 4 M2 for any complete correct method SC3 for 2096 or 2097 seen M1 for xcos70 = 5 or equivalent 3 (a) 14.619cm 3 5 M1 for x  or equivalent cos70 M2 for 72  14.622  2x7x14.62cos20 or equivalent (b)(i) 8.39cm 4 A1 only if answer given as 8.4cm

2 1 x7x14.62sin20 (b)(ii) 17.5cm 3 M2 for 2 or other complete correct method B2 for area ACE = 68.7 or height of triangle ACE = 13.7 or height of triangle ABE = 6.74 or angle BAE = 53.4o (c) 33.68cm2 to 33.7cm2 5 or angle ABE = 73.2o M2 for subsequent complete correct method 4 (a) 0.75, 0.8, 0.6 1,1,1 On correct branches

1 Accept 20 or 5% (b)(i) 0.05 2 M1 for 0.25 x 0.2 or equivalent 19 Accept 400 or 4.75% (b)(ii) 0.0475 3 FT M2 for (b)(i) x [1 – (b)(i)] or equivalent FT SC1 for [1 – (b)(i)] seen 13 Accept 20 or 65% (c) 0.65 3 M2 for complete correct method SC1 for (0.25 x 0.8) and (0.75 x 0.6) seen Accept 81 or 40.5% (d)(i) 0.405 2 200 M1 for (their 0.75) x (their 0.6) x 0.9 Accept fractional form or 6.6% (d)(ii) 0.066(4…) 2 M1 for (their 0.405)3

5 (a) A and D 2 SC1 for D and G

(b) D and F 2 SC1 for B and G

(c) G, (0, -1) 1,2 SC2 for A, (-1, -2) or B, (-1, -1) or E, (2,2)

6 6 (d) B and E,   1, 2 Accept   0  0  B1 for (4, 1), B1 for (3, 1), B1 for (1,0) and (2,0) (e)(i) (1, 0), (2, 0), (4, 1), (3, 1) 3 SC2 if answer left in matrix or column vector form

(e)(ii) Shear, scale factor 2, x-axis invariant 1,1,1 S1 for correct scale 6 (a) Correct curve drawn 6 P4 for 7 points correctly plotted (±1mm), -1 for each error C1 for a smooth curve drawn through points

(b)(i) -2.75 to –2.65 1

(b)(ii) 4.6 to 5.2 2 B1 for evidence of using x = 1.7 on the graph to find y

(c)(i) y = 5x + 1 1 Allow f(x) or equivalent for y

Correct line drawn on graph 2 FT only if answer to (c)(i) is y = ±5x ±1 (c)(ii) -2.2 to –2.1 1 -0.25 to –0.15 1 2.25 to 2.4 1

AMˆ B  CMˆ D , Aˆ  Cˆ , Bˆ  Dˆ 2 Any two of the three pairs of equal angles stated 7 (a)(i) Correct reason 1 At least one correct reason – e.g. angles in same segment

Allow √40cm (a)(ii) 6.32cm 2 10 x M1 for  or equivalent x 4

(b)(i) p 1

(b)(ii) -2.5q 1

(b)(iii) p – 2.5q 1 FT for (b)(i) + (b)(ii)

(b)(iv) p - q 1

(c) p – 2.5q  k(p – q) 1 Convincing explanation required

8 (a)(i) 21 2 M1 for (66, 67 or 68) – 46

Median = 64 1

(a)(ii) Quartiles = 39 and 87 1,1

IRQ = 48 1 FT but not 75 – 25 = 50

M1 for using mid-interval values (condone one error) (a)(iii) 64.5 4 M1 for fx M1 for dividing by 100 – only if previous M1+M1 awarded

(a)(iv) 20  C  40 1

(b)(i) Width 3cm, Area 30cm2 1 Both mentioned

(b)(ii) x = 13, y = 11, z = 5.5 1,1,1

9 (a) 36000  (50 x 30) 2 SC1 for 36000 seen

(b) 5x(x + 5) 2 SC1 for (x + 5) seen

5x(x + 5) + 36000 = 50 x 30 x 25 M2 for 5x(x + 5) + 36000 = 50 x 30 x 25 or equivalent (c)(i) 4 A1 for 5x2 + 25x = 1500 simplify to x2 + 5x - 300 A1 for completion of proof

 5  1225 M2 for (x + 20)(x – 15) or (c)(ii) -20, 15 4 2 A1 for each correct answer (c)(iii) 20cm and 15cm 1 Correct answers only

Correct scale 1

y = 600 1 10 (a) y = 0.01x 2 B1 for line through (0, 0) or line with gradient 0.01

y = 200 for 0 to 30000 1 y = 0.015x –250 for 30000 to 80000 2

(b)(i) $60000 1

(b)(ii) $20000 to $50000 1, 1 SC1 for $(0 or 1) to $30000

M1 for use of y = 150 seen (b)(iii) $15000 2 SC1 for $25000 or $40000 or $60000