2017 VCAA Further Mathematics Exam 1 Solutions PDF

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http://www.learning-with-meaning.com/ 2017 VCAA Further Mathematics Exam 1 Solutions © itute 2017

SECTION A Data analysis 1

2

3

4

Core 5

6

7

8

9

10

11

12

D B D D B E E D A A D D Recursion and financial modelling 17 18 19 20 21 22 A D C D E A SECTION B Module 1: Matrices 1 2 3 4 5 6 B E C C A D Module 2: Networks and decision mathematics 1 2 3 4 5 6 B C A D C E Module 3: Geometry and measurement 1 2 3 4 5 6 D D B B C B Module 4: Graphs and relations 1 2 3 4 5 6 B C B E D C SECTION A Data analysis

13

14

15

16

B D D

A

23 D

24 B

7 A

8 A

7 D

8 B

7 E

8 A

actual , deseasonalised actual deseasonalised = = 0.625× actual = (1− 0.375)× actual 1.6

D

Q16 1.6 =

A

Recursion and financial modelling Q17

A

Q18

D

Q19

C

Q20

D

Q21

7 C

8 D

Core

680 − 125 ≈ $0.072 4 × 1920

E

Q22

A

28.42 ≈ 0.004 7105. 41 Interest = 7233. 83 × 0. 004 = 28. 94 Principal addition = 7500.00 − 7233.83 = 266.17 Payment = 266.17 − 28.94 = 237.23

D

Q23 Interest rate =

Q1

D

Q2

B

Q3

D

Q4 3 < log10 (area ) < 4 , 10 3 < area < 10 4

D

Q5 30 % of 300 = 90

B

Q6

E

Q7

E

Q8

D

Q9 17.7 − 18.4 = −0.7

A

Q10 z =

22 + 19 + 22 + 43 19 + 22 + 43 + 37 = 26.5 , = 30. 25 4 4 26.5 + 30.25 = 28.375 2

Q15

x − x − 0.3 − 0.02 = −0.8 = 0.4 sx

Q24 N = 120 , I % = 4. 35 , PV = 245 000 , PMT = −1800 , P/Y = 12 , C/Y = 12 , FV = −108 219. 1611 N = 60 , PV = 108 219. 1611, PMT = −2000 , FV = 0 , P/Y = 12, C/Y = 12 , I % ≈ 4.14

B

A

Q11

D

Q12

D

Q13

B

Q14

D

1 2017 Further Maths Trial Exam 1 Solutions

© itute 2017

http://www.learning-with-meaning.com/ SECTION B Module 1: Matrices

Module 3: Geometry and measurement

Q1 θ =

360 = 72 5

D

Q1

B

Q2

E

Q3 ∆ ≠ 0

C

Q4

C

Q5

A

Q4 V =

Q6 aij + bij = (2 i + j) + (i − j ) = 3i

D

Q5

C

Q7 Let Fn+ 1 = Fn = F0 .

Q6 r = 102 − 82 = 6

B

1  0 0  0

sin θ sin 26° = , θ ≈ 50 ° or 130 ° 7 4 The third angle: 180 − 50 − 26 = 104° or 180− 130 − 26 = 24°

E

Q2 XZ =

38.52 + 24.0 2 ≈ 45.4

D

Q3 139 ° E, 25 ° E, 3 °W, 58 ° W

0 0 0 0 0 0 0. 65    1 0 0 0 . 25 0 . 75 0 0 F + B F0 =   0 0 1 0 0. 20 0. 95 0  0    0 0 1 0. 10 0. 05 0. 05 1  1 0 0 0 0. 65 0 0 0      0 . 25 0 . 75 0 0  0 1 0 0    B= F −    0.20 0. 95 0  0 0 0 1 0  0  0 0 0 1  0.10 0. 05 0. 05 1    17 500  Y − 10 000  J  .: B =   − 1650  A    − 5850  D

 0.3 0.2 V 40  29      0.2 0.2 W 15 = 13       X Y Z 20  33 X = 1 − 0.3 − 0.2 = 0.5 Y = 1− 0.2 − 0.2 = 0.6 40 X + 15Y + 20Z = 33 , Z = 0.2 0.2 ×40 + 0.2 ×15 + 20W = 13 , W = 0.1

1 π × 52 × 1.8 + π × 52 × 16 ≈ 1304 3

B

Q7

Q8 Shaded area ≈

1 1 × 100 2 sin 60° − × π × 502 ≈ 403 2 2

A

Module 4: Graphs and relations

Q1

B

Q2

C

Q3 100 = k × 5 2 , k = 4

B

Q4 500 + 240 + 200 = 940

E

Q5

D

Q6 2a + 3c = 69.50 and a + 5c = 78.50 .: a =16 and c = 12.5 .: 3 a + 4 c = 98. 00

C

A

Q8

A

Module 2: Networks and decision mathematics

Q7 150 x + 50 ×

Q1

B

Q2

C

Q3

A

Q4 CGJ: 4 + 3 + 5 = 12

D

Q5 Critical path CFHM

C

Q6

E

Q7

D

Q8 The minimum cut is Cut B

B

2017 Further Maths Trial Exam 1 Solutions

B

x = 0.8× 200 + 250 , x = 2. 35 2

Q8

C D

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