3-D Shapes and volume

Transcription

1 -D Shapes and Volume Mark Scheme 1 Level IGCSE Subject Maths Exam Board Edexcel Topic Shape, Space and Measures Sub Topic -D Shapes and volume Booklet Mark Scheme 1 Time Allowed: Score: Percentage: 57 minutes /47 /100 Grade Boundaries: A* A B C D E U >85% 75% 70% 60% 55% 50% <50%

2 $!# % " $ 1. π r 9 = 100 oe 5 ( r =).5677 for.5 or for value rounding to.54 ( ) 9 2 ".5..." 2 ( h =) for 8.27 or for value rounding to for answer rounding to 108 (π ) If both s scored, award 5 marks for an answer which rounds to 108 Total 5 marks 2. πr 2 x 4r 2 x 4π r / =125π/6 oe 24 r 16 r = 125 oe r = 125/8 oe r = (125/8) M2 Any equation based on cylinder 2 spheres = space oe h = 4r must be implicit for award of M2 {decimal form: 12.6r 8.4r =65.4 (1 dp or better)} If not M2 then for πr 2 x 4r or better One occurrence of r in correct equation. awrt to 2.5 Ans dep on M Total 5 marks

3 . 2 2 π π oe or (using ) or (using.14) (rounded or truncated to at least sig figs) or 2 π 5.1 (5.1.7) or or M2 for one of 2 π or value in range inc or π oe or value in range inc or NB. Accept.14(...) or 22/7 in place of π 282 for answer in range inc 4. 2 π.4 8. or or π.4 or or π.4 or 2.12 or for awrt π or 8( ) May be rounded or truncated to at least 2 sf ( if.14 used) oe or May be rounded or truncated to at least 2 sf 57 for answer rounding to 57

4 6. (a) 0.5 x (11 + 7) x 10 (b) 90 x for (0.5 x 2 x 10) + (7 x 10) + (0.5 x 2 x 10) ft Their area in (a) x 12 ft =π 4.5 l 10 l = or l = π For exact expression or answer which rounds to 9.2 sin (AVO) = 4.5/ 9.20 (= ) For a correct expression for sin AVO or cos AVB cos (AVB) = ( )/ 2 x 9.2 x 9.2 (= ) awrt x 10 x 12 (= 60) or 1 x 8 (= 104) or 8 x 10 (= 80) One correct face 0.5 x 10 x 12 (= 60) and 0.5 x 10 x 12 (= 60) and 1 x 8 (= 104) and 1 x 8 (= 104) and 8 x 10 (= 80) or 2 x 60 and 2 x 104 and dep on above (exactly 5 correct faces ) Award M0A0 for 0.5 x 10 x 12 8 and M0A0 for 0.5 x 10 x 12 = 60 followed by 60 8, etc 9. (A =) 0.5 x (4 + k) x (= 5 6) oe k + 4 = 10 6 (k =) or (k =) oe (k =) (k 4) oe correctly isolating k Accept 2(5 2 2) but don't accept followed by 5 2 2

5 10. 12π for circumference accept value which rounds to π or 60π correct expression for surface area 110 accept awrt 110 (SF) e.g 111 If full Surface Area given, then award 2 marks as long as you see60π oe in working ( for 12 oe) Do not isw πr 2 = 81π or 4r 2 = 81 M2 for r = 4.5 or r = 81 4 (=4.5) 4 "4.5" ft for "r" dep on first 82 4 for r = 81 oe (may be seen in two stages) 4

6 12. (Slant Height =) (5a) 2 + (12a) 2 (= 1a) correct use of Pythagoras condone missing brackets (total surface area = ) π (5a) 2 + π 5a 1a oe or π (5a) 2 + π 5a (5a) 2 + (12a) 2 (=90 πa 2 ) eg. 90 πa 2 = 60π oe or π (5a) 2 + π 5a 1a = 60π oe V = 1 π (5 "2") 2 12 "2" (=100πa ) or V = 1 π oe or k = 1 "2") 2 12 "2" ( cao dep on first must have either 25a 2 or (5a) 2 dep on first for equation formed (need not be simplified) must have either 25a 2 or (5a) 2 a = 2 dep on first NB. For the award of this mark, brackets must be present or the value for r 2 evaluated correctly for the candidate s value of a Total 6 marks