ADVANCED PROGRAMME MATHEMATICS: PAPER II MARKING GUIDELINES

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GRADE 2 EXAMINATION NOVEMBER 206 ADVANCED PROGRAMME MATHEMATICS: PAPER II MARKING GUIDELINES Time: hour 00 marks These marking guidelines are prepared for use by examiners and sub-examiners, all of

1 GRADE 2 EXAMINATION NOVEMBER 206 ADVANCED PROGRAMME MATHEMATICS: PAPER II MARKING GUIDELINES Time: hour 00 marks These marking guidelines are prepared for use by examiners and sub-examiners, all of whom are required to attend a standardisation meeting to ensure that the guidelines are consistently interpreted and applied in the marking of candidates' scripts. The IEB will not enter into any discussions or correspondence about any marking guidelines. It is acknowledged that there may be different views about some matters of emphasis or detail in the guidelines. It is also recognised that, without the benefit of attendance at a standardisation meeting, there may be different interpretations of the application of the marking guidelines.

2 GRADE 2 EXAMINATION: ADVANCED PROGRAMME MATHEMATICS: PAPER II MARKING GUIDELINES Page 2 of MODULE 2 STATISTICS QUESTION. (a) P( X = ) 7 0 = 5 5 = 0, 20 (5) (b) 5 = 5 (2) (c) Px ( ) > 0,95 0 n n 0,95 0 > 5 5 n < 0,05 5 n log < log 0,05 5 n >, 25 people (8).2 (a)!! 8!! = (5) (b) = or 0,007 (5) (c) = (8) []

3 GRADE 2 EXAMINATION: ADVANCED PROGRAMME MATHEMATICS: PAPER II MARKING GUIDELINES Page of QUESTION 2 2. (a) y = 0,8,5x () (b) r = 0,98 Data lie close to the regression line. (2) (c) y = 0,8,5(5) =,52 (2) (d) Reliable but caution is required as although extrapolation occurs, correlation is very strong. (2) 2.2 (a) () (b) x 0 2 PX ( = x) () (c) E[ X] = 0 2 = 0, (2) [20]

4 GRADE 2 EXAMINATION: ADVANCED PROGRAMME MATHEMATICS: PAPER II MARKING GUIDELINES Page of QUESTION. (a) A 96% confidence interval for p is: ( 0,8)( 0, 2) 0,8 ± 2, ,78 ;0,859 (6) ( ) (b) 96% of the time the interval will contain the population proportion. (2) 2.2 (a) ~ N ( µ ; σ ) σ = µ 5 2µ µ P( x< 2µ ) = P z < µ 5 = P( z <, 67) = 0,5 0, 525 = 0,9525 (8) (b) µ µ 0,8 = = 0,8 2 = µ 52 µ = 2,52 (7) [2]

5 GRADE 2 EXAMINATION: ADVANCED PROGRAMME MATHEMATICS: PAPER II MARKING GUIDELINES Page 5 of QUESTION. A one-tailed test should be used as Gareth would like to see if there has been an increase in his travel time from last year to this year. (2).2 H : µ = 5,7 0 H : µ > 5,7 Rejection region: reject H 0 if z >, 75 Test Statistic: 7, 5,7 z = =,5026, 2 8 Conclusion: since z <,75, we fail to reject the HH 0 at the % level of significance and suggest insufficient evidence to support the claim, hence no significant increase in Gareth's journey time. (0) [2] QUESTION Arnie Michael Connor For entrance : Px ( 2) = PA ( M C') PA ( M' C) PA ( ' M C) PA ( M C) 6 = = (6) = (6) 56 [2] Total for Module 2: 00 marks

6 GRADE 2 EXAMINATION: ADVANCED PROGRAMME MATHEMATICS: PAPER II MARKING GUIDELINES Page 6 of MODULE FINANCE AND MODELLING QUESTION. R2 000 R5 000 R T 0 T 8 T 2 T 5 T 2,62%, comp monthly,8%, comp quart (6) , ,08 = 6, , ,08 = 5 25, ,08 = 27 98, ,6 5 25, ,7 = ,59 OR , =,66 8,66 0, = 8 90, ,570 0,08 = 9 7, ,289 0,08 = , 59 (0) [6]

