PPE Paper 1 November 2015 Higher Tier Edexcel Style Mark Scheme Commissioned by The PiXL Club Ltd.

Transcription

1 PPE Paper November 05 Higher Tier Edexcel Style Mark Scheme Commissioned by The PiXL Club Ltd. --

2 Question (part) Working Answer Mark Notes M for any two of 7, 0 and 0.5 seen or 40 or 40 or M for 4 0 or 40 or 7 40 or7. 40 or or A for Physics with correct comparative figure(s) M for correct method to find figure(s) to compare, eg (4/60)*00 (=40) oe or oe (=5.8) C for Physics with 40% or 5.8 or and oe (a) Key: 7 = 7 3 M for unordered stem and leaf diagram (condone errors, number misplaced counts as one error) A for correctly ordered and fully correct diagram NB: ignore commas between leaves, stems could be 60,70,80,90 B for key e.g. 7 = 7 3 (b) 77 B ft 4 (a) x + 8y B for x + 8y oe [B for x or 8y seen] {Note: 8y seen with no working gets B0 4x + x = 6x gets B0} 4 (b) c + 4r B for c +4r oe [B for c or 4r oe seen] Ignore any Left Hand Side = c + 4r {Note: ignore units or use of p }

3 5 (a) -3,-,,0 B cao ( each error or omission) 5 (b) 4m 0 m.5 M for 4m 0, condone use of = sign or > A for y.5 oe as final answer M for method to find area of one rectangle, eg 0 9 (=80) or 0 (=40) M (dep) for subtracting from/by given area, eg (6 80 ) (=36) or 40 6 (=4) M for final step from complete method shown, eg 0 "36" 3 or 4 3 A cao M for a correct expression for the area of one rectangle, eg (9 + 3) (0 x) or 9 x M (dep) for a correct equation eg (9 + 3) (0 x) + (9 x) = 6 M for correct method to isolate x, eg 3x = 4 A cao Yes with correct working 4 M for a complete method with relative place value correct. Condone multiplication error, addition not necessary. M (dep) for addition of all the appropriate elements of the calculation. A for or 37p (spare) C ft (dep on M) for correct decision for their total cost M for a complete grid with not more than multiplication error, addition not -3-

4 necessary M (dep) for addition of all the appropriate elements of the calculation A for or 37p (spare) C ft (dep on M) for correct decision for their total cost *8 (i) *8 (ii) 9 (a) 80 0 = ( x 70) 40 Reasons 8.5 x M for 80-0 or 70 seen M for 80 ( x 70) or 0 70 A cao B for two out of three of: angles on a line add to; 80 isosceles triangle (accept sides equal or angles equal); sum of the angles in a triangle is equal to 80 for two out of three of: angles on a line add to; 80 isosceles triangle (accept sides equal or angles equal); exterior angle of a triangle is equal to the sum of the interior opposite angles B cao 9 (b).37 x 0-3 B cao 0 Diagram 4 M arc radius 4 cm centre B within the guidelines M angle bisector from A to BC within the guidelines A for clear indication that inside of arc is being identified as correct region for the first condition, or that side of straight line nearer to C is identified as correct region for the second condition. (Note that only of the Ms need be awarded for this A mark to be awarded) A fully correct region -4-

5 Ignore any drawing outside the given triangle (a) 0 0 B for 0 0 or equivalent (b) 3 4 B for answer in range 3-4 inclusive (c) M for A for 0800 cao M for ( ) 0 A for 680 cao 3 (a) 3(t 4) = t + 6t = t + 6t t = + 4t = t B 6t or M correctly isolating their terms in t or their constant terms in an equation A cao 3 (b) (x y) 3(x y) = x y 3x + 6y -x + 4y PTO M x y or 3x 6y or 3x + 6y A x + 4y or 4y x [SC: B for x 8y or x + 4y with or without working if M0 scored] 3 (c) (x 5)(x + 7) x + 4x 5x 35 = x + 9x 35 x + 9x 35 M out of 3 terms correct with correct signs Or all 4 terms correct ignoring any sign errors A cao 4 (a) x x x 3 x 3 x 5 3 M for a continual prime factorisation (at least two consecutive steps correct) or at least two stages of a factor tree correct M for a fully correct factor tree or list,,,3,3,5-5-

