1. AS Maths
Decision Paper
June 2013
Model Answers

2. Grade Boundaries
Grade A B C D E
Marks 64 59 54 50 46

4. A 1
B 2
C 3
D 4
E 5
F 6

5. Initial Match
A 1
B 2
C 3
D 4
E 5
F 6
A 1
B 2
C 3
D 4
E 5
F 6
One Solution
𝑭→𝟏↛𝑩→𝟒
𝑨→𝟑↛𝑪→𝟐↛𝑬→𝟔
One Final Match
A3, B4, C2, D5, E6, F1

6. 5
Comp Swaps
2, 12, 17, 18, 5, 13
2, 12, 17, 18, 5, 13
2, 5, 12, 17, 18, 13
2, 5, 12, 13, 17, 18
2, 5, 12, 13, 17, 18

7. EG = 2.3
AB = 2.5
IJ = 2.9
AC = 3.1
AD = 3.2
HJ = 3.4
GJ = 3.6
BE = 3.9
FI = 5.4
Total = 30.3
Total = 30.3

8. B E H A D G J C F I

9. FI

10. AD

12. A → B → C → D → E → F → A 15 13 10 26 27 12
= 103
It is a TOUR, that maybe IMPROVED upon

13. A → C → D → F → B → E → A 11 10 15 15 24 27
= 102

14. 77 e) Because it has a LOWER BOUND of 77 10 C D 12 10 + 12 + 13 + 19 = A F 19 = 23 12 13 E 11 C B F 77

16. Police Car A A → B → D → K → G Police Car E E → C → D → K → G21 19
Police Car E
E → C → D → K → G 10 12 11 5 15
Police Car J
J → L → I → H → G 16 7 15 21 14 6 15 9 10 20 21

17. ii) B would appear 4 times ( 𝑛 2 = 8 2 =4)
ODD VERTICES at A, C, L and G
AC (12) + LG (15) = 27
AL (11) + CG (15) = 26
Repeat
AG (21) + CL (9) = 30
Total = = 160
ii) B would appear 4 times ( 𝑛 2 = 8 2 =4)
Total of all times = 134 minutes

19. A B C D E
Line 10 36 16 2
Line 20 32
Line 30 4
Line 40
Line 60 16
Line 70 4 4
Line 20 16
Line 30
Line 40
Print B 4

20. A B C D E
Line 10 11 7 1
Line 20 7
Line 30 4
Line 40
Line 60 7
Line 70 4 1
Line 20 4
Line 30 3
Line 40
Line 60 4
Line 70 3 1
Line 20 3
Line 30 1
Line 40

21. A B C D E
Line 60 3
Line 70 1 3
Line 20 3
Line 30
Line 40
Print B 1
HCF (of A and B )

22. 6𝑥+4𝑦+3𝑧≥420
6𝑥+4𝑦+3𝑦≥420
6𝑥+7𝑦≥420
6𝑥+6𝑦+4𝑦≥480
6𝑥+6𝑦+4𝑧≥480
6𝑥+10𝑦≥480
6𝑥+4𝑦+4𝑦≤720
6𝑥+4𝑦+4𝑧≤720
3𝑥+5𝑦≥240
6𝑥+8𝑦≤720
3𝑥+4𝑦≤360
𝑆𝑜 𝑦=𝑧

24. 𝑃=4𝑥+5𝑦 𝑂𝑏𝑗𝑒𝑐𝑡𝑖𝑣𝑒 𝑙𝑖𝑛𝑒 4𝑥+5𝑦=20 Or 4𝑥+5𝑦=100 𝑊ℎ𝑒𝑛 𝑥=0, 𝑦=20
3𝑥+4𝑦=360
𝑂𝑏𝑗𝑒𝑐𝑡𝑖𝑣𝑒 𝑙𝑖𝑛𝑒
4𝑥+5𝑦=20 Or
4𝑥+5𝑦=100
6𝑥+7𝑦=420
𝑊ℎ𝑒𝑛 𝑥=0, 𝑦=20
𝑊ℎ𝑒𝑛 𝑦=0,𝑥=25
𝑭𝒆𝒂𝒔𝒊𝒃𝒍𝒆 𝑹𝒆𝒈𝒊𝒐𝒏
𝑶𝒃𝒋𝒆𝒄𝒕𝒊𝒗𝒆 𝑳𝒊𝒏𝒆
3𝑥+5𝑦=240
𝑦=0

25. 𝑃=4𝑥+5𝑦
Maximum Profit £480 (120 Gold (𝑥), 0 Silver(𝑦), 0 Bronze 𝑧 .
𝑃=2𝑥+12𝑦
Maximum Profit £1080 (0 Gold (𝑥), 90 Silver(𝑦), 90 Bronze 𝑧 .