7 GRADE 2 EXAMINATION: ADVANCED PROGRAMME MATHEMATICS: PAPER II MARKING GUIDELINES Page 7 of QUESTION = 0,06 0, =,06 n 0,06 n n = 5,890 quarters = years, 5 or 6 months OR 0,06 0, = 0,06 0, = ( ),06 n ( n ) n = 5,890 quarters = years, 5 or 6 months [2] QUESTION. 000 = 0 00( r) r = 8,55% 0 00 = ( r) r = 8,57% (6) , = ,20 (6) 0, , (8 2 ) = 8 8,20 () ,052 0, = ,86 Yes, it will cover the costs (8) [2] 2 QUESTION. T = (2) ( 2) ( ) 2 = 6 T = ( 2) (2) ( ) = 6 T 5 = (2) ( 2) ( ) = 6 (5)

8 GRADE 2 EXAMINATION: ADVANCED PROGRAMME MATHEMATICS: PAPER II MARKING GUIDELINES Page 8 of.2 T n decreasing discrete exponential y-int, and no x-int n () 5. Pn = 5 r 5 = 5 29, 7r 20 ( Pn P ) n 2 = Pn r P n , 7r 70 = (5 29,7 r) r(5 29,7 r)( ) 20 r = 0,27 ('solve' function) (9) [8] QUESTION 5 5. Single data points, not joined by a curve Measurements taken at intervals; measurements between intervals not considered (2) < prey < 800 (2) (2) 5. rate of decrease : steeper gradient (2) 5.5 (a) b rate of deadly interactions between predator and prey () (b) /c = life span of predator; hence predators live for shorter periods OR cf = how many predators die in each cycle; hence more predators die in each cycle. Fewer predators implies increase in prey populations or slower decline. () 5.6 C prey initially increasing and predator initially decreasing with tendency to equilibrium. () [8] QUESTION 6 6. G (2) 6.2 (2) 6. T n = 2, T n, T = () = 2 n n < 9,9 = 9 () [2] Total for Module : 00 marks

9 GRADE 2 EXAMINATION: ADVANCED PROGRAMME MATHEMATICS: PAPER II MARKING GUIDELINES Page 9 of MODULE MATRICES AND GRAPH THEORY QUESTION. 2 ( ) = z z = x 2y = and x y = x = 2, y = (8).2 (a) false (2) (b) false (2) (c) true (2) (d) true (2) [6] QUESTION 2 2. (a) translation units right and unit down () (b) yes () (c) M 2 5 = 2 (2) 2.2 (a) shear of factor, y-axis invariant () (b) no () (c) determinant () (d) det = area of figure and image unchanged () 2. tan A = A = 7,565 o cos, sin, cos 0 sin 0 sin, cos, sin 0 cos0 0,9 0,92 = 0,92 0,9 (8) [22]

10 GRADE 2 EXAMINATION: ADVANCED PROGRAMME MATHEMATICS: PAPER II MARKING GUIDELINES Page 0 of QUESTION , 6 0, 0, 7 6 = 2 5 2,, 6 5 OR , 6 0 0, 0 0 x 0 0 y 0 0 z = x 5 y = = z 0 2 (8).2 6(t ) 2(6t 9) (8 27) = 0 6t 27 = 0 t =,5 (6). scale factor of,5: w = (2) [6] QUESTION. VW (2).2 triangular inequality does not hold (2). W V R Q U P S T W or W V R U Q P S T W (). PSTW = 5 2 x 2 < 5 x < 5 so x = (6) []

11 GRADE 2 EXAMINATION: ADVANCED PROGRAMME MATHEMATICS: PAPER II MARKING GUIDELINES Page of QUESTION 5 5. English, Swahili (2) 5.2 E X (8) Z (5) S (72) F (6) P (58) A (60) E (85) = 2 min (8) 5. E P (65) A (60) F (62) S (6) X (62) Z (5) E (50) = 08 min OR E Z (50) X (5) S (62) F (6) A (62) P (60) E (65) = 08 min OR any other acceptable circuit < 2 min (0) [20] QUESTION edges (2) = 0 (2) 6. (8) Vertices,,,,, Vertices,,,, 2, Vertices,,, 2, 2, Vertices,,, 2, 2, [2] Total for Module : 00 marks Total: 00 marks

ADVANCED PROGRAMME MATHEMATICS MARKING GUIDELINES

GRADE EXAMINATION NOVEMBER 4 ADVANCED PROGRAMME MATHEMATICS MARKING GUIDELINES Time: hours marks These marking guidelines are prepared for use by examiners and sub-examiners, all of whom are required to