6 A for x or (b) e.g. 6, 30 M for two numbers with an HCF of 6 or for two numbers with a LCM a multiple of 5 A for two numbers with an HCF of 6 and a LCM a multiple of 5 (eg (6, 30), (, 30), ) M for 3 and 3 5 or for 3 5 A for two numbers with an HCF of 6 and a LCM a multiple of 5 eg (6, 30) (, 30) = x 3 = Or (/6)+(3/0)=(7/5) (7/5) x 300 = M for 6300 or 50 seen M for oe or or 90 seen M (dep on at least previous M) for A cao Or PTO M for (/6)+(3/0) or (7/5) oe M for (7/5) 300 or 40 seen or (7/5) or (8/5) oe seen M (dep on at least previous M) for or 60 seen or (8/5) 300 A cao 6 (a) 3. B cao 6 (b). M for 3.8 k or k or k.6 or.6 k where k can be any value A cao -6-

7 6 (c) Reason B for correct reason e.g. because the IQR ignores extreme values 7 (a) 00 < C 400 B cao 7 (b) 7,8,7,37,45,50 B cao 7 (c) Correct cumulative frequency diagram B ft for all 6 points plotted correctly ( sq) at top end of intervals dep on sensible table B ft (dep on previous B) for points joined by curve/line segments [SC: B ft from sensible table for 6 points plotted not at ends but consistently within each interval and joined or 5 points correctly plotted at the top end of intervals] 7 (d) 7 9 M Line drawn up to the cumulative frequency graph at 700 or correct reading at 700 ± ½ square or 3 33 seen A ft graph 8 (a) ED 6 = ED = 8 4 M for 4 6 oe or 6 4 oe or 4 8 oe or 8 4 oe (accept all these written as ratios) A cao 8 (b) : 6 = AC : CD (5 (4 + 6)) 4 0 M 5 5 oe A cao M (5 (4 + 6)) 4 A cao -7-

8 9 (a) 9 (b) 9, -3, 3 M for 5 ( +.5) A cao B for all three correct (B one or two correct) B ft for all 7 points plotted correctly ± square B ft (indep) for a smooth curve through 6 or 7 of their plotted points provided at least B awarded in (a), with 6 or 7 points correctly plotted and (, 3) & (, 3) not joined with a straight line 0 πxl = πx h + x = 4x h² = 3x² π x h + x = πx Alternative h + x = x h + x = 4x h = 3x (a) AB = AO + OB 3 x 4 B for curved surface area of one of the shapes e.g. πxl or πx M for for attempt to equate surface areas e.g πxl = πx or l = x M for attempt to connect h and x using Pythagoras s theorem e.g. h + x = 4x A for 3x or 3x PTO Alternative B for h² + x² = l² oe M for attempt to equate surface areas e.g. π x h + x = πx oe M (dep) for attempt to square both sides of their formula e.g. h + x = A for 3x or 3x a + 3b B for a + 3b or 3b a SC B for attempt to equate surface areas in terms of r, rather than x 4x -8-

9 (b) OP = a + (3b a) (a + b) is parallel to a + b 3 M for a ± 5 ('3b a') 3b ± 3 5 A for 6 5 a b oe ('a - 3b') = 6 5 a b A for 6 (a + b) is parallel to a + b oe 5 = 6 5 (a + b) (a) parallel B cao (b) - B cao (c) /7 M use of reciprocal e.g. / 9 3/ or square root e.g. 3-3, A or 79 seen or 7 seen or 7 seen cao (a) (7/9), (/9); (7/9), (/9), (7/9), (/9); B for (7/9), (/9) on LH branch B for (7/9), (/9), (7/9), (/9) on RH branch 3 (b) 8/8 3-9-

10 4 x = x= x = 36 x = (36/99) = (4/) or 0000x = x = 3636 x = (3636/9999) = (4/) or 9900x = 3600 etc 5 (a) Proof 3 M for 00x = or 0000x = M (dep) for subtraction of both sides A for (36/99) = (4/) from correct proof. M starts long/short division of into 4, set out correctly, with 0.36 seen on the top of the bus stop (oe) with a remainder of 7 (5, -4) M(dep) Remainder of 4 after the remainder of 7 seen in correct place A At least remainders of 4 and one of 7 seen in the correct place and with a statement that the decimal will recur with a cycle length because the remainders have a cycle length. B for (5, -4) (B for (a, 4) or (5,b) where a 5 or 3 and b 4). 5 (b) (-, ) B for (,) (B for (a,) or (,b) where a and b ). -0-