Question 11
Question
In the question paper above.
Mark scheme
11(a)(ii) Triangle drawn at (1, 0), (1, –2), (4, –2) 2 B1 for two correct vertices or for triangle reflected in y = –x 11(b) Rotation 3 B1 for each 90 clockwise oe (–1, 5) Trace ID: PC-A5C66EEC6F Re-uploading, mirroring or re-hosting this file on any other website or domain is unauthorised and traceable. Licensed for hosting on papacambridge.com only. PapaCambridge Downloaded from PapaCambridge - https://papacambridge.com/ 12(a) 2.3 × 105 cao 1 12(b) 3.78 × 1032 cao 2 B1 for figs 378 or M1 for 42 × 1031 or 0.42 × 1032 or 1031(4.2 × 10 – 4.2) oe or 1032(4.2 – 4.2 ÷ 10) oe 12(c) 2 × 1017 cao 2 1 ( M1 for 8 ×1051 3 oe ) 13(a) or { } 1 13(b) 9 1 14 12 nfww 4 B2 for x = 15 or M1 for 180 – 2x = 135 + x oe M1 for 360 ÷ (2 × their x) oe 180 ( n − 2 ) or = 135 + their x oe n 15 6 10 2 B1 for [ 40 =] 2 10 or [ 160 =] 4 10 or answer 3 40 16(a) [x =] 35 2 B1 for each [y =] 105 16(b) Angle at the centre of a circle is twice the 1 angle at the circumference 16(c) 21π cao 3 360 − 150 M2 for × π × 62 oe 360 150 or M1 for × π × 62 oe 360 210 If 0 scored, SC1 for × π × k oe 360 Trace ID: PC-A5C66EEC6F Re-uploading, mirroring or re-hosting this file on any other website or domain is unauthorised and traceable. Licensed for hosting on papacambridge.com only. PapaCambridge Downloaded from PapaCambridge - https://papacambridge.com/ 17(a) 8 3 4 B3 for AC equivalent to 8 3 but not in 24 the form a b e.g. 3 OR 12 M2 for [ AC =] oe cos30 12 or M1 for = cos30 oe AC 3 B1 for cos 30 = 2 17(b) 6 nfww 3 d M2 for = sin30 oe 12 or M1 for recognition that the shortest distance is the perpendicular from B to AC. 18(a) 4π × 42 M2 4π × 42 πr 2 + πr × 12 = + π × 42 M1 for πr 2 + πr × 12 or + π × 42 2 2 Correct cancelling or factorising π A1 leading to r2 + 12r – 48 = 0 18(b) 2 21 – 6 or 2( 21 − 3) 4 B3 for –6 ± 84 or better −12 ± 336 or B2 for or better 2 or (r + 6)2 = 84 or better −12 ± 122 − 4 × [1] × −48 or M1 for 2 2 or for (r + 6) – 36 – 48 [= 0] Trace ID: PC-A5C66EEC6F Re-uploading, mirroring or re-hosting this file on any other website or domain is unauthorised and traceable. Licensed for hosting on papacambridge.com only. PapaCambridge Downloaded from PapaCambridge - https://papacambridge.com/ 19(a) −8 2 −8 k 8 B1 for or or −4 k −4 4 19(b) 8 and –16 4 ( ) B1 for 4 10 = 160 soi 2 M2 for x + 4 = [±] 12 or (–4 – x ) = [±]12 −8 ± 24 or (x + 16)(x – 8) [=0] or 2 or M1 for ( 4 + x )2 + ( 7 − 3)2 = 4 10 oe 19(c) y = –2x + 10 nfww 5 7−3 M1 for [grad AB =] oe 4 − −4 M1 for perp line = –1 ÷ their grad (AB) B1 for (2, 6) M1 for their (2, 6) substituted into y = their mx + c oe 20(a) 1 1 3 1 or x −6 final answer B1 for or x −6 9x 6 9 x6 1 B2 for 9 [−]9 or final answer [ −]9x−6 or x6 or M1 for 3–2 oe to a maximum of 2 marks if final answer incorrect If 0 scored SC1 for answer xk kx6 ,[ −]9xk or − 9 20(b) 2 3 M2 for x = 2(1 – 2x) oe or better x= oe 5 1 or M1 for 49 = 72 or 7 = 49 2 soi or for equating their powers with a common base Trace ID: PC-A5C66EEC6F Re-uploading, mirroring or re-hosting this file on any other website or domain is unauthorised and traceable. Licensed for hosting on papacambridge.com only. PapaCambridge Downloaded from PapaCambridge - https://papacambridge.com/ 21 2x − 5 5 M2 for (2x – 5)(x + 4) final answer or M1 for 2x(x + 4) – 5(x + 4) a − 3b or x(2x – 5) + 4(2x – 5) or for (2x + p)(x + q) where pq = –20 or p + 2q = 3 M2 for (a – 3b)(x + 4) or M1 for a(x + 4) – 3b(x + 4) or x(a – 3b) + 4(a – 3b) 22(a) x3 – x2 – 21x + 45 final answer 3 B2 for correct unsimplified answer or for simplified final answer with 3 out of 4 terms correct or B1 for correct expansion of two given brackets with at least 3 terms out of 4 correct 22(b) Correct labelled sketch 4 B1 for positive cubic positive cubic Crossing x-axis at –5 B2 for 2 roots only and graph which Repeated root and local minimum at (k, • crosses x-axis at –5 (root must be 0) where k > 0 (if labelled must be 3) labelled) Crossing y-axis at 45 only • has a repeated root at (k, 0) where k > 0 (does not need to be labelled but if labelled should be 3) or B1 for a correctly labelled root at 3 or 45 –5 or for a repeated root at (k, 0) where k > 0 –5 [3] (does not need to be labelled but if labelled should be 3) B1FT for a single intercept on y-axis labelled at 45 but not if line y = 45. FT from part (a) for their 45 Trace ID: PC-A5C66EEC6F Re-uploading, mirroring or re-hosting this file on any other website or domain is unauthorised and traceable. Licensed for hosting on papacambridge.com only. PapaCambridge Downloaded from PapaCambridge - https://papacambridge.com/