2019 VCAA Further Mathematics Exam 1 Solutions PDF

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http://www.learning-with-meaning.com/

2019 VCAA Further Mathematics Exam 1 Solutions

Q13

SECTION A Data analysis 1 2 B B 9 10 E A

Core 3 D 11 A

4 D 12 B

5 C 13 E

6 D 14 E

7 B 15 D

8 B 16 C

Recursion and financial modelling 17 18 19 20 21 D C A C C

22 E

23 C

24 B

SECTION B Module 1: Matrices 1 2 3 4 5 6 C D E E B A Module 2: Networks and decision mathematics 1 2 3 4 5 6 E C C A B A Module 3: Geometry and measurement 1 2 3 4 5 6 D A C E C D Module 4: Graphs and relations 1 2 3 4 5 6 B D E D B C SECTION A Data analysis

7 A

8 E

7 B

8 D

7 D

8 B

7 E

8 C

E Day no. 3 med 5 med

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2 24

3 40 28

4 28 40

5 51 33

6 33 37

7 37 37

Q14

E

Q15

D

Q16

C

Recursion and financial modelling

Q17 A1 = 10 , A2 = 24 , A3 = 2 × 24 + 4 = 52

D

Q18

C

Q19

A

Q20

3.6 ×300 000 = 900 .00 , n = 12 100 n

C

Q21 500.00 r = 580.00 , r = 1.16 , b = 580.00 r = 672.80

C

30 000 − 18 480 = 0.16 3 × 24 000

E

Q22 Unit cost =

75   Q23 995.491+  ≈ 1001.71 × 100  12 

Core

Q1 11+ 4 + 2 = 17

B

Q2

B

8 37

C

12

r   Q24 20 000 1 +  = 20 732 100 12 ×   12

Q3 log10 100 000 = 5 , 7 + 1 = 8

D

Q4 89 − 40 = 49

D

Q5 75 − 57 = 18

C

Q6

1 (95% + 68% ) = 81.5% 2

r 20 732   , r ≈ 3.60  1+  = × 100 12 20 000   12   r  r effective = 1 +  − 1 ×100% = 3.66   100 × 12  Difference ≈3.66 −3. 60 = 0.06

D

Q7 2.5% × 160 = 4

B

Q8

B For

Against

Male Female Q9

E

Q10 − 0. 893743 ≈ − 0. 945

A

Q11 b = r

ssleep scoffee

= − 0. 770 ×

1.12 ≈ − 0.55 1.56

Q12

A B 1

2019 VCAA Further Mathematics Exam 1 Solutions

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B

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

Module 3: Geometry and measurement

Module 1: Matrices

Q1 4 × 27.43 = 109.72

D A

Q1

C

Q2

 7 Q2 6× 7 + 6× 8 = [6 6] ×   8 

D

Q3

Q3

E

Q4 E → C → A→ D → B → E , repeat cycle every 5 questions. E Q5

B

Q6

A 14

1 4π 52 + π 52 ≈ 236 2

(

)

C

Q4

E

Q5

C

Q6

114 − 104 × 60 = 40 min later, i.e. 6.30 pm 15

D

15

.62 .62 .62  0.80 0.20 0. 40  0.80 0.20 0.40        0.05 0.60 0.10  ≈ 0.05 0.60 0. 10  ≈ .14 .14 .14  .24 .24 .24  0.15 0.20 0. 50  0.15 0.20 0.50 

Q7 Radius =

18.85 311 ≈ 11.0 ≈ 3.00 , height ≈ 2π π × 3 .00 2

D

Q7 W can receive directly from U , V and Y , but Y cannot send directly to U , V and W . A

Q8 Area of the square with the circle centres as its vertices minus π r2  2  = 4r 2 − π r 2 B the area of four quarter-circles= (2r ) − 4  4  

Q8 m = 0.8 m + 0.48 s and 0. 48s = 12 , .: s = 25 and m = 60 E m + s = 85

Module 4: Graphs and relations

Module 2: Networks and decision mathematics

Q1

E

Q2 Add two edges to make all vertices with even degree.

C

Q3 Capacity = sum of forward maximum flow= 14

C

Q4 The two graphs have different number of vertices and .: cannot be isomorphic. A

Q1 2. 4 −1 = 1.4

B

Q2

D

Q3 c + d = 16 , 7c + 13d = 178 .: d = 11

E

q−0 8− 0 = , q = 20 0− (− 10) − 6 − (− 10)

D

Q4

Q5 Sale = 35 (65 − 40 ) = 875 , fixed cost 875 − 250 = 625 Q6

Volume of pineapple juice 300 x 3 2x , ≥ , y≤ ≥ Volume of mango juice 200 y 2 3

B C

Q5 MD + DE + EA + AB + EG + GC + GF = 203

B

Q6

A

Q7 Line VW and line ST are parallel.

Q7

B

Q8 They meet during 2 < t ≤ 6 , Jenny will have walked 518 m and Alan will have walked 900 − 518 = 382 m C

Q8 Critical path: 51 G: LST − EST = 16 − 6 = 10 , I : 22 − 12 = 10 , N : 29 − 19 = 10 D

E